# Patent

## Title
Interferometer for determining characteristics of an object surface, including processing and calibration

## Abstract

Disclosed is a system including: (i) an interferometer configured to direct test electromagnetic radiation to a test surface and reference electromagnetic radiation to a reference surface and subsequently combine the electromagnetic radiation to form an interference pattern, the electromagnetic radiation being derived from a common source; (ii) a multi-element detector; (iii) one or more optics configured to image the interference pattern onto the detector so that different elements of the detector correspond to different illumination angles of the test surface by the test electromagnetic radiation; and (iv) an electronic processor coupled to the detector, wherein the electronic processor is configured to process information measured by the detector to determine information about a test object having the test surface. The measurements made by the detector elements provide ellipsometry/reflectometry data for the test surface.

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
Under 35 U.S.C § 119(e), the present application claims priority to U.S. Provisional Patent Application Ser. No. 60/645,448, filed Jan. 20, 2005 and entitled “INTERFEROMETER FOR DETERMINING CHARACTERISTICS OF AN OBJECT SURFACE,” the contents of which is incorporated herein by reference.


BACKGROUND
The invention relates to interferometry.
Interferometric techniques are commonly used to measure the profile of a surface of an object. To do so, an interferometer combines a measurement wavefront reflected from the surface of interest with a reference wavefront reflected from a reference surface to produce an interferogram. Fringes in the interferogram are indicative of spatial variations between the surface of interest and the reference surface.
A scanning interferometer scans the optical path length difference (OPD) between the reference and measurement legs of the interferometer over a range comparable to, or larger than, the coherence length of the interfering wavefronts, to produce a scanning interferometry signal for each camera pixel used to measure the interferogram. A limited coherence length can be produced, for example, by using a white-light source, which is referred to as scanning white light interferometry (SWLI). A typical scanning white light interferometry (SWLI) signal is a few fringes localized near the zero optical path difference (OPD) position. The signal is typically characterized by a sinusoidal carrier modulation (the “fringes”) with bell-shaped fringe-contrast envelope. The conventional idea underlying SWLI metrology is to make use of the localization of the fringes to measure surface profiles.
SWLI processing techniques include two principle trends. The first approach is to locate the peak or center of the envelope, assuming that this position corresponds to the zero optical path difference (OPD) of a two-beam interferometer for which one beam reflects from the object surface. The second approach is to transform the signal into the frequency domain and calculate the rate of change of phase with wavelength, assuming that an essentially linear slope is directly proportional to object position. See, for example, U.S. Pat. No. 5,398,113 to Peter de Groot. This latter approach is referred to as Frequency Domain Analysis (FDA).
Scanning interferometry can be used to measure surface topography and/or other characteristics of objects having complex surface structures, such as thin film(s), discrete structures of dissimilar materials, or discrete structures that are underresolved by the optical resolution of an interference microscope. Such measurements are relevant to the characterization of flat panel display components, semiconductor wafer metrology, and in-situ thin film and dissimilar materials analysis. See, e.g., U.S. Patent Publication No. US-2004-0189999-A1 by Peter de Groot et al. entitled “Profiling Complex Surface Structures Using Scanning Interferometry” and published on Sep. 30, 2004, the contents of which are incorporated herein by reference, and U.S. Patent Publication No. US-2004-0085544-A1 by Peter de Groot entitled “Interferometry Method for Ellipsometry, Reflectometry, and Scatterometry Measurements, Including Characterization of Thin Film Structures” and published on May 6, 2004, the contents of which are incorporated herein by reference.
Other techniques for optically determining information about an object include ellipsometry and reflectometry. Ellipsometry determines complex reflectivity of a surface when illuminated at an oblique angle, e.g. 60°, sometimes with a variable angle or with multiple wavelengths. To achieve greater resolution than is readily achievable in a conventional ellipsometer, microellipsometers measure phase and/or intensity distributions in the back focal plane of the objective, also known as the pupil plane, where the various illumination angles are mapped into field positions. Such devices are modernizations of traditional polarization microscopes or “conoscopes,” linked historically to crystallography and mineralogy, which employs crossed polarizers and a Bertrand lens to analyze the pupil plane birefringent materials.
Conventional techniques used for thin film characterization (e.g., ellipsometry and reflectometry) rely on the fact that the complex reflectivity of an unknown optical interface depends both on its intrinsic characteristics (material properties and thickness of individual layers) and on three properties of the light that is used for measuring the reflectivity: wavelength, angle of incidence, and polarization state. In practice, characterization instruments record reflectivity fluctuations resulting from varying these parameters over known ranges. Optimization procedures such as least-squares fits are then used to get estimates for the unknown parameters by minimizing the difference between measured reflectivity data and a reflectivity function derived from a model of the optical structure.
SUMMARY
In at least one embodiment, an interferometry method and apparatus is disclosed that produces angularly resolved interference signals from a test surface over a range of wavelenghths. The information related to each wavelength may be extracted mathematically or in hardware. Furthermore, the optical hardware for obtaining the angularly resolved interference signals from the test surface is interchangeable with optical hardware useful for other surface characterization tasks, such as conventional interferometric surface profiling. Accordingly, an interferometry system is disclosed that is capable of operating in an ellipsometry mode for providing complex reflectivity information of the test surface for a range of angles, wavelengths, and polarizations, and a profiling mode for providing information about the test surface over a range of test surface locations.
We now summarize various aspects and features of the invention.
In general, in one aspect, the system includes: (i) an interferometer configured to direct test electromagnetic radiation to a test surface and reference electromagnetic radiation to a reference surface and subsequently combine the electromagnetic radiation to form an interference pattern, the electromagnetic radiation being derived from a common source; (ii) a multi-element detector; and (iii) one or more optics configured to image the interference pattern onto the detector so that different elements of the detector correspond to different illumination angles of the test surface by the test electromagnetic radiation.
Embodiments of the system may include any of the following features.
The interferometer may include an interference objective having a pupil plane. Furthermore, the one or more optics may image the interference pattern at the pupil plane to the multi-element detector. Also, the interferometer may be configured to image EM radiation emitted from the common source to the pupil plane of the interference objective. By way of example, the interference objective be a Mirau objective or a Michelson objective.
The one or more optics may be configured to be selective adjusted to image the test surface onto the detector or to image the interference pattern onto the detector so that different elements of the detector correspond to different illumination angles of the test surface by the test electromagnetic radiation. In other words, the detector in the system can alternate between recording an optical profile of the test surface and recording angularly resolved interference data about the test surface.
In some embodiments, the test EM radiation can be reflected from the test surface. Alternatively, in other embodiments, the test EM radiation can be transmitted through the test surface.
The interferometer may include a scanning stage to adjust the relative optical path length between the test and reference EM radiation when they form the optical interference pattern.
The system may further include the common source. For example, the common source may be a broadband source. The interferometer may also include a scanning stage to adjust the relative optical path length between the test and reference EM radiation when they form the optical interference pattern, and the scanning stage may be configured to vary the optical path length over a range larger than a coherence length for the common source.
The interferometer may further include one or more polarization elements positioned to adjustably control the polarization content of the interference pattern measured by the detector
The system may further include an electronic processor coupled to the detector, wherein the electronic processor is configured to analyze information about the interference pattern to determine angularly resolved information about a test object having the test surface. For example, the test object may have at least one layer adjacent the test surface.
In general, in another aspect, an apparatus is disclosed including: (i) an interferometer configured to direct test light to a test surface and subsequently combine it with reference light to form an interference pattern, the test and reference light being derived from a common source; (ii) an electronic detector; and (iii) one or more optics configured to direct at least a portion of the combined light to the detector so that different regions of the detector correspond to different illumination angles of the test surface by the test light.
Embodiments of the apparatus may include any of the following features.
The interferometer may include a beam splitter configured to separate input light derived from the common source into the test light and the reference light, and a reference surface positioned to reflect the reference light before it is combined with the test light. The test light is configured to reflect from the test surface, and the beam splitter in the interferometer is positioned to recombine the test and reference light after they reflect from the respective test and reference surfaces.
The interferometer may further includes a lens to focus the test light to the test surface. The lens defines a pupil plane and the one or more optics image the pupil plane onto the detector. The common source is spatially extended, and the input light is imaged from the common source to the pupil plane. A field stop can be positioned to define the spatial extent of the test light on the test surface.
The interferometer can include an interference objective having a pupil plane. For example, the interference objective can be a Mirau interference objective or a Michelson interference objective. The one or more optics can image the interference pattern at the pupil plane to the multi-element detector.
The detector can include multiple detector elements with different detector elements corresponding to different illumination angles of the test surface by the test light.
The test and reference light derived from the common source can be in the visible portion of the electromagnetic spectrum. Alternatively, they can be in the ultraviolet, near-infrared, or infrared portions of the electromagnetic spectrum.
The test light is configured to reflect from the test surface. Alternatively, in some embodiments, the test light is configured to transmit through the test surface.
The apparatus can further include a translation stage configured to adjust the relative optical path length between the test and reference light when they form the interference pattern. For example, the apparatus can further include a base for supporting a test object having the test surface, and the translation stage can be configured to move at least a portion of the interferometer (such as an interference objective in the interferometer) relative to the base.
The apparatus can further include the common source. The translation stage can be configured to vary the optical path length over a range larger than a coherence length for the common source. The common source can be a broadband source spanning more than 50 nm (or more than 100 nm, or even more than 200 nm) at full width half maximum.
In certain embodiments, the common source can be a tunable source. For example, the apparatus can further include an electronic processor coupled to the detector and the tunable source, and configured to process images recorded by the detector for different wavelength settings of the tunable source. In such cases, the interferometer can include a reference surface positioned to reflect the reference light, wherein the reference surface is further positioned to produce a non-zero optical path length difference with the test light at the interference pattern.
The interferometer can further include one or more polarization elements positioned to adjust the polarization content of the interference pattern measured by the detector. For example, the one or more polarization elements can include a first polarizer positioned to receive input light from the common source from which the test and reference light are derived. In one case, for example, the one or more polarization element can further include a second polarizer positioned to receive the combined light before it reaches the detector. In another case, for example, the first polarizer is further positioned to receive the combined light before it reaches the detector. Furthermore, the one or more polarization elements can include a quarter-wave plate positioned to receive input light from the common source from which the test and reference light are derived and the combined light before it reaches the detector.
The interferometer can include a lens to focus the test light to the test surface, and the one or more polarization elements can include a first polarizer positioned to cause the test light to be linearly polarized prior to being focused by the lens. For example, the first polarizer can cause the test light to have a polarization at the test surface that varies azimuthally between s- and p-polarized light. The first polarizer can be positioned to also cause the combined light to be linearly polarized at the detector. Alternatively, the one or more optics can further include a second polarizer positioned to cause the combined light to be linearly polarized at the detector. For example, the first and second polarizers can have a common orientation.
Different locations on the detector can correspond to different combinations of Fresnel reflection coefficients for s- and p-polarized light at the detector. The relative combination of the s- and p-polarized reflection coefficients can depend on an azimuthal coordinate on the detector and the angle dependence of the Fresnel coefficients depends on a radial coordinate.
The interferometer can include a beam splitter positioned receive input light from the common source along a first direction and direct the combined light toward the detector along a second direction different from the first direction.
The apparatus can further include an electronic processor coupled to the detector, wherein the electronic processor is configured to process information measured by the detector to determine information about a test object having the test surface. For example, the test object can includes one or more layers on a substrate. In certain embodiments, the electronic processor can extract angularly resolved reflectivity information about the test surface from the detector measurement, and determine the information about the test object based on the angularly resolved information. For example, the information can include a refractive index estimate for a portion of the test object and/or a thickness estimate for a layer in the test object. The electronic processor can be configured to determine the information about the test object based on a comparison between data based on the information measured by the detector and a model for the test object. For example, the model can provide an estimate for the measured information as a function of one or more parameters for the test object, and wherein the comparison selects values for the one or more parameters to optimize the fit between the measured information and that provided by the model.
The apparatus can further include a translation stage configured to adjust the relative optical path length between the test and reference light when they form the interference pattern, wherein the electronic processor is configured to analyze an interference intensity signal measured at each of multiple locations across the detector and produced by scanning the translation stage. Furthermore, the electronic processor can be configured to determine the correspondence between the different regions of the detector and the different illumination angles of the test surface by the test light based on the frequency of the intensity signal at different locations on the detector.
Also, the electronic processor can be configured to extract angularly resolved and wavelength-resolved information about the test surface based on the intensity signals measured across the detector. For example, the electronic processor can be configured to transform the interference signal at different locations of the detector into a frequency domain to extract the angularly resolved and wavelength-resolved information.
The interferometer can includes one or more polarization elements positioned to adjust the polarization content of the interference pattern measured by the detector. As a result, the electronic processor can be configured to extract angularly resolved, wavelength-resolved, and polarization-resolved information about the test surface based on the intensity signal measured across the detector. For example, the angularly resolved, wavelength-resolved, and polarization-resolved information can be complex reflectivity information about the test surface.
The electronic processor can be configured to select a subset of each of the interference intensity signals, the subsets corresponding to a selected interface in the test object, and process the subsets of interference intensity signals to determine information about the test object related to the selected interface.
The electronic processor can store calibration information about the optical properties of the interferometer and use the calibration information and the information measured by the detector to determine the information about the test object.
The apparatus can be configured to adjustably switch between a first mode of operation in which the combined light is directed to the detector so that different regions of the detector correspond to different illumination angles of the test surface by the test light and a second mode of operation in which different regions of the detector correspond to the different regions of the test surface illuminated by the test light to enable a profiling mode of operation.
For example, the apparatus can further include a stage configured to adjust the position of the detector relative to the one or more optics to switch between the first and second modes of operation. The apparatus can also include an electronic controller coupled to the detector stage and configured to adjustably cause the stage to switch between the first and second modes of operation.
In another example, the one or more optics can include a first set of one or more optics for operating in the first mode of operation and a second set of one or more optics for operating in the second mode of operation. The apparatus can include a multi-position optics holder supporting the first and second set of optics and configured to adjustably position one of the first and second sets and not the other of the first and second sets in the path of the combined light being directed to the detector to switch between the first and second modes.
The multi-positioned lens holder can be motorized, and the apparatus can further include an electronic controller coupled to the motorized multi-position optics holder to selectively cause the multi-position optics holder to switch between the first and second modes of operation.
In yet another example, the apparatus can further include a second set of one or more optics, a beam splitter positioned to direct a first portion of the combined to light to the first of optics and direct a second portion of the combined light to the second set of optics, and a second electronic detector. The second set of optics is configured to direct the second portion of the combined light to the second electronic detector so that different regions of the second detector correspond to the different regions of the test surface illuminated by the test light, corresponding to the second mode.
The apparatus can further include an electronic processor coupled to the detector and configured to process information measured by the detector in each mode of operation to determine information about a test object having the test surface. The electronic processor is configured to use information derived in one mode of operation to assist in determining further information about the test object when using the other mode of operation.
For example, the information derived in the first mode may correspond to a refractive index of a portion of the test object, and the electronic processor can be configured to determined a phase change on reflection (PCOR) based on the refractive index to assist in determining topography information when operating in the second mode. In another example, the information derived in the second mode corresponds to an estimate for the surface roughness of the test surface, and the electronic processor can be configured to use the surface roughness estimate to process information measured by the detector in the first mode to determine information about the test object.
The interferometer can include a multi-position mount (e.g., a turret) configured to support multiple objectives and position a selected objective in the path of input light from the common source, the multiple objectives including at least one interference objective. The multi-position mount can be motorized, and the apparatus can further include an electronic controller coupled to the multi-position mount to selectively cause the mount to switch between objectives. For example, the multiple objectives can include two different interference objectives, only one of which includes a polarization optic. The multiple objectives can also include one or more non-interferometric objectives, each of which when positioned in the path of the input light enables the apparatus to operate in a non-interferometric, microscope mode.
In general, in another aspect, an interferometry method is disclosed, including: (i) directing test light to a test surface over a range of illumination angles; (ii) subsequently combining the test light with reference light to form an interference pattern, wherein the test and reference light are derived from a common source; and (iii) directing at least a portion of the combined light to a multi-element detector so that different elements of the detector correspond to different illumination angles of the test surface by the test light.
Embodiments of the method may include any of the following features.
The combined light can be directed to the detector by imaging a pupil plane for the test light to the detector.
The method may further include measuring an interference signal at each of multiple elements of the detector as a function of varying an optical path length difference between the test and reference light.
The test light, reference light, and combined light can be selectively polarized.
The method can further include determining information about a test object having the test surface based on a signal measured at different detector elements. For example, determining the information about the test object can include determining a reflectivity for the test surface with respect to different illumination angles and wavelengths. The reflectivity can be a complex reflectivity with respect to the different illumination angles and wavelengths, for a selected polarization state. Determining the information about the test object further can include comparing the measured reflectivity to an estimate for the reflectivity based on a model of the test object.
As part of a calibration step, the method may further include determining a relationship between different illumination angles of the test surface by the test light and different elements of the detector based on the frequency of the interference signal at different detector elements. Also, the method may further include determining the location of an optical axis for the combined light on the detector based on the frequency of the interference signal at different detector elements. Also, the method may further include determining the rate at which the optical path length difference is varied by based on the frequency of the interference signal at different detector elements.
As part of a further calibration, the test surface may have known reflection properties, and the method may further include calibrating reflection parameters of an interferometer used to direct the test light and combine it with the reference light based on a signal measured at different detector elements and the known reflection parameters of the test surface. The method may further include repeating the steps with a second test surface having known reflection properties, and further calibrating reflection parameters of the interferometer based on signals measured at the different detector elements and the known reflection parameters of the test surfaces.
The method may further include features corresponding to those listed for the apparatus described above.
In general, in another aspect, an apparatus is disclosed including: an interferometry system configured to operate in each of a first mode that measures reflectivity of a test surface over a range of angles and wavelengths and a second mode that measures one or more properties of the test surface over across a range of test surface locations.
Embodiments of the apparatus may include any of the following features.
The apparatus can be configured to selectively switch between the first and second modes. Alternatively, the apparatus can be configured to simultaneously provide measurements in both modes.
The interferometer can include at least one electronic detector, and in the first mode different elements of the detector correspond to different illumination angles of the test surface by test light in the interferometry system. The first mode can corresponds to an ellipsometry mode that measures the reflectivity of the test surface over the range of angles and wavelengths for one or more selected polarizations. Alternatively, the first mode can corresponds to an reflectometry mode that measures the reflectivity of the test surface over the range of angles and wavelengths for unpolarized light. To operate in the first mode, the interferometer can image a pupil plane for test light directed to the test surface to the detector.
In the second mode, different elements of the detector correspond to different locations of the test surface illuminated by test light in the interferometry system. Specifically, the interferometer is configured to image the test surface to the detector. The second mode can be a profiling mode.
The apparatus can further include an electronic processor coupled to the interferometry system and configured to process information measured by the interferometry system in each mode of operation to determine information about a test object having the test surface. Furthermore, he electronic processor can be configured to use information derived in one mode of operation to assist in determining further information about the test object when using the other mode of operation.
The interferometry system can be further configured to selectively operate in non-interferometric microscopy mode to measure non-interferometric optical images of the test surface.
In general, in another aspect, a method is disclosed including: (i) using an interferometry system to measure a test surface in a first mode of operation that measures reflectivity of the test surface over a range of angles and wavelengths; and (ii) using the same interfometry system to measure the test surface in a second mode of operation that interferometrically profiles a topography of the test surface.
The method may further include using the same interferometry system to measure the test surface in a third mode of operation that produces one or more non-interferometric, microscope images of the test surface.
As used herein, “light” is not limited to electromagnetic radiation in the visible spectral region, but rather refers generally to electromagnetic radiation in any of the ultraviolet, visible, near infrared, and infrared spectral regions.
Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. In case of conflict with any document incorporated by reference, the present disclosure controls.
Other features, objects, and advantages of the invention will be apparent from the following detailed description.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic diagram of an interferometry system 100 configured to operate in an ellipsometry mode.
FIG. 2 is a graph showing an example of an interferometry signal measured a detector element when the optical path length difference (“OPD”) between the test and reference light in interferometry system 100 is varied, where the OPD is expressed by frame number.
FIG. 3 is a schematic diagram of interferometry system 100 reconfigured to operate in a profiling mode.
FIG. 4 shows plots of a data collected by a detector element for a test object having 1-micron thick silicon dioxide film on a silicon substrate. The left plot shows interferometry signal measured by the detector element as a function of frame number during the OPD scan. The right plot shows the Fourier transform of the interferometry signal with respect to wavenumber, with spectral magnitude being shown by solid trace and spectral phase being shown by the dotted trace.
FIG. 5 shows plots of experimentally derived, complex reflectivity coefficients for a selected angle of incidence (43 degrees) and a selected wavelength (576 nm) as a function of azimuth angle for a 675-nm thick silicon dioxide monolayer film on a silicon substrate. The left plot shows the spectral component Z (top curve being the real component and the bottom curve being the imaginary component) and the right plot shows the corresponding values for z (top curve being the real component and the bottom curve being the imaginary component), which scales Z with respect to a system calibration.
FIG. 6 shows a plot of the interferometry signal for a 5-micron thick film of silicon dioxide on silicon to demonstrate how portion of the signal can be selected to isolate a selected interface in the structure.
FIG. 7 is a schematic diagram of another embodiment for interferometry system 100.
FIG. 8 is a schematic diagram of yet another embodiment for interferometry system 100.
FIG. 9 is a schematic diagram of interferometry system 100 showing how various components can be adjusted in an automated fashion under the control an electronic processor.



Like reference numerals in different drawings refer to common elements.
DETAILED DESCRIPTION
Conventional techniques used for thin film characterization (e.g., ellipsometry) rely on the fact that the complex reflectivity of an unknown optical interface depends both on its intrinsic characteristics (e.g., material properties and thicknesses of individual layers) and on three properties of the light that is used for measuring the reflectivity: wavelength, angle of incidence, and polarization state. In practice, ellipsometry instruments record reflectivity fluctuations resulting from varying these parameters over known ranges. Optimization procedures such as least-squares fits are then used to get estimates for the unknown parameters by minimizing the difference between measured reflectivity data and a reflectivity function derived from a model of the optical structure.
Embodiments disclosed herein provide an interferometry system and method for rapidly collecting a large number of reflectivity data points over a wide range for all three optical characteristics of the probe beam (i.e., wavelength, angle of incidence, and polarization state) for a selected region of a test surface. Furthermore, the same instrument can switch from this ellipsometry mode of operation to a profiling mode to provide laterally resolved information about the test surface. Moreover, information determined in the ellipsometry mode can be used to improve the accuracy of the information obtained in the profiling mode. For example, the ellipsometry mode can provide information about the material properties of the test object having the test surface to create more accurate topography maps of the various optical interfaces, the top surface (air interface), for example, being of particular interest.
Exemplary Apparatus
FIG. 1 is a schematic diagram of an interferometry system 100. A spatially extended source 102 directs input light 104 to an interference objective 106 via relay optics 108 and 110 and beam splitter 112. The relay optics 108 and 110 image input light 104 from spatially extended source 102 to an aperture stop 115 and corresponding pupil plane 114 of the interference objective 106 (as shown by the dotted marginal rays 116 and solid chief rays 117).
In the embodiment of the FIG. 1, interference objective 106 is of the Mirau-type, including an objective lens 118, beam splitter 120, and reference surface 122. Beam splitter 120 separates input light 104 into test light 122, which is directed to a test surface 124 of a test object 126, and reference light 128, which reflects from reference surface 122. Objective lens 118 focuses the test and reference light to the test and reference surfaces, respectively. The reference optic 130 supporting reference surface 122 is coated to be reflective only for the focused reference light, so that the majority of the input light passes through the reference optic before being split by beam splitter 120.
After reflecting from the test and reference surfaces, the test and reference light are recombined by beam splitter 120 to form combined light 132, which is transmitted by beam splitter 112 and relay lens 136 to form an optical interference pattern on an electronic detector 134 (for example, a multi-element CCD or CMOS detector). The intensity profile of the optical interference pattern across the detector is measured by different elements of the detector and stored in an electronic processor (not shown) for analysis. Unlike a conventional profiling interferometer in which the test surface is imaged onto the detector, in the present embodiment, relay lens 136 (e.g., a Bertrand lens) images different points on the pupil plane 114 to corresponding points on detector 134 (again as illustrating by dotted marginal rays 116 and solid chief rays 117).
Because each source point illuminating pupil plane 114 creates a plane wave front for test light 122 illuminating test surface 124, the radial location of the source point in pupil plane 114 defines the angle of incidence of this illumination bundle with respect to the object normal. Thus, all source points located at a given distance from the optical axis correspond to a fixed angle of incidence, by which objective lens 118 focuses test light 122 to test surface 124. A field stop 138 positioned between relay optic 108 and 110 defines the area of test surface 124 illuminated by test light 122. After reflection from the test and reference surfaces, combined light 132 forms a secondary image of the source at pupil plane 114 of the objective lens. Because the combined light on the pupil plane is then re-imaged by relay lens 136 onto detector 134, the different elements of the detector 134 correspond to the different illumination angles of test light 122 on test surface 124.
Polarization elements 140, 142, 144, and 146 define the polarization state of the test and reference light being directed to the respective test and reference surfaces, and that of the combined light being directed to the detector. Depending on the embodiment, each polarization element can be a polarizer (e.g., a linear polarizer), a retardation plate (e.g., a half or quarter wave plate), or a similar optic that affects the polarization state of an incident beam. Furthermore, in some embodiments, one or more of the polarization elements can be absent. Moreover, depending on the embodiment, beam splitter 112 can be polarizing beam splitter or a non-polarizing beam splitter. Details of various embodiments for these polarization elements are described further below. In general, because of the presence of polarization elements 140, 142 and/or 146, the state of polarization of test light 122 at test surface 124 can be a function of the azimuthal position of the light in pupil plane 114.
In the presently described embodiment, source 102 provides illumination over a broad band of wavelengths (e.g., an emission spectrum having a full-width, half-maximum of more than 50 nm, or preferably, even more than 100 nm). For example, source 102 can be a white light emitting diode (LED), a filament of a halogen bulb, an arc lamp such as a Xenon arc lamp or a so-called supercontinuum source that uses non-linear effects in optical materials to generate very broad source spectra (>200 nm). The broad band of wavelengths corresponds to a limited coherence length. As in conventional scanning interferometer, a translation stage 150 adjusts the relative optic path length between the test and reference light to produce an optical interference signal at each of the detector elements. For example, in the embodiment of the FIG. 1, translation stage 150 is a piezoelectric transducer coupled to interference objective 106 to adjust the distance between the test surface and the interference objective, and thereby vary the relative optical path length between the test and reference light at the detector.
FIG. 2 shows an exemplary interference signal measured by one of the detector elements as the translation stage varies the relative optical path length between the test and reference light. The interference signal is modulated by a contrast envelope corresponding to the coherence length of the source. The reference surface is positioned in the interferometer so that a zero optical path length difference between the test and reference light corresponds to a position of the test surface that is in focus with respect to objective lens 118. Thus, maximum contrast is generally observed when the test surface is in this in-focus position relative to the interference objective. A measurement is performed by scanning the translation stage over a range larger than the coherence length so that the contrast envelope is captured in a sequence of intensity patterns measured at the detector.
The interference signal measured at each detector element is analyzed by the electronic processor, which electronically coupled to both detector 134 and translation stage 150. In the presently described embodiment, the electronic processor transforms the interference signal into the frequency domain, for example, by using a Fourier transform, to extract the phase and amplitude information for the different wavelength components of the light source. Preferably, the source spectrum is broad so that many independent spectral components can be calculated with this procedure. As will be described in greater detail below, the amplitude and phase data relate directly to the complex reflectivity of the test surface, which can be analyzed to determine information about the test object. Generally, the electronic processor uses information from a separate calibration to correct the measurement for the reflectivity of the reference mirror and other optical characteristics of the interferometer. Because of the arrangement of interferometry system 100, each detector element of electronic detector 134 provides reflectivity measurements at a multiplicity of wavelengths produced by source 102, for a specific angle of incidence and polarization state (according to the orientations of polarization elements 140, 142, 144 and/or 146). The collection of detector elements thus covers a range of angles of incidence, polarization states and wavelengths, which maximizes the ability of the instrument to properly characterize unknown optical structures.
A number of calibration procedures can be used to derive the complex reflectivity of the test surface from the measured interference signals. For example, a calibration measurement can be made with a mirror made of known bulk material (opaque or transparent) as the test object, and a spectral filter can be used to isolate a selected wavelength from the source. The interference signals measured on the detector can then be processed to determine the angle of incidence corresponding to each detector element and the speed of the scanning stage used for data acquisition. The latter information is useful to properly match the interference signal spectral components to their respective wavelengths. Additional measurements using objects of known optical properties can also be used to derive the properties of the interferometer and imaging system on a pixel-by-pixel basis. For example, a calibration may include the steps of calculating the transmission of the system for each wavelength and at each detector position. Similarly, polarization effects such as phase offsets introduced between orthogonal states of polarization can also be measured for each detector element and for each wavelength if required. Specific details for certain embodiments of the calibration are described further below.
To switch interferometry system 100 from an ellipsometry mode for a determining the complex reflectivity of the test surface, to a profiling mode for determining, for example, the topography of the test surface, it is sufficient to change the properties of the imaging system so that the image of the part comes in focus on the detector instead of the image of the source. As shown in FIG. 3, this can be accomplished, for example, by replacing the relay lens 136 by another lens 236 and keeping the detector position fixed. In this case, the input light from source 102 continues to be imaged to pupil plane 114, however, the points on 124 are imaged to corresponding points on detector 134 (as indicated by marginal rays 216 and chief rays 217 from source 102).
Measurement Model
To demonstrate the analysis of the interference signals obtained by interferometry system 100, we consider an embodiment in which polarization elements 140 and 144 are linear polarizers, polarization elements 142 and 146 are absent, and beam splitter 112 is a non-polarizing beam splitter. The effect of the linear polarizer 140 is to create an identical linear polarization state at every point in pupil plane 114. As a result, the polarization of the light incident on test surface 124 is linear, but its orientation with respect to the plane of incidence is a function of the azimuthal location of the source point at the pupil plane. For example, the source points that belong to a pupil diameter that is parallel to the direction of the linear polarization in the pupil plane will generate illumination light that is linearly polarized within the plane of incidence at the test surface (this is called the P polarization state). Similarly, the source points that belong to a diameter that is perpendicular to the direction of the linear polarization in the pupil plane will generate illumination light that is linearly polarized perpendicularly to the plane of incidence (this is called the S polarization state). Source points that do not belong to these two diameters will create illumination light on the test surface that has a mix of S and P polarization states. This is relevant because the reflectivity coefficients for the test surface are different for S and P polarized light.
The two linear polarizers can have a number of relative orientations that will dictate the content of the interference signal detected by the detector. For example, if the polarizers are parallel then the measured interference signal will depend solely on S-polarized test light being incident on the test surface for one diameter of the pupil plane and depend solely on P-polarized test light being incident on the test surface for an orthogonal diameter of the pupil plane (and similarly, for the reference light incident on the reference surface). This is attractive because the difference between the magnitude and phase of S and P reflectivities is the basis for ellipsometry. If desired, therefore, simplified processing of the data can be restricted to these two diameters. On the other hand, using the data over the entire pupil plane requires taking into account the mix of the two polarization states, but provides more data points and thus increases the resolution of the measurement.
The following analysis applies to the arrangement with the two linear polarizers aligned parallel to one another. In this case, the amount of test light that is transmitted through the second linear polarizer (polarization element 144) to detector 134 can be expressed as:




  
    
      
        
          E
          out
        
        =
        
          
            1
            2
          
          ⁢
          
            (
            
              
                
                  
                    cos
                    ⁡
                    
                      (
                      θ
                      )
                    
                  
                  2
                
                ⁢
                
                  rp
                  ·
                  tp
                
              
              -
              
                
                  
                    sin
                    ⁡
                    
                      (
                      θ
                      )
                    
                  
                  2
                
                ⁢
                
                  rs
                  ·
                  ts
                
              
            
            )
          
          ⁢
          
            E
            in
          
        
      
    
    
      
        (
        1
        )
      
    
  




where θ is the azimuth angle measured with respect to the direction of the polarizers, rp and rs are the complex reflection coefficients of the object surface for P and S polarization states (known as the “Fresnel reflection coefficients”), tp and ts are the transmission coefficients for P and S polarization states for the round trip through the interference objective 106 and the main beam splitter 112 and Eout is the complex amplitude of the electric field. This model assumes that the optics are free from birefringence and that reflection off the object surface is also free from mechanisms that would mix the S and P polarizations states. For example, a uniaxial material with its axis along the local surface normal can be characterized in this context, however, a material having in-plane birefringence requires a different model.

In practice, the same model applies for the reference light that propagates along the reference leg of the interferometer, however, the reflection and transmission coefficients are a priori different:




  
    
      
        
          E
          out
          r
        
        =
        
          
            1
            2
          
          ⁢
          
            (
            
              
                
                  
                    cos
                    ⁡
                    
                      (
                      θ
                      )
                    
                  
                  2
                
                ⁢
                
                  
                    rp
                    r
                  
                  ·
                  
                    tp
                    r
                  
                
              
              -
              
                
                  
                    sin
                    ⁡
                    
                      (
                      θ
                      )
                    
                  
                  2
                
                ⁢
                
                  
                    rs
                    r
                  
                  ·
                  
                    ts
                    r
                  
                
              
            
            )
          
          ⁢
          
            E
            
              i
              ⁢
              
                
              
              ⁢
              n
            
          
        
      
    
    
      
        (
        2
        )
      
    
  




The interference pattern that is measured at the detector for a given source wavelength λ and a given source point at the pupil plane consists of a modulating term that is proportional to the product EoutEout:

Intensity(k,α,z)=|Eout|2+|Erout|2+2|Eout||Erout|cos(2k cos(α)z+φ(k,α))

where k=2π/λ, λ is the wavelength of the light, z is the vertical location of the test surface during a mechanical scan relative to a zero optical path length difference between the test and reference light, α is the angle of incidence of the light at the test surface (which depends on the source point location at the pupil) and φ is a phase difference between the test and reference electric fields. In practice, the signal measured at a given detector location is the sum of all such signals generated by the various wavelengths present in the source spectrum. As a result, a Fourier transformation of the signal allows separating these contributions into complex spectral components corresponding to very narrow wavelength ranges. Note that in order to assign a calculated spectral component to a specific source wavelength one should take into account the correction factor cos(α), which shifts the location of these spectral components. This correction factor involves knowing the angle of incidence of light at each pixel of the detector. A calibration of the optical system can be used for this task and is discussed further below.

FIG. 4 (left side plot) shows a representative interference signal measured by a given detector element of detector 134 (corresponding to a given location in the pupil plane) when measuring a 1003-nm thick silicon dioxide film on silicon. FIG. 4 (right side plot) shows the result of Fourier transforming the interference signal to yield the spectral magnitude and phase as function of wavelength (or the corresponding wavenumber k). The variation in the spectral magnitude and phase is a result of the variation of the Fresnel reflection coefficient as a function of the wavelength (or wavenumber).
In certain embodiments, the frequency transform processing is applied to a region of interest within the image of the pupil plane on the detector. For example, the region of interest can be an annulus, which defines a given range of angles of incidence at the test surface. The azimuthal location of a pixel (i.e., one of the detector elements) within this annulus defines the mix of S and P polarization that illuminates the test surface and the radial distance of the pixel to the optical axis defines the angle of incidence. Furthermore, it can be useful to extract (possibly using interpolation) the spectral components as described above over multiple circles within the region of interest. These components calculated over one such circle can be written in the form:




  
    
      
        
          
            Z
            
              α
              ⁢
              
                
              
              ⁢
              λ
              ⁢
              
                
              
              ⁢
              θ
            
          
          =
          
            
              L
              λ
            
            ⁢
            
              I
              
                α
                ⁢
                
                  
                
                ⁢
                λ
                ⁢
                
                  
                
                ⁢
                θ
              
            
            ⁢
            
              exp
              ⁡
              
                (
                
                  i
                  ⁢
                  
                    
                  
                  ⁢
                  
                    φ
                    
                      α
                      ⁢
                      
                        
                      
                      ⁢
                      λ
                      ⁢
                      
                        
                      
                      ⁢
                      h
                    
                  
                
                )
              
            
            ⁢
            
              (
              
                
                  
                    
                      cos
                      ⁡
                      
                        (
                        θ
                        )
                      
                    
                    2
                  
                  ⁢
                  
                    ρ
                    
                      α
                      ⁢
                      
                        
                      
                      ⁢
                      λ
                    
                  
                
                -
                
                  
                    
                      sin
                      ⁡
                      
                        (
                        θ
                        )
                      
                    
                    2
                  
                  ⁢
                  
                    τ
                    
                      α
                      ⁢
                      
                        
                      
                      ⁢
                      λ
                    
                  
                
              
              )
            
          
        
        ⁢
        
          

        
        ⁢
        with
        ⁢
        
          

        
        ⁢
        
          
            ρ
            
              α
              ⁢
              
                
              
              ⁢
              λ
            
          
          =
          
            
              
                
                  rp
                  
                    α
                    ⁢
                    
                      
                    
                    ⁢
                    λ
                  
                
                
                  rs
                  
                    α
                    ⁢
                    
                      
                    
                    ⁢
                    λ
                  
                
              
              ⁢
              
                
              
              ⁢
              and
              ⁢
              
                
              
              ⁢
              
                τ
                
                  α
                  ⁢
                  
                    
                  
                  ⁢
                  λ
                
              
            
            =
            
              
                ts
                
                  α
                  ⁢
                  
                    
                  
                  ⁢
                  λ
                
              
              
                tp
                
                  α
                  ⁢
                  
                    
                  
                  ⁢
                  λ
                
              
            
          
        
      
    
    
      
        (
        4
        )
      
    
  




where the subscripts denote a functional dependence, α is the angle of incidence corresponding to the radius of the circle at the pupil plane, λ is the wavelength of light, θ is the azimuthal angle measured with respect to the linear polarizers, h is a height offset of the object surface, L is a real scaling factor related to the source intensity or signal strength and I is a complex function that represents the variations of the light intensity across the source as well as phase and amplitude variations occurring in the optics.

The electronic processor can use the above formula as the key model for the measurement process. For example, the processor can Fourier transform the interference signals recorded by the detector to yield the component Z for different wavelengths and angles, of incidence and by inversion extract the complex ratio rp/rs that relates to the test surface being characterized (e.g., based on Eq. 4). This ratio is called the ellipsometric ratio and can also be expressed as:




  
    
      
        
          ρ
          
            α
            ⁢
            
              
            
            ⁢
            λ
          
        
        =
        
          
            
              rp
              
                α
                ⁢
                
                  
                
                ⁢
                λ
              
            
            
              rs
              
                α
                ⁢
                
                  
                
                ⁢
                λ
              
            
          
          =
          
            
              tan
              ⁡
              
                (
                
                  Ψ
                  
                    α
                    ⁢
                    
                      
                    
                    ⁢
                    λ
                  
                
                )
              
            
            ⁢
            
              exp
              ⁡
              
                (
                
                  i
                  ⁢
                  
                    
                  
                  ⁢
                  
                    Δ
                    
                      α
                      ⁢
                      
                        
                      
                      ⁢
                      λ
                    
                  
                
                )
              
            
          
        
      
    
    
      
        (
        5
        )
      
    
  




where Ψ and Δ are the two well-known ellipsometric parameters. Standard ellipsometry algorithms can then be used to calculate some optical properties of the test object, for example, the thickness and refractive index of transparent films.

For example, for the case of a homogeneous test surface devoid of films, the electronic processor can readily calculate the complex refractive index of the material according to the expression:




  
    
      
        
          n
          ⁡
          
            (
            λ
            )
          
        
        =
        
          
            n
            0
          
          ⁢
          
            tan
            ⁡
            
              (
              α
              )
            
          
          ⁢
          
            
              1
              -
              
                
                  
                    4
                    ⁢
                    
                      
                    
                    ⁢
                    
                      ρ
                      
                        α
                        ⁢
                        
                          
                        
                        ⁢
                        λ
                      
                    
                  
                  
                    
                      (
                      
                        1
                        +
                        
                          ρ
                          
                            α
                            ⁢
                            
                              
                            
                            ⁢
                            λ
                          
                        
                      
                      )
                    
                    2
                  
                
                ⁢
                
                  
                    sin
                    ⁡
                    
                      (
                      α
                      )
                    
                  
                  2
                
              
            
          
        
      
    
    
      
        (
        6
        )
      
    
  




where n0 is the refractive index of the ambient medium, usually air. The technique provides in this case the complex refractive index over the entire source spectrum. Data calculated over multiple angles of incidence can be averaged to improve the measurement resolution.

In another example, for the case of a transparent monolayer having an unknown thickness t and known refractive indices n0, n1, n2 of the ambient, film and substrate materials, the electronic processor can determine the unknown thickness t according to the following equations:




  
    
      
        
          
            α
            0
          
          =
          α
        
        ⁢
        
          
        
        ,
        
          
            α
            1
          
          =
          
            
              
                
                  n
                  0
                
                ⁡
                
                  (
                  λ
                  )
                
              
              
                
                  n
                  1
                
                ⁡
                
                  (
                  λ
                  )
                
              
            
            ⁢
            
              sin
              ⁡
              
                (
                
                  α
                  0
                
                )
              
            
          
        
        ,
        
          
            
              α
              2
            
            =
            
              
                
                  
                    n
                    1
                  
                  ⁡
                  
                    (
                    λ
                    )
                  
                
                
                  
                    n
                    2
                  
                  ⁡
                  
                    (
                    λ
                    )
                  
                
              
              ⁢
              
                sin
                ⁡
                
                  (
                  
                    α
                    1
                  
                  )
                
              
            
          
          ⁢
          
            

          
          ⁢
          
            
              
                r
                
                  01
                  ⁢
                  p
                
              
              =
              
                
                  tan
                  ⁡
                  
                    (
                    
                      
                        α
                        0
                      
                      -
                      
                        α
                        1
                      
                    
                    )
                  
                
                
                  tan
                  ⁡
                  
                    (
                    
                      
                        α
                        0
                      
                      +
                      
                        α
                        1
                      
                    
                    )
                  
                
              
            
            ,
            
              
                r
                
                  12
                  ⁢
                  p
                
              
              =
              
                
                  tan
                  ⁡
                  
                    (
                    
                      
                        α
                        1
                      
                      -
                      
                        α
                        2
                      
                    
                    )
                  
                
                
                  tan
                  ⁡
                  
                    (
                    
                      
                        α
                        1
                      
                      +
                      
                        α
                        2
                      
                    
                    )
                  
                
              
            
          
          ⁢
          
            

          
          ⁢
          
            
              
                r
                
                  01
                  ⁢
                  s
                
              
              =
              
                -
                
                  
                    sin
                    ⁡
                    
                      (
                      
                        
                          α
                          0
                        
                        -
                        
                          α
                          1
                        
                      
                      )
                    
                  
                  
                    sin
                    ⁡
                    
                      (
                      
                        
                          α
                          0
                        
                        +
                        
                          α
                          1
                        
                      
                      )
                    
                  
                
              
            
            ,
            
              
                r
                
                  12
                  ⁢
                  s
                
              
              =
              
                -
                
                  
                    sin
                    ⁡
                    
                      (
                      
                        
                          α
                          1
                        
                        -
                        
                          α
                          2
                        
                      
                      )
                    
                  
                  
                    sin
                    ⁡
                    
                      (
                      
                        
                          α
                          1
                        
                        +
                        
                          α
                          2
                        
                      
                      )
                    
                  
                
              
            
          
          ⁢
          
            

          
          ⁢
          
            
              A
              =
              
                r
                
                  01
                  ⁢
                  p
                
              
            
            ,
            
              B
              =
              
                
                  r
                  
                    12
                    ⁢
                    p
                  
                
                +
                
                  
                    r
                    
                      01
                      ⁢
                      p
                    
                  
                  ⁢
                  
                    r
                    
                      01
                      ⁢
                      s
                    
                  
                  ⁢
                  
                    r
                    
                      12
                      ⁢
                      s
                    
                  
                
              
            
            ,
            
              C
              =
              
                
                  r
                  
                    12
                    ⁢
                    p
                  
                
                ⁢
                
                  r
                  
                    01
                    ⁢
                    s
                  
                
                ⁢
                
                  r
                  
                    12
                    ⁢
                    s
                  
                
              
            
          
          ⁢
          
            

          
          ⁢
          
            
              D
              =
              
                r
                
                  01
                  ⁢
                  s
                
              
            
            ,
            
              E
              =
              
                
                  r
                  
                    12
                    ⁢
                    s
                  
                
                +
                
                  
                    r
                    
                      01
                      ⁢
                      p
                    
                  
                  ⁢
                  
                    r
                    
                      01
                      ⁢
                      s
                    
                  
                  ⁢
                  
                    r
                    
                      12
                      ⁢
                      p
                    
                  
                
              
            
            ,
            
              F
              =
              
                
                  r
                  
                    01
                    ⁢
                    p
                  
                
                ⁢
                
                  r
                  
                    12
                    ⁢
                    p
                  
                
                ⁢
                
                  r
                  
                    12
                    ⁢
                    s
                  
                
              
            
          
          ⁢
          
            

          
          ⁢
          
            X
            =
            
              
                
                  -
                  
                    (
                    
                      B
                      -
                      
                        
                          ρ
                          
                            α
                            ⁢
                            
                              
                            
                            ⁢
                            λ
                          
                        
                        ⁢
                        E
                      
                    
                    )
                  
                
                ±
                
                  
                    
                      
                        (
                        
                          B
                          -
                          
                            
                              ρ
                              
                                α
                                ⁢
                                
                                  
                                
                                ⁢
                                λ
                              
                            
                            ⁢
                            E
                          
                        
                        )
                      
                      2
                    
                    -
                    
                      4
                      ⁢
                      
                        (
                        
                          C
                          -
                          
                            
                              ρ
                              
                                α
                                ⁢
                                
                                  
                                
                                ⁢
                                λ
                              
                            
                            ⁢
                            F
                          
                        
                        )
                      
                      ⁢
                      
                        (
                        
                          A
                          -
                          
                            
                              ρ
                              
                                α
                                ⁢
                                
                                  
                                
                                ⁢
                                λ
                              
                            
                            ⁢
                            D
                          
                        
                        )
                      
                    
                  
                
              
              
                2
                ⁢
                
                  (
                  
                    C
                    -
                    
                      
                        ρ
                        
                          α
                          ⁢
                          
                            
                          
                          ⁢
                          λ
                        
                      
                      ⁢
                      F
                    
                  
                  )
                
              
            
          
          ⁢
          
            

          
          ⁢
          
            t
            =
            
              
                iλ
                
                  4
                  ⁢
                  
                    
                  
                  ⁢
                  π
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      n
                      1
                    
                    ⁡
                    
                      (
                      λ
                      )
                    
                  
                  ⁢
                  
                    cos
                    ⁡
                    
                      (
                      
                        α
                        1
                      
                      )
                    
                  
                
              
              ⁢
              
                log
                ⁡
                
                  (
                  X
                  )
                
              
            
          
        
      
    
    
      
        (
        7
        )
      
    
  




where log is the complex natural logarithm function, i=√{square root over (−1)} and the sign in the calculation of X is chosen according to the resulting value of t, which must be real positive. The processing of the data obtained by interferometry system 100 provides multiple estimates of t, because the measurement is performed for multiple values of α and λ. These multiple estimates can be used to solve for a possible ambiguity in the film thickness associated with the term X in Eq. 7 and to improve the measurement resolution. In other embodiments, the electronic processor can derive one or more of the refractive indices of the test object from the measurement data based on a similar set of equations.

For more general cases, the electronic processor can use, for example, the “scattering matrix” approach to calculate the reflection coefficients of an test surface as a function of its unknown parameters (refractive indices, film thicknesses, layer roughness, refractive index gradients, etc). The reflection coefficient functions are applied to calculate the ellipsometric parameters Ψmodel and Δmodel for guess values of the unknown parameters. An iterative algorithm is then used to vary these parameters in order to minimize the sum of the squared differences between the measured ellipsometric coefficients and corresponding model coefficients:

χ2=Σ(Ψαλ−Ψαλmod el)2+Σ(Δαλ−Δαλmod el)2  (8)

Alternative merit functions can be defined that include for example weighting factors for the different wavelengths and angles of incidence. Such approaches are described, for example, in R. M. A. Azzam and N. M. Bashara, “Ellipsometry and Polarized Light,” Elsevier Science B.V., ISBN 0 444 87016 4 (paperbook), 1987.

System Calibration
In certain embodiments, a first step of the system calibration includes calculating the angle of incidence of a beam bundle at the test surface based on the location of the source point in the pupil plane. In other words, we want to assign an angle of incidence α to each pixel in the detector corresponding to the image of the pupil plane. This can be accomplished, for example, by performing a measurement with a narrowband filter so that the light detected by the detector is essentially monochromatic and has a known wavelength. In this case, Equation (3) shows that the frequency of the interference signal is proportional to the source wavelength and the angle of incidence through the relationship k cos α. The signal frequency can be calculated by a Fourier transform of the signal and the angle of incidence can be derived from the knowledge of the scan rate of the translation stage and the source wavelength.
Furthermore, to the extent the scan rate of the translation stage is initially unknown, it can be determined by locating the pixel on the detector whose interference signal has the largest frequency. According to the frequency's dependence on the relationship k cos α, this pixel corresponds to normal incidence (i.e., α=0), and so the stage speed can be extracted directly from the measured frequency and knowledge of the source wavelength.
Note that a priori information on the way the microscope objective maps angles in object space onto pupil positions can also be used to improve the quality of this calibration. For example, a typical objective is corrected for coma (a geometric aberration), which implies that the ray mapping at the pupil should nominally obey the so-called “Abbé sine condition.” This condition means that the radial distance of a source point from the optical axis at the pupil is directly proportional to the sine of the angle of incidence in object space. One can thus calculate the angle of incidence for each pixel and then fit a global function derived from the sine condition to provide an analytical function mapping pupil position to angle of incidence.
In certain embodiments, the procedure outlined above can be repeated for different nominal source wavelengths so that chromatic variations of the angular mapping are taken into account. A by-product of the fitting procedure is the pixel position of the optical axis at the pupil. That information is also recorded as a function of wavelength and can be used later on to apply corrections to angle of incidence calculations.
For certain embodiments, the second stage of the calibration involves calculating the value of the various system parameters that relate the observable Z expressed in Eq. (4) to the ellipsometric ratio.
For example, this can accomplished by measuring two samples that have known optical properties, for example calibration wafers typically used with ellipsometers. For each angle of incidence and wavelength of interest the electronic processor determines the spectral components Z as a function of azimuth angle θ as in Eq. (4) for both samples. The ratio of these components is then calculated, yielding the complex ratio z as a function of θ:




  
    
      
        
          
            z
            
              α
              ⁢
              
                
              
              ⁢
              λ
              ⁢
              
                
              
              ⁢
              θ
            
          
          =
          
            
              
                Z
                
                  α
                  ⁢
                  
                    
                  
                  ⁢
                  λ
                  ⁢
                  
                    
                  
                  ⁢
                  θ
                
                a
              
              
                Z
                
                  α
                  ⁢
                  
                    
                  
                  ⁢
                  λ
                  ⁢
                  
                    
                  
                  ⁢
                  θ
                
                b
              
            
            =
            
              
                
                  L
                  λ
                  a
                
                
                  L
                  λ
                  b
                
              
              ⁢
              
                exp
                ⁡
                
                  (
                  
                    
                      i
                      ⁢
                      
                        
                      
                      ⁢
                      
                        φ
                        
                          α
                          ⁢
                          
                            
                          
                          ⁢
                          λ
                          ⁢
                          
                            
                          
                          ⁢
                          ha
                        
                      
                    
                    -
                    
                      i
                      ⁢
                      
                        
                      
                      ⁢
                      
                        φ
                        
                          α
                          ⁢
                          
                            
                          
                          ⁢
                          λ
                          ⁢
                          
                            
                          
                          ⁢
                          hb
                        
                      
                    
                  
                  )
                
              
              ⁢
              
                
                  
                    
                      
                        cos
                        ⁡
                        
                          (
                          θ
                          )
                        
                      
                      2
                    
                    ⁢
                    
                      ρ
                      
                        α
                        ⁢
                        
                          
                        
                        ⁢
                        λ
                      
                      a
                    
                  
                  -
                  
                    
                      
                        sin
                        ⁡
                        
                          (
                          θ
                          )
                        
                      
                      2
                    
                    ⁢
                    
                      τ
                      
                        α
                        ⁢
                        
                          
                        
                        ⁢
                        λ
                      
                    
                  
                
                
                  
                    
                      
                        cos
                        ⁡
                        
                          (
                          θ
                          )
                        
                      
                      2
                    
                    ⁢
                    
                      ρ
                      
                        α
                        ⁢
                        
                          
                        
                        ⁢
                        λ
                      
                      b
                    
                  
                  -
                  
                    
                      
                        sin
                        ⁡
                        
                          (
                          θ
                          )
                        
                      
                      2
                    
                    ⁢
                    
                      τ
                      
                        α
                        ⁢
                        
                          
                        
                        ⁢
                        λ
                      
                    
                  
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        or
        ⁢
        
          

        
        ⁢
        
          
            z
            
              α
              ⁢
              
                
              
              ⁢
              λ
              ⁢
              
                
              
              ⁢
              θ
            
          
          =
          
            
              zs
              
                α
                ⁢
                
                  
                
                ⁢
                λ
              
            
            ⁢
            
              
                
                  
                    
                      cos
                      ⁡
                      
                        (
                        θ
                        )
                      
                    
                    2
                  
                  ⁢
                  
                    ρ
                    
                      α
                      ⁢
                      
                        
                      
                      ⁢
                      λ
                    
                    a
                  
                
                -
                
                  
                    
                      sin
                      ⁡
                      
                        (
                        θ
                        )
                      
                    
                    2
                  
                  ⁢
                  
                    τ
                    
                      α
                      ⁢
                      
                        
                      
                      ⁢
                      λ
                    
                  
                
              
              
                
                  
                    
                      cos
                      ⁡
                      
                        (
                        θ
                        )
                      
                    
                    2
                  
                  ⁢
                  
                    ρ
                    
                      α
                      ⁢
                      
                        
                      
                      ⁢
                      λ
                    
                    b
                  
                
                -
                
                  
                    
                      sin
                      ⁡
                      
                        (
                        θ
                        )
                      
                    
                    2
                  
                  ⁢
                  
                    τ
                    
                      α
                      ⁢
                      
                        
                      
                      ⁢
                      λ
                    
                  
                
              
            
          
        
      
    
    
      
        (
        9
        )
      
    
  




where zsαλ and ταλ are unknown complex numbers and the a or b superscripts identify one or the other calibration sample. ραλa and ραλb are calculated using the ratio of the reflection coefficients for the two materials. These coefficients are themselves calculated using the known material properties and known film thicknesses (if present) of the calibration samples. The electronic processor can then use a solver, for example a least-squares solver based on the Levenberg-Marquardt algorithm, to find the value of the two unknown parameters that minimize the difference between the quantities calculated on both sides of Equation (9). The process is repeated for other angles of incidence and wavelengths.

In a further step, if desired, the maps zsαλ and ταλ are filtered and/or fitted to analytical functions. It is then possible to reprocess the spectral components obtained for each sample and derive another calibration parameter, the function J:




  
    
      
        
          
            J
            
              α
              ⁢
              
                
              
              ⁢
              λ
              ⁢
              
                
              
              ⁢
              θ
            
          
          =
          
            
              
                Z
                
                  α
                  ⁢
                  
                    
                  
                  ⁢
                  λ
                  ⁢
                  
                    
                  
                  ⁢
                  θ
                
                a
              
              
                
                  
                    
                      cos
                      ⁡
                      
                        (
                        θ
                        )
                      
                    
                    2
                  
                  ⁢
                  
                    ρ
                    
                      α
                      ⁢
                      
                        
                      
                      ⁢
                      λ
                    
                    a
                  
                
                -
                
                  
                    
                      sin
                      ⁡
                      
                        (
                        θ
                        )
                      
                    
                    2
                  
                  ⁢
                  
                    τ
                    
                      α
                      ⁢
                      
                        
                      
                      ⁢
                      λ
                    
                  
                
              
            
            =
            
              
                L
                λ
                a
              
              ⁢
              
                I
                
                  α
                  ⁢
                  
                    
                  
                  ⁢
                  λ
                  ⁢
                  
                    
                  
                  ⁢
                  θ
                
              
              ⁢
              
                exp
                ⁡
                
                  (
                  
                    i
                    ⁢
                    
                      
                    
                    ⁢
                    
                      φ
                      
                        α
                        ⁢
                        
                          
                        
                        ⁢
                        λ
                        ⁢
                        
                          
                        
                        ⁢
                        ha
                      
                    
                  
                  )
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        or
        ⁢
        
          

        
        ⁢
        
          
            J
            
              α
              ⁢
              
                
              
              ⁢
              λ
              ⁢
              
                
              
              ⁢
              θ
            
          
          =
          
            
              
                
                  Z
                  
                    α
                    ⁢
                    
                      
                    
                    ⁢
                    λ
                    ⁢
                    
                      
                    
                    ⁢
                    θ
                  
                  b
                
                
                  
                    
                      
                        cso
                        ⁡
                        
                          (
                          θ
                          )
                        
                      
                      2
                    
                    ⁢
                    
                      ρ
                      
                        α
                        ⁢
                        
                          
                        
                        ⁢
                        λ
                      
                      b
                    
                  
                  -
                  
                    
                      
                        sin
                        ⁡
                        
                          (
                          θ
                          )
                        
                      
                      2
                    
                    ⁢
                    
                      τ
                      
                        α
                        ⁢
                        
                          
                        
                        ⁢
                        λ
                      
                    
                  
                
              
              ⁢
              
                zs
                
                  α
                  ⁢
                  
                    
                  
                  ⁢
                  λ
                
              
            
            =
            
              
                L
                λ
                a
              
              ⁢
              
                I
                
                  α
                  ⁢
                  
                    
                  
                  ⁢
                  λ
                  ⁢
                  
                    
                  
                  ⁢
                  θ
                
              
              ⁢
              
                exp
                ⁡
                
                  (
                  
                    i
                    ⁢
                    
                      
                    
                    ⁢
                    
                      φ
                      
                        α
                        ⁢
                        
                          
                        
                        ⁢
                        λ
                        ⁢
                        
                          
                        
                        ⁢
                        ha
                      
                    
                  
                  )
                
              
            
          
        
      
    
    
      
        (
        10
        )
      
    
  




In practice, the two expressions for J shown in Equation (10) can be averaged. The calculated values of J as a function of angle of incidence, wavelength and azimuth angle are then stored by the electronic processor in a calibration file along with the definition of the function ταλ.
Note that the procedure outlined above could be extended to more than two samples in order to benefit from redundancy in the calculation.
In certain embodiments, another step of the calculation involves establishing the exact angular orientation of the polarizers with respect to the coordinate system of the pupil as seen by the detector. This can be done, for example, by observing that Equation (9) is periodic in θ with a period π. It follows that the phase of the even components of the Fourier transform of the ratio z is a direct measurement of the angular offset of the polarizer. Accordingly, this calculation can be performed before determining zsαλ and ταλ.
Characterization of an Unknown Test Object
In certain embodiments, by using the stored calibration information, the electronic processor can characterize an unknown test object as follows. The interference data recorded for an unknown object surface are processed as for the calibration and yield rings of data according to Equation (4), where the superscript c denotes the unknown test object:

Zαλθ=cLλcIαλθexp(iφαλhc)(cos(θ)2ραλc−sin(θ)2ταλ)  (11)

Each ring is processed using the calibration information. First, the function J is retrieved for the specific angle of incidence and wavelength and a new complex ratio is calculated:




  
    
      
        
          
            z
            
              α
              ⁢
              
                
              
              ⁢
              λ
              ⁢
              
                
              
              ⁢
              θ
            
          
          =
          
            
              
                Z
                
                  α
                  ⁢
                  
                    
                  
                  ⁢
                  λ
                  ⁢
                  
                    
                  
                  ⁢
                  θ
                
                c
              
              
                J
                
                  α
                  ⁢
                  
                    
                  
                  ⁢
                  λ
                  ⁢
                  
                    
                  
                  ⁢
                  θ
                
              
            
            =
            
              
                
                  L
                  λ
                  c
                
                
                  L
                  λ
                  a
                
              
              ⁢
              
                exp
                ⁡
                
                  (
                  
                    
                      i
                      ⁢
                      
                        
                      
                      ⁢
                      
                        φ
                        
                          α
                          ⁢
                          
                            
                          
                          ⁢
                          λ
                          ⁢
                          
                            
                          
                          ⁢
                          hc
                        
                      
                    
                    -
                    
                      i
                      ⁢
                      
                        
                      
                      ⁢
                      
                        φ
                        
                          α
                          ⁢
                          
                            
                          
                          ⁢
                          λ
                          ⁢
                          
                            
                          
                          ⁢
                          ha
                        
                      
                    
                  
                  )
                
              
              ⁢
              
                (
                
                  
                    
                      
                        cos
                        ⁡
                        
                          (
                          θ
                          )
                        
                      
                      2
                    
                    ⁢
                    
                      ρ
                      
                        α
                        ⁢
                        
                          
                        
                        ⁢
                        λ
                      
                      c
                    
                  
                  -
                  
                    
                      
                        sin
                        ⁡
                        
                          (
                          θ
                          )
                        
                      
                      2
                    
                    ⁢
                    
                      τ
                      
                        α
                        ⁢
                        
                          
                        
                        ⁢
                        λ
                      
                    
                  
                
                )
              
            
          
        
        ⁢
        
          

        
        ⁢
        or
        ⁢
        
          

        
        ⁢
        
          
            z
            
              α
              ⁢
              
                
              
              ⁢
              λ
              ⁢
              
                
              
              ⁢
              θ
            
          
          =
          
            
              
                Z
                
                  α
                  ⁢
                  
                    
                  
                  ⁢
                  λ
                  ⁢
                  
                    
                  
                  ⁢
                  θ
                
                c
              
              
                J
                
                  α
                  ⁢
                  
                    
                  
                  ⁢
                  λ
                  ⁢
                  
                    
                  
                  ⁢
                  θ
                
              
            
            =
            
              
                η
                
                  α
                  ⁢
                  
                    
                  
                  ⁢
                  λ
                
              
              ⁡
              
                (
                
                  
                    
                      
                        cos
                        ⁡
                        
                          (
                          θ
                          )
                        
                      
                      2
                    
                    ⁢
                    
                      ρ
                      
                        α
                        ⁢
                        
                          
                        
                        ⁢
                        λ
                      
                      c
                    
                  
                  -
                  
                    
                      
                        sin
                        ⁡
                        
                          (
                          θ
                          )
                        
                      
                      2
                    
                    ⁢
                    
                      τ
                      
                        α
                        ⁢
                        
                          
                        
                        ⁢
                        λ
                      
                    
                  
                
                )
              
            
          
        
      
    
    
      
        (
        12
        )
      
    
  




where ηαλ and ραλc are unknown complex parameters independent of the azimuth angle θ. A numerical solver is applied again to find the value of these parameters that provide the best match between the measured ratio z and the model on the right hand side of Equation (12). An important result of the calculation is the parameter ραλc, which is the ellipsometric ratio for the unknown object surface.

As described above with reference, for example, to Eqs. 6-8, the electronic processor can process the ellipsometric ratio according to a model of the test object to extract information about the test object, such as the refractive index and/or thickness of one or more layers.
The graphs in FIG. 5 show experimental data derived using the above analysis for a 675-nm thick SiO2 monolayer on a silicon substrate. The graphs show the real and imaginary parts of Zαλθc (left side plot) and zαλθ (right side plot) measured experimentally for α=43° and λ=576 nm. As shown, the derived ratio zαλθ exhibits the π-periodicity expected from the model in Equation (12).
Note that in order to create the ring of data defined in Equation (11), the location of the optical axis at the detector should be known. This location may have changed since the calibration. For example, because the instrument may have been switched from the surface characterization mode to the topography mode, one cannot assume that the projection of the center of the pupil at the detector remains constant. Hence, in certain embodiments, a preliminary step of the process can involve calculating the frequency spectrum at each detector element, deriving a nominal mean frequency for each pixel (e.g., the mean frequency can be calculated as the centroid of the measured spectrum), and analyzing the map of mean frequency to find the location of the pupil center. As mentioned in the calibration section above, the mean frequency for a given source spectrum is expected to scale with the cosine of the angle of incidence in object space. Hence, the pupil location where the mean frequency is maximum corresponds to the optical axis. In some embodiments, this location can be calculated by fitting an even function—such as a parabola—to the map of mean frequencies and defining the apex of the parabola as the location of the optical axis. Alternatively, a preliminary measurement can be performed with a narrowband filter inserted in the system, as in the system calibration.
For simplicity and ease of expression, the procedures outlined in the above sections are based on certain assumptions about the nature of the test surface and the optical system. However, more advanced models can be used for more complicated cases to extract information about the test object from the interference signals measured by system 100. For example, a different model can be used when the test structure may exhibit birefringence, while the calibration procedure based on non-birefringent calibration samples remains the same.
Additional Configurations of the Polarization Elements
The analytical sections above were based on an embodiment in which polarization elements 140 and 144 are linear polarizers oriented parallel to one another, polarization elements 142 and 146 are absent, and beam splitter 112 is non-polarizing. In another embodiment, an analytically equivalent configuration that guarantees the parallelism of the linear polarizers involves removing polarization elements 140 and 144, and having polarization element 142 being a linear polarizer, because it is positioned in the path of both the input light being directed to the interference objective and the combined light being directed to the detector. In another embodiment, polarization elements 140 and 144 can be linear polarizers that oriented orthogonal to one another, in which case the amount of light coming back from the object is a periodic function of the azimuthal position multiplied by an azimuth-independent weighted sum of the S and P reflectivity. Such information can also be processed to determine information about the test object.
In yet another embodiment, polarizing elements 140, 144 and 146 are absent, whereas the beam splitter 112 is of the polarizing type and polarization element 142 is a quarter wave plate. Proper alignment of the quarter wave plate with its fast and slow axes at 45° from the polarization axis defined by beam splitter 112 results in a circular polarization state at every point of the pupil. The contribution of S and P polarizations in the detected interference signal is then to first-order independent of the azimuthal position of the source points. It is thus possible to combine the information collected over groups of detector elements that reside at fixed distances from the optical axis to improve the signal to noise ratio of the overall measurement. Note that depending on the nature of the quarter wave plate more advanced processing may be required to account for example for the variation of retardance with wavelength, which introduces a small azimuthal dependence on the polarization state of the source points at the pupil. This can be modeled mathematically using, for example, Jones matrices and vectors, as is known in the art.
In yet another embodiment, polarization element 140 is absent, beam splitter 112 is of the polarizing type, polarization element 142 is a quarter wave plate, polarization element 144 is absent, and polarization element 146 is a linear polarizer attached to interference objective 106. Because of the linear polarizer, this embodiment is analytically equivalent to the first embodiment with parallel linear polarizers. However, the addition of a polarizing beam splitter and quarterwave plate improves the light efficiency of the system when a different microscope objective (without polarizer attached) is mounted to the system, for use, for example, in the profiling mode of operation. As described in greater detail below, switching back and forth between different microscope objectives can be accomplished with an objective turret, which can be motorized under the control of the electronic processor for a production line instrument.
Reflectometry Mode
In yet another embodiment, polarization elements 140, 142, 144 and 146 are all absent and the beam splitter is of the non polarizing type. For a typical broadband source such as the filament in a halogen bulb or the emissive material of a white-light LED, the illumination input light is unpolarized, which means that for every source point at the pupil the polarization state can be described as an equal mix of S and P polarization components. In this case the measured signal is expected to be again independent from the azimuthal source position to the first order. In this case the system is capable of measuring the amount of light reflected by the object for different angles of incidence, as in a reflectometer. However, contrary to a conventional reflectometer that captures light one wavelength at a time, interferometry system 100 can capture all source wavelengths in the course of a single measurement. These spectral components are separated using the analysis of the signal in the frequency domain described above. While this reflectometry mode of operation does not provide as much information about the test surface reflectivity as the ellipsometry modes described above, the reflectometry information is still sensitive to variations in the properties of the test object. For example, the reflectometry data can be compared to models of the test object to determine the material composition at a given location in a heterogeneous sample, refractive indices, thicknesses, and/or the presence or absence of defects.
Selective Signal Analysis for Thin Film Samples
When the test object includes one or more films, the multiple interfaces produce multiple reflections that contribute the interference signal measured at each detector element. For the case of a broadband light source, the interference signal measured at various locations at in pupil plane have a limited coherence length, as shown by the signal envelope in FIG. 2 and FIG. 4 (left side). When the film is sufficiently thick that the round-trip optical thickness is larger than the coherence length, the measured signal consists of multiple separable signals, each signal corresponding to an interface between two materials.
An example of such a signal is shown in FIG. 6 for a 5-μm thick silicon dioxide (SiO2) film on silicon (Si). In this case, the weaker signal to the right corresponds to the air/SiO2 interface. The larger signal in the center corresponds to the SiO2/Si interface. The weak signal on the left is due to a double pass reflection of light in the SiO2 layer. In this case, it is possible to process each portion of the signal corresponding to a given interface independently to simplify the sample model (e.g., limit the number of unknown parameters) and thereby simplify or improve the robustness of the analysis.
For example, in certain embodiments, the electronic processor may process the portion of the signal corresponding to the air/top layer interface so that the analysis becomes equivalent to measuring an infinitely thick slab of the top layer material. In this case the refractive index of the material can be readily calculated using Equation (6) and there is no need to include in the modeling the effect of underlying layers and possibly complex structures such as those found on patterned semiconductor wafers.
Furthermore, in certain embodiments, after the electronic processor analyzes the portion of the signal corresponding to the top interface, the processing can be repeated for the entire signal (or other portions of the signal) by including the signal portions corresponding to the underlying interface. The model required to process the ellipsometry data is more complicated in this case, however, because the initial processing yields the refractive index of the top layer, the processing is simpler than it would have been in the absence of the initial processing. For example, the refractive index of a thick monolayer can be first calculated using Equation (6) when processing the rightmost signal. Assuming the substrate material is known, the processing of the entire interference signal (including the entire trace shown in FIG. 6, for example) yields new ellipsometric parameters that provide the film thickness using Equation (7). The benefit is the ability to separate the calculation of the refractive index and physical thickness.
For the case of a multilayer stack made of sufficiently thick layers, one can apply a bootstrap procedure that starts with the first signal yielding the refractive index of the first layer. The processing of the first and second signals simultaneously then yields the thickness of the first layer and the refractive index of the second layer. The processing of the first, second and third signals then yields the thickness of the second layer and the refractive index of the third layer, and so on. The benefit again is that one does not need to use an ellipsometric model that includes all interfaces at once with all materials and thicknesses being unknowns, as is common in conventional ellipsometers.
Even for small film thicknesses that cause the interference signal associated with each interface to partially overlap, it may still be possible to isolate a portion of the interference signal corresponding to a given interface and separately process that portion. See, for example, U.S. patent application Ser. No. 10/941,649 entitled “METHODS AND SYSTEMS FOR INTERFEROMETRIC ANALYSIS OF SURFACES AND RELATED APPLICATIONS” and published as U.S. Patent Publication No. US-2005-0078318-A1, the contents of which are incorporated herein, which describes such techniques in the context of a profiling mode.
Profiling Mode Analysis
As described above, interferometry system 100 can switch from an ellipsometry (or reflectometry) mode for a determining reflectivity information about the test surface, to a profiling mode for determining, for example, the topography of the test surface. As shown in FIG. 3, this can be accomplished, for example, by replacing the relay lens 136 by another lens 236 that images test surface to the detector (rather than image the pupil plane to the detector). This configuration corresponds to a conventional scanning interferometer for surface profiling. In what follows, a mathematical formalism for the surface profiling operation is described.
For a bulk material test object (i.e., no thin film structure), the interference phase φ to first order in the angular wavenumber k=2π/λ with respect to a reference datum plane in the test leg can be expressed as:

φ(k)=2nk (h−ζ)+(γpart+γsys)+(τpart+τsys)(k−k0),  (13)

where k0 is the nominal wavenumber, ζ is the scan coordinate for the translation stage, γpart is the part surface phase change on reflection (PCOR), and γsys is the system phase offset attributable to the interferometer system. The value γsys includes PCOR contributions from the interferometer optics and any constant offsets resulting, e.g., from the starting position of the scan ζ. The linear dispersions coefficients τpart and τsys correspond to the phase offsets γpart and γsys, respectively. The phase offsets γpart, γsys are evaluated at the nominal wavenumber k0. The index of refraction n for air and is assumed to be independent of wavenumber. Those skilled in the art will appreciate that the teachings of the invention can be extended to denser transparent media than air by taking into account the wavenumber dependence of material index. All of the terms in Eq. 13 are potentially a function of field position x,y, although for the subsequent description, the variables n, ζ, k0 are assumed to be constant over the field of view.

Because of the broad band radiation from the light source, interference fringes are only produced when the optical path difference (OPD) between the reference and measurement legs are within the coherence length of the broadband radiation. Thus, scanning interferometric measurements can be considered a “coherence profiling” mode in that it uses the broadband nature of the interference effect, e.g., the localization of fringe contrast or equivalently, the measurement of the rate of change of interference phase with wavenumber. As a result, the interference signal I measured by each detector element can be expressed as:

I=1+V[h+(τsys+τpart)/2n−ζ]cos[2nk0(h−ζ)+γpart+γsys]  (14)

where V is the fringe contrast envelope. The envelope V is proportional to the Fourier Transform of the spectral distribution of the light from the light source.

For a symmetric contrast envelope, the peak value of the fringe contrast envelope is given by the scan position for which dφ/dk=0. This is the stationary phase position, where the interference phase is the same independent of wave number, and all of the interference patterns add up constructively. More generally, it can be shown that the stationary phase condition dφ/dk=0 corresponds to the centroid of the fringe contrast envelope V. The phase gap G between the stationary phase position and the nearest zero phase point φ=0 position is given by

G=(γpart+γsys)−k0 (τsys+τpart).  (15)

This is a constant phase offset, independent of wavenumber k, but dependent on the system and part parameters. The phase φ0 is the phase at the nominal wavenumber k0 (with respect to a ζ=0 scan position), e.g., from Eq. (13) we have

φ0=2nk0h+(γpart+γsys).  (16)

From Eq. 14 it can be seen that the maximum or peak fringe contrast occurs at the scan position ζ=h+(τsys+τpart)/2n. Thus, in one data processing embodiment, the electronic processor, when operating in the profiling mode, determines the fringe-contrast envelope V as a function of ζ, e.g., by electronic or digital conversion, for every detector pixel. It then determines the scan position ζmax for which the envelope V reaches a specific value, e.g., its maximum or peak value. The corresponding height h for each location on the test object is this scan position minus the dispersion offset:

h=ζmax−(τsys−τpart)/2n.  (17)

In another signal processing method, the coherence profiling intensity signal is Fourier transformed with respect to the scan position ζ into the frequency domain (i.e., with respect to frequency wave number k). The phase of the transformed data corresponds directly to the phase φ(k) in Eq. 13. From this phase, the signal processor calculates the phase derivative dφ/dk, and determines height h for each detector pixel according to:




  
    
      
        h
        =
        
          
            
              1
              
                2
                ⁢
                n
              
            
            ⁢
            
              
                d
                φ
              
              
                d
                k
              
            
          
          -
          
            
              
                (
                
                  
                    τ
                    sys
                  
                  -
                  
                    τ
                    part
                  
                
                )
              
              /
              2
            
            ⁢
            n
          
        
      
    
    
      
        (
        18
        )
      
    
  




where the derivative dφ/dk is calculated for ζ=0. Eq. 18 follows directly from Eq. 13.

From Eqs. 17 and 18, one sees that surface height measurements based on coherence profiling data can be more accurately calculated by accounting, e.g., by calibration, for PCOR dispersion for the interferometry system and the test part (e.g., τpart and τsys). To the extent the PCOR factors are constant across the field of view, not accounting for them will only introduce overall shift in the surface profile and the resulting surface topography is accurate. However, when the PCOR factors change because of, for example, variations in the surface material, they should be accounted for to provide a more accurate surface topography profile.
In addition to coherence profiling, surface height measurements can also be based on interferometric phase profiling data where the interferometric phase φ(k) is measured directly for one or more wavenumbers k. For example, phase shifting interferometry (PSI) techniques can be used for such measurements. From Eq. 13, it is clear that if direct interferometric phase measurements are used to determine height h, accounting for PCOR γpart and γsys (and PCOR dispersion τpart and τsys for wave numbers other than the nominal wave number k0) improves the accuracy of the height measurement.
Generally, the sensitivities to particular noise sources for coherence profiling measurements differ from those for phase profiling measurements, thus a particular technique may be preferable for a particular application, or they may be used to complement one another. One drawback of many phase profiling measurements, however, is the measured phase φ(k) includes 2π fringe ambiguity. For relatively smooth surfaces, relative fringe ambiguity over the surface may be interpolated from the data of multiple detector pixels using standard fringe unwrapping procedures. More generally, however, it is preferable to have an independent measurement, such as coherence profiling data, to remove such fringe ambiguity. Thus, to obtain absolute surface profile measurements, the coherence profiling height measurement can be used alone, or it can be used to remove the absolute fringe ambiguity from the phase profiling measurement, which may be more accurate than the coherence measurement in some cases.
In one such embodiment, the height h determined from a coherence profiling measurement is used to calculate an absolute phase profiling height measurement h′ based on phase profiling data for the phase φ0=φ(k0) according to:




  
    
      
        
          h
          ′
        
        =
        
          
            1
            
              2
              ⁢
              
                nk
                0
              
            
          
          ⁢
          
            {
            
              
                (
                
                  
                    φ
                    0
                  
                  -
                  
                    γ
                    part
                  
                  -
                  
                    γ
                    sys
                  
                
                )
              
              -
              
                2
                ⁢
                π
                ⁢
                
                  
                
                ⁢
                
                  Int
                  ⁡
                  
                    [
                    
                      
                        
                          (
                          
                            
                              φ
                              0
                            
                            -
                            
                              γ
                              part
                            
                            -
                            
                              γ
                              sys
                            
                          
                          )
                        
                        -
                        
                          (
                          
                            2
                            ⁢
                            
                              k
                              0
                            
                            ⁢
                            nh
                          
                          )
                        
                      
                      
                        2
                        ⁢
                        π
                      
                    
                    ]
                  
                
              
            
            }
          
        
      
    
    
      
        (
        19
        )
      
    
  




where Int [ ] returns the nearest integer to its argument. Eq. 19 can be applied independently to every point x,y on the part surface. Again, as is apparent from Eq. 19, accounting for PCOR γpart and γsys improves the accuracy of the absolute phase profiling measurement. Moreover, Eq. 19 implicitly depends on PCOR dispersion values τpart and τsys through the coherence profiling determination of h.

For more complex samples, such as those with thin films, the profiling formalism is more complicated because reflections from underlying surfaces will also contributed the interference signal. Where the limited coherence length of input light is small enough relative to film thickness to separate the interferometry signal into portions corresponding to each interface, the electronic processor can isolate that portion of the interferometry signal corresponding to the interface of interest and process it using the general formalism described above to extract the surface topography for that interface. Furthermore, even for small film thicknesses that cause the interference signal associated with each interface to partially overlap, it may still be possible to isolate a portion of the interference signal corresponding to a given interface and separately process that portion. See, for example, U.S. patent application Ser. No. 10/941,649 entitled “METHODS AND SYSTEMS FOR INTERFEROMETRIC ANALYSIS OF SURFACES AND RELATED APPLICATIONS” and published as U.S. Patent Publication No. US-2005-0078318-A1, which was incorporated by reference above. In yet further embodiments, the electronic processor can use the model-based techniques disclosed in U.S. patent application Ser. No. 10/795,579 entitled “PROFILING COMPLEX SURFACE STRUCTURES USING SCANNING INTERFEROMETRY” and published as U.S. Patent Publication No. US-2004-0189999-A1, the contents of which is incorporated herein by reference, to determine profile information for complex surface structures.
Additional Embodiments for Profiling
Instead of switching out relay lens 136, in further embodiments, for example, the relay lens can be left alone and detector 134 can be translated to a position where the test surface is in focus. This is shown schematically in FIG. 7, which shows detector 134 coupled to a motorized translation stage 760 under the control of electronic processor 770 to adjust the detector position for receiving combined light 132 relative to the rest of the interferometry system 700. The translation stage allows the system to switch between a first position corresponding the ellipsometry mode, in which the pupil plane is imaged to the detector, and a second position corresponding to the profiling mode, in which the test surface is imaged to the detector.
In yet a further embodiment, shown schematically in FIG. 8, a beam splitter 810 can split the combined light 132 received from the rest of the interferometry system 800 into two channels with two corresponding multi-element detectors 880 and 890, with one channel using relay optics 875 to image pupil plane 114 to the first detector 880 to provide the ellipsometry mode measurement and the other channel using relay optics 885 to image the test surface to the second detector 890 to simultaneously provide the profiling mode measurement. Both detectors are coupled to electronic processor 870, which analyze the detector images as described above.
Various combinations of these approaches are also possible. For example, the system can include optics that image the pupil plane to a first portion of a common electronic detector and image the test surface to a second portion of the common electronic detector. In this case, the different portions of the common electronic detector can be considered to be separate detectors.
Multi-Mode Operation and Applications
FIG. 9 shows a schematic diagram of how various components in interferometry system 100 can be automated under the control of electronic processor 970, which, in the presently described embodiment, can include an analytical processor 972 for carrying out mathematical analyses, device controllers 974 for controlling various components in the interferometry system, a user interface 976 (e.g., a keyboard and display), and a storage medium 978 for storing calibration information, data files, a sample models, and/or automated protocals.
First, the system can include a motorized turret 910 supporting multiple objectives 912 and configured to introduce a selected objective into the path of input light 104. One or more of the objectives can be interference objectives, with the different interference objectives providing different magnifications. Furthermore, in certain embodiments, one (or more) of the interference objectives can be especially configured for the ellipsometry mode of operation by having polarization element 146 (e.g., a linear polarizer) attached to it. The remaining interference objectives can be used in the profiling mode and, in certain embodiments, can omit polarization element 146 so as to increase light efficiency (such as for the embodiment described above in which beam splitter 112 is a polarizing beam splitter and polarization element is 142 is a quarter wave plate). Moreover, one or more of the objectives can be a non-interferometric objective (i.e., one without a reference leg), each with a different magnification, so that system 100 can also operate in a conventional microscope mode for collecting optical images of the test surface (in which case the relay lens is set to image of test surface to the detector). Turret 910 is under the control of electronic processor 970, which selects the desired objective according to user input or some automated protocol.
Next, the system includes a motorized stage 920 (e.g., a tube lens holder) for supporting relay lenses 136 and 236 and selectively positioning one of them in the path of combined light 132 for selecting between the first mode (e.g., an ellipsometry or reflectometry mode) in which the pupil plane 114 is imaged to the detector and the second mode (e.g., profiling or microscope mode) in which the test surface is imaged to the detector.
Motorized stage 920 is under the control of electronic processor 970, which selects the desired relay lens according to user input or some automated protocol. In other embodiments, in which a translation stage is moved to adjust the position of the detector to switch between the first and second modes, the translation is under control of electronic processor. Furthermore, in those embodiments with two detection channels, each detector is coupled to the electronic processor 970 for analysis.
Furthermore, the system can include motorized apertures 930 and 932 under control of electronic processor 970 to control the dimensions of field stop 138 and aperture stop 115, respectively. Again the motorized apertures are under the control of electronic processor 970, which selects the desired settings according to user input or some automated protocol.
Also, translation stage 150, which is used to vary the relative optical path length between the test and reference legs of the interferometer, is under the control electronic processor 970. As described above, the translation stage can be coupled to adjust the position of the interference objective relative to a mount 940 for supporting test object 126.
Alternatively, in further embodiments, the translation stage can adjust the position of the interferometry system as a whole relative to the mount, or the translation stage can be coupled to the mount, so it is the mount that moves to vary the optical path length difference.
Furthermore, a lateral translation stage 950, also under the control of electronic processor 970, can be coupled to the mount 940 supporting the test object to translate laterally the region of the test surface under optical inspection. In certain embodiments, translation stage 950 can also orient mount 940 (e.g., provide tip and tilt) so as to align the test surface normal to the optical axis of the interference objective.
Finally, an object handling station 960, also under control of electronic processor 970, can be coupled to mount 940 to provide automated introduction and removal of test samples into system 100 for measurement. For example, automated wafer handling systems known in the art can be used for this purpose. Furthermore, if necessary, system 100 and object handling system can be housed under vacuum or clean room conditions to minimize contamination of the test objects.
The resulting system provides great flexibility for providing various measurement modalities and procedures. For example, the system can first be configured in the microscope mode with one or more selected magnifications to obtain optical images of the test object for various lateral positions of the object. Such images can be analyzed by a user or by electronic processor 970 (using machine vision techniques) to identify certain regions (e.g., specific structures or features, landmarks, fiducial markers, defects, etc.) in the object. Based on such identification, selected regions of the sample can then be studied in the ellipsometry mode to determine sample properties (e.g., refractive index, underlying film thickness(es), material identification, etc.).
Accordingly, the electronic processor causes stage 920 to switch the relay lens to the one configured for the ellipsometry mode and further causes turret 910 to introduce a suitable interference objective into the path of the input light. To improve the accuracy of the ellipsometry measurement, the electronic processor can reduce the size of the field stop via motorized aperture 930 to isolate a small laterally homogenous region of the object. After the ellipsometry characterization is complete, electronic processor 970 can switch the instrument to the profiling mode, selecting an interference objective with a suitable magnification and adjusting the size of field stop accordingly. As described above, the profiling mode captures interference signals that allow reconstructing the topography of, for example, one or more interfaces that constitute the object. Notably, as described in greater detail below, the knowledge of the optical characteristics of the various materials determined in the ellipsometry mode allows for correcting the calculated topography for thin film or dissimilar material effects that would otherwise distort the profile. See, for example, U.S. patent application Ser. No. 10/795,579 entitled “PROFILING COMPLEX SURFACE STRUCTURES USING SCANNING INTERFEROMETRY” and published as U.S. Patent Publication No. US-2004-0189999-A1, which was incorporated by reference above. If desired, the electronic processor can also adjust the aperture stop diameter via motorized aperture 932 to improve the measurement in any of the various modes.
When used in conjunction with automated object handling system 960, the measurement procedure can be repeated automatically for a series of samples. This could be useful for various process control schemes, such as for monitoring, testing, and/or optimizing one or more semiconductor processing steps.
For example, the system can be used in a semiconductor process for tool specific monitoring or for controlling the process flow itself. In the process monitoring application, single/mulit-layer films are grown, deposited, polished, or etched away on unpatterned Si wafers (monitor wafers) by the corresponding process tool and subsequently the thickness and/or optical properties are measured using the interferometry system disclosed herein (for example, by using the ellipsometry mode, the profiling mode, or both). The average, as well as within wafer uniformity, of thickness (and/or optical properties) of these monitor wafers are used to determine whether the associated process tool is operating with targeted specification or should be retargeted, adjusted, or taken out of production use.
In the process control application, latter single/mulit-layer films are grown, deposited, polished, or etched away on patterned Si, production wafers by the corresponding process tool and subsequently the thickness and/or optical properties are measured with the interferometry system disclosed herein (for example, by using the ellipsometry mode, the profiling mode, or both). Production measurements used for process control typical include a small measurement site and the ability to align the measurement tool to the sample region of interest. This site may consists of multi-layer film stack (that may itself be patterned) and thus requires complex mathematical modeling in order to extract the relevant physical parameters. Process control measurements determine the stability of the integrated process flow and determine whether the integrated processing should continue, be retargeted, redirected to other equipment, or shut down entirely.
Specifically, for example, the interferometry system disclosed herein can be used to monitor the following equipment: diffusion, rapid thermal anneal, chemical vapor deposition tools (both low pressure and high pressure), dielectric etch, chemical mechanical polishers, plasma deposition, plasma etch, lithography track, and lithography exposure tools. Additionally, the interferometry system disclosed herein can be used to control the following processes: trench and isolation, transistor formation, as well as interlayer dielectric formation (such as dual damascene).
Combining Information from Different Modes
One powerful feature of interferometry system 100 is that not only is it possible to gather rapidly and in automated fashion information about the test object for a variety of measurement modes, but also, that information determined from one mode of operation can be used to improve the accuracy of the measurement in the other mode of operation.
For example, when in the ellipsometry mode of operation, the electronic processor can determine the optical properties of various materials present at different locations on an object (for example copper lines separated by dielectric regions on a semiconductor wafer). In such cases, each material typically requires a separate measurement. Once these properties are known it is possible to calculate the phase change on reflection (PCOR) undergone by light reflecting off the object surface. As described above in the profiling analysis section, these phase changes are material dependent and affect the topography measurement. For example, copper regions appear lower than they truly are with respect to the dielectric regions. However, the knowledge of the material dependent phase changes determined in the ellipsometry mode allows the electronic processor to correct the topography map to obtain the true surface topography. In practice, the phase change on reflection for a given angle of incidence and wavelength affects the measured signal as a contribution to the parameter φ in Equation 20. For example, one can write:

φαλφαλsystem−φαλpart  (20)

where φαλsystem is a characteristic of the instrument and φαλpart is the phase change on reflection for that particular measurement location. In the case of bulk materials such as thick metal films the surface characterization technique yields a refractive index calculated for example using Equation (6). The electronic processor can then calculate the value of the phase change of reflection for light reflecting off the metal at various angles of incidences and wavelengths using the complex argument of the Fresnel coefficients of reflection. For more complicated surface structures the optimization of the merit function in Equation (8) yields the optical properties of the structure. The scattering matrix technique then calculates the phase change of reflection as a function of angle of incidence and wavelength. As described above in the profiling analysis section, when a low numerical aperture (NA) interference objective is used for topography measurements the correction for the effect of the phase change on reflection amounts simply to subtracting from the surface height the calculated phase change divided by the wavenumber used for surface height calculation (e.g., as shown in Eq. 16). For high-NA interference objectives the correction results from the modeling of the interferometer: the model sums the interference signals generated by various source points at various wavelengths with the appropriate weights for an object point of height h=0. The sum interference signal is analyzed with the same algorithm used for topography measurement and yields an effective height h′, which is simply the height offset due to the combination of phase changes on reflection. The value h′ is then subtracted from the experimental topography map at the locations corresponding to the particular surface structure.

In another example, the accuracy of the measurement in the ellipsometry mode is improved when the object surface is normal to the optical axis of the interference objective (i.e., there is no tip and tilt of the object surface relative to the interference objective). This can be accomplished by having the electronic processor switch to the topography mode and performing repeated measurements of the surface tip and tilt while adjusting part orientation. As described above, the procedure can be automated with a motorized tip/tilt stage 960, which makes the instrument self aligning. Once the part is properly nulled the instrument can switch back to the surface characterization mode (e.g., an ellipsometry mode or a reflectometry mode).
In yet another example, the topography mode of measurement can also be used to measure the surface roughness of a top layer. This information can then be included in the ellipsometric model of the surface. Similarly, the topography of the top surface potentially provides information about the thickness uniformity of a film. This information can be used to best select the size of the field stop that defines the measurement area in surface characterization mode. For example, one may want to select a small region where the thickness is nominally constant.
Furthermore, in those embodiments in which a portion of the interference signal is selected to isolate a corresponding interface in the test object, it is possible to measure the film optical thickness or physical thickness (if the refractive index is known) in the topography mode. This a priori information on thickness can then be fed to the surface characterization mode and provide accurate guess values for the ellipsometry model.
Narrow-band Tunable Source
In yet another embodiment, light source 102 in system 100 of FIG. 1 is replaced by a tunable monochromatic source under the control of the electronic processor. For example, the source can be a tunable laser diode or a broadband source incorporating a tunable spectral filter to produce a tunable spectral output (e.g., a monochromator, a spectral filter wheel, or a tunable liquid crystal filter.) Furthermore, the position of reference mirror 122 is adjusted so that the optical path length difference between the test light and reference light when the test surface is in-focus with respect to the interference objective is non-zero. Detector 134 records the interference pattern produced by the combined light as the wavelength of the source is scanned. There is no mechanical motion of the object with respect to the interferometric objective in this case. Because of the adjustment in the position of the reference mirror and the resulting non-zero optical path length difference between the test and reference legs of the interferometer, the scanning of the source frequency produces an interference signal that is measured at each detector element. This interference signal is sometimes referred to as a “channel spectrum.”
When operating in the ellipsometry mode (as in FIG. 1), the intensity of the interference signal measured at each detector element corresponds to Eq. 4, except that “z” is fixed at the non-zero optical path length difference, and the wavenumber k is varied. During analysis, the electronic processor determines the wavelength-dependent, complex reflectivity of the test surface from the interference cross-term in Eq. 4 using a analytical framework similar to that shown above. For example, the interference signal at each detector element can be Fourier transformed, filtered to select the portion of the transformed signal corresponding to the cross-term, and then inversed Fourier transformed to give the magnitude and phase of the signal with respect to wavelength. This magnitude and phase can then be related as to ellipsometry parameters in a similar fashion to that described above. When operating in the profiling mode (as in FIG. 3), the interference signal in the present embodiment can be Fourier transformed, and variations in the phase at the non-zero optical path length difference coordinate in the transform over the various detector elements can be related changes in the topography of the test surface. Information from the other coordinates in the Fourier transform can also be analyzed to provide topography information.
Accordingly, this narrow-band, tunable source embodiment can also operate in the various modes of operation and for the various applications described above.
Additional Embodiments
The embodiments shown in FIGS. 1 and 3 implement an interference objective of the Mirau-type, in which the beam splitter in the interference objective directs the reference light back along the optical axis for the test light. In other embodiments, interferometry system 100 can instead use a different type of interference objective, such as a Michelson objective, in which the beam splitter directs the reference light away from the optical axis of the test light (e.g., the beam splitter can be oriented at 45 degrees to the input light so the test light and reference travel at right angles to one another). In such cases, the reference surface can be positioned outside of the path of the test light.
In another embodiment, the interference objective can be of the Linnik-type, in which the case the beam splitter is positioned prior to the objective lens for the test surface (with respect to the input light) and directs the test and reference light along different paths. A separate objective lens is used to focus the reference light to the reference lens. In other words, the beam splitter separates the input light into the test and reference light, and separate objective lenses then focus the test and reference light to respective test and reference surfaces. Ideally the two objective lenses are matched to one another so that the test and reference light have similar aberrations and optical paths.
Additional interferometer configurations are also possible. For example, the system can be configured to collect test light that is transmitted through the test sample and then subsequently combined with reference light. For such embodiments, for example, the system can implement a Mach-Zehnder interferometer with dual microscope objectives on each leg.
The light source in the interferometer may be any of: an incandescent source, such as a halogen bulb or metal halide lamp, with or without spectral bandpass filters; a broadband laser diode; a light-emitting diode; a combination of several light sources of the same or different types; an arc lamp; any source in the visible spectral region; any source in the IR spectral region, particularly for viewing rough surfaces & applying phase profiling; and any source in the UV spectral region, particularly for enhanced lateral resolution. For broadband applications, the source preferably has a net spectral bandwidth broader than 5% of the mean wavelength, or more preferably greater than 10%, 20%, 30%, or even 50% of the mean wavelength. For tunable, narrow-band applications, the tuning range is preferably broad (e.g., greater than 50 nm, greater than 100 nm, or greater than even 200 nm, for visible light) to provide reflectivity information over a wide range of wavelengths, whereas the spectral width at any particular setting is preferable narrow, to optimize resolution, for example, as small as 10 nm, 2 nm, or 1 nm. The source may also include one or more diffuser elements to increase the spatial extent of the input light being emitted from the source.
Furthermore, the various translations stages in the system, such as translation stage 150, may be: driven by any of a piezo-electric device, a stepper motor, and a voice coil; implemented opto-mechanically or opto-electronically rather than by pure translation (e.g., by using any of liquid crystals, electro-optic effects, strained fibers, and rotating waveplates) to introduce an optical path length variation; any of a driver with a flexure mount and any driver with a mechanical stage, e.g. roller bearings or air bearings.
The electronic detector can be any type of detector for measuring an optical interference pattern with spatial resolution, such as a multi-element CCD or CMOS detector.
Software
The analysis steps described above can be implemented in computer programs using standard programming techniques. Such programs are designed to execute on programmable computers or specifically designed integrated circuits, each comprising an electronic processor, a data storage system (including memory and/or storage elements), at least one input device, and least one output device, such as a display or printer. The program code is applied to input data (e.g., images from the detector) to perform the functions described herein and generate output information (e.g., refractive index information, thickness measurement(s), surface profile(s), etc.), which is applied to one or more output devices. Each such computer program can be implemented in a high-level procedural or object-oriented programming language, or an assembly or machine language. Furthermore, the language can be a compiled or interpreted language. Each such computer program can be stored on a computer readable storage medium (e.g., CD ROM or magnetic diskette) that when read by a computer can cause the processor in the computer to perform the analysis and control functions described herein.
A number of embodiments of the invention have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the invention.

## Claims

1. An apparatus comprising:
an interferometer configured to direct test light to a test surface and subsequently combine it with reference light to form an interference pattern, the test and reference light being derived from a common source;
an electronic detector;
one or more optics configured to direct at least a portion of the combined light to the detector so that different regions of the detector correspond to different illumination angles of the test surface by the test light; and
an electronic processor coupled to the detector, wherein the electronic processor is configured to process information measured by the detector to determine information about a test object having the test surface;
wherein the electronic processor stores calibration information about the optical properties of the interferometer and uses the calibration information and the information measured by the detector to determine the information about the test object.

2. The apparatus of claim 1, wherein the detector comprises multiple detector elements and the calibration information comprises a relationship between different illumination angles of the test surface by the test light and different elements of the detector.

3. The apparatus of claim 1, wherein the calibration information comprises the location of an optical axis for the combined light on the detector.

4. The apparatus of claim 1, wherein the calibration information comprises reflection parameters of the interferometer.

5. The apparatus of claim 1, wherein the test object comprises one or more layers on a substrate.

6. The apparatus of claim 1, wherein the electronic processor extracts angularly resolved reflectivity information about the test surface from the detector measurement, and determines the information about the test object based on the angularly resolved information.

7. The apparatus of claim 1, further comprising a translation stage configured to adjust the relative optical path length between the test and reference light when they form the interference pattern, wherein the electronic processor is configured to analyze an interference intensity signal measured at each of multiple locations across the detector and produced by scanning the translation stage.

8. The apparatus of claim 7, wherein the electronic processor is configured to determine the correspondence between the different regions of the detector and the different illumination angles of the test surface by the test light based on the frequency of the intensity signal at different locations on the detector.

9. The apparatus of claim 7, wherein the electronic processor is configured to extract angularly resolved and wavelength-resolved information about the test surface based on the intensity signals measured across the detector.

10. The apparatus of claim 9, wherein the electronic processors configured to transform the interference signal at different locations of the detector into a frequency domain to extract the angularly resolved and wavelength-resolved information.

11. The apparatus of claim 10, wherein the interferometer comprises one or more polarization elements positioned to adjust the polarization content of the interference pattern measured by the detector, and wherein the electronic processor is configured to extract angularly resolved, wavelength-resolved, and polarization-resolved information about the test surface based on the intensity signal measured across the detector.

12. The apparatus of claim 11, wherein the angularly resolved, wavelength-resolved, and polarization-resolved information is reflectivity information about the test surface.

13. The apparatus of claim 1, wherein the information about the test object comprises a refractive index estimate for a portion of the test object.

14. The apparatus of claim 1, wherein the information about the test object comprises a thickness estimate for a layer in the test object.

15. The apparatus of claim 7, wherein the electronic processor is configured to select a subset of each of the interference intensity signals, the subsets corresponding to a selected interface in the test object, and process the subsets of interference intensity signals to determine information about the test object related to the selected interface.

16. The apparatus of claim 1, wherein the electronic processor is configured to determine the information about the test object based on a comparison between data based on the information measured by the detector and a model for the test object.

17. The apparatus of claim 16, wherein the model provides an estimate for the measured information as a function of one or more parameters for the test object, and wherein the comparison selects values for the one or more parameters to optimize the fit between the measured information and that provided by the model.

18. An apparatus comprising:
an interferometer configured to direct test light to a test surface and subsequently combine it with reference light to form an interference pattern, the test and reference light being derived from a common source;
an electronic detector;
one or more optics configured to direct at least a portion of the combined light to the detector so that different regions of the detector correspond to different illumination angles of the test surface by the test light; and
an electronic processor coupled to the detector, wherein the electronic processor is configured to process information measured by the detector to determine information about a test object having the test surface;
wherein the test object comprises one or more layers on a substrate and the information about the test object comprises information about the layers.

19. The apparatus of claim 18, wherein the information about the layers comprises an estimate of a thickness of one or more of the layers.

20. The apparatus of claim 18, wherein the information about the layers comprises an estimate of an optical property of one or more of the layers.

21. The apparatus of claim 20, wherein the optical property comprises an index of refraction.

22. The apparatus claim 18, wherein the information about the layers comprises information related to the composition of one or more of the layers.

23. The apparatus of claim 18, wherein the electronic processor extracts angularly resolved reflectivity information about the test surface from the detector measurement, and determines the information about the test object based on the angularly resolved information.

24. The apparatus of claim 18, further comprising a translation stage configured to adjust the relative optical path length between the test and reference light when they form the interference pattern, wherein the electronic processor is configured to analyze an interference intensity signal measured at each of multiple location across the detector and produced by scanning the translation stage.

25. The apparatus of claim 24, wherein the electronic processor is configured to determine the correspondence between the different regions of the detector and the different illumination angles of the test surface by the test light based on the frequency of the intensity signal at different locations on the detector.

26. The apparatus of claim 24, wherein the electronic processor is configured to extract angularly resolved and wavelength-resolved information about the test surface based on the intensity signals measured across the detector.

27. The apparatus of claim 26, wherein the electronic processor is configured in transform the interference signal at different locations of the detector into a frequency domain to extract the angularly resolved and wavelength-resolved information.

28. The apparatus of claim 27, wherein the interferometer comprises one or more polarization elements positioned to adjust the polarization content of the interference pattern measured by the detector, and wherein the electronic processor is configured to extract angularly resolved, wavelength-resolved, and polarization-resolved information about the test surface based on the intensity signal measured across the detector.

29. The apparatus of claim 28, wherein the angularly resolved, wavelength-resolved, and polarization-resolved information is reflectivity information about the test surface.

30. The apparatus of claim 18, wherein the information about the test object comprises a refractive index estimate for a portion of the test object.

31. The apparatus of claim 24, wherein the electronic processor is configured to select a subset of each of the interference intensity signals, the subsets corresponding to a selected interface in the test object, and process the subsets of interference intensity signals to determine information about the test object related to the selected interface.

32. The apparatus of claim 18, wherein the electronic processor is configured to determine the information about the test object based on a comparison between data based on the information measured by the detector and a model for the test object.

33. The apparatus of claim 32, wherein the model provides an estimate for the measured information as a function of one or more parameters for the test object, and wherein the comparison selects values for the one or more parameters to optimize the fit between the measured information and that provided by the model.

34. The apparatus of claim 18, wherein the electronic processor stores calibration information about the optical properties of the interferometer and uses the calibration information and the information measured by the detector to determine the information about the test object.

35. An interferometry method, comprising:
directing test light to a test surface over a range of illumination angles;
subsequently combining the test light with reference light to form an interference pattern, wherein the test and reference light are derived from a common source;
directing at least a portion of the combined light to a multi-element detector so that different elements of the detector correspond to different illumination angles of the test surface by the test light; and
determining calibration information based on interference signals measured by the detector elements.

36. The method of claim 35, further comprising determining information about a test object having the test surface based on interference signals measured by the detector elements.

37. The method of claim 35, wherein the combined light is directed to the detector by imaging a pupil plane for the test light to the detector.

38. The method of claim 35, wherein the determining calibration information comprises measuring the interference signal at each of multiple elements of the detector as a function of varying an optical path length difference between the test and reference light.

39. The method of claim 38, wherein the determining calibration information comprises determining relationship between different illumination angles of the test surface by the test light and different elements of the detector based on the frequency of the interference signal at each of different detector elements.

40. The method of claim 38, wherein the determining calibration information comprises determining the location of an optical axis for the combined light on the detector based on the frequency of the interference signal at different detector elements.

41. The method of claim 38, wherein the determining calibration information further comprises determining the rate at which the optical path length difference is varied by based on the frequency of the interference signal at different detector elements.

42. The method of claim 35, wherein the test surface has known reflection properties, and the method further comprises calibrating reflection parameters of an interferometer used to direct the test light and combine it with the reference light based on a signal measured at different detector elements and the known reflection parameters of the test surface.

43. The method of claim 42, further comprising repeating the steps with a second test surface having known reflection properties, and further calibrating reflection parameters of the interferometer based on signals measured at the different detector elements and the known reflection parameters of the test surfaces.

44. The method of claim 35, wherein the test light, reference light, and combined light are selectively polarized.

45. The method of churn 35, wherein determining the information about the test object comprises determining a reflectivity for the test surface with respect to different illumination angles and wavelengths.

46. The method of claim 45, wherein the reflectivity is a complex reflectivity with respect to the different illumination angles and wavelenghths, for a selected polarization state.

47. The method of claim 45, wherein determining the information about the test object further comprises comparing the measured reflectivity to estimate for the reflectivity based on a model of the test object.

48. An interferometry method comprising;
directing test light to a surface of a test object over a range of illumination angles, wherein the test object comprises the test object comprises one or more layers;
subsequently combining the test light with reference light to form an interference pattern, wherein the test and reference light are derived from a common source;
directing at least a portion of the combined light to a multi-element detector so that different elements of the detector correspond to different illumination angles of the test surface by the test light; and
determining information based on interference signals measured by the detector elements, wherein the information about the test object comprises information about the layers.