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WO2008151266A2 - Interférométrie pour déterminer des caractéristiques de la surface d'un objet à l'aide d'un éclairage spatialement cohérent - Google Patents

Interférométrie pour déterminer des caractéristiques de la surface d'un objet à l'aide d'un éclairage spatialement cohérent Download PDF

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WO2008151266A2
WO2008151266A2 PCT/US2008/065863 US2008065863W WO2008151266A2 WO 2008151266 A2 WO2008151266 A2 WO 2008151266A2 US 2008065863 W US2008065863 W US 2008065863W WO 2008151266 A2 WO2008151266 A2 WO 2008151266A2
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test
light
detector
information
source
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PCT/US2008/065863
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English (en)
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WO2008151266A3 (fr
Inventor
Xavier Colonna De Lega
Peter De Groot
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Zygo Corporation
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Priority claimed from US11/758,252 external-priority patent/US7884947B2/en
Application filed by Zygo Corporation filed Critical Zygo Corporation
Publication of WO2008151266A2 publication Critical patent/WO2008151266A2/fr
Publication of WO2008151266A3 publication Critical patent/WO2008151266A3/fr

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/02041—Interferometers characterised by particular imaging or detection techniques
    • G01B9/02043—Imaging of the Fourier or pupil or back focal plane, i.e. angle resolved imaging
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/02055—Reduction or prevention of errors; Testing; Calibration
    • G01B9/02056—Passive reduction of errors
    • G01B9/02057—Passive reduction of errors by using common path configuration, i.e. reference and object path almost entirely overlapping
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/02055—Reduction or prevention of errors; Testing; Calibration
    • G01B9/0207—Error reduction by correction of the measurement signal based on independently determined error sources, e.g. using a reference interferometer
    • G01B9/02072—Error reduction by correction of the measurement signal based on independently determined error sources, e.g. using a reference interferometer by calibration or testing of interferometer
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/02083—Interferometers characterised by particular signal processing and presentation
    • G01B9/02084—Processing in the Fourier or frequency domain when not imaged in the frequency domain
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/02083—Interferometers characterised by particular signal processing and presentation
    • G01B9/02088—Matching signals with a database
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/0209—Low-coherence interferometers
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B2290/00—Aspects of interferometers not specifically covered by any group under G01B9/02
    • G01B2290/70—Using polarization in the interferometer

Definitions

  • 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).
  • SWLI scanning white light interferometry
  • 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. Patent No. 5,398,113 to Peter de Groot. This latter approach is referred to as Frequency Domain Analysis (FDA).
  • FDA Frequency Domain Analysis
  • 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 September 30, 2004, the contents of which are incorporated herein by reference, and U.S. Patent Publication No.
  • 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.
  • 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.
  • an interferometry method and apparatus that produces angularly resolved interference signals from a test surface over a range of wavelengths.
  • the information related to each wavelength may be extracted mathematically or in hardware.
  • 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.
  • 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.
  • an apparatus in one aspect, includes: an interferometer configured to direct broadband spatially coherent test light to a test surface of a test object over a range of illumination angles and subsequently combine it with reference light to form an interference pattern, the test and reference light being derived from a common source; a multi-element detector; and one or more optics configured to direct at least a portion of the combined light to the detector so that different elements of the detector correspond to different illumination angles of a region of the test surface illuminated by the test light.
  • the apparatus includes the common source.
  • the common source may be a broadband spatially coherent source.
  • the broadband source is a source spanning more than 50 nm at full width half maximum, more than 100 nm at full width half maximum, more than 500 nm at full width half maximum, or more than 1000 nm at full width half maximum.
  • the interferometer includes an interference objective having a pupil plane, and where the one or more optics image the interference pattern at the pupil plane to the multi-element detector.
  • input light is directed from the common source to the pupil plane.
  • the input light directed to the pupil plane may be spatially coherent at the pupil plane.
  • the common source may output a beam having a waist, and the waist of the beam imaged to the pupil plain.
  • a field stop may be positioned to define the spatial extent of the test light on the test surface.
  • the interference objective is configured to focus the test light to a test spot at the test surface.
  • the width of the test spot may be about equal to the width of a diffraction spot of the interference objective at the test surface, about 150% or less of the width of a diffraction spot of the interference objective, or about 200% or less of the width of a diffraction spot of the interference objective.
  • the numerical aperture of the interference objective may be greater than 0.7 or 0.0.
  • the width of the test spot is about 1 ⁇ m or less or about 0.5 ⁇ m or less.
  • the common source includes a light source optically coupled to an optical fiber configured to provide spatially coherent output light.
  • the light source includes one or more of: a lamp element, a laser, a light emitting diode, a light emitting diode array.
  • the optical fiber includes a single mode fiber and/or a photonic bandgap fiber.
  • the optical fiber includes an optically nonlinear material.
  • the fiber interacts with light from the light source propagating along the fiber to provide output light with a broader spectral range than the light source.
  • the common source includes a resonant cavity configured to provide spatially coherent output light.
  • the apparatus includes an optical element configured to operate selectively to reduce the spatial coherence of the test light.
  • the apparatus includes an electronic processor coupled to the detector.
  • the electronic processor is configured to process information measured by the detector to determine information about the test object.
  • the test object includes one or more layers on a substrate.
  • 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.
  • the apparatus may include a translation stage configured to adjust the relative optical path length between the test and reference light when they form the interference pattern.
  • the electronic processor may be configured to analyze an interference intensity signal measured at each of multiple locations across the detector and produced by scanning the translation stage.
  • the electronic processor is configured, in a first mode, 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.
  • the electronic processor is configured, in a first mode, to extract angularly resolved and wavelength-resolved information about the test surface based on the intensity signals measured across the detector.
  • 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.
  • the model provides an estimate for the measured information as a function of one or more parameters for the test object, and where 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 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.
  • the translation stage is configured to vary the optical path length over a range larger than a coherence length for the common source.
  • the one or more optics are configured to direct at least a portion of the combined light to the detector so that different elements of the detector correspond to different locations on the region of the test surface illuminated by the test light.
  • the electronic processor is configured, in a second mode, to process information measured by the different elements of the detector corresponding to different locations on the region of the test surface illuminated by the test light to determine information about a test object having the test surface.
  • a method includes: directing broadband spatially coherent test light to a test surface of a test object over a range of illumination angles and subsequently combining it with reference light to form an interference pattern, the test and reference light being derived from a common source; and 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 a region of the test surface illuminated by the test light.
  • the common source is a broadband spatially coherent source.
  • the common source may be a broadband spatially coherent source.
  • the broadband source is a source spanning more than 50 nm at full width half maximum, more than 100 nm at full width half maximum, more than 500 nm at full width half maximum, or more than 1000 nm at full width half maximum.
  • the directing spatially coherent test light to the test surface includes using an optical system to direct the test light to illuminate a test spot on the surface, where the width of the test spot at the test surface is about equal to a diffraction spot of the optical system at the test surface.
  • Some embodiments include processing angularly resolved information measured by the detector to determine information about the test object.
  • Some embodiments include: adjusting the relative optical path length between the test and reference light when they form the interference pattern and analyzing an interference intensity signal measured at each of multiple locations across the detector and produced by adjusting the relative optical path length.
  • the adjusting the relative optical path length includes varying the optical path length over a range larger than a coherence length for the common source.
  • Embodiments may include any of the features or characteristics found in the various embodiments described above.
  • light and “optical” does not only refer to visible electromagnetic radiation; rather such terms include electromagnetic radiation in any of the ultraviolet, visible, near-infrared, and infrared spectral regions.
  • spatially coherent light is to be understood to refer to light where the oscillation of the electromagnetic field is substantially correlated for two or more points spatially separated in a direction transverse to the direction of propagation of the light.
  • 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, hi 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.
  • Figure 1 is a schematic diagram of an interferometry system 100 configured to operate in an ellipsometry mode.
  • Figure 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.
  • OPD optical path length difference
  • Figure 3 is a schematic diagram of interferometry system 100 reconfigured to operate in a profiling mode.
  • Figure 4 shows plots of a data collected by a detector element for a test object having
  • 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.
  • Figure 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.
  • Figure 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.
  • Figure 7 is a schematic diagram of another embodiment for interferometry system 100.
  • Figure 8 is a schematic diagram of yet another embodiment for interferometry system 100.
  • Figure 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.
  • Figure 10 is a schematic diagram of yet another embodiment for interferometry system 100.
  • Figure 11 is a schematic diagram of interferometry system 100 configured to operate in an ellipsometry mode, featuring broadband, spatially coherent illumination.
  • 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 Figure 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).
  • 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.
  • test and reference light 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).
  • 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.
  • relay lens 136 e.g., a Bertrand lens
  • relay lens 136 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).
  • 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.
  • 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 optics 108 and 110 defines the area of test surface 124 illuminated by test light 122.
  • 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.
  • 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.
  • one or more of the polarization elements can be absent.
  • 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.
  • 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 ran).
  • 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 ran.
  • 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.
  • 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.
  • 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.
  • Figure 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.
  • 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.
  • 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.
  • the source spectrum is broad so that many independent spectral components can be calculated with this procedure.
  • 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.
  • 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.
  • 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.
  • 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.
  • a calibration may include the steps of calculating the transmission of the system for each wavelength and at each detector position.
  • 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.
  • interferometry system 100 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 Figure 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).
  • 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.
  • 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.
  • 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).
  • 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 amount of test light that is transmitted through the second linear polarizer (polarization element 144) to detector 134 can be expressed as:
  • E out -[cos( ⁇ ) ⁇ p -tp -sm( ⁇ ) 2 rs -ts)E m (1)
  • ⁇ 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
  • E out is the complex amplitude of the electric field.
  • the interference pattern that is measured at the detector for a given source wavelength ⁇ and a given source point at the pupil plane consists of a modulating term that is proportional to the product E oul E o r uj :
  • ⁇ 2 ⁇ / ' ⁇
  • ⁇ 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
  • ⁇ is the angle of incidence of the light at the test surface (which depends on the source point location at the pupil)
  • ⁇ is a phase difference between the test and reference electric fields.
  • 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.
  • Figure 4 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.
  • Figure 4 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).
  • the frequency transform processing is applied to a region of interest within the image of the pupil plane on the detector.
  • 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.
  • VUk p ⁇ 2* . and ,_ - . "- ⁇ 4) rs a ⁇ tp, a ⁇ where the subscripts denote a functional dependence, a is the angle of incidence corresponding to the radius of the circle at the pupil plane, ⁇ is the wavelength of light, ⁇ is the azimuthal angle measured with respect to the linear polarizers, A is a height offset of the object surface, L is a real scaling factor related to the source intensity or signal strength and / 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.
  • 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: where ⁇ and ⁇ 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.
  • the electronic processor can readily calculate the complex refractive index of the material according to the expression:
  • « 0 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.
  • the electronic processor can determine the unknown thickness t according to the following equations:
  • the processing of the data obtained by interferometry system 100 provides multiple estimates of t, because the measurement is performed for multiple values of a and ⁇ . 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.
  • 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.
  • 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 ⁇ model and ⁇ model 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:
  • 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.
  • 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.
  • Equation (3) shows that the frequency of the interference signal is proportional to the source wavelength and the angle of incidence through the relationship £cos ⁇ .
  • 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.
  • 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.
  • 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 "Abbe 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.
  • 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.
  • the second stage of the calibration involves calculating the value of the various system parameters that relate the observable Z expressed in in Eq. (4) to the ellipsometric ratio.
  • 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 ⁇ 9as in Eq. (4) for both samples. The ratio of these components is then calculated, yielding the complex ratio z as a function of &.
  • the maps zs a ⁇ and ⁇ a ⁇ 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 : (10)
  • Equation (10) 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 ⁇ a ⁇ - Note that the procedure outlined above could be extended to more than two samples in order to benefit from redundancy in the calculation.
  • 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 ⁇ with a period ⁇ . 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 zs a ⁇ and ⁇ a ⁇ .
  • 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:
  • K M L c ⁇ I a ⁇ exp(/ ⁇ ⁇ e )(cos( ⁇ ?) 2 Pl x - sin(#) 2 ⁇ a ⁇ ) (11)
  • Equation (12) J a ⁇ where ⁇ a ⁇ and p a ° ⁇ are unknown complex parameters independent of the azimuth angle ⁇ .
  • 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 p a c ⁇ , which is the ellipsometric ratio for the unknown object surface.
  • 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 Figure 5 show experimental data derived using the above analysis for a
  • the derived ratio z a ⁇ exhibits the ⁇ -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.
  • 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.
  • the mean frequency for a given source spectrum is expected to scale with the cosine of the angle of incidence in object space.
  • the pupil location where the mean frequency is maximum corresponds to the optical axis.
  • 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.
  • a preliminary measurement can be performed with a narrowband filter inserted in the system, as in the system calibration.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • this embodiment is analytically equivalent to the first embodiment with parallel linear polarizers.
  • 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.
  • 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.
  • polarization elements 140, 142, 144 and 146 are all absent and the beam splitter is of the non polarizing type.
  • 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.
  • the measured signal is expected to be again independent from the azimuthal source position to the first order.
  • the system is capable of measuring the amount of light reflected by the object for different angles of incidence, as in a refiectometer.
  • 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.
  • the multiple interfaces produce multiple reflections that contribute the interference signal measured at each detector element.
  • the interference signal measured at various locations at in pupil plane have a limited coherence length, as shown by the signal envelope in Figure 2 and Figure 4 (left side).
  • the measured signal consists of multiple separable signals, each signal corresponding to an interface between two materials.
  • FIG. 6 An example of such a signal is shown in Figure 6 for a 5- ⁇ m thick silicon dioxide (SiO 2 ) film on silicon (Si).
  • SiO 2 silicon dioxide
  • the weaker signal to the right corresponds to the air/ SiO 2 interface.
  • the larger signal in the center corresponds to the SiO 2 /Si interface.
  • the weak signal on the left is due to a double pass reflection of light in the SiO 2 layer, hi 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.
  • 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.
  • 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.
  • 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.
  • 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 Figure 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.
  • 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 Figure 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.
  • ⁇ (k) 2nk(h - ⁇ ) + (r part + r sys ) + ( ⁇ part + ⁇ sys )(k - k 0 ) , (13)
  • PCOR part surface phase change on reflection
  • the value / ⁇ 3 includes PCOR contributions from the interferometer optics and any constant offsets resulting, e.g., from the starting position of the scan ⁇ .
  • the linear dispersions coefficients ⁇ part and T 5 ⁇ 8 correspond to the phase offsets
  • 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.
  • the interference signal / measured by each detector element can be expressed as:
  • 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.
  • 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 d ⁇ /dk 0 corresponds to the centroid of the fringe contrast envelope V.
  • the electronic processor when operating in the profiling mode, determines the fringe-contrast envelope Fas a function of ⁇ , e.g., by electronic or digital conversion, for every detector pixel. It then determines the scan position ⁇ m ⁇ X 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:
  • the coherence profiling intensity signal is Fourier transformed with respect to the scan position ⁇ into the frequency domain (i.e., with respect to frequency wave number k).
  • the phase of the transformed data corresponds directly to the phase ⁇ (k) in Eq. 13. From this phase, the signal processor calculates the phase derivative d ⁇ /dk , and determines height h for each detector pixel according to:
  • 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., ⁇ part and r ⁇ ). 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.
  • surface height measurements can also be based on interferometric phase profiling data where the interferometric phase ⁇ (k) is measured directly for one or more wavenumbers k.
  • 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 ⁇ part and ⁇ (and PCOR dispersion ⁇ part and ⁇ sys for wave numbers other than the nominal wave number ko) improves the accuracy of the height measurement.
  • 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 is the measured phase ⁇ (k) includes 2 ⁇ fringe ambiguity.
  • relative fringe ambiguity over the surface may be interpolated from the data of multiple detector pixels using standard fringe unwrapping procedures.
  • 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.
  • 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 ⁇ part and ⁇ improves the accuracy of the absolute phase profiling measurement. Moreover, Eq. 19 implicitly depends on PCOR dispersion values ⁇ part and T ⁇ ys through the coherence profiling determination of A.
  • the profiling formalism is more complicated because reflections from underlying surfaces will also contributed the interference signal.
  • 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.
  • the electronic processor can use the model- based techniques disclosed in U.S. Patent Application Serial 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.
  • the relay lens can be left alone and detector 134 can be translated to a position where the test surface is in focus.
  • Figure 7 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.
  • 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.
  • 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.
  • the different portions of the common electronic detector can be considered to be separate detectors.
  • Figure 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 protocols.
  • the system can include a motorized turret 910 supporting multiple objectives
  • One or more of the objectives can be interference objectives, with the different interference objectives providing different magnifications.
  • 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).
  • 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.
  • 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 refiectometry 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.
  • the translation is under control of electronic processor.
  • each detector is coupled to the electronic processor 970 for analysis.
  • 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.
  • 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.
  • the translation stage can be coupled to adjust the position of the interference objective relative to a mount 940 for supporting test object 126.
  • 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.
  • a lateral translation stage 950 can be coupled to the mount 940 supporting the test object to translate laterally the region of the test surface under optical inspection.
  • 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.
  • 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.
  • automated wafer handling systems known in the art can be used for this purpose.
  • system 100 and object handling system can be housed under vacuum or clean room conditions to minimize contamination of the test objects.
  • 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.).
  • sample properties e.g., refractive index, underlying film thickness(es), material identification, etc.
  • 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.
  • 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.
  • 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.
  • the profiling mode captures interference signals that allow reconstructing the topography of, for example, one or more interfaces that constitute the object.
  • 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 Serial 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.
  • the electronic processor can also adjust the aperture stop diameter via motorized aperture 932 to improve the measurement in any of the various modes.
  • 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.
  • the system can be used in a semiconductor process for tool specific monitoring or for controlling the process flow itself, hi 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.
  • 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.
  • 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).
  • interferometry system 100 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.
  • 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 ⁇ in Equation 20. For example, one can write:
  • ⁇ a s j lem is a characteristic of the instrument and ⁇ rt is the phase change on reflection for that particular measurement location.
  • 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.
  • 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).
  • NA numerical aperture
  • 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.
  • 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.
  • 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).
  • 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.
  • system 100 in the profiling mode shown in Figure 3 is modified to also allow concurrent angularly resolved (e.g. reflectometry or ellipsometry) measurement.
  • lens 236 is placed such that the points on surface 124 are imaged to corresponding points on detector 134 (as indicated by marginal rays 216 and chief rays 217 from source 102), thereby allowing a surface profiling measurement to determine, for example, a topography measurement.
  • beam splitter 1101 is placed between lens 236 and detector 134 to divert a portion of combined light 132 to form a second beam 1104.
  • Beam 1104 is directed to field stop 1110 and on through relay lens 1136 to form an optical interference pattern on electronic detector 1134 (as indicated by chief rays 1117 and marginal rays 1116).
  • 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.
  • Pupil plane 114 is imaged onto the detector by relay lens 1136 such that different points on the pupil plane 114 are imaged to corresponding points on detector 1134.
  • 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.
  • 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.
  • combined light 132 forms a secondary image of the source at pupil plane 114 of the objective lens.
  • field stop 1110 can be a fixed aperture, a series of user-selectable physical apertures or a user-programmable aperture such as that created using a spatial light modulator (for example a pixelated LCD filter). It is possible to create effective apertures with arbitrary shapes. It is also possible to locate an effective aperture which restricts the measurement to any arbitrary location on the object surface within the field of view of the optics.
  • interferometry system 100 operates to acquire angularly resolved information about an area or areas of the surface of object 126 using detector 1134 while concurrently obtaining surface profile information using detector 134.
  • both an ellipsometry/reflectometry measurement and a surface profile measurement may be acquired during a single scan of interference objective 106.
  • Information from concurrent measurements can be combined to supplement, confirm, or improve the other.
  • a first aperture can be created at a location A.
  • An angularly resolved measurement then provides the optical properties of the object at that location.
  • the procedure is repeated at a location B.
  • the measured optical property information can then be used to improve a concurrent profile measurement. For example, using the measured optical property information, it is possible to calculate the height offset that would be reported in a concurrently measured profile map covering locations A and B due to the difference in optical properties. Such optical effects in the profile map are reduced by correcting for the calculated height offsets, resulting in a corrected topography map.
  • interferometry system 100 can provide semiconductor wafer metrology in an integrated circuit production line. Increased throughput can insure that the system does not become a bottleneck which slows the entire line.
  • Narrow-band Tunable Source in yet another embodiment, light source 102 in system 100 of Figure 1 is replaced by a tunable monochromatic source under the control of the electronic processor.
  • 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.)
  • 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.
  • 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.”
  • 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.
  • the electronic processor determines the wavelength-dependent, complex reflectivity of the test surface from the interference cross-term in Eq. 4 using an analytical framework similar to that shown above.
  • 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.
  • 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.
  • this narrow-band, tunable source embodiment can also operate in the various modes of operation and for the various applications described above.
  • the test object is illuminated with spatially coherent light.
  • Light is said to be spatially coherent when the oscillation of the electromagnetic field is substantially correlated (i.e., has a substantially fixed phase relationship) for points spatially separated in a direction transverse to the direction of propagation.
  • the electromagnetic field at points on a cross-section of the beam will oscillate in a correlated way.
  • the use of spatially coherent light allows for diffraction limited or near-diffraction limited illumination of areas on the test object. In certain embodiments, this allows for illumination and measurement of small, well-defined regions of the test surface. Further, in some embodiments, the spatially coherent illuminating light can be spectrally broadband, allowing for wavelength resolved measurements, as described above. For example, referring to Figure 11, interferometer system 100 operates in an ellipsometry mode, as shown in Figure 1 , but with a broadband spatially coherent illumination system 1000 (described in more detail below), replacing elements 102, 108, and 138.
  • a broadband spatially coherent illumination system 1000 described in more detail below
  • light source 1001 is coupled to optical fiber 1002 to generate spatially coherent input light 104 (the chief rays of which are indicated by solid lines).
  • Input light 104 is spatially coherent across face 1003 of fiber 1002.
  • input light 104 is collimated by collimator lens 1004.
  • the collimated beam is expanded by expander lens 1005 to match the size of objective pupil aperture stop 115, re- collimated by lens 110, and directed to pupil plane 114 of interference objective 106.
  • shape of the light beam is Gaussian (or nominally Gaussian) the beam waist may be imaged pupil plane 114.
  • 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.
  • 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.
  • 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.
  • the pupil plane 114 is imaged onto the detector.
  • relay lens 136 images different points on the pupil plane 114 to corresponding points on detector 134.
  • Illumination system 1000 provides spatially coherent 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).
  • 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.
  • Such broadband, spatially coherent illumination can be provided by a number of types of sources.
  • optical fiber 1002 is a so called "monomode" fiber.
  • a monomode fiber supports only a single (or, in some cases, a few) spatial mode for light propagating along the fiber. See, e.g., Encyclopedia of Laser Physics and Technology, available at http://www. ⁇ -photonics.com/single_mode_fibers.html.
  • output light 104 contains primarily light in the supported spatial mode. The light across output face 1003 is thereby well correlated, yielding spatially coherent output light 104.
  • Monomode fibers are typically capable of supporting a single spatial mode over a range of wavelengths.
  • light source 1001 is a broadband source (e.g.
  • the optical fiber 1002 includes a photonic bandgap material
  • fiber 1002 may also be a monomode fiber, supporting a single (or few) spatial mode for light over a very wide range of wavelengths (e.g. a range spanning wavelengths from the infra-red and above to the ultraviolet and below). See, e.g.
  • fiber 1002 contains nonlinear material which acts to further broaden the spectral range of light input into the fiber. Nonlinear effects (e.g. Raman scattering or four wave mixing) occur as the light propagates along the fiber, producing light at wavelengths other than those present in the input light.
  • light source 1001 may be a relatively narrowband source, with spectral broadening provided by fiber 1002 to produce broadband output light 104.
  • illumination system 1000 includes a resonant cavity capable of producing a spatially coherent output beam.
  • light source 1001 may include a resonant cavity pumped by a source (e.g. a laser, LED, or LED array) to excite the cavity to resonate at a single (or a few) spatial mode of the cavity. The output of the cavity will thereby be spatially coherent.
  • fiber 1002 may be removed, with input light 104 deriving directly from light source 1001 (e.g., as the output beam of the resonant cavity).
  • the cavity may include a filter which acts to limit the number of spatial modes which are supported by the resonant cavity.
  • coherent illumination differs from cases in which the measurement object is illuminated by light with a low degree of spatial coherence (e.g., when using a spatially incoherent extended source imaged at pupil plane 114 to provide Koehler illumination).
  • a spatially incoherent illuminating light beam will produce a large spot size at test object 126 (e.g., a spot size significantly wider than the diffraction spot of interference obj ective 106) .
  • test light 122 is spatially coherent, and may be focused to a small spot size at test object 126.
  • the focused beam at test object 126 is, in this case, the convolution of the geometrical point spread function of interference objectivelO ⁇ by its diffraction spot.
  • the geometrical point spread is defined as the irradiance distribution at the object of point sources in pupil plane 114, when all diffraction effects are ignored.
  • the geometric point spread of interference objective 106 depends on, for example, optical aberrations in the objective, and can be reduced or even eliminated using correction techniques know in the art.
  • the diffraction spot is, on the other hand, the irradiance distribution at object 126 due to diffraction effects including, for example, effects of apertures, obscurations, etc along the objective.
  • the spot size at test object 126 can approach or essentially equal the width of the diffraction spot at the test object.
  • the diffraction spot can be, for example, a fraction of a micrometer for the central lobe of the illumination spot.
  • interferometry system 100 in an ellipsometry mode, can determine angle, wavelength, and polarization resolved information (e.g. complex reflectance information) for a small, well defined region of test surface 124 of test object 126. Such a measurement can be repeated over multiple areas on test surface 124.
  • test object 126 For example, complex reflectance measurements taken at multiple test spots across test surface 124 can be analyzed to map out properties of test object 126 such as film thickness, material type, index of refraction etc. Such information could, for example, be used to improve a surface profile measurement made using interferometry system 100 operating in a profiling mode.
  • spatially coherent illumination differs from illumination by light with a low degree of spatial coherence in another respect.
  • light diffusely reflected from test surface 124 will combine incoherently (i.e. with a random phase relationship) at detector 134.
  • the intensity of the combined electromagnetic field at detector 134 corresponding to the diffusely reflected light will average to zero.
  • the diffusely reflected light will therefore have no contribution to the interference signal measured by detector 134.
  • such signals may still be analyzed using, for example, model based techniques in which the measured signal is compared to, for example, model signals calculated using the full Maxwell's equations and/or exemplary signals based on known reference samples. Examples of such techniques are be found in U.S. Provisional Patent Application No. 60/876,748, entitled APPARATUS AND METHOD FOR MEASURING CHARACTERISTICS OF SURFACE FEATURES and filed on December 22, 2006, which is incorporated herein by reference.
  • interferometry system 100 includes an optical element (e.g. a diffuser) which may be selectively switched into the beam path to reduce the spatial coherence of the illuminating light.
  • an optical element e.g. a diffuser
  • one may provide the option of Koehler illumination by imaging the spatially coherent light source (i.e. fiber face 1003) onto a diffuser (not shown) placed within aperture stopl 15 of interference objective 106.
  • broadband spatially coherent illumination source with interferometry system 100 in an ellipsometry mode
  • such a source can be used similarly in a variety of other modes, including the profiling mode described above.
  • 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).
  • the reference surface can be positioned outside of the path of the test light.
  • 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.
  • 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.
  • the two objective lenses are matched to one another so that the test and reference light have similar aberrations and optical paths.
  • the system can be configured to collect test light that is transmitted through the test sample and then subsequently combined with reference light.
  • 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.
  • 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.
  • the tuning range is preferably broad
  • the source may also include one or more diffuser elements to increase the spatial extent of the input light being emitted from the source.
  • the interferometer can be configured such that some or all of the interferometer's optical elements are reflective elements. For example, in applications where input light is in the UV or extreme UV (EUV) spectral, refractive optical elements using typical materials would absorb a substantial amount of the light. In such applications all refractive elements in the interferometer could be replaced by reflective elements such as, for example, curved mirrors.
  • the various translations stages in the system 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.
  • interferometer system 100 outputs measurement information to, for example, a user display, a printer, a machine-readable medium or storage device, a electronic controller, etc.
  • the output data can automatically control a further device or devices (e.g., integrated circuit processing and/or metrology tools).
  • 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.

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Abstract

L'invention concerne un dispositif qui comprend: un interféromètre conçu pour diriger de la lumière d'essai à large bande spatialement cohérente sur une surface d'essai d'un objet soumis à l'essai sur une plage d'angles d'éclairage, et combiner ultérieurement cette lumière avec une lumière de référence afin de former un motif d'interférence, la lumière d'essai et la lumière de référence étant obtenues à partir d'une source commune; un détecteur à éléments multiples; et un ou plusieurs systèmes optiques conçus pour diriger au moins une partie de la lumière combinée vers le détecteur, de manière à faire correspondre les différents éléments du détecteur avec les différents angles d'éclairage d'une région de la surface d'essai éclairée par la lumière d'essai.
PCT/US2008/065863 2007-06-05 2008-06-05 Interférométrie pour déterminer des caractéristiques de la surface d'un objet à l'aide d'un éclairage spatialement cohérent WO2008151266A2 (fr)

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US94200107P 2007-06-05 2007-06-05
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US11/758,252 US7884947B2 (en) 2005-01-20 2007-06-05 Interferometry for determining characteristics of an object surface, with spatially coherent illumination
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US8649024B2 (en) 2010-12-03 2014-02-11 Zygo Corporation Non-contact surface characterization using modulated illumination
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US7139081B2 (en) * 2002-09-09 2006-11-21 Zygo Corporation Interferometry method for ellipsometry, reflectometry, and scatterometry measurements, including characterization of thin film structures
US7106454B2 (en) * 2003-03-06 2006-09-12 Zygo Corporation Profiling complex surface structures using scanning interferometry
DE10327019A1 (de) * 2003-06-12 2004-12-30 Carl Zeiss Sms Gmbh Verfahren zur Bestimmung der Abbildungsgüte eines optischen Abbildungssystems
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WO2013105922A3 (fr) * 2011-12-12 2013-09-19 Zygo Corporation Caractérisation de surface sans contact utilisant un éclairage modulé
US8896827B2 (en) 2012-06-26 2014-11-25 Kla-Tencor Corporation Diode laser based broad band light sources for wafer inspection tools
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