WO2009149103A1 - Détection et classification par interférométrie de défauts - Google Patents

Détection et classification par interférométrie de défauts Download PDF

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Publication number
WO2009149103A1
WO2009149103A1 PCT/US2009/045999 US2009045999W WO2009149103A1 WO 2009149103 A1 WO2009149103 A1 WO 2009149103A1 US 2009045999 W US2009045999 W US 2009045999W WO 2009149103 A1 WO2009149103 A1 WO 2009149103A1
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Prior art keywords
sample
phase
defect
light
signal
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PCT/US2009/045999
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English (en)
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Hwan J. Jeong
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Jeong Hwan J
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Priority claimed from US12/190,144 external-priority patent/US7864334B2/en
Application filed by Jeong Hwan J filed Critical Jeong Hwan J
Priority to EP09759262.0A priority Critical patent/EP2286175A4/fr
Priority to JP2011512587A priority patent/JP5444334B2/ja
Priority to CN200980121352.XA priority patent/CN102089616B/zh
Publication of WO2009149103A1 publication Critical patent/WO2009149103A1/fr
Priority to US12/959,194 priority patent/US7986412B2/en

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/84—Systems specially adapted for particular applications
    • G01N21/88—Investigating the presence of flaws or contamination
    • G01N21/95—Investigating the presence of flaws or contamination characterised by the material or shape of the object to be examined
    • G01N21/9501—Semiconductor wafers
    • 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
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/84—Systems specially adapted for particular applications
    • G01N21/88—Investigating the presence of flaws or contamination
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01L—SEMICONDUCTOR DEVICES NOT COVERED BY CLASS H10
    • H01L21/00—Processes or apparatus adapted for the manufacture or treatment of semiconductor or solid state devices or of parts thereof
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/41—Refractivity; Phase-affecting properties, e.g. optical path length
    • G01N21/45—Refractivity; Phase-affecting properties, e.g. optical path length using interferometric methods; using Schlieren methods

Definitions

  • This patent specification relates to common-path interferometry. More particularly, the patent specification relates to high resolution common-path interferometric imaging for use in detecting and classifying defects in micro lithographic devices such as semiconductor devices and integrated circuits and defects in photolithographic reticles.
  • Optical defect detection technology has been one of the key technologies limiting our ability to make ever smaller transistors. It has, up till now, provided both high performance and high throughput, which other technologies like electron beam microscopy could not offer.
  • the geometries employed in IC chips have continued to decrease, it has become harder to detect defects reliably.
  • Design rules of future generations of IC chips are so small that there is a real possibility that none of the current optical defect detection technologies will work. Therefore, in order to extend the life of optical inspection technology into future equipment generations, a major overhaul of optical defect detection technology is needed.
  • Optical defect detection systems in use today include both bright field systems and dark field systems. Unlike bright field systems, dark field systems attempt to exclude the unscattered illumination beam from the image. However, limitations of the current dark field and bright field defect detection systems exist which cause difficulty in reliably detecting defects, especially as the design rules progressively decrease.
  • Separate path interferometric techniques have been proposed according to which two beams, probe and reference beams, are generated using a beam splitter and brought to an image sensor through different paths or subsystems. For example, separate path systems designed for defect detection are discussed in US Patent Nos. 7,061,625, 7,095,507, 7,209,239 and 7,259,869.
  • phase-contrast microscopes are designed to provide a fixed amount of phase control to specular component, usually ⁇ / y or - 71 A - These systems commonly use extended light sources such as an arc or halogen lamp. Although they are generally suitable for observing biological samples, conventional phase-contrast microscopes are not generally well suited for detecting the wide variety of defects that exist in semiconductor wafers and/or reticles.
  • US patent No. 7,295,303 discusses approaches similar to phase-contrast microscopy that are not well suited for detecting a wide variety of defects that exist in semiconductor wafers and/or reticles.
  • U.S. Patent No. 7,365,858 and U.S. Application Publication No. 2005/0105097 Al discuss a system for imaging biological samples. Two modes of operation are discussed, a "phase mode" and an "amplitude mode.” The goal in the discussed amplitude mode is to obtain high contrast raw images. In phase mode, the discussed techniques
  • a common-path interferometric imaging system for the detection and classification of defects in a sample.
  • the system includes an illumination source for generating light, which includes wavelengths as short as EUV (13.5nm) and wavelengths as long as 10 microns in the far infrared, directed toward the sample; an optical imaging system for collecting a portion of the light from the sample including a scattered component of the light that is predominantly scattered by the sample, and a specular component of the light that is predominantly undiffracted, or specularly reflected or transmitted, by the sample; a variable phase controlling system for adjusting the relative phase of the scattered component and the specular component and a sensing system for measuring the intensity of the combined scattered and specular components, and a processing system to determine from outputs of the sensing system if points on the sample are likely to include defects.
  • An accurate positioning system allows the intensity signal from each point on the sample to be accurately referenced to and compared with a reference signal for that point by a computer. If the difference exceeds predetermined positive and negative thresholds, then this location on the sample is recorded and displayed as a possible defect location along with the level of the sample and reference signals corresponding to that location.
  • the reference signal with which the signal from the sample is compared may be generated by a computer from the pattern image that is expected to be on the sample, assuming the defect is not present. If multiple copies of the pattern are available and some are known to be defect free, or the defects are known to be randomly distributed, then the reference signal can be generated by a similar common-path interferometric imaging system using the same phase shift and wavelength to scan the corresponding position on one or more neighboring die on the same wafer, or the corresponding position on one or more die on a similar wafer.
  • FIG. 1 shows an example of an interferometric defect detection system, according to some embodiments
  • Figs. 2a and 2b show an example of a phase controller and attenuator, according to some embodiments
  • FIG. 3 shows an example of an interferometric defect detection system, according to some embodiments.
  • FIGs. 4a and 4b show an example for changing optical path length, according to some embodiments.
  • Fig. 5 shows an example of a movable mirror used to change the optical path length, according to some embodiments
  • FIG. 6 shows an example of an interferometric defect detection system making use of a moveable mirror phase controller, according to some embodiments
  • Figs. 7a - 7 c show an example of a compensation plate with Fourier filter strips for use with an interferometric defect detection system, according to some embodiments
  • FIG. 8 shows an example of a placement of a folding prism for the illumination light, according to some embodiments.
  • Fig. 9 shows a phase controller combined with a polarization rotator, according to some embodiments.
  • Fig. 10 shows an example of a polarization controller, according to some embodiments.
  • FIG. 11 shows an example of a continuously -variable attenuator using polarization, according to some embodiments
  • Fig. 12 shows an example implementation of a system using the type of attenuator shown in Fig. 11;
  • Figs. 13a-13c show further detail of the system in the vicinity of the pupil or aperture stop, according to some embodiments.
  • Fig. 14 shows an example of an attenuator having both ⁇ /2 and ⁇ /4 plates, according to some embodiments
  • Fig. 15 shows an example of an interferometric defect detection system with high incidence angle illumination, according to some embodiments
  • Fig. 16 shows an example of an interferometric defect detection system with high incidence angle illumination and a variable attenuator, according to some embodiments
  • Fig. 17 shows an example of an interferometric defect detection system with a low-flare high-incidence angle illumination, according to some embodiments
  • Fig. 18 shows an example of an interferometric defect detection system with low- flare high-incidence angle illumination and a variable attenuator, according to some embodiments
  • Fig. 19 shows an example of an interferometric defect detection system with an azimuthally rotatable high incidence angle illumination, according to some embodiments
  • Fig. 20 shows an example of an interferometric defect detection system with an azimuthally rotatable high incidence angle illumination with a variable attenuator for the specular component, according to some embodiments
  • Fig. 21 shows an example of an interferometric defect detection system with an azimuthally rotatable high incidence angle illumination, according to some embodiments
  • Fig. 22 shows an example of an interferometric defect detection system with an azimuthally rotatable high incidence angle illumination with a variable attenuator for the specular component, according to some embodiments
  • Fig. 23 shows an example of an interferometric defect detection system with illumination through transmissive samples, according to some embodiments
  • Fig. 24 shows an example of a sample inspection system incorporating both reflection and transmission modes, according to some embodiments
  • Figs. 25 through 27 show various examples of waveplates for use in operation of a detection system in a sequential multiple wavelength mode, according to some embodiments
  • Fig. 28 shows an example system configuration for two wavelengths, according to some embodiments.
  • Fig. 29 shows an example of an interferometric defect detection system having a low incidence angle illumination with an extended light source, according to some embodiments
  • Fig. 30 shows an example of an interferometric defect detection system having a high incidence angle illumination with an extended light source, according to some embodiments
  • Fig. 31 shows an example of an interferometric defect detection system having a high incidence angle illumination with an extended light source and phase control in the path of the scattered light, according to some embodiments;
  • Figs. 32a and 32b show the shapes of the defects used for numerical simulations herein;
  • Figs. 33 through 35b are graphs showing results of numerical simulations
  • Fig. 36 shows plots of simulated enhanced contrast of an image of a 40 nm defect by attenuating the intensity of the specular component by 96%;
  • Fig. 37 shows plots of simulated enhanced contrast of an image of a 20 nm defect by attenuating the intensity of the specular component by 99.9%;
  • Fig. 38 shows plots of simulated signal intensity and the phase of 20 nm defect as an example
  • Fig. 39 shows plots of simulated phases of defect signals from 20 nm particle and 20 nm void
  • Fig. 40 shows plots of spatial frequency bandwidths of defect signal components
  • Fig. 41 shows an example of system configuration for the reduction of the number of sample scans
  • Figs. 42a through 42c compare the magnitude of interference term with that of dark field term for different defect sizes and sample reflectivities;
  • Figs. 43a and 43b show the design examples of catadioptric imaging system
  • Figs. 44a through 44f show coherent uniform illuminator designs
  • Figs. 45a through 45f show autofocus system designs
  • Figs. 46a through 46e show serrated aperture and its performances.
  • inventive body of work A detailed description of the inventive body of work is provided below. While several embodiments are described, it should be understood that the inventive body of work is not limited to any one embodiment, but instead encompasses numerous alternatives, modifications, and equivalents, as well as combinations of features from the different embodiments. In addition, while numerous specific details are set forth in the following description in order to provide a thorough understanding of the inventive body of work, some embodiments can be practiced without some or all of these details. Moreover, for the purpose of clarity, certain technical material that is known in the related art has not been described in detail in order to avoid unnecessarily obscuring the inventive body of work.
  • reticle and “mask” are used herein interchangeably and refer to a patterned object that is used as a master to create other patterned objects.
  • the optical field can be described with complex amplitudes. Complex amplitudes can be conveniently represented in a Cartesian or in a polar coordinate system. It is represented by real and imaginary parts in a Cartesian coordinate system and amplitude and phase in a polar coordinate system. Therefore, the three phrases: "complex amplitude”, “real and imaginary parts,” and “amplitude and phase” are equivalent to each other as used herein, and the three terms are treated equivalently and can be exchanged with one another.
  • the word “light” is used as shorthand for electromagnetic radiation having a relatively wide range of possible wavelengths, as discussed below.
  • specular component of reflection in practice is “substantially specular,” meaning that it includes not only specularly reflected light but can also include a relatively small amount of scattered light.
  • each field component of the ray is defined as follows. [0061] b ⁇ ⁇ b ⁇ exp(i ⁇ b ); Complex amplitude of the specular component, where ⁇ b is the phase of specular component which can be set to zero without losing the generality of the signal equation,
  • S ⁇ g ⁇ e ⁇ p('( ⁇ g + ⁇ b ) > Complex amplitude of any stray light present. Stray light is undesirable non-image-forming light which is generated by unwanted reflections from lens surfaces and mechanical components.
  • the light intensity that an image sensor detects can be expressed as follows.
  • the light intensity, /, detected by a detector element at the image plane is the sum of the squares of the electric field amplitudes for the specular, scattered and stray light components and is given by:
  • b * , a * and s * are the complex conjugates of b , a and s respectively.
  • the specular component, b is separated out in equation (Ia) because it can be physically separated from other image intensity components at the pupil plane. Note that all complex amplitudes are functions of position on the sample. Additionally, only relative phases between different components matter. Therefore, the absolute phase of specular component, ⁇ b , does not play any role and can be set to zero without losing generality. Also notice that if ⁇ b is set to zero, the complex amplitude of the specular component defines the direction of the real axis of the complex plane coordinate system used herein. [0072] The optical path length difference of the stray light with respect to the specular component is assumed to be larger than the coherence length of the illumination light. Therefore, stray light is added incoherently, without considering its relative phase, in the equation (1).
  • Equation (Ic) shows that the image comprises not only a defect signal, s, but also many other unwanted components.
  • components other than the defect signal need to be removed to the extent possible. This is commonly done by die-to-die subtraction of the image of, e.g., neighboring die from the image of the current die.
  • die-to-die subtractions for example, [(current die image) - (left die image)] and [(current die image) - (right die image)] are required in order to correctly identify defect signals. Defects that show up in both subtracted images belong to a current die. Defects that show up in only one of the two subtracted images belong to neighboring dies.
  • Equation (2c) is a general defect signal equation. Note that the definition of defect herein includes not only the defects of interest but also the defects of little or no interest. A good example of the defects of little interest is sample pattern noise. The sample pattern noise is actually not a noise but a defect as this term is used herein. That is, s, the defect signal includes the sample pattern noise as well as the defect signal of interest. Detailed discussions on sample pattern noise will be presented in later sections. Equation (2c) shows that the comparison of the two signals with and without a defect present is a mixed bag of different signal components. The first four terms constitute the dark field signal because they exist even if the specular component is filtered out (herein they will sometimes be called the "dark field term").
  • the interference term (herein it will be sometimes called the "interference part"). That is, the last term originates from interference between the defect signal amplitude and the specular component.
  • the sign and magnitude of the interference term depends not only on the strength of the specular component but also on the relative phase between the defect signal amplitude and the specular component. If the phase difference between the defect signal and the specular component is ⁇ 90° then the defect signal may not be detected.
  • the solutions described herein can be described at least theoretically in connection with signal equation (2c), but it should be understood that theoretical explanations can pertain to idealized circumstances that should not limit the practical aspects of the operation of embodiments disclosed in this patent specification.
  • the signal equation shows the importance of controlling the relative phase between the defect signal amplitude and the specular component for consistent performance.
  • both the sign and the magnitude of the interference term can be controlled. For example, if we set the relative phase to zero, the magnitude of the interference term attains a positive maximum. If we set the relative phase to 180°, the magnitude of the interference term attains a minimum (or a negative maximum).
  • controlling the relative phase between the specular and scattered components can be used to maximize the magnitude of interference term, and can also be used to change its sign. It should be understood that references to maximizing in this patent specification refer to at increasing a parameter preferably but not necessarily to a practical maximum thereof, and references to minimizing refer to reducing a parameter preferably but not necessarily to a practical minimum thereof.
  • the defect size can be estimated from the amplitude information and the defect type can be determined from the phase information.
  • the optical signal amplitude of the defect does not directly provide the physical size of the defect. Rather, it provides only an Optical size' of the defect.
  • the relationship between the physical size and the optical size can be complicated making it difficult to estimate the physical size of the defect accurately from the optical signal amplitude alone.
  • a more accurate characterization of defects allows a more accurate decision as whether or not they likely require repair. This possibility will be explored in a later section of Catch-all Mode.
  • Accurate defect classification is usually as important as reliable defect detection because it can save time in the defect review process which is one of the more expensive processes in semiconductor manufacturing.
  • the relative phase can be controlled by controlling either the phase of the specular component or the phase of the scattered component. However, it is usually easier to control the phase of the specular component because the etendue of the specular component is much smaller than that of the scattered component.
  • the control of the relative phase between scattered and specular components is one of the key features of the interferometric defect detection and classification technology disclosed herein. Its importance will be demonstrated with examples in later sections.
  • noiseless parametric amplification This kind of amplification is called “noiseless parametric amplification" where b is the amplification parameter.
  • a basic theoretical explanation for the noiseless amplification is as follows. Both the magnitude of the interference term and the photon noise are proportional to ⁇ b ⁇ . Therefore, the signal-to-noise ratio, the ratio between the two quantities, is independent of b .
  • the factor '2' in the interference term comes from the fact that there are actually two signal amplifiers that coherently work with each other. One amplifier is represented by bs * and the other amplifier is represented by b *s. They are mutually coherent but can either be mutually constructive or destructive depending on the relative phase between the defect signal and the specular component.
  • the two amplifiers need to be configured to work in a mutually constructive way by controlling the relative phase between the defect signal and the specular component.
  • the mutual construction becomes a maximum when the relative phase is set to either 0° or 180°.
  • a complete mutual destruction happens when the relative phase is ⁇ 90°.
  • the story is different.
  • equation (Ib) there is only one noise amplifier which is represented by ⁇ b ⁇ in the equation and is the main source of photon noise. This means that the specular component can amplify the signal two times more than the signal-noise.
  • the specular component can increase the signal-to-noise ratio of the signal up to two times the intrinsic signal-to-noise ratio inherent in the signal itself if the dynamic range of the image sensor is sufficiently large.
  • the price paid for the factor '2' is that the relative phase between the scattered and the specular components must be controlled in order to maximize the amplification. Therefore, increasing the signal-to-noise ratio requires phase control. Phase control requires knowledge about the relative phase in order to add more information to the signal. Thus, the increase in the signal-to-noise ratio does not violate the law of information conservation.
  • the intrinsic signal-to-noise ratio is the ratio between the signal and the signal- noise, the noise contained in the signal itself. Signal-noise is also called intrinsic noise.
  • the dynamic range of a detector is the ratio between the maximum signal range of the detector and the minimum detectable signal, which is usually assumed to be the noise level of the detector. Dynamic range is usually defined as the total number of gray levels the detector can provide, i.e. the maximum signal range divided by the noise level.
  • No electronic amplifiers, including even the cleanest electronic amplifiers, such as the dynodes inside a photo-multiplier tube, can increase the signal-to-noise ratio. They can only reduce the signal-to-noise ratio.
  • the noiseless amplification by the specular component is special in the sense that it can actually increase the signal-to-noise ratio. It is the best amplifier known so far. It is the most suitable amplifier for weak signals such as the signals from tiny defects and it beats all electronic amplifiers in performance. [0088]
  • the systems and methods disclosed herein fully utilize the power of the noiseless amplification by the specular component in order to reliably detect tiny defects.
  • the interfero metric detection herein is a version of homodyne detection in which the two interfering beams have the same temporal frequency.
  • the specular component is a double-edged sword. If it is utilized as an amplifier by controlling its phase properly, its benefit can be huge. However, if it is not utilized, it does not stay neutral but becomes harmful in that it can be a major source of photon noise. This additional noise indicates that bright field inspection systems can perform even worse than dark field inspection systems in certain instances. This is one of the reasons why the existing bright field systems do not perform consistently.
  • One of main ideas described herein is utilizing the specular component in the most beneficial way.
  • the examples shown in the following tables demonstrate the power of noiseless amplification. Examples are selected to represent the real world of high-end defect detection in the future.
  • the relative phase between the specular and scattered components is set to 0° or 180° in order to maximize the noiseless amplification.
  • the defect signal level in a single pixel of a typical high-end image sensor such as scientific grade CCD, TDI CCD (Time Delay and Integration CCD), etc. is considered.
  • Detector noise is assumed to be additive and independent of the signal level.
  • Light intensities are expressed in the unit of light-generated electrons in the detector rather than photons in the light beam because what we eventually care about is the number of electrons generated in the detector.
  • the defect signal is very weak compared with the detector noise but still quite strong compared with its intrinsic noise.
  • the first table below shows how an undetectably weak defect signal for conventional defect detection system can become an easily detectable signal through a large, noiseless amplification provided by a strong specular component and a large image sensor dynamic range.
  • the signal-to-noise ratio was increased from 0.25 to 12.0 by the noiseless amplification process.
  • the second table below shows how even an extremely feeble signal from a tiny defect can become a detectable signal through a large noiseless amplification provided by the strong specular component and a large dynamic range of the image sensor. Notice that, in this case, the signal is weak compared even with its intrinsic noise. However, the signal-to-noise ratio increased from 0.005 to a sizablel .69 by the noiseless amplification process. It shows the possibility of relatively reliable detection of even a single photon signal.
  • the signal-to-noise ratio of the amplified signal is larger than the intrinsic signal-to-noise ratio of the signal itself. This is one of the amazing powers of the technique disclosed herein that to the inventor's knowledge has not been previously appreciated or expected.
  • the signal-to-noise ratios are still less than two times the intrinsic signal-to-noise ratios due to the limited amplification of the signals.
  • the tables show us the importance of the noiseless amplification of signals by the specular component for the detection of small or tiny defects in the future. Noiseless amplification allows us to detect very weak defect signals reliably even with a noisy image sensor as long as the intrinsic signal-to-noise ratio of the signal is reasonably high.
  • the intrinsic signal-to-noise ratio is the ratio between the signal and the signal-noise which is the noise contained in the signal itself. It will be shown through examples in the later section of Limitations of Dark Field Mode that a large amount of noiseless signal amplification by the specular component can be achieved even with samples having low reflectivity.
  • the quality of the first stage amplifier is the most important.
  • the specular component provides the possibility of noiseless first stage signal amplification.
  • the systems and methods disclosed herein can take advantage of this by controlling the amplitude of the specular component and by controlling the relative phase between the defect signal amplitude and the specular component.
  • a high signal-to-noise ratio means high sensitivity and a low false detection rate in defect detection.
  • Noiseless amplification of the defect signal using the specular component is one of the key features of interferometric defect detection and classification technology disclosed herein. Generally, the higher the noiseless amplification, the better the signal-to-noise ratio.
  • High noiseless amplification benefits from a strong specular component.
  • an unattenuated strong specular component is generally preferred herein. This is the opposite of conventional microscopy where the specular component is either blocked off or severely attenuated to enhance the contrast of the raw images.
  • the specular component should be attenuated when the dynamic range of the image sensor is too limited for the application.
  • the phase controller can also be used for the deamplification of unwanted defect signals.
  • a good example is wafer pattern noise which is actually not a noise but an unwanted defect signal. In most defect detection applications, it is desirable to suppress wafer pattern noise. If the suppression of wafer pattern noise is more important than amplifying the defect signals of interest, the phase controller can be set to minimize the wafer pattern noise rather than maximizing the defect signals of interest. More concrete discussions on pattern noise will be presented later.
  • the terms "sample pattern noise”, “wafer pattern noise”, “pattern noise”, “sample noise” and “wafer noise” refer to the same kind of noise and will be used interchangeably herein.
  • the spatial frequency band width of the interference term is different from that of the dark field term.
  • the spatial frequency band width of the interference term is smaller than that of the dark field term in a common path configuration. (See Fig. 40 for example.)
  • the defect image formed by the interference term is spatially wider than the defect image formed by the dark field term. This implies that the frequency bandwidth of the interference term is narrower. This can be beneficial because it can lead to a higher throughput.
  • a smaller bandwidth allows a coarser sampling of the sample image which allows a larger field of view for the imaging system with an image sensor of the same size. A higher throughput can normally be achieved with a larger field of view.
  • the bandwidth of the dark field term is fixed as long as the numerical aperture of the imaging system is fixed; it does not depend on the ray angle of the specular component.
  • the bandwidth of the interference term depends not only on the numerical aperture of the imaging system but also on the ray angle of the specular component.
  • the spatial frequency bandwidth of the interference term can be minimized by minimizing the ray angle of the specular component.
  • the ray angle of the specular component becomes a minimum when the direction of the illumination light is normal or near-normal to the sample surface.
  • a normal or near- normal illumination of the sample can be chosen for a higher throughput.
  • Normal or near-normal illumination carries an additional advantage, in that it makes the polarization more uniform across the pupil compared to a high angle incidence illumination. A more uniform polarization across the pupil leads to a higher interference term.
  • the spatial shape of the interference term is just the shape of the amplitude point spread function (APSF) of the imaging system and is thus fixed. Even if the spatial frequency of the specular component is not zero, it does not change the shape of the interference term. Its only effect is to provide the interference term with a non-zero carrier frequency.
  • APSF amplitude point spread function
  • the interference term can be expressed as the multiplication of the amplitude point spread function, APSF, with the carrier frequency term. That is, the carrier frequency term can always be factored out and be treated separately. If we treat the carrier frequency term separately, there is no difference between the shape of the subtracted image of a tiny defect and the APSF. This allows a fast numerical deconvolution of the defect image with the sampling functions of finite width attributable to a detector array.
  • the width of the sampling function is the width of the light-sensitive area in each pixel of the image sensor.
  • a high sensitivity or a high dynamic range usually requires a large light-sensitive area.
  • the finite size of the detectors in the array serves to reduce maximum signal amplitude somewhat and deconvolution is equivalent to magnifying the image.
  • the optical image magnification can be replaced with a fast numerical deconvolution. Replacing optical magnification with a numerical deconvolution reduces optical system cost.
  • the penetration depth of the illumination light into the sample surface It is sometimes useful to control the penetration depth of the illumination light into the sample surface. For example, if a defect that needs to be detected is located on or close to the sample surface, a shallow penetration of the illumination light will be generally preferred to detect the defect more reliably. In an opposite case where a defect that needs to be detected is located at the bottom of a deep trench, a deep penetration of the illumination light will generally be preferred to detect the defect more reliably.
  • the penetration depth of the illumination light cannot be controlled arbitrarily. However, if the printed patterns around the defect on the sample are oriented in one direction, the penetration depth of the illumination light can be controlled to some degree by controlling the polarization of the illumination light. For example, if the polarization direction of the illumination light is set to be parallel to the direction of the printed patterns on the sample, the illumination light penetrates the least amount.
  • the polarization direction of the illumination light is set to be perpendicular to the direction of the printed patterns, the illumination light penetrates most deeply. This way of controlling the penetration depth of the illumination light can be useful in defect detection because a high proportion of printed patterns have a preferred edge direction.
  • the penetration of the illumination light can still be too deep even with the polarization of the illumination light oriented parallel to the direction of printed patterns. In this case, we can consider implementing a high incidence angle for the illumination. Note that an incidence angle is defined as the angle between the light ray and the surface normal, not the surface itself.
  • High incidence angle illumination can lead to throughput reduction because it requires a finer sampling grid in order to accurately sense the signal. This leads to either a higher magnification ratio or a smaller field of view for the same detector size.
  • a beneficial effect with a high angle illumination If a high angle illumination is combined with s-polarized light, it can reduce the penetration of the illumination light into the surface of the sample much more effectively than a low incidence angle illumination. Note that an extremely high angle incidence is called "grazing incidence”.
  • the reduction of the penetration of the illumination light into the wafer surface can also reduce the so-called "wafer pattern noise". Wafer pattern noise arises when the printed patterns on the wafer vary slightly from die to die due to variations in the manufacturing processes across the wafer.
  • wafer pattern noise There are two kinds of wafer pattern noise. One is called axial or longitudinal wafer pattern noise and the other is called lateral wafer pattern noise. High angle illumination can reduce the longitudinal wafer pattern noise. Lateral wafer pattern noise can be reduced by good Fourier filtering and softening the edges of apertures and obscurations. An effective and practical way of softening the edges of apertures and obscurations is described in a later section called Serrated Aperture. [00107] Strictly speaking, wafer pattern noise is actually not a noise at all. It is rather a kind of defect signal that we are not interested in.
  • the reduction of the illumination light penetration can be significant if the surface profile of the wafer is relatively flat or if the direction of wafer pattern edges tend to be parallel to the direction of the s-polarization of the illumination light.
  • the benefit can be less significant if the wafer has as many x-direction edges as y-direction edges or the directions of the pattern edges are not substantially parallel to the direction of the s-polarization of illumination light.
  • the implementation of high angle incidence illumination can be very costly. Therefore, the benefit against cost should be carefully analyzed before making a decision to employ high incidence angle illumination.
  • Penetration depth control of the illumination light is not the only reason for the polarization control of the illumination light.
  • the interaction of the polarized light with the defect and its surrounding patterns is usually complicated and needs experimental measurement and/or numerical modeling to predict. Real cases often defy intuition.
  • the polarization direction can be varied to improve defect detection.
  • the interferometric defect detection systems can be configured in many different ways. Many examples include a common path and a provision for controlling the relative phase between the defect signal and the specular component. In this section, general system configurations will be provided. Concrete design examples and subsystem examples will be presented later in other sections. [00112] 1. Example of System Configuration. Fig. 1 shows an example of an interferometric defect detection system 100. A light beam 118 is generated by illumination source 112 which in one example is a coherent source such as a laser. Any wavelength can be used provided it is possible to make the basic components of the interferometric imaging system.
  • illumination source 112 which in one example is a coherent source such as a laser. Any wavelength can be used provided it is possible to make the basic components of the interferometric imaging system.
  • Beam 118 is reflected towards the surface of the sample 110 and illuminates the sample surface as shown. Beam 118 covers the f ⁇ eld-of-view of the image sensor at the surface of sample 110.
  • Sample 110 can be a wafer, reticle, or other sample being inspected.
  • the sample 110 scatters (or diffracts) part of the illumination beam and specularly reflects another part (and a part may be absorbed).
  • the scattered and specularly reflected portions of the incident beam are referred to herein as the "scattered component" and "specular component” respectively.
  • the scattered component is represented by beams 128, and the specular component is represented by beam 124.
  • a high-resolution optical imaging system including a front-end lens system 116 and a back-end lens system 114 is arranged to collect both the scattered and specular components of light and directs them to an image sensor 140.
  • Aberrations in the imaging system can cause the relative phase between the specular and the scattered components to vary from one scattered ray to another scattered ray. This kind of phase variation can degrade the system performance. Therefore, the imaging system is preferably substantially diffraction-limited, i.e., has only small amounts of aberrations.
  • the design and manufacturing of such imaging systems are well-known arts.
  • the front-end lens system is usually designed to be telecentric on the sample side in order to achieve uniform performance across the field.
  • the telecentricity does not need to be perfect.
  • a substantial amount of telecentricity error, such as a few degrees is usually tolerable.
  • Back-end lens system 114 does not need to be telecentric.
  • the image of the sample needs to be magnified by a large amount, typically 10Ox or even more.
  • the magnification of the sample image is usually achieved by making the focal length of back-end lens system 114 longer than that of front-end lens system 116. In order to achieve high performance, the focus of the imaging system needs to be accurately maintained during the sample scan.
  • image sensor 140 may also include controller 142, which is described in greater detail below.
  • a high sensitivity and high dynamic range are preferred in the image sensor.
  • controller 142 such as a computer or like machine, that is adapted (e.g., via instructions such as software embodied in a computer-readable or machine-readable medium) to control the operation of the various components of the system.
  • Controller 142 is configured to control the operation of system 100 and includes a processing unit (“processor") 152 electrically connected to sensor system 140 and adapted to receive and process digitized raw electronic signal therefrom and form processed image signals, as described in greater detail below.
  • processor processing unit
  • processor 152 is configured to process raw signal and compare it to other signals (e.g., digital images of adjacent fields, or idealized fields, such as stored in memory unit 154) to determine if a defect is present, and to characterize the defect, as explained in greater detail below.
  • signals e.g., digital images of adjacent fields, or idealized fields, such as stored in memory unit 1504.
  • the term "electronic or electrical signal” includes both analog and digital representations of analog physical quantities or other information.
  • Controller 142 is configured to receive electronic raw signal from sensor system 140 and process the signal to characterize or classify the defect in the sample.
  • controller 142 includes a processor 152, which is or includes any processor or device capable of executing a series of software instructions and includes, without limitation, a general- or special-purpose microprocessor, finite state machine, controller, computer, central-processing unit (CPU), graphical-processing unit (GPU), field- programmable gate array (FPGA), or digital signal processor.
  • processor 152 which is or includes any processor or device capable of executing a series of software instructions and includes, without limitation, a general- or special-purpose microprocessor, finite state machine, controller, computer, central-processing unit (CPU), graphical-processing unit (GPU), field- programmable gate array (FPGA), or digital signal processor.
  • CPU central-processing unit
  • GPU graphical-processing unit
  • FPGA field- programmable gate array
  • Memory unit (“memory”) 154 is operably coupled to processor 152.
  • the term “memory” refers to any processor-readable medium, including but not limited to RAM, ROM, EPROM, PROM, EEPROM, disk, floppy disk, hard disk, CD- ROM, DVD, or the like, on which may be stored a series of instructions executable by processor 152.
  • controller 142 includes a port or drive 156 adapted to accommodate a removable processor-readable medium 158, such as CD-ROM, DVD, memory stick or like storage medium.
  • the defect detection and classification methods described herein may be implemented in various embodiments in a machine-readable medium (e.g., memory 154) comprising machine readable instructions (e.g., computer programs and/or software modules) for causing controller 142 to perform the methods and the controlling operations for operating system 100.
  • machine readable instructions e.g., computer programs and/or software modules
  • the computer programs run on processor 152 out of memory 154, and may be transferred to main memory from permanent storage via disk drive or port 156 when stored on removable media 158, or via a network connection or modem connection when stored outside of controller 142, or via other types of computer or machine-readable media from which it can be read and utilized.
  • the computer programs and/or software modules may comprise multiple modules or objects to perform the various methods of the present invention, and control the operation and function of the various components in system 100.
  • the type of computer programming languages used for the code may vary between procedural code-type languages to object- oriented languages.
  • the files or objects need not have a one to one correspondence to the modules or method steps described depending on the desires of the programmer.
  • the method and apparatus may comprise combinations of software, hardware and firmware.
  • Firmware can be downloaded into processor 142 for implementing the various example embodiments of the invention.
  • Controller 142 also optionally includes a display unit 146 that can be used to display information using a wide variety of alphanumeric and graphical representations.
  • display unit 146 is useful for displaying raw signals or processes signals.
  • Controller 142 also optionally includes a data-entry device 148, such as a keyboard, that allows a user of system 100 to input information into controller 142 to manually control the operation of system 100.
  • controller 142 is operably connected to or is part of sensor system 140. In another example embodiment, controller 142 is operably connected to a sample positioning system 150 for positioning the sample and an actuator 144 for adjusting the phase using phase controller and attenuator 122. Controller 142 is shown only in system 100 of Fig. 1 for ease of illustration, however it can be included in all example embodiments described herein.
  • both the scattered component 128 and specular components 124 pass through the same optical system.
  • this embodiment is a type of common path interferometer system. This feature is advantageous for the stability of the system performance. This is because any disturbances to the common path interferometer are likely to affect both optical paths by the same amount and the relative phase difference between scattered and specular components is likely to be maintained.
  • the phase controller and attenuator 122 is installed in the path of the specular component 124.
  • the specular component passes through a phase controller 122 and its relative phase can be adjusted to maximize defect detection sensitivity or to determine both the phase and the amplitude of each defect signal.
  • Scattered light beams 128 are passed through a compensation plate 130 to compensate the otherwise large amount of path length difference between the specular and scattered components.
  • the axial position of the compensation plate is very flexible because the optical path length of the light ray does not depend on the axial location of the compensation plate. That is, the compensation plate does not need to be placed in the same plane with the phase controller even though most of the figures show the compensation plate and the phase controller in the same plane in order to emphasize the fact that the compensation plate compensates for the otherwise longer optical path length of the phase controller. It can be placed significantly above or below the phase controller.
  • the flexibility in the axial location of the compensation plate facilitates the mechanical designs around the compensation plate.
  • phase control is an advantageous feature and can be utilized to dramatically improve the defect detection capability and is discussed in greater detail below.
  • the specular component 124 can also be attenuated to improve image contrast by adding a pinhole stop in its path or a reflective coating on one of the surfaces of phase controller components.
  • the reflected portion of specular component 124 is represented in Fig. 1 with beam 126.
  • the phase controller and attenuator are located at the primary pupil plane or aperture stop, which advantageously avoids power loss and complexity due to an additional pupil relay system, beam splitters and other components that may be needed otherwise.
  • Bright sources are preferred in many applications because they allow a clean spatial separation of the specular component from the scattered component at a pupil conjugate plane of the optical imaging system. Bright sources also make the Fourier filtering very effective thanks to a small footprint for the specular component at the pupil plane. Both a clean separation of the specular component from the scattered component and an effective Fourier filter are important for the best performance of the systems and methods disclosed herein. In general, the brighter the source, the better. The brightest sources currently available are lasers. Therefore, lasers are the preferred sources for many applications. [00130] The sample can be illuminated with a laser in either coherent or incoherent fashion.
  • incoherent illumination with a laser has significant drawbacks in that it not only usually requires a costly speckle buster but also makes Fourier filtering much less effective compared with coherent illumination. Therefore, coherent illumination with a laser source is preferred.
  • the methods of achieving uniform illumination intensity across the whole field are presented in a later section on Coherent Uniform Illuminator.
  • the laser can be either a continuous-wave type or a pulsed type such as mode- locked or Q-switched laser.
  • the laser can have multiple temporal modes or a finite temporal bandwidth. However, a single spatial mode is usually preferred for the coherent illumination.
  • the phase controller 122 should be placed at or close to the pupil or a pupil conjugate of the optical imaging system in order to be able to spatially separate the specular component from the scattered component in a clean fashion and also to achieve uniform performance over the whole imaging field.
  • the optical system is relatively simple and there is no need for a conjugate of the aperture stop of the optical imaging system.
  • the phase controller 122 is placed at or close to the aperture stop plane of the imaging system in Fig. 1. Placing the phase controller at or close to the aperture stop plane of the optical imaging system is preferred for many applications because it does not require additional optical parts that are not only bulky and costly but also can reduce image quality and energy efficiency.
  • the phase controller can be made quite small and does not to take much space or interfere with other system components.
  • Phase Controller Figs. 2a and 2b show an example of a phase controller and attenuator.
  • a phase controller is used to change the relative phase between scattered and specular components of light from the sample. Note that absolute phase is generally not of interest. Rather, it is the relative phase between scattered and specular components that is generally of interest. Therefore, the phase controller can be installed in the path of either the specular or scattered component.
  • phase controller installed in the path of the specular component
  • the phase controller may be installed in the path of the scattered component.
  • One technique for changing the phase is to change the optical path length of the beam.
  • the optical path length can be changed easily by varying the thickness of the optical material that the beam passes through.
  • These kinds of phase controllers can be made in many different ways.
  • One way is to overlap two wedged glass plates as shown in Fig. 2a.
  • Phase controller 122 makes use of an upper glass wedge 222 and a lower glass wedge 220.
  • Incoming light beam 124 enters the lower wedge 220 and at least a portion passes through the upper wedge 222 as light beam 212.
  • the optical path length of the passing-through beam is changed.
  • the upper wedge 222 can be moved rightward to increase the path length and leftward to decrease the path length.
  • the air gap between the upper wedge and lower wedge can cause the specular component beam to walk off the desired path.
  • This can cause the wavefront of the specular component to be tilted at the image plane.
  • the tilted wavefront can lead to performance variation across the field, especially in the high sensitivity mode of operation which will be described in later sections.
  • This problem can be fixed easily.
  • the specular component beam can be brought back to its desired path by slightly tilting the whole phase controller block in the opposite direction to the beam walk-off direction.
  • the amount of tilt required can be determined by measuring the wavefront tilt of the specular component at the image plane.
  • the wavefront tilt appears as a linear phase variation of the specular component across the field. Therefore, it can be measured during the phase controller calibration process which will be described in the next paragraph.
  • phase controller needs to be calibrated before use.
  • the calibration can be done purely mechanically by precisely measuring the dimensions and positions of the optical parts of the controller. However, a better way is doing it optically, which can be done without difficulty.
  • the phase controller can be calibrated using a step- phase object, such as phase mask consisting of a two-dimensional array of islands, each island having a small path difference from its surrounds.
  • the image of the step-phase object shows contrast reversal around the phase-step area as the phase of the specular component passes the 90° point.
  • the image contrast hits the extrema at zero and at a 180° phase angle of the specular component.
  • phase controller can be accurately calibrated.
  • Other patterns such as a small pit, small island, a narrow valley, narrow mesa, etc. can also be used for the calibration.
  • This calibration process provides the phase reference, or zero phase shift point, as well.
  • phase references should all be the same if the imaging system is perfect. However, real imaging systems cannot be made perfect. Some variation of phase reference values across the field is expected to exist due to phase controller tilt, aberrations, field curvature, etc. The linear part of the variation of phase reference values across the field can be removed by slightly tilting the whole phase controller block. The nonlinear parts of the variation originate from the imperfections in the imaging system. [00140] The first order effect of an imaging system imperfection is a variation of phase reference values across the field.
  • phase reference values across the field are a good indicator of the quality of the imaging system.
  • the variation of phase reference values across the field is less important for the catch-all mode and dark field mode of operation which is presented in later sections. However, this can become an issue for the high sensitivity mode of operation which will be presented in a later section. This is because it can make the performance of the high sensitivity mode of operation vary across the field. Therefore, it is important to maintain the quality of the imaging system high.
  • Gouy phase there is another phase called Gouy phase that needs to be calibrated.
  • Gouy phase is described below in a later section called
  • an attenuator is added to the kind of phase controller shown in Fig. 2a by putting a reflective coating on one or more of the surfaces of phase controller components.
  • a reflective coating 224 is positioned at a surface of lower wedge 220 as shown. According to this example, a portion of incoming beam 124 is reflected by coating 224 and dumped as represented by dump beam
  • the attenuation amount can be step-varied by putting several coatings with different reflectance in a row and making the component movable.
  • Fig. 2b shows an example of a reflective coating 224 a viewed along the line
  • coating 224 is made up of three different reflective coatings 230, 232 and 234, arranged as shown in the direction of arrow 240.
  • moving lower wedge 220 By moving lower wedge 220, different levels of attenuation can be achieved.
  • FIG. 3 shows another example of an interferometric defect detection system
  • the phase of the scattered component, represented by beams 128 are varied using the glass wedges 324.
  • Coherent light source 112 generates illumination beam 118 which is reflected toward the surface of sample 110.
  • the scattered component of the reflected light is represented by beams 128 and the specular component is represented by beam 124.
  • the effective path length and therefore the phase of the scattered component is changed. Specular component
  • Front-end lens system 316 and back-end lens system 314 collect the light from sample 110 and focus the light on the image sensor
  • FIGs 4a and 4b Another way of changing the optical path length is shown in Figs 4a and 4b.
  • an optically transparent liquid 410 is injected between electrodes 420 and 422 of a ring capacitor.
  • the thickness of the liquid 410 is varied by varying the voltage across the capacitor electrodes 420 and 422.
  • Liquid crystal rather than regular liquid can also be used for liquid 410.
  • the optical path length is varied by just changing the average orientation of the liquid crystal molecules.
  • Fig. 4b shows a plan view of the structure of Fig. 4a in the direction along B-B'. Upper electrode 420 is shown along with liquid 410.
  • a movable slightly wedged glass plate or transparent film strip can also be used as a simple continuously-variable phase controller.
  • this kind of phase- controller inevitably deviates the ray path from its ideal path and consequently affects the system performance adversely.
  • Fig. 5 shows an example of a movable mirror used to change the optical path length, according to some embodiments.
  • the system includes a movable member 530 having a reflective surface.
  • Incoming specular reflection beam 520 is partially reflected from surface 534 of member 530.
  • Scattered light beams 510 and 512 are reflected from fixed reflective member 536.
  • a movable mirror type phase controller has been found to be especially useful for applications using extremely short wavelength light, like a vacuum ultraviolet light or extreme ultraviolet light which might be used in future generation defect detection systems. This is because it is relatively difficult to find or develop transmissive optical materials for these wavelengths.
  • phase controlling mirror does not always need to be highly reflective.
  • a low reflectivity is preferred because attenuating the specular component is useful in achieving proper image contrast.
  • bare glass without any coating can provide adequate reflectivity in some instances.
  • a phase controller can be constructed using electro-optical components.
  • Fig. 6 shows an example of an interferometric defect detection system making use of a moveable mirror phase controller.
  • Incoming light beam 618 is directed toward the surface of sample 610 which could be a wafer, reticle, or other sample being inspected.
  • the scattered component, represented by beams 510 and 512, pass through lens system 616 and are reflected from reflective member 536 before passing through lens system 614 which directs the beams toward the image sensor 640.
  • the specular component beam 520 is reflected from the surface of moveable reflective member 530 as described with respect to Fig. 5.
  • a discretely- variable phase controller can be used.
  • one choice of phase values for the discrete Iy -variable phase controller is 0°, ⁇ 180°, and ⁇ 90°.
  • three discrete phase selections may work in some applications such as catch-all mode of operation which will be described in a later section.
  • one choice of phase values is 0°, and ⁇ 120°. Reducing the number of phase selections to two, e.g. ⁇ 0°, 180° ⁇ or ⁇ 90°, -90° ⁇ is less preferred for many applications since the sign of the interference term cannot be matched to that of the dark field term for both amplitude- type defects and phase-type defects.
  • a discretely variable phase controller can be made in many different ways.
  • One way of making a discretely variable phase controller is by either depositing thin films of the correct thickness on a substrate or etching out the substrate by a correct depth.
  • discretely variable phase controllers can have different physical shapes than continuously variable phase controllers, they are not conceptually considered as a different kind of phase controller but considered as a subset of continuously variable phase controllers because a continuously variable phase can be operated in a discrete fashion.
  • a single phase controller can be shared by multiple wavelengths or employed with broadband illumination. However, in this case, precise phase controls for all wavelengths is relatively difficult to achieve.
  • phase of the phase controller can be varied rapidly, the system can be operated in a heterodyne mode.
  • Heterodyne mode is a good choice if there is significant amount of 1/f noise.
  • a rapid change of the phase of the phase controller can be achieved in many different ways. For example, it can be achieved by rapidly moving one of the glass pieces of the phase controller shown in Fig. 2a. If the phase controller is made of electro-optical materials, a very rapid phase change can be achieved by controlling the phase controller electro-optically.
  • a heterodyne system is relatively difficult to implement in scanning systems, especially in fast scanning systems, but is relatively easy to implement in non-scanning systems such as static or stepping systems.
  • Blocking unwanted light at a pupil plane or aperture stop is called Fourier filtering because the light amplitude distribution at a pupil plane or aperture stop is the Fourier transform of the light amplitude distribution at the object plane.
  • Fourier filtering is a desirable feature in many applications because it can effectively reduce the amount of light reaching the detector array that is diffracted by the Manhattan mask or wafer patterns. It reduces not only photon noise but also sample pattern noise. It also makes the intensity of the light more uniform across the field. [00155] A more uniform light intensity allows for better use of the dynamic range of the image sensor for noiseless signal amplification.
  • Figs. 7a - 7c show an example of a compensation plate with opaque Fourier filter strips for use with an interferometric defect detection system having near normal illumination.
  • compensation plate 730 is shown with narrow Fourier filter strip members 750, 752, 754 and 756.
  • Scattered light near the specular beam is blocked by an opaque blocking plate 732, which contains an aperture of width p just wide enough to pass the specular beam.
  • an opaque blocking plate 732 which contains an aperture of width p just wide enough to pass the specular beam.
  • light scattered by the x- and y- wafer pattern geometries lands on the filter strip members 750, 752, 754 and 756 at the pupil plane or aperture stop. In this way, this kind of unwanted light can be filtered out very effectively.
  • a couple of crossed strips of opaque material such as metal are all that is needed.
  • the Fourier filters block not only the diffracted light from periodic patterns, but also the diffracted light from non-periodic patterns such as long lines or edges oriented in the perpendicular direction to the Fourier filter strips.
  • strip members 750, 752, 754 and 756 do not block much of the defect signal light while blocking most of the unwanted light generated by the Manhattan patterns on the mask or wafer.
  • This kind of Fourier filter that blocks unwanted light in two-directions is called a two-dimensional Fourier filter. Two-dimensional Fourier filtering is much more effective than a one- dimensional Fourier filter in blocking unwanted light from a 2-dimensional pattern on the sample.
  • a two dimensional Fourier filter makes the intensity of the image much more uniform across the field compared with a one dimensional Fourier filter.
  • Uniform image intensity is important for many applications because it allows us to fully utilize the dynamic range of image sensor for the amplification of the defect signal.
  • an effective two dimensional Fourier filter is essential for a high, noiseless amplification of weak defect signals. It improves the useful dynamic range of the image sensor.
  • the width of the Fourier filter does not need to be uniform and can be varied across the pupil in order to block the unwanted light more effectively.
  • the unwanted light is usually more intense in the proximity of the specular component at the pupil plane. Therefore, Fourier filter strips usually need to be tapered to optimize their performance. Tapered Fourier filter strips, which are wider in the middle and narrower at their extremities, will be generally more effective in blocking the unwanted light while minimizing their impact on obscuring signal light.
  • Fourier filters can have dual functions. Fourier filter strips can also be used as an aperture stop for the specular component by extending their inner ends to the region where the specular component passes. If the aperture stop needs to be variable, then the Fourier filter strips should be made movable along their length directions. Mechanical abrasion between moving Fourier filters and the fixed compensation plate can easily be avoided by putting a big enough gap between the Fourier filter strips and the compensation plate.
  • Putting a sizable gap between the Fourier filter strips and the compensation plate does not affect the performance of the imaging system because moving the compensation plate in any direction does not affect the optical path length of any ray.
  • two-dimensional Fourier filtering is achieved not only simply and easily but also with minimal impact to the signal light.
  • Fig. 7a shows an upper glass wedge 722 and a lower glass wedge 720.
  • Fig. 7b shows a cross-sectional view of the arrangement of Fig. 7a along the line C-C according to some embodiments.
  • Compensation plate 730 is shown with an opening, in which are disposed upper glass wedge 722 and lower glass wedge 720.
  • Fig. 7c shows a cross-sectional view of the arrangement of Fig. 7a along the line D-D' according to some embodiments.
  • Compensation plate 730 is shown with an opening in which are disposed upper glass wedge 722 and lower glass wedge 720 having a reflective surface 724. Relative motion between the upper and lower glass wedges is achieved by extension arm 726 and actuator 770, which are connected to the upper glass wedge 722.
  • extension arm 726 and actuator 770 which are connected to the upper glass wedge 722.
  • the center of the illumination input prism 780 and the small pupil stop of diameter p for the specular beam are diagonally opposite each other in Figs, 7 and 8.
  • the compensation plate and phase controller are located in the same or nearly the same plane in order to emphasize the fact that the compensation plate compensates optical path lengths for the phase controller.
  • this is not necessary because the axial location of the compensation plate is very flexible, as previously explained.
  • the flexibility in the axial location of the compensation plate can alleviate mechanical conflicts or difficulties around the Fourier filters and phase controller.
  • Fourier plane blockers to eliminate pattern diffraction other than that arising from the Manhattan patterns on the sample are added if needed.
  • This kind of special Fourier blockers usually needs to be custom-designed and can be implemented in many different ways. For example, additional metal strips can be introduced in the pupil plane.
  • Another way is to insert a glass plate or a pellicle containing printed patterns in the pupil plane.
  • This kind of flexibility allows an almost perfect filtering of noise-generating light for almost any kind of wafer or mask pattern.
  • the blocking of signal light can impact the final defect signal in two ways: it not only reduces the total amount of signal light but also makes the image of a defect a little fuzzier through diffraction.
  • There is usually an optimum amount of Fourier filtering that depends on the patterns on the wafer.
  • the amount of Fourier filtering which is desirable depends on the particular application and can be determined without undue experimentation by one skilled in the art.
  • a Fourier filter does not always need to be made with opaque materials like metal strips. It can be made with semi-transparent materials or even completely transparent materials such as dielectric films. These kinds of Fourier filters can be very effective in increasing the signal or the visibility of some patterns or features. For some applications such as the observation of complicated patterns or features, a very sophisticated Fourier filter can be used in order to increase the image visibility.
  • the Fourier filter made of an absorbing material like metal can become hot during operation, especially in industrial applications where powerful light sources are usually used.
  • a hot Fourier filter not only causes mechanical problems but also optical problems because it can heat the surrounding air, which in turn can distort the wavefront of the signal light. However, this kind of heat problem can be resolved or mitigated by flowing gas with high heat conductivity like helium around the Fourier filter. Helium gas is especially suitable because its refractive index is very low and therefore not very sensitive to its density.
  • specular component cannot be precisely defined because there are no clear boundaries between specular and scattered components.
  • the specular component must be of finite size and therefore contain some, even an extremely tiny amount of scattered (or diffracted) component. Therefore, the specular component actually means a combination of both unscattered (or undiffracted) light and low angle scattered light.
  • specular component as used herein is allowed to contain some amount of low angle scattered component.
  • the characteristics of the specular component can be varied by changing the amount of low angle scattered light it contains. Varying the size of the specular stop is one of the simplest devices that can be used to change the amount of scattered light in the specular beam. A larger specular stop puts more scattered components into the specular beam and vice versa. The important thing is that the stop size is directly related to the spatial uniformity of the specular component at the image plane. A larger stop provides less spatial uniformity of specular component at the image plane because it passes more scattered light and vice versa. In other words, a larger specular stop averages less of the local variations of image intensity and vice versa.
  • a larger specular stop spatially averages less of the local variations of the complex amplitude of the specular component at the image plane and vice versa. That is, the specular stop averages spatially not only the intensity or amplitude but also the phase variation of the specular component across the field of view.
  • the complex amplitude of the specular component at the image plane is a convolution of sample reflectivity function with the diffraction pattern of the specular stop at the image plane.
  • the defect signal may be poorly characterized by the limited number of gray levels available, even though the whole dynamic range of the detector is fully utilized by the noiseless amplification of the signal.
  • some amount of attenuation of the specular component is needed to achieve proper contrast in the raw images.
  • the attenuation of the specular component using the specular stop has an incidental effect of making the specular component more uniform across the field.
  • Another advantageous feature with the specular aperture is that it does not create a ghost image because the reflected light can be easily removed from the optical system.
  • an attenuator with a reflective coating can produce a ghost image through a second reflection with another surface.
  • the specular stop may have to absorb a lot of light energy for proper attenuation of the specular component and consequently will become very hot. This can cause not only mechanical problems but also optical problems because the hot stop can heat the surrounding air and the heated air in turn can distort the wavefront.
  • this kind of heat problem can be mitigated by filling the lens cavities with a gas with high heat conductivity and low refractive index like helium. Helium gas is a good choice because its refractive index is very low and therefore insensitive to its density.
  • the second drawback is the phase change of the specular component with the pinhole size.
  • This kind of phase change is called "Gouy phase shift". This is an intrinsic phenomenon and therefore cannot be easily avoided.
  • Gouy phase shift is static and therefore can easily be mapped over the field and compensated. Therefore, the phase change of the specular component associated with specular stop size needs to be attended to but is not a show stopper.
  • the specular stop may well turn out to be the size of a pinhole.
  • the reflective counterpart of a pinhole is a tiny mirror (pinmirror) that reflects a portion of incoming light.
  • the choice of specular aperture type and shape depends on the application and the design of the optical system. Transmissive and reflective pinholes share the same optical properties.
  • the specular beam stop and Fourier filter components are shown as separate components to emphasize their separate functions. However, in actual system designs, it may be preferable to combine the two separate components into one to simplify the mechanical design and also to minimize potential mechanical conflicts.
  • the two components can be combined into one by either extending the Fourier filter strips inwards or extending the specular beam or pinhole aperture outwards. In the combined design, the size of the pinhole stop can be adjusted by moving the Fourier filter strips along their long directions.
  • a variable phase controller requires some kind of mechanical or electrical actuator. The most convenient place to put an actuator may be right next to the phase controller. However, placing an actuator right next to the phase controller may block too much of the signal light. In some examples, the actuator is placed at the periphery of the optical imaging system, which is an attractive choice because it provides more space for the actuator. However, the drawback of this choice is that it requires some mechanism to transfer the actuator motion to the phase controller. The motion transfer mechanism must span the pupil radius and can block the signal light. However, according to some embodiments, the problem of light blocking is resolved by making use of the fixed locations of Fourier filters. By installing the motion transfer mechanism like moving or rotating wires on the top of or below Fourier filter blocking strips, further blocking of light can be avoided.
  • a motion transfer member 726 is provided that runs along the path of Fourier filter member 754. Motion transfer member 726 is driven by actuator 770 and moves the top wedge shaped glass piece in the variable phase shift mechanism. Similarly, motion transfer mechanisms for other parts like variable pinhole stops or wave plates can also be implemented in much the same way to minimize additional light blockage. Enough space for motion transfer mechanisms can easily be procured because the axial location of the compensation plate is very flexible.
  • phase controller and its actuator unavoidably obscure (or block) some of the signal light. This kind of light blockage reduces not only the total amount of signal light that can reach the image sensor but also reduces the resolving power of the optical system by diffracting light. This is an undesirable side effect which is minimized to the maximum extent possible.
  • both optical components and the actuator of the phase controller should be made as small as possible or the actuator should be placed at the periphery of the optical imaging system.
  • Fig. 8 shows an example of a placement of a folding prism for the illumination light, according to some embodiments.
  • Compensation plate 830 is arranged with Fourier filter strips 850, 852, 854 and 856 in a fashion similar to that shown in Fig. 7a.
  • an additional small reduction of obscuration can be achieved by placing the folding prism 880 for the illumination light beam 818 in line with the Fourier filter strip 850 as shown.
  • softening of the edges of the obscurations and the optical imaging system's aperture stop can reduce the undesirable side effect of edge diffraction. An effective and practical way of softening the edges of apertures and obscurations is described in a later section of Serrated Aperture.
  • Fig. 9 shows a phase controller combined with a polarization rotator suitable for some embodiments.
  • Fig. 9 shows a lower wedged glass plate 920 having a reflective coating 924, an upper moveable wedged glass plate 922 and a variable specular stop 950.
  • a rotatable ⁇ /2 plate 960 is positioned above the variable pinhole stop 950.
  • Incoming specular light beam 916 is partially reflected by coating 924, and a portion of the beam 912 passes through the moveable wedged glass plate 922, the stop 950 and the rotatable ⁇ /2 plate 960.
  • Fig. 9 is somewhat limited in that it cannot transform the polarization of an incoming specular component to an arbitrary type of polarization.
  • the arrangement can rotate an incoming linear polarization in any direction.
  • no polarizations other than linear polarizations are needed to maximize the defect detection sensitivity. This has been found to be the case for semiconductor wafers and reticles. Therefore, a simple polarization control device shown in Fig. 9 will be adequate for a wafer or reticle defect detection.
  • Fig. 10 shows a lower wedged glass plate 1020 having a reflective coating 1024, an upper moveable wedged glass plate 1022 and a variable stop 1050.
  • a rotatable ⁇ /2 plate 1060 and a rotatable ⁇ /4 plate 1062 are positioned above the variable pinhole stop 1050.
  • Incoming specular light beam 1016 is partially reflected by coating 1024, and a portion of the beam 1012 passes through the moveable wedged glass plate 1022, the stop 1050, the rotatable ⁇ /2 plate 1060 and the rotatable ⁇ /4 plate 1062.
  • the portion of the scattered component whose polarization is orthogonal to that of specular component does not interfere with the specular component and consequently contributes to the dark field part of the image.
  • this portion of the orthogonal polarization in the scattered component can be filtered out in order to increase the image contrast or reduce photon noise. Filtering the orthogonal polarization in the scattered light beam can be achieved by inserting appropriate waveplates into the path of the scattered component to linearly polarize the unwanted polarization component, removing this unwanted component with a linear polarizer and then converting the remaining light to match the polarization of the interfering specular beam.
  • the amount of attenuation can be varied by putting several different reflective coatings in a row, each having a different reflectivity, and make them movable as shown in Fig. 2b.
  • This kind of attenuator is simple and does not require additional optical components. However, these kinds of attenuators can generate a ghost image due to the highly reflective surface.
  • a continuously -variable attenuator can be used.
  • One way to make a continuously- variable attenuator is to utilize the polarization property of light. It is well-known that a continuously-variable attenuator can be constructed by rotating a polarizer around the axis of a linearly polarized beam , or alternatively, rotating the polarization direction of a beam passing through a fixed polarizer.
  • Fig. 11 shows an example of a continuously-variable attenuator using a polarizing beam splitter.
  • Fig. 12 shows an example implementation of a system using the type of attenuator shown in Fig. 11.
  • Figs. 13a-13c show further detail of the system in the vicinity of the pupil or aperture stop, according to some embodiments.
  • polarized laser beam 1116 enters a polarization beam splitter 1164 which reflects s-polarized light 1126 while transmitting p-polarized light 1110.
  • the amount of specular component that passes through the polarization beam splitter can be controlled in a continuous fashion.
  • the p-polarized light beam 1110 pass through moveable wedged glass plate 1122 and variable aperture stop 1150 as previously described.
  • the rotatable ⁇ /2 plate 1160 on the output side can be used to reorient the polarization of the exiting light in any direction.
  • Fig. 14 shows an example of an attenuator having both ⁇ /2 and ⁇ /4 plates which can be used to achieve any polarization state.
  • Beam 1416 enters a fixed polarization beam splitter 1464 which reflects the s-polarized light 1426 while transmitting p-polarized light 1410.
  • the amount of specular component that passes through the polarization beam splitter can be controlled in continuous fashion.
  • the p- polarized light 1410 passes through moveable wedged glass plate 1422 and variable stop 1450 as previously described.
  • the rotatable ⁇ /2 plate 1460 and the rotatable ⁇ /4 plate 1468 on the output side can be used to reorient the polarization of the exiting light in any state.
  • interferometric defect detection system 1200 includes an illumination source 1212 which generates a coherent beam 1218. Beam 1218 is directed towards the surface of the sample 1210 as shown.
  • the sample 1210 can be a wafer, reticle, or other sample being inspected.
  • the scattered component from sample 1210 is represented by beams 1228, and the specular component is represented by beam 1224.
  • a high- resolution optical system including lens systems 1214 and 1216 collects both the scattered and specular components of light and directs them to an image sensor 1240.
  • Subsystem 1270 is positioned in the path of specular component 1224 and includes a phase controller, variable attenuator, and one or more polarization rotators such as described and shown with respect to Figs.
  • Scattered light beams 1228 are passed through a compensation plate 1230 to compensate for the path length difference between the specular and scattered components.
  • a beam dump 1226 accepts the portion of specular component 1224 that is attenuated by the variable attenuator.
  • Fig. 13a compensation plate 1330 is shown with narrow Fourier filter strip members 1350, 1352, 1354 and 1356. Illumination beam 1318 is reflected toward the sample (not shown) using prism 1380.
  • Subsystem 1370 is positioned as shown and includes a phase controller, variable attenuator, and one or more polarization rotators such as described and shown with respect to Figs. 11 and 14.
  • Figs. 13b and 13c show cross-sectional views of the arrangement of Fig. 13a along the line E-E' and F-F' respectively.
  • compensation plate 1330 is shown with an opening in which are disposed the various components of subsystem 1370.
  • Polarization beam splitter 1364 reflects the s-polarized light while transmitting p-polarized light.
  • the amount of specular component that passes through the polarization beam splitter can be controlled in a continuous fashion.
  • P-polarized light passes through moveable wedged glass plate 1322 and variable stop 1350.
  • the rotatable ⁇ /2 plate 1360 on the output side can be used to reorient the polarization of the exiting light in any direction.
  • High incidence-angle illumination One source of noise that can be considered is the wafer pattern noise that arises when the printed patterns on the wafer vary slightly from die to die due to the variation of manufacturing process across the wafer. The wafer pattern noise increases with the penetration depth of the illumination light into the wafer surface. Therefore, it is sometimes desirable to reduce the penetration of the illumination light into the wafer surface.
  • This method has a couple of drawbacks.
  • the increase of spatial frequency bandwidth requires a finer sampling of the image to detect the interference term faithfully. This can reduce the throughput of the catch-all mode of operation which will be described in later sections.
  • the systems and methods disclosed herein are flexible with respect to the incidence angle of illumination. The systems and methods can accommodate not only a low incidence angle but also a high incidence angle. Figs. 15 through 18 show examples of this.
  • FIG. 15 shows an example of an interfero metric defect detection system with high incidence angle illumination.
  • Interferometric defect detection system 1500 includes an illumination source beam 1518 which is directed towards the surface of the sample 1510 as shown.
  • the sample 1510 can be a wafer, reticle, or other sample being inspected.
  • the scattered component from sample 1510 is represented by beams 1528, and the specular component is represented by beam 1524.
  • a high-resolution optical system including lens systems 1514 and 1516 collects both the scattered and specular components of light and directs them to an image sensor 1540.
  • Subsystem 1570 is positioned in the path of specular component 1524 and includes a phase controller and attenuator such as described and shown with respect to Figs. 2a and 2b.
  • Scattered light beams 1528 are passed through a compensation plate 1530 to equalize path lengths for the specular and scattered components.
  • a beam dump 1526 accepts the portion of the specular component 1524 that is rejected by the attenuator.
  • Fig. 16 shows an example of an interferometric defect detection system with high incidence angle illumination and a variable attenuator.
  • Interferometric defect detection system 1600 includes an illumination source beam 1618 which is directed towards the surface of the sample 1610 as shown.
  • the sample 1610 can be a wafer, reticle, or other sample being inspected.
  • the scattered component from sample 1610 is represented by beams 1628, and the specular component is represented by beam 1624.
  • a high- resolution optical system which includes lens systems 1614 and 1616, collects both the scattered and specular components of light and directs them to an image sensor 1640.
  • Subsystem 1670 is positioned in the path of specular component 1624 and includes a phase controller and variable attenuator such as described and shown with respect to Figs. 9-11 and 14. Scattered light beams 1628 are passed through a compensation plate 1630 to equalize the path lengths of the specular and scattered components.
  • a beam dump 1626 accepts the portion of the specular component 1624 that is rejected by the variable attenuator.
  • Fig. 17 shows an example of an interfere metric defect detection system with a low image flare and high-incidence angle illumination. Flare is illumination light reflected or scattered by the lens surfaces on its way to the sample which winds up on the sensing plane.
  • Interferometric defect detection system 1700 includes an illumination source beam 1718 which is directed towards the surface of the sample 1710 as shown.
  • the sample 1710 can be a wafer, reticle, or other sample being inspected.
  • the scattered component from sample 1710 is represented by beams 1728, and the specular component is represented by beam 1724.
  • a high-resolution optical imaging system including lens systems 1714 and 1716 collects both the scattered and specular components of light and directs them to an image sensor 1740.
  • Subsystem 1770 is positioned in the path of specular component 1724 and includes a phase controller and attenuator such as described and shown with respect to Figs. 2a and 2b.
  • Scattered light beams 1728 are passed through a compensation plate 1730 to equalize the path lengths of the specular and scattered components.
  • a beam dump 1726 accepts the portion of specular component 1724 that is rejected by the attenuator.
  • Fig. 18 shows an example of an interferometric defect detection system with low image flare and high-incidence angle illumination and a variable attenuator, according to some embodiments.
  • Interferometric defect detection system 1800 includes an illumination source beam 1818 which is directed towards the surface of the sample 1810 as shown.
  • the sample 1810 can be a wafer, reticle, or other sample being inspected.
  • the scattered component from sample 1810 is represented by beams 1828, and the specular component is represented by beam 1824.
  • a high-resolution optical system including lens systems 1814 and 1816 collects both the scattered and specular light components and images them on an image sensor 1840.
  • Subsystem 1870 is positioned in the path of specular component 1824 and includes a phase controller and variable attenuator such as described and shown with respect to Figs. 9-11 and 14. Scattered light beams 1828 are passed through a compensation plate 1830 to equalize the path lengths of the specular and scattered components.
  • a beam dump 1826 accepts the portion of specular component 1824 that is rejected by the variable attenuator.
  • Azimuthal Rotation of Illumination Light generally depends not only on the polar angle but also on the azimuthal angle of incidence of the illumination light.
  • Azimuthal angle is defined as the angle between the pattern on the sample and a normal projection of the incident beam onto the sample.
  • An effective way of covering the practical azimuthal angles is to put a rotatable prism or mirror at the conjugate location of the sample. This scheme is shown in Figs. 19 through 22. The configuration of Figures 19 and 20 is more flexible because the illumination system and collection system share only the high power part of lens system.
  • FIG. 19 shows an example of an interfero metric defect detection system with an azimuthally rotatable high incidence angle illumination.
  • Interferometric defect detection system 1900 includes an illumination source beam 1918 which is directed towards a rotatable and tiltable surface 1920 such as a mirror or prism.
  • the reflected beam passes through lens systems 1912 and 1916 and is directed towards the surface of the sample 1910 as shown.
  • the sample 1910 can be a wafer, reticle, or other sample being inspected.
  • the scattered component from sample 1910 is represented by beams 1928, and the specular component is represented by beam 1924.
  • a high-resolution optical system including lens systems 1914 and 1916, and beam splitter 1972 collects both the scattered and specular components of light and directs them to an image sensor 1940.
  • Subsystem 1970 is positioned in the path of specular component 1924 and includes a phase controller and attenuator such as described and shown with respect to Figs. 2a and 2b. Scattered light beams 1928 are passed through a compensation plate 1930 to compensate for path length differences between the specular and scattered components.
  • a beam dump 1926 accepts the portion of specular component 1924 that is rejected by the attenuator.
  • Subsystem 1970 has to move with the rotation of the mirror 1920 to follow the beam around the periphery of the pupil.
  • the optical efficiency of this scheme can be no greater than 25% because of the transmission and reflection through the beamsplitter. If a polarizing beamsplitter is used for surface 1972 and a quarter wave plate is employed in the illumination path between the beamsplitter and the sample then a much higher efficiency is possible.
  • Fig. 20 shows an example of an interferometric defect detection system with an azimuthally rotatable high incidence angle illumination and with a variable attenuator for the specular component, which may find applications.
  • Interferometric defect detection system 2000 includes an illumination source beam 2018 which is directed towards a rotatable surface 2020 such as a mirror or prism.
  • the reflected beam passes through lens systems 2012 and 2016 and is directed towards the surface of the sample 2010 as shown.
  • the sample 2010 can be a wafer, reticle, or other sample being inspected.
  • the scattered component from sample 2010 is represented by beams 2028, and the specular component is represented by beam 2024.
  • a high-resolution optical system including lens systems 2014 and 2016, and beam splitter 2072 collects both the scattered and specular components from the sample and directs them to an image sensor 2040.
  • Subsystem 2070 positioned in the path of specular component 2024, includes a phase controller and variable attenuator such as described and shown with respect to Figs. 9-11 and 14. Subsystem 2070 should move with the rotation of the mirror 2020 to follow the beam around the periphery of the pupil. Scattered light beams 2028 are passed through a compensation plate 2030 to equalize path lengths for the specular and scattered components.
  • a beam dump 2026 accepts the portion of the specular component 2024 that is attenuated by the variable attenuator.
  • Figs. 21 and 22 show possible configurations.
  • Fig. 21 shows an example of an interferometric defect detection system with an azimuthally rotatable, high incidence angle illumination.
  • Interferometric defect detection system 2100 includes an illumination source beam 2118 which is directed towards a rotatable and tiltable surface 2120 such as a mirror or prism. The reflected beam is directed towards the surface of the sample 2110 as shown.
  • the sample 2110 can be a wafer, reticle, or other sample being inspected.
  • the scattered component from sample 2110 is represented by beams 2128, and the specular component is represented by beam 2124.
  • a high-resolution optical system including lens systems 2114 and 2116, and beam splitter 2172 collects both the scattered and specular components of light and directs them to an image sensor 2140.
  • Subsystem 2170 is positioned in the path of specular component 2124 and includes a phase controller and attenuator such as described and shown with respect to Figs. 2a and 2b. Subsystem 2170 should move with the rotation of the mirror 2120 to follow the beam around the periphery of the pupil. Scattered light beams 2128 are passed through a compensation plate 2130 to equalize path lengths of the specular and scattered components.
  • FIG. 22 shows an example of an interferometric defect detection system with an azimuthally rotatable high incidence angle illumination with a variable attenuator for the specular component that may be suitable for some applications.
  • Interferometric defect detection system 2200 includes an illumination source beam 2218 which is directed towards a rotatable and tiltable surface 2220 such as a mirror or prism. The reflected beam is directed towards the surface of the sample 2210 as shown.
  • the sample 2210 can be a wafer, reticle, or other sample being inspected.
  • the scattered component from sample 2210 is represented by beams 2228, and the specular component is represented by beam 2224.
  • a high-resolution optical system including lens systems 2214 and 2216, and mirror 2272 collects both the scattered and specular components of light and directs them to an image sensor 2240.
  • Subsystem 2270 positioned in the path of specular component 2224 and includes a phase controller and variable attenuator such as described and shown with respect to Figs. 9-11 and 14. Subsystem 2270 should move with the rotation of the mirror 2220 to follow the beam around the periphery of the pupil.
  • Scattered light beams 2228 are passed through a compensation plate 2230 to equalize path lengths of the specular and scattered components.
  • a beam dump 2226 accepts the portion of specular component 2224 that is attenuated by the variable attenuator.
  • An azimuthal rotation of the illumination beam can be very effective in increasing the defect detection sensitivity, if it is combined with polarization control.
  • Polarization control of the illumination does not need to be mechanically coupled with the azimuthal rotation of the illumination light. Therefore, the two controls can be implemented independently without difficulty. Note that when the azimuthal direction of the illumination beam is changed, then the phase controller in the path of the specular component should also be rotated around the lens axis in order to follow the illumination beam path.
  • Transmissive Configuration Some samples like reticles and biological tissues can be more transmissive than reflective. In order to inspect transmissive samples, the system can be configured in a transmission mode.
  • Fig. 23 shows an example of an interferometric defect detection system designed to pass illumination through transmissive samples. The only significant difference from the embodiments previously described is the illumination path. [00217] Other aspects remain the same.
  • Interferometric defect detection system 2300 includes an illumination source which generates a coherent beam 2318. Beam 2318 is directed towards the transmissive sample 2310 as shown.
  • the sample 2310 can be, for example, a reticle or a biological sample being inspected.
  • the scattered component from sample 2310 is represented by beams 2328, and the specular component is represented by beam 2324.
  • a high-resolution optical system including lens systems 2314 and 2316 collects both the scattered and specular components of light and directs them to an image sensor 2340.
  • Subsystem 2370 is positioned in the path of the specular component 2324 and can include a phase controller, an attenuator, and/or one or more polarization controllers such as described and shown with respect to Figs. 2a-b, 9-11 and 14.
  • Scattered light beams 2328 are passed through a compensation plate 2330 to equalize the path lengths of the specular and scattered components.
  • a beam dump 2326 accepts the portion of specular component 2324 that is rejected by the variable attenuator.
  • Most reticles are both transmissive and reflective. However, they are usually used in transmission mode.
  • the transmission, not the reflectivity, of the reticle is the final concern.
  • the complex transmission coefficient of a point on a reticle can be determined by measuring the intensity of the transmitted light using a number of different phase shifts. Therefore, the transmissive configuration described herein can be used for the inspection of reticles, especially phase- shit reticles, very effectively in terms of both performance and cost.
  • System 2400 includes a reflective inspection subsystem 2402a and a transmissive inspection subsystem 2402b.
  • a single source beam 2418 is directed toward sample 2410, which is, for example, a reticle.
  • sample 2410 which is, for example, a reticle.
  • the reflected and transmitted light beams are detected by two separate image sensors 2440a and 2440b simultaneously.
  • Phase control and attenuation are achieved through each respective subsystem 2470a and 2470b. There is no change of working principles from those previously described herein.
  • the aforementioned controls of relative phase, specular amplitude, azimuthal rotation and polarization can be implemented.
  • a die-to-die image subtraction technique usually cannot be used.
  • the reference image of a defect-free reticle can be generated from reticle data used to make the reticle pattern. This is a heavy computational task usually done by computer. Then, the image of an actual reticle is compared with the computer-generated image of a defect-free reticle to find defects. In order to facilitate fast data processing, the image of a defect- free reticle must be generated very quickly.
  • a fully coherent illumination source such as a laser minimizes the amount of computation required for reticle image construction, thus allowing fast image construction with minimal computational resources.
  • Sequential Multiple Wavelengths In this configuration, only one image sensor may be used and one wavelength at a time may be used to detect defects. The hardware is simpler but the operation takes more time compared with the configuration for simultaneous multiple wavelength operation.
  • the continuously variable phase controller does not need to be modified to accommodate different wavelengths but wave plates for amplitude attenuation and polarization control should be modified to handle different wavelengths.
  • Figures 25 through 27 show some possible means for changing the ⁇ /2 plates.
  • Fig. 25 shows an example of a carousel 2510 holding two ⁇ /2 wave plates, each for a different inspection wavelength.
  • Fig. 26 shows an example of a carousel 2610 holding three ⁇ /2 wave plates, each optimal for a different wavelength.
  • Fig. 27 shows an example of a carousel 2710 holding four ⁇ /2 wave plates for four different wavelengths. Modifications analogous to those shown in Figs. 25-27 can be applied to ⁇ /4 plates. When the wavelength is switched, the wave plates are switched accordingly. Wave plate switching is achieved by rotating the waveplate carousel by an appropriate amount.
  • Fig. 28 shows an example system configuration for two wavelengths.
  • System 2800 for inspection of sample 2810 uses two separate illumination source beams 2818a and 2818b having two different wavelengths.
  • the two wavelengths are combined and separated by a dichroic wavelength splitter 2872.
  • the two wavelengths share the same front end of the collection optics 2816, which is usually the most critical and also the most expensive part of the whole optical system. By sharing the front end of the collection optics 2816, the system achieves not only simplicity but also stability.
  • the back-end lens components, 2812 and 2814 which are usually of low optical power and therefore are less expensive, are separated in order to give maximum flexibility in phase control, magnification adjustment, and sensor choices.
  • Subsystems 2870a and 2870b are used to control the phase and attenuation such as shown and described with respect to Figs. 2a-b, 9-11 and 14.
  • Each wavelength also uses its own compensation plate 2830a and 2830b, and image sensor 2840a and 2840b.
  • 266 nm and 532 nm wavelengths are used.
  • the technology for producing these two wavelengths is mature and a single laser system can provide both wavelengths, thus reducing cost.
  • shorter wavelengths such as 193 nm, vacuum ultraviolet, extreme ultraviolet, etc., can be used to get higher sensitivity.
  • shorter wavelengths are harder to handle.
  • more than two wavelengths are implemented by adding more wavelength splitters in the back-end optical paths.
  • phase controllers can be placed in the same pupil plane next to each other to eliminate wavelength splitters and save image sensors.
  • a configuration makes the mechanical designs more difficult and increases the pupil obscuration.
  • the system can be configured so that multiple wavelengths or broad band illumination share the same phase controller. Such a configuration saves on the number of phase controllers but makes a precise control of the phases difficult.
  • Extended Source For many applications single spatial mode lasers, which produce a very coherent beam, are the preferred light sources as previously discussed. However, in some embodiments, light sources other than single mode lasers can also be used. For example, an extended source like an arc lamp can be used as shown in Figs. 29 through 31. An extended source is defined herein as an incoherent source whose etendue is much larger than the square of its wavelength.
  • Fig. 29 shows an example of an interferometric defect detection system having a low incidence angle illumination system and employing an extended source.
  • Incoming illumination beam 2918 is directed toward sample 2910 using beam splitter 2972.
  • the specular reflected component is represented by beam 2924 and passes through a phase controller and attenuator 2970 that is analogous to any of the subsystems shown and described with respect to Figs. 2a-b, 9-11 and 14.
  • the scattered component represented by beams 2928 pass through a compensation plate 2930.
  • Front end optical system 2916 and back end optical system 2914 collect and direct the light from the sample towards imaging sensor 2940.
  • Fig. 30 shows an example of an interferometric defect detection system having a high incidence angle illumination with an extended light source.
  • Incoming light beams 3018 are directed toward sample 3010 using beam splitter 3072.
  • the specular reflected component is represented by beam 3024 which passes through a phase controller and attenuator 3070 that are analogous to any of the subsystems shown and described with respect to Figs. 2a-b, 9-11 and 14.
  • the scattered component represented by beams 3028 pass through compensation plate 3030.
  • Front end optical system 3016 and back end optical system 3014 collect and direct the light towards imaging sensor 3040.
  • FIG. 31 shows an example of an interferometric defect detection system having a high incidence angle illumination with an extended light source and phase control in the path of the scattered light.
  • Incoming illumination beam 3118 is directed toward sample 3110 using beam splitter 3172.
  • the specular reflected component is represented by beam 3124 and passes through a compensation plate 3130.
  • the scattered component represented by beams 3128 pass though phase controllers and attenuators 3170 that are analogous to any of the subsystems shown and described with respect to Figs. 2a-b, 9-11 and 14.
  • Front end optical system 3116 and back end optical system 3114 collect and direct the light towards imaging sensor 3140.
  • An extended source has an advantage of spreading light energy uniformly over wider areas of the imaging system lens components.
  • High Sensitivity Mode This mode targets specific types of defects, particularly the kinds of defects which can adversely affect chip production yield.
  • the relative phase between the scattered component and the specular component is usually set to maximize the defect signal. However, the relative phase can also be set to minimize wafer pattern noise or maximize the signal-to-noise ratio of defect signals. In most cases, these are equivalent to each other.
  • the signal-to-noise ratio can be increased up to two times the intrinsic signal-to-noise ratio through noiseless amplification of the signal by the specular component.
  • noiseless amplification is important for the detection of weak defect signals.
  • the desirable or ideal relative phase value can be determined experimentally. For example, the catch-all-mode which will be introduced in the next section can be run on the sample to determine the optimal phase value experimentally.
  • the optimum relative phase for detection can be set based on theory or numerical simulations.
  • the relative phase can be varied by changing the phase of either or both the specular or scattered component. But, in practice it is usually much easier to change the phase of the specular component because the specular component usually has a lower etendue. Therefore, in all numerical simulations, the phase of the specular component is varied to get optimum relative phase values. Even though the numerical simulations are limited to specific type of defects, the systems and methods disclosed herein are generally applicable for the detection of any kind of defects. [00241] Figs. 32a and 32b show the shapes of the defects used for the numerical simulations herein. The defects are cylindrically-shaped having a height or depth the same as their diameter. Fig.
  • Fig. 32a shows a particle type defect 3210 having a height and diameter of "d.”
  • Fig. 32b shows a void type defect 3212 having a depth and diameter of "d.”
  • the defect material is assumed to be the same as the sample material.
  • phase defects because they introduce phase change, not amplitude change, to the reflected light. Being phase only, they are at an extreme end of a full spectrum of possible defect types.
  • phase type defects Another extreme type of defect is an amplitude-only defect.
  • Amplitude only defects have opposite characteristics to phase defects; they have zero height but different reflectivity than their surrounding areas.
  • Most real defects are neither a pure phase type nor a pure amplitude type. They generally have both phase and amplitude differences from their surrounds. Only the signals from phase type defects are simulated in this section, however, the equations and computer program used for the simulations are so general that they can handle other types of isolated cylindrical defects.
  • NA numerical aperture
  • Equation (3) can be rewritten as follows.
  • the part in the first angled bracket represents a pure phase object and the part in the second angled bracket represents a pure amplitude object with zero reflectivity.
  • any tiny defect can be decomposed into a pure phase defect and a pure amplitude defect.
  • Normal illumination with unit intensity can be simply expressed as follows.
  • V (a, ⁇ ) The complex amplitude of the reflected light, V (a, ⁇ ) , at the pupil becomes: V(a, ⁇ ) ⁇ Pupil(p) x Defocus(p) x Q(a, ⁇ )
  • Figs. 33 - 35b show numerical simulation results using the above program.
  • Fig. 33 shows simulation results for a 40 nm diameter defect.
  • Curve 3310 shows simulated results for a conventional bright field mode system and curves 3312 and 3314 show simulated results of the interfero metric methods disclosed herein using a high sensitivity mode and phase angles of 144° and -36° applied to the specular component, respectively.
  • Curve 3316 shows simulated results for a conventional dark field system.
  • Fig. 34 shows simulation results for a 20 nm diameter defect.
  • Curve 3410 shows simulated results for a conventional bright field mode system.
  • Curves 3412 and 3414 show simulated results for the interferometric methods disclosed herein using a high sensitivity mode introducing phase angles of 117° and -63° to the specular component, respectively.
  • Curve 3416 plots simulated results for a conventional dark field system.
  • Fig. 35a shows simulation results for a 10 nm diameter defect.
  • Curve 3510 shows simulated results of a conventional bright field mode system.
  • Curves 3512 and 3514 show simulated results of the interferometric methods disclosed herein using a high sensitivity mode introducing phase angles of 104° and —76° to the specular component, respectively.
  • Curve 3516 shows simulated results for a conventional dark field system.
  • BF in the figure's legend means a conventional system using bright field mode and is included in the figures for comparison purposes.
  • "HS” in the figure's legend means high sensitivity mode.
  • the angle ⁇ s is not the phase angle introduced to the specular component. Rather, ⁇ s is the sum of the phase angle introduced to the specular component and the innate phase angle difference between the defect signal and the specular component.
  • the innate phase angle difference is the phase angle difference that a conventional bright field mode system will have.
  • the innate phase angle differences in the simulated defect signals are —144°, —117° and —104° for 40 nm, 20 nm and 10 nm defects respectively. These innate phase angle differences are quite different from 0° or ⁇ 180°. This is the reason why a conventional bright field inspection mode can perform neither well nor stably.
  • the phase controller either adds or subtracts an appropriate amount of phase angle to make the total phase angle difference 0° or ⁇ 180° between the defect and its surround.
  • the phase controller added 144°, 117° and 104° respectively to the innate signals from 40 nm, 20 nm, and 10 nm defects to make the total phase differences 0°.
  • the phase controller also adds -36°, -63° and -76° respectively to the innate defect signals from 40 nm, 20 nm, and 10 nm defects to make the total phase difference -180°.
  • the dark field signal could be higher than those shown in the figures if it happens to interfere constructively with the scattered light by the surrounding patterns. That kind of interference is not controllable and relies completely on luck. Therefore, it is generally expected that the dark field defect signal will become too low to be detected reliably for defects whose size is smaller than a quarter of the wavelength. In the near future, a significant portion of critical defects in semiconductor wafers are expected to be much smaller than a quarter of the wavelength. In fact, line widths are expected to approach a quarter wavelength where the wavelength is 193 nm divided by the index of refraction of water at 193 nm. Therefore, the future of current dark field inspection technologies looks poor.
  • the required phase change on the specular component to make the relative phase between the defect signal and the specular component be 0° or 180° is not necessarily ⁇ 90°, even though the defects used in simulations are phase objects.
  • the amount of phase change required on the specular component for a maximum defect signal depends on the size of the phase object. This is a critical difference between this inspection technology and phase-contrast microscopy where a fixed ⁇ 90° phase is added to the specular component for maximum image contrast. Even these simple examples show that continuous variability of the relative phase between the defect signal and the specular component is desirable for reliable defect detection. If the signals from more general defects were simulated, they would show even more clearly the desirability of having continuous variability in the phase controller.
  • phase controller For example, if the signals from pure amplitude defects are simulated, the optimum phase value for the phase controller will be 0° or 180°. These phase values are very different from those shown in the examples of pure phase defects. Actually, the phase controller should be able to provide any phase shift value in order to be able to detect all kinds of defects reliably. Thus, the continuous variability of the phase controller is not just desirable but really necessary if we want to reliably detect defects.
  • the systems and methods disclosed herein employ a phase controller that can vary the relative phase in a substantially continuous manner.
  • the defect signals are boosted or amplified significantly over the conventional bright field signal by varying the relative phase appropriately. Furthermore, the signal amplification becomes more significant when the defect size gets smaller. Another advantage of operating in a maximum defect signal mode is improved signal stability. This is because the first order signal sensitivity to external perturbation is zero if the signal intensity is an extremum. Thus, the systems and methods disclosed herein can provide much higher defect detection sensitivity along with better stability.
  • the phase controller can also be used for the deamplification of unwanted defect signals.
  • a good example is wafer pattern noise, which is actually not a noise but a defect signal. In most defect detection situations, it is desirable to suppress wafer pattern noise. If suppression of wafer pattern noise is more important than amplifying the defect signals of interest, the phase controller can be set to minimize the wafer pattern noise rather than maximizing the defect signals of interest.
  • the bright field signal is still sizable. However, the important thing is that this is true for the defect type used in the simulation.
  • the bright field signal can be much smaller for some types of real defects.
  • the defect signal can be written more explicitly.
  • the defect signal, s is the difference between the raw signal from the defect and the specular component. (Refer to equation (3).) Therefore, the defect signal amplitude at the location of the defect becomes where Rd is the reflectivity of the defect h is the height of the defect Equation (17) tells us that if; where R sur is the reflectivity of the surrounding area the defect signal is purely imaginary. That is, ⁇ s , the phase difference between the defect
  • both the bright field, 3521, and dark field signals, 3522 are virtually zero.
  • the signal may be completely recovered by controlling the relative phase between the scattered and specular components.
  • a 90° relative shift generates interference signal 3523, and a -90° relative phase shift generates signal 3524.
  • This example demonstrates the power of the interferometric detection systems and methods disclosed herein.
  • signal curve 3312 is slightly larger in absolute amplitude than signal curve 3314. This is because the dark field term and the interference term shown in equation (2c) carry the same signs and add constructively for curve 3312. However, for curve 3314, the dark field term and the interference term carry opposite signs and add destructively. Therefore, in this specific example, curve 3312 is a better choice for defect detection than curve 3312. In this specific example, the difference between the two choices is small. However, in cases of real defects, the difference between the two choices can be significant. The high sensitivity mode of operation allows us to choose the optimum signal curve for any specific type of defect.
  • the defect signal Due to the diffraction from the sharp edge of the imaging system aperture, the defect signal usually changes signs as the signal measurement point moves toward the peripheral part of the signal as shown in Fig. 33 through Fig. 35b. Therefore, if the signal needs to be integrated spatially to maximize the total signal, it is important to convert all parts of the signal to positive values before the integration.
  • the amount of noise is spatially uniform because the main noise sources are the detector noise and the photon noise from the specular component, both of which are spatially uniform. Therefore, the signal has the highest signal-to-noise ratio at the center or peak of the signal and a lower signal-to-noise ratio in its periphery.
  • a strong specular component means high noiseless amplification of the defect signal.
  • High noiseless amplification of defect signals leads to high defect contrast in the subtracted image. This, in turn, leads to a more sensitive and stable defect detection system. Therefore, a strong specular component is generally preferred.
  • a strong specular component increases the contrast of subtracted images, but decreases the contrast of raw images.
  • the contrast of concern for defect detection is the contrast of the subtracted images, not the raw, images before subtraction. This criterion is quite the opposite of all conventional microscopes including phase-contrast types and their derivatives, which endeavor to increase the contrast of raw images.
  • Fig. 36 shows an image of a 40 nm defect that was given enhanced contrast by attenuating the intensity of the specular component by 96%.
  • Curve 3610 shows the results after attenuating the specular component, while curve 3612 shows the results before attenuating the specular component.
  • Fig. 37 shows an enhanced contrast of the image of 20 nm defect achieved by attenuating the intensity of the specular component by 99.9%.
  • Curve 3710 shows the results after attenuating the specular component, while curve 3712 shows the results before attenuation. Note that the amounts of attenuation used in the simulations are excessive. They are neither recommended nor practical in many cases, but were used to demonstrate the capability of the technique for contrast enhancement.
  • contrast enhancement must be used with care with these and other undesirable side effects in mind. Note that illuminating a larger area on the sample and employing a proportionally larger detector array can reduce the possibility of sample damage by intense illumination light while preserving throughput, but this usually requires a more expensive instrument design. [00280] Fortunately, even though the specular component was attenuated severely in the simulations to show the contrast enhancement clearly, most actual cases do not require that much contrast enhancement thanks to a large dynamic range of the image sensors used in current defect detection systems.
  • Moderate contrast enhancement is not only very acceptable with current practice but also preferred considering the current need for signal amplification, the efficiency of light energy use and system throughput.
  • An important conclusion can be derived from the shape of the defect images 3610 in Fig. 36 and 3710 in Fig. 37.
  • the shape of the defect images indicates that the interference term is dominant even with a large amount of attenuation of the specular component. Even if the attenuation is 99.9%, the interference term is still dominant.
  • the interference term is formed by the noiseless amplification of the signal by the specular component and a low reflectivity of the sample has nearly the same effect as a high attenuation of the specular component.
  • the dominance of the interference term even with a very high attenuation of the specular component can be interpreted to mean that the noiseless signal amplification by the specular component works very effectively, even with samples of extremely low reflectivity.
  • all the systems and methods disclosed herein which depend on the noiseless signal amplification by the specular component work well with virtually any kind of sample.
  • the smaller the defect the more effective the noiseless amplification of the defect signal by the specular component. More accurate supporting examples will be shown in a later section on "The Limitations of Dark Field Mode.”
  • the catch-all mode is based on the determination of both the amplitude and the phase of the defect signal. Because the defect signal is completely determined by its amplitude and the phase, if the noise is low enough, the catch-all mode can, in principle, catch virtually all the different kinds of defects in one run. [00284] Defects can be classified much more accurately if both their amplitude and the phase information is available.
  • the size of the defect can be estimated from the amplitude information and from the phase information it can be determined if the defect is a particle type or void type, or mesa type or valley type.
  • An example will be given in the section "Three Scan Method.”
  • a more accurate defect classification is a huge time saver in the defect review process, which is usually very costly.
  • the defect review usually requires the use of expensive but slow electron microscopes.
  • the information collected in the catch-all mode of operation can be very useful for the proper setup of other modes of operation.
  • the utilization of the catch-all mode for the proper setup of other operation modes will not only cut down the setup time but also make a fast automatic setup possible.
  • the catch-all mode can also be used for the setup of the catch-all mode itself. For example, the catch-all mode can be operated multiple times with different numbers of sample scans, each corresponding to a different phase shift, and also with different polarizations.
  • the catch-all mode is a powerful mode.
  • a single run of the catch-all mode requires multiple scans of the sample.
  • its throughput is not expected to be much lower compared with other modes because it can catch all different kinds of defects with a single run and there is no need for sample loading/unloading between multiple scans.
  • the throughput reduction will be handsomely compensated by the throughput increase in the defect review process. Therefore, the catch-all-mode is expected to be a popular mode of operation even with its lower throughput.
  • Equation (2c) shows that the interference term contains the amplitude and cosine of the relative phase of the defect signal.
  • the interference term contains the amplitude and cosine of the relative phase of the defect signal.
  • at least three scans of the sample need be used. Two scans are not enough because there is another unknown, the whole dark field term.
  • the phase of the specular component needs to be set differently for each scan. This can be achieved by calibrating the phase controller. A calibration method for the phase controller is described in a previous section.
  • the initial phase value of the specular component is not important, so any phase setting of the specular component can be used.
  • the phase value of the specular component for the first scan of sample is ⁇ b and the phase changes are ⁇ j and ⁇ 2 for second and third scan
  • the complex amplitudes of the specular component for the first, second and third scans are expressed as follows:
  • die-to-die subtracted intensities contain the needed amplitude and phase information of the defect signal. Therefore, these die-to-die subtracted intensities need to be stored for the whole wafer. This seems to require an unrealistic amount of memory space. But, in reality, it does not require much memory space because the data are nonzero only in areas around defects, which are extremely sparse in reality. Only data of nonzero or larger values than the predetermined threshold value need to be stored. Data of zero or values smaller than the threshold value do not need to be stored.
  • the amplified defect signal intensity, I s for this case has the following simple expression:
  • I s is a raw signal intensity. Its magnitude depends not only on the intensity of illumination light but also on the intensity of the specular component. Therefore, in order to make the defect signal more consistent, I s should be normalized against the intensities of the illumination light beam and the specular component.
  • the illumination can be made relatively uniform across the field but the intensity of the specular component can vary significantly over the whole field. An exact measurement of the intensity variation of the specular component is difficult. Fortunately, exact values of the local intensity of the specular component are not needed. Approximate values are fine for normalization purpose. Local intensity values of the specular component can be approximated by the local average of the total light intensity in most cases. Therefore, the raw amplified defect signal intensity, I s can be properly normalized as follows.
  • hocai is the local average of total light intensity at image plane
  • I s ' is the normalized intensity of the amplified defect signal. Iu normalizes
  • I s and Iiocai normalizes ⁇ b ⁇ .
  • Defects are usually detected by comparing the peak value of 11 with a preset value called threshold. More elaborate defect detection algorithms can also be used to improve the overall performance.
  • I s ' 2 can be spatially integrated and the integrated value, rather than the peak value, can be compared with a predefined threshold value.
  • a numerical deconvolution of the defect image with the finite width of detector element can also be applied along with other methods. A fast numerical deconvolution method will be described in the section "Spatial Frequency Bandwidth.”
  • the normalized intensity of the amplified defect signal not only reveals the existence of a defect but also provides crucial information about the size of the defect.
  • the optical signal does not directly provide the physical size information of defects. Rather, it provides only the Optical size' of defects directly.
  • the relationship between the physical size and the optical size can be complicated. Therefore, it is hard to estimate the physical size of the defect accurately from the optical signal alone.
  • the phase of the defect signal ⁇ s relative to the specular component, becomes:
  • phase information provides additional critical information for a more accurate defect classification. For example, phase information determines immediately if the defect is a particle, void, mesa, or a valley type. An accurate and reliable defect classification is just as important as reliable defect detection. Existing technologies rely on partial amplitude information only for defect classification, and this results in very unreliable defect classification.
  • the systems and methods disclosed herein allow using both amplitude and phase information for defect classification. The use of both quantities allows a much more accurate and reliable defect classification.
  • Fig. 38 shows plots of the signal intensity and the phase of a 20 nm defect as an example. Curve 3810 is the signal intensity and curve 3812 is the corresponding phase.
  • Equation (37) can be normalized with illumination intensity and used to evaluate the strength of the dark field signal and this will determine if the dark field mode of operation can be used to reliably find defects.
  • Equations (35) through (39) can be especially useful in real systems because it does not take much computing time to calculate them and they are the least sensitive to random noise thanks to an equal division of the phase angle.
  • the amplified defect signal intensity, equation (38) or (39), is the intensity of the whole, not just the real part, of the defect signal and, therefore, a true indicator of the existence of the defect. By comparing it with a predefined threshold, we can tell if the defect is sufficiently large to be of concern. If the defect is of concern, we can characterize it by calculating the complex amplitude of its signal using equations (35) and (36). This gives some crucial information about what kind of defect it is. [00312] For example, Fig. 39 shows plots of the phases of defect signals from a 20 nm particle and a 20 nm void. Curve 3910 shows the phases of the 20mn void, and curve 3912 shows the phase of the 20mn particle.
  • defect size is comparable to or larger than the resolution of the collection optics and noise is also low, we can even deconvolve the complex amplitude of the defect signal with the complex amplitude of the point spread function of the imaging optics to get a more detailed picture of the defect.
  • This capability will help defect classification become much more accurate. More accurate defect classification leads to significant time saving in the defect review process which is usually a very costly and slow because defect review usually requires the use of expensive but slow electron microscopes. Therefore, the throughput reduction due to multiple sample scans will be handsomely compensated by the throughput increase in the defect review process.
  • the image sensor has a large dynamic range, then we can boost the interference part of the whole signal by a large amount. In this case, the dark field part of the whole signal can be so small that we may be able to use the two scan method to speed up the catch-all mode of the operation.
  • Four Scan Method A simple choice for the four phase values of the specular component is 0, ⁇ , — and . If we scan the sample four times with 0, ⁇ , — and
  • the amplified defect signal intensity, I s for this case has the following simple expression:
  • This four scan method provides simpler equations. However, its main drawback is that the relative phase angle between defect signal and specular component can be as large as 45°. Notice that the maximum relative phase angle for the three scan method is 30°. This fact can make this four scan method less sensitive to some defects than the three scan method.
  • different phase values than ⁇ 0, ⁇ , — and ⁇ can be chosen. Possible different choices are ⁇ 0, — , — and — ⁇ , ⁇ ⁇ — , ⁇ — ⁇ , etc. However, these other choices involve the use of a regression method to determine the defect signal and make the analytical expression of defect signal more complicated.
  • the error function is defined as follows in a least-square regression.
  • Equations (73) and (74) are the general best solutions for the complex amplitude of amplified defect signal.
  • Equation (75) can be normalized with illumination intensity and used to evaluate the strength of the dark field signal. By evaluating the strength of the dark field signal, we can tell if the dark field mode of operation can be used to find the defects.
  • the regression process for the catch-all mode can be done analytically. Therefore, operation in the catch-all mode does not require excessive computing time even if the sample is scanned a lot more than three times in order to obtain more reliable defect signals. Hence, more scans mean lower throughput. However, if the signal-to-noise ratio is low or a high signal-to-noise ratio is needed, more sample scans can significantly help. For example, an accurate study of defect signals can benefit from a supply of defect signals of high signal-to-noise ratio and this can be easily obtained by running the catch-all mode with a large number of sample scans.
  • heterodyne mode suffers less 1/f noise and so is able to provide cleaner measurement data generally.
  • the heterodyne method can be implemented with relative ease in static or stepping systems, however, it is usually hard to implement in scanning systems, especially in fast scanning systems.
  • Contrast Enhancement If the dynamic range of the image sensor is saturated, then, the contrast of the image needs to be increased in the catch-all mode to preserve signal integrity. In this case the same contrast enhancement technique described in the high sensitivity mode section can be used.
  • Polarization Diversity As mentioned previously, the strength of the defect signal can depend on the polarization states of the illumination light and also the scattered light. Therefore, if the defects of interest are composed of different kinds of defects, whose signal strengths depend on polarization states differently, then in order to capture all the different kinds of defects, images need to be collected with multiple different polarization states. This is called polarization diversity. In theory coping with polarization diversity could take a lot of scans with different combinations of phase shift and polarization settings. In practice this is not usually practical, and good judgment is required to balance throughput with the probability of missing a small defect or two. A basic understanding of optical physics can help in coping with polarization diversity. For example, as long as the defect and its neighboring patterns do not have helical structures, the polarization combinations employed can be limited to linear polarization combinations.
  • NA complex amplitude distribution of the optical signal collected by the collection lens is
  • the maximum spatial frequency of the interference term can be only approximately.
  • Fig. 40 which compares the spatial frequency bandwidth of the defect signal component with normal incidence of illumination, with the dark field spatial frequency bandwidth.
  • Curve 4010 shows the interference term and curve 4012 shows the dark field term.
  • NA 2NA all mode is , not .
  • the Nyquist-Shannon ⁇ ⁇ sampling theorem states that the spatial frequency of the image sampling should be at least two times the maximum spatial frequency of the image in order to pick up all information in the image and to avoid signal aliasing. Note that the Nyquist-Shannon sampling theorem applies to image sensors because image sensors are a kind of sampling device. [00349] This means that if we use the same image sensor for all modes, the image magnification for the catch-all mode does not need to be as high as that of the high sensitivity mode or dark field mode to pick up all the needed information about the defect and to prevent signal aliasing.
  • the same image sensor can cover a larger field of view at the sample plane in the catch-all mode.
  • a larger field of view means a higher throughput.
  • the throughput reduction of the catch-all mode due to multiple sample scans can be significantly compensated by the increase in the field of view.
  • future generations of interferometric defect detection systems may be able to use the same image magnification for both the high sensitivity mode and the catch-all mode.
  • the dark field mode may not be operational with an image magnification higher than that for the other modes of operation due to the low intensity of this signal component. If the illumination ray path is fixed, the image magnification does not need to be changed. This suggests that the same fixed image magnification may be used for all modes of operation in future generations of interferometric defect detection systems.
  • a single fixed image magnification will not only make the imaging system more stable while reducing the manufacturing cost of the system but also simplify its operation.
  • the Ny quist- Shannon sampling theorem assumes a delta function as the sampling function. But, any real sampling function cannot be a delta function. Real sampling functions must have finite widths, otherwise, they cannot sense the signal. Image sensors are a kind of spatial sampling device. The width of the sampling function is the width of the light-sensitive area in each pixel of the image sensor. A high sensitivity or high dynamic range usually requires a large light-sensitive area. Therefore, the Nyquist- Shannon sampling theorem is applied to real systems with appropriate modification. However, the general arguments presented here still hold.
  • a standard way of eliminating the negative effect of the finite width of sampling functions is to deconvolve the image with the sampling function. This is equivalent to the inverse Fourier filtering in which the Fourier transform of the image is multiplied with the inverse of the Fourier transform of the sampling function.
  • the process of deconvolution usually requires too much computing resources to be practical. This is especially true for high speed defect detection.
  • the process can be greatly simplified so it can be performed quickly. Simplification of the deconvolution process is very limited for arbitrary images. However, great simplification of the deconvolution process is possible for the subtracted images of tiny defects whose sizes are much smaller than the wavelength. This is because the interference term is dominant in the subtracted image of the tiny defect and the shape of the interference term is the same as the shape of the amplitude point spread function (APSF) of the imaging system and thus fixed as long as the numerical aperture of the imaging system is fixed.
  • APSF amplitude point spread function
  • Fig. 33 through Fig. 37 confirm this fact. Even if the spatial frequency of the specular component is not zero, it does not change the shape of the interference term. Its effect is to provide the interference term with a nonzero carrier frequency. [00355] If the specular component is composed of a single ray, the interference term can be expressed as the multiplication of the APSF with the carrier frequency term. That is, the carrier frequency term can be factored out and be treated separately. If we treat the carrier frequency term separately, the difference between the subtracted image of a tiny defect and the APSF is their strengths.
  • the deconvolution process reduces to the point-by- point rescaling of the signal function.
  • the rescaling function can easily be generated by taking the ratio between the ideal APSF, which is not affected by the finite width of the sampling function, and the real APSF which is affected by the finite width of the sampling function.
  • the deconvolution process is a simple point-by-point multiplication of the defect image with the rescaling function. This is an extremely fast process in modern computers. Thus, in this case, the deconvolution process can be performed extremely fast for the images of tiny defects. Notice that noise is not amplified or affected in a statistical sense by the deconvolution process as long as it is evenly distributed statistically in the spatial frequency domain. Deconvolution makes the image look like it is being sampled with an array of delta- functions, referred to as a comb-function, with the same spacing as the detector array.
  • Fig. 41 shows an example system 4100.
  • the illumination beam 4118 enters the imaging system near the pupil plane and is folded by a small prism so that it strikes the sample at near normal incidence.
  • the specular beam component, 4124, and the scattered component, 4128, from the sample 4110 are split into two beams using a beam splitter, 4172, located near the pupil and between the high NA lens assembly, 4116, and the low NA lens assembly, 4114.
  • a phase controller 4112 and a compensation plate, 4130 is installed in each beam path.
  • Each phase controller sets the relative phase between scattered and specular components to one of the pre-selected values.
  • Two separate image sensors, 4140 measure the intensities of two separate images simultaneously.
  • a single sample scan can produce two image data sets at the same time. Consequently, the total number of sample scans can be reduced to half in the example system. Further reduction of the number of sample scans can easily be achieved by further splitting each of the two beams using additional beam splitters.
  • phase controller sets the relative phase between scattered and specular components to one of the pre-selected values.
  • Multiple separate image sensors simultaneously measure the intensities of multiple separate images.
  • Cascaded beam splittings can be performed as many times as needed as long as the physical space allows them.
  • This method can also be applied to a high-sensitivity mode of operation when the targeted defects contain multiple different kinds of defects each of which require a different phase setting for optimum detection. In this case, each phase controller is set to an optimal phase value for the best detection of each different kind of defect.
  • the dark field mode is not a good choice for the detection of tiny defects whose sizes are smaller than — .
  • the dark field mode is a good choice for the speedy detection of large defects because it produces strong enough signals for a variety of different kinds of large defects and a single scan of the sample is usually enough. Note that if one wants to know the strength of the dark field signal beforehand, the catch-all mode may be employed on the sample first.
  • the dark field mode is finding the best focus for the image sensor. This is because the dark field mode blocks out the specular component which does not carry any focus information but still can affect the image critically during image focusing through its interference with the scattered component.
  • the dark field mode does not need as high a dynamic range on the image sensor as other operational modes because it does not have a specular component. More important characteristics of the image sensor system for the dark field mode are high sensitivity and finer pixels.
  • Limitations of Dark Field Mode The dark field mode is easy to operate because it does not require the manipulation of a phase controller. Also, it can catch a variety of defects with a single sample scan.
  • the dark field mode is usually the first choice if the signal is strong enough or the noiseless amplification of the signal by the specular component is insignificant due to the weak specular component.
  • the dark field mode has severe limitations in finding tiny defects due to its lack of noiseless signal amplification capability.
  • Fig. 42a shows the dark field part, 4210, and interference part, 4220, of the defect signal from a 80 nm isolated defect on a sample surface of only 1% reflectivity. The reflectivity of the defect itself is assumed to be 100% in all simulated cases.
  • Fig. 42a shows that even if the defect is relatively large and the reflectivity of the sample surface is very low, the interference part of the signal is larger than the dark field part.
  • Fig. 42b shows the dark field part, 4230, and interference part, 4240, of the defect signal from a 40 nm isolated defect on a sample surface of only 0.1% reflectivity. That is, the reflectivity of the surrounding area is only one thousandth of the defect reflectivity. This shows that if the size of the defect is smaller than quarter wavelength, even with extremely low reflectivity of the sample, the interference part of the defect signal is larger than the dark field part.
  • Fig. 42c shows the dark field part, 4260, and interference part, 4250, of the defect signal from a 20 nm isolated defect on a sample of only 0.1% reflectivity.
  • the dark field part is significantly smaller than the interference part. If the reflectivity of the sample is larger, the interference part dominates even more. Therefore, we can say that in almost all practical situations, the interference term will dominate for all samples. That is, the technique of the phase control and noiseless amplification described herein work well for all the different types of wafers and reticles likely to be encountered in practice. This is another important advantage of the systems and methods disclosed herein. It turns out that dark field mode is useful only when the size of the defect is roughly larger than a quarter wavelength.
  • a high quality imaging system is one of the key components and the most expensive part of most optics-based inspection systems.
  • the systems and methods disclosed herein can be used with a wide variety of imaging systems including dioptric, catoptric, and catadioptric systems. Dioptric and catoptric designs are better known for this type of application. Numerous books, patents, and other literature exhaustively cover dioptric and catoptric designs.
  • Catadioptric designs are less known but can be very high performing. Design examples of two high performing catadioptric imaging systems will be presented here. The designs are based on US Patent No. 5,031,976. The first design example is shown in Fig. 43a. The design prescription is shown below.
  • This design is for single wavelength applications. A wavelength of 266 nm was chosen for the example design. All lenses and the two catadioptric components 4313,
  • fused silica 4311 are made of fused silica in the example design.
  • the refractive index value of fused silica is assumed to be 1.499684 for 266 nm wavelength.
  • other lens materials such as calcium fluoride, lithium fluoride, etc. can also be used.
  • Lens component 4311 is a plano-convex lens with a reflective coating on the flat side, which faces the sample 4310 spaced 1.5 mm away. The central part of the reflective coating is removed to allow the light from the sample to pass through the lens. After passing through the lens 4311 the image beam passes through another lens element
  • Another way of introducing the near normal incidence illumination beam 4316 is through a second, small, off-axis hole in the reflective coating on surface 4314 on lens/mirror element 4313. This assures that the specular component from the sample 4310 is reflected from the opposite side of surface 4314 and therefore follows a very similar path as the scattered component from the sample to the detector plane. This illumination method produces less flare because the illumination beam passes through fewer optical components.
  • All the lens elements do not need to be made of the same material.
  • lenses located at a high laser intensity area can be made with a more laser- damage-resistant material like calcium fluoride and the rest can be made with fused silica.
  • All lens surfaces are spherical. No aspheric surface is needed even though aspheric surfaces can be used to improve performance further or to reduce the number of lens components.
  • No lens surface has extreme curvature either. All these lens characteristics lead to moderate manufacturing tolerances. Thus, the lens system shown in Fig. 43a can be manufactured without any extreme difficulty.
  • the numerical aperture of the design is 0.9. Its field of view covers quite a large 1.0 mm diameter field.
  • the magnification is chosen to be 20Ox, but it can be changed easily without affecting the quality or performance of the system.
  • the design Strehl ratio is 0.996 or higher over the whole field.
  • the diameter of the aperture stop is 47 mm.
  • the compensation plate 4315 lies close the lens pupil and in an interferometric imaging application would contain the phase controller and the Fourier filter blocking strips.
  • the clear aperture diameter of the compensation plate is nearly the same as the 47 mm diameter of the aperture stop. This is large enough to install a phase controller in the middle without incurring excessive central obscuration.
  • the design also has very low field curvature and distortion.
  • the only drawback of the design is its small working distance which is 1.5 mm in the example design.
  • the example design may not work for applications such as reticle inspection, which typically requires a large working distance because of the pellicle protection. However, the design is well suited for other applications such wafer inspection, which do not require a large working distance.
  • Fig. 43b shows another catadioptric design example. The design prescriptions are shown below.
  • This design is similar to the previous design in the part between the sample surface 4331 and the intermediate image 4332, however near the pupil plane it contains a dichroic wavelength splitter 4333 which divides the beam in two legs, with one leg 4334 being the 266 nm portion and the other 4335 the 532 nm portion. Each leg contains its own compensation plate 4336 and phase controller (not shown).
  • the refractive index values of fused silica are assumed to be 1.499684 for 266 nm and 1.460705 for the 532 nm wavelength.
  • the refractive index values of calcium fluoride are assumed to be 1.462084 for the 266 nm and 1.435358 for the 532 nm wavelength.
  • the refractive index value of BK7 glass is assumed to be 1.519473 for the 532 nm wavelength.
  • the design has similar characteristics to the single wavelength design.
  • the lens system can be manufactured without extreme difficulty.
  • the numerical aperture and the field of view are the same as those of the previous design.
  • the physical size is also similar. However, it is designed for two wavelength applications.
  • the wavelengths are chosen to be 266 nm and 532 nm. Other wavelengths can also be chosen with the same design form. It has a wavelength splitter and two separate phase controllers contained in each compensation plate so as to be able to independently handle two wavelengths.
  • the front-end lens system is shared by both wavelengths.
  • the back-end lens systems are completely separated to maximize the design flexibility.
  • the design Strehl ratios are at least 0.996 for the 266 nm wavelength and at least 0.985 for the 532 nm wavelength over the whole field.
  • the field curvature and distortion are also very low.
  • the design can be easily modified to accommodate more wavelengths by inserting more wavelength splitters into the back-end lens systems. These design examples are applicable to the defect detection systems described herein.
  • Fig. 44a shows this method.
  • the first lens 4401 purposely introduces an appropriate amount of spherical aberration to the input beam 4402 which has a gaussian shape as shown in curve 4407.
  • Spherical aberration from the first lens redistributes the energy in the beam as it propagates through free space.
  • a gaussian beam can be converted into a tophat-shaped uniform beam.
  • the second lens 4403 is used because the spherical aberration not only redistributes light energy but also introduces wavefront distortion.
  • the second lens corrects the wavefront distortion introduced by the first lens so that the energy distribution at focal plane 4405 is shown by curve 4406.
  • the relay system usually needs at least two lenses separated from each other. This is because the relay system not only needs to relay the tophat beam profile but also has to preserve the flat wavefront at the illumination field. Sometimes, it is very hard to procure space for the relay system. Usually, lots of mechanical interference problems arise. The problem becomes more severe if the relay system needs to be a zoom system. The embodiments described herein can alleviate these problems. [00387]
  • Fig. 44b shows the workings of the present invention according to some embodiments. In brief, the gaussian input beam profile 4420 is converted into a profile 4421 that is shaped to form an envelope over a sine-function.
  • the beam is incident on a phase plate 4425 that has grooves positioned where the sine function goes negative that produce 180 degree phase changes in the transmitted beam. Further propagation of the beam through free space converts it into a tophat intensity profile 4423 at the sample plane 4426.
  • Diffraction theory tells us that the far-field diffraction pattern of a sinc- function-like beam is tophat-shaped.
  • the described embodiments like the prior art, use a beam profile converter 4427 but, the beam profile converter does not convert an input beam profile to a tophat profile. It converts the input gaussian beam profile into another nonuniform beam profile 4421.
  • the converted beam profile 4421 at image plane 4424 is actually more nonuniform than the input beam profile 4420.
  • the profile of the converted beam 4421 should look more or less like the envelope of a sine-function.
  • the beam profile converter 4427 converts the input beam profile to a desirable profile without introducing a wavefront distortion.
  • the beam profile converter introduces an appropriate amount of spherical aberration through the first lens 4428 (or lens group) and corrects the wavefront distortion introduced by lens 4428 with the second lens 4429 (or lens group).
  • the present embodiment uses another optical component called a "phase- stepper" placed after the beam profile converter.
  • the phase stepper can be made by forming unequally spaced grooves with a square profile on a glass substrate as shown in Fig.44b. Precision grooves on a glass substrate can be made in many different ways. For example, they can be made by patterning the grooves with a lithography technique followed by either precision etching or deposition of a glass material.
  • the phase stepper changes the phases of selected portions of the incident wavefront in a discreet fashion. The amount of phase step needed is about 180°.
  • Fig.44c shows a configuration according to another embodiment. It has a transform lens 4430 which transforms the sinc-function-like beam 4422 into a tophat beam at its focal plane 4426.
  • the function of the transform lens in this design is the same as a long free space propagation path in the previous design. Basically, both free space propagation and the transform lens perform a Fourier transform of the input beam profile.
  • the size of the tophat beam depends on the size of the input beam to the transform lens and also on the focal length of the transform lens; it is inversely proportional to the size of the input beam and proportional to the focal length of the transform lens. [00393] By choosing the right input beam size and/or focal length for the transform lens, the size of the tophat beam at the illumination field can be controlled.
  • a transform lens becomes a valuable alternative to free space propagation when space is too limited to meet the distance requirement of equation (82). If a transform lens needs to have a longer focal length than the physical path length available, a telephoto lens can be used as a transform lens. In the opposite cases where a longer overall length is desired, a reverse- telephoto lens can be used as a transform lens.
  • a lens or lenses are in the beam propagation path.
  • the transform lens is simpler and more flexible in its configuration than the image relay lenses needed in the prior art systems.
  • the embodiments have advantages over the prior art including those employing lenses in the beam propagation path.
  • Fig. 44d shows an example of a superuniform beam profile 4460.
  • the described techniques are well-suited for the generation of a superuniform beam which can be easily generated by shaping the beam profile on the input side of the phase-stepper like an envelope of the Fourier transform of the targeted superuniform beam profile. Actually, the described techniques are so flexible that it can be used for the generation of a wide variety of other beam profiles such as a beam profile with multiple humps.
  • Fig. 44e shows the result of trying to achieve a tophat profile without using a beam profile converter.
  • the input gaussian beam, 4440 is passed through a phase-stepper, 4425, which changes the phase without changing the general beam profile as shown by curve 4441.
  • the final result at the illumination field 4426, curve 4442, is preferable to a gaussian profile but not as good as is obtained with a profile converter. This system is simpler because it does not need a beam profile converter. However, the beam at the illumination field is either less uniform and/or less energy-efficient than those shown in Fig.44b and 44c.
  • Fig. 44f shows only two separate illumination fields to illustrate the working principle clearly. However, more than two illumination fields can be achieved easily by inserting a grating which generates more than two diffraction orders or by inserting multiple diffraction gratings. The locations of the illumination fields can be controlled by choosing the pitch and orientation of the grating(s) properly. In Fig. 44f, the orientation of the grating is set to be the same as that of phase stepper in order to show the working principle clearly, but, that is not a requirement. The grating orientation can be set to any direction in order to place the illumination fields at predetermined positions. [00400] High energy efficiency and good inter-field uniformity can also be achieved by designing the profile of the grating grooves properly.
  • the depth and shape of the groove can be adjusted to achieve well matched illumination uniformity in each field.
  • extremely high energy efficiency can be achieved by blazing the grating groove profiles.
  • interferometric defect detection system is not an exception. In principle, interfero metric defect detection system can be operated without an autofocus system if the environment is quiet and the sample stage is extremely precise. However, these ideal conditions rarely are available in the real world. Therefore, it will be usually preferred to have an autofocus system to insure stable performance of the whole system.
  • An autofocus system is usually an important subsystem. Its performance is usually crucial to the performance of the whole system. However, performance alone is not the only requirement for an autofocus system. It must fit to an available space. Also, its cost must be reasonable. Described embodiments of the present invention address these issues.
  • a single channel configuration is shown in Fig. 45 a, which shows the focus system located relative to the high NA and low NA imaging lens groups 116 and 114 respectively and the compensation plate 130.
  • the focusing system uses a single spatial-mode laser 4501 as a light source.
  • Semiconductor lasers are excellent candidates. However, laser beams are usually not very stable in their position and pointing direction. Because of their inherent instability, it is preferable not to couple lasers directly into an autofocus optical system. Unstable laser beams can introduce errors into the focus signal.
  • lasers are not directly coupled to the autofocus optical system. Instead, the laser beam passes through a long single-mode optical fiber 4502.
  • the single-mode fiber preferably at least a foot long in order to dissipate the cladding modes which are usually excited by an imperfect coupling of the laser light into the fiber.
  • the single-mode optical fiber is a passive device that can stabilize the beam position and pointing direction by converting the original instabilities in the source to an output intensity change which can be calibrated out easily.
  • the variation in beam position and pointing direction changes the coupling efficiency of the laser beam into the single-mode-fiber.
  • the change of coupling efficiency at the input end induces a change of intensity at the output end.
  • the use of single-mode fiber as a beam stabilizer is an important feature, according to some embodiments.
  • the output end of the fiber is conjugated (or imaged) on the sample plane 110 and on the position sensitive detector (PSD) surface 4511. Because the autofocus ray is focused obliquely on the sample surface by lens 4503, a focal shift of the sample surface causes a lateral movement of the laser beam at the PSD surface 4511. However, a small tilt in the sample moves the beam over the aperture of imaging lens 4504 but does not change its position on the position sensitive detector 4511. Thus the system measures sample focus position but not sample tilt. Thus, by reading the beam position from the PSD, we can determine the amount of focus change of the sample.
  • a computer or controller connected to the PSD reads the PSD output and processes it to estimate the focus error. If the focus error is larger than a predetermined value, the computer or controller takes corrective action by sending an appropriate focus correction signal to the focus actuator 4518.
  • the focus error detection and the corrective action can be run in an open or closed loop.
  • PSDs are readily available and provide a variety of choices.
  • the described embodiment preferably does not use a beam splitter to couple the auto focus ray into or out of the imaging system. Instead, it uses small prisms (or mirrors) 4505. This method of light coupling has the following advantages over the beam splitter.
  • the aberrations of auto focus optics can be made very small because of the small etendue of the beams.
  • S-polarization which has the electrical field parallel to the sample surface, has less variation of reflectivity and phase than p-polarization on most samples. This means that s-polarized light can provide more consistent performance than p-polarized light.
  • s-polarized light is used as shown in Fig. 45a through 45c. S-polarization is represented by arrays of circular dots in the beam paths. There are several different ways to ensure that only s-polarized light is picked up from the source. One way is simply to install a polarizer in the beam path. Another way is to use a polarization-preserving single mode fiber between the source laser and the entrance to the auto focus optical system.
  • the polarization-preserving fiber accepts both s- and p- polarizations but transmits one polarization while attenuating the other polarization quickly. By rotating the core of fiber to the correct direction, the polarization-preserving fiber can be made to transmit only s-polarization. If the light coming out from the laser source is polarized, the polarization-preserving single mode fiber can provide significantly higher energy efficiency than other kinds of fibers.
  • a generic problem of most auto focus systems is that there is a time delay between focus error sensing and its correction due to time delays in the focus signal processor and the slow response of the focus-error correction system. This becomes one of the main focus error sources in high speed scanning systems where a sample is scanned quickly underneath the imaging system. In this case, in order to reduce the focus error, the focus error should be detected in advance of the imaging of the sample and focus error correction signals should be fed- forward to the focus-error correction system.
  • the autofocus beam In order to detect the focus error in advance, the autofocus beam must land on the sample surface at a forward position in the sample scan direction. This requires the autofocus system to shift the autofocus beam position laterally at the sample surface in order to accommodate changes in scan speed and direction. The autofocus beam position at the sample surface can be easily shifted laterally, by laterally moving the output end of the fiber. This method works because, as stated previously, the output end of the fiber is imaged on the sample surface.
  • a tiltable glass plate 4512 can be used as shown in Fig. 45a.
  • the beam can be laterally shifted by tilting the glass plate. If the input beam is shifted, the output beam is shifted a corresponding amount as well. Maintaining the relative position between the beam and the PSD can be done by introducing a tiltable glass plate in front of the PSD or by simply moving the position of the PSD 4511.
  • a single-channel autofocus system shown in Fig. 45a is usually not very stable because it is sensitive to mechanical structure instabilities or temperature changes.
  • One way to reduce this kind of problem is to set up multiple channels in a symmetrical way.
  • the multiple channel autofocus system configured in a symmetrical way can be made to be insensitive to a common mode mechanical shift.
  • Fig. 45b shows an example of multichannel autofocus systems. It has two channels configured in a symmetrical way.
  • the beam position shift at the sample plane is achieved by tilting glass plates 4512.
  • the PSDs are shifted by direct shift mechanisms 4511.
  • Fig. 45c shows another example of a two-channel autofocus system.
  • both input and output beams are shifted by tilting the glass plates and consequently, the PSDs do not need to be shifted.
  • This configuration uses fewer parts but makes the beam alignments more difficult because the two channels are coupled by sharing the tiltable glass plates.
  • beam splitters 4513 are used to direct the return beams to PSDs.
  • One issue is the loss of light energy.
  • the use of non-polarizing beam splitters sacrifices at least 75% of the available light energy. Energy loss may be acceptable for most samples but may not be acceptable for samples of very low reflectivity.
  • Another issue is that a part of the return beam from one channel enters back into the source laser of the other channel. That is, channels interfere with each other at their sources. This interference destabilizes the source lasers and can cause focus errors. In order to make the source lasers stable, they can be optically isolated from each other. There are two solutions to this problem.
  • One solution is to arrange the beam paths of the two channels so that they do not overlap with each other, as shown in Fig. 45 d. In this arrangement, the return beam can still hit the core of the optical fiber, however, whenever this happens, the direction of the return beam deviates too far off from the acceptance angle of the single mode fiber for the return beam to be coupled into the fiber.
  • the other solution is to use polarization beam splitters rather than non- polarizing ones and put Faraday rotators 4514 in the beam paths as shown in Fig. 45b and 45c.
  • a polarization beam splitter transmits p-polarization and reflects s-polarization. Therefore, the laser beams that pass through a polarization beam splitter are completely linearly polarized.
  • the Faraday rotators preferably are designed to rotate the angle of the incoming linear polarization by 45°.
  • the beams pass through the Faraday rotators 4514 two times, once in their incoming paths and a second time in their return paths.
  • the linear polarization of the laser beams is rotated by 90° by the two Faraday rotators.
  • the originally p-polarized light that passed through the beam splitter in the incoming path is converted into s-polarization at the beam splitter in the return path.
  • the beam splitter in the return path reflects the whole beam toward the PSD and does not transmit the return laser beam toward source laser.
  • Faraday rotators isolate the source lasers from each other. If the beam splitters 4513 and position sensitive detectors 4511 are rotated properly about the beam axis, the laser beams can be 100% s- polarized when they are incident on the sample.
  • this method allows us to achieve high energy efficiency, no inter-channel interference and s-polarization on sample surface at the same time.
  • Fig. 45e shows the top view of a two-channel autofocus system.
  • the autofocus channels are rotated relative to the sample in order to avoid light from either laser which is diffracted from the sample entering into the outgoing beam path. This method is usually very effective in avoiding diffracted light from the sample because diffracted light is usually very localized in the x- and y-directions at the pupil plane.
  • the two channels are placed close to each other. If there is mechanical drift or creeping, two channels placed close to each other are likely to drift or creep in the same direction.
  • the focus signal extracted from multiple channels can be made insensitive to this kind of common-mode motion of the channels.
  • 45f shows another example of a multi-channel configuration.
  • the optical paths of the two channels cross over at the focus point on the sample but otherwise are completely separated.
  • This configuration requires more parts but is more energy-efficient and also does not require Faraday rotators.
  • the beam path alignments will be easier with this configuration because the two channels are not coupled at all.
  • the embodiments not only perform better but also are simpler and more flexible in its physical arrangement. [00426] The important features of new autofocus system are summarized below.
  • Symmetrical dual or multiple channels arranged so as to have less sensitivity to environmental disturbances.
  • Most optical systems require at least one aperture that defines the numerical aperture.
  • Most apertures are made of a thin metal plate with a sizable hole in the middle. These kinds of apertures are easy to produce, however, the sharp edges on these apertures produce a long-range diffraction in the image plane, which in turn causes long-range interferences between the different parts of the image. Long-range interference is one of the major contributors to wafer pattern noise.
  • the aperture edges preferably are softened. That is, the transition between the 100% transmission area and no transmission area should not be abrupt but gradual. A gradual transition can be achieved in many different ways. Aperture edge serration is one of them. An aperture edge serration method is chosen because it has many advantages over other methods if it is done correctly. One advantage is that serrations can be made easily; they can be machined directly into a thin metal plate or they can be created by etching using conventional semiconductor fabrication techniques.
  • FIG. 46a A schematic diagram of the serrated aperture is shown in Fig. 46a.
  • the serrations of aperture 4606 have periodic structures 4608, not random pitches. Serrations of non-periodic or random structures are not considered in this patent specification because their diffraction patterns do not have desirable forms. Even with perfectly periodic structures, a large amount of diffraction is unavoidable because of sudden transmission changes of the serration edges.
  • the diffraction pattern from periodic serrations can be broken into discrete orders.
  • the lowest order, the zeroth order originates from the circular average of the transmitted field and consequently is not affected by the sharp edges of the serrations. This means that the diffraction pattern of zeroth order is the same as that from a truly gradually-transiting aperture.
  • the diffraction pattern of zeroth order is what we want to get from the serrated aperture.
  • N Total number of serrations 3 : Fourier transform operator
  • the far field diffraction pattern produced by an object is the Fourier transform of the object's transmission pattern.
  • the coordinates p and r should be scaled properly.
  • p and r In order for p and r to be a Fourier transform variable pair, if one of p and r is scaled with wavelength, the other should be scaled with the focal length.
  • the most popular scaling convention is that p is scaled with the focal length and r with the wavelength.
  • p is expressed with the unit of focal length, it becomes identical with the image space direction cosine of the ray that passes through the pupil point at p from the center.
  • NA numerical aperture
  • the image space position coordinate expressed with the wavelength unit and the image space ray direction cosine constitute a convenient Fourier transform variable pair.
  • the diffraction formula derived uses properly scaled coordinate systems.
  • the diffraction formula does not change when the coordinate scaling is switched between the two conventions. Therefore, the reader can switch between the two scaling conventions freely without worrying about a change in the diffraction formula. Switching the scaling convention is actually equivalent to changing the interpretation of the coordinate variables. Such a change of interpretation can provide more intuition to the diffraction formula.
  • the diffraction formula will be derived for coherent normal illumination only. This is because the diffraction for an incoherent case is just the intensity summation of multiple coherent cases and the diffraction formula for an oblique illumination case can be immediately derived from a normal illumination case using the "shift theorem" of the Fourier transform.
  • Serrations can have a variety of different tooth shapes. The details of the diffraction pattern depend on the shape of the teeth. Fig. 46a shows serrations with linear teeth as an example. However, the properties of each diffraction order which are of the most concern do not depend on the shape of the serration teeth but depend on the serration pitch only. [00440] P(p, ⁇ ) , the amplitude transmission of a serrated aperture, can be expressed as follows.
  • the Fourier transform of second term can be obtained using Weighted Hankel Transform: where:
  • C k can be expressed as follows:
  • equation (87) can be expressed as follows:
  • Equation (95) shows that whole diffraction is composed of discrete diffraction orders. If we take out the zeroth order from the second term, then:
  • Equation (97) is the final result of the derivation of the diffraction formula. Unfortunately, it still has a one-dimensional integration that needs to be carried out numerically. However, a numerical one-dimensional integration can be done much more accurately and quickly than the numerical two-dimensional integration that is required for the numerical two-dimensional Fourier transform. [00448]
  • the first two terms in equation (97) constitute the zeroth diffraction order, which is what we want to have from the serrated aperture. If we write down the zeroth diffraction order separately:
  • Equation (97) The last term in equation (97) is all higher diffraction orders which we have to exclude from the image sensor. However, we do not need to care about all nonzero diffraction orders because only the first diffraction order is strongest and comes closest to the zeroth order at the image plane. All other higher orders are not only weaker than the first order but also, more importantly, land further away from the zeroth order at the image plane than the first order. Therefore, in order to make the serrated aperture work, we need to take a look at only the first diffraction order and make sure it lands outside the image sensor. If we take out the first diffraction order from the last term in equation (97), then:
  • Both the sharp edges of the aperture and any sharp edges of any obscuration can produce long range diffraction effects.
  • the same serration technique used for apertures can be applied to obscurations in order to reduce long range diffraction effects by any obscuration. Thanks to Babinet's principle, the diffraction formula for a serrated obscuration is identical to that for the serrated aperture except for the reversal of the amplitude sign. (Reference: "Principles of Optics", Max Born and Emil Wolf, Cambridge University Press, 1999.) Therefore, no new derivation of diffraction formula for obscurations is needed.
  • the analytical diffraction formula is so general it can be applied to serrations with any teeth shape. However, we still should do numerical evaluations of the formula to see the behavior of the diffraction pattern.
  • the serrations with linear tooth shape as shown in Fig. 46a perform well and are easy to manufacture. Therefore, serrations with linear tooth shape are chosen for the numerical evaluations of the diffraction pattern.
  • the function w(p) is expressed as follows:
  • Serrated apertures produce images which extend less far than an unserrated aperture. This feature is exactly what we wanted from serrated apertures.
  • Serrations reduce long range diffraction amplitudes, but, they also reduce the peak height of the zeroth diffraction order because they unavoidably reduce the effective aperture area. This is an undesirable side effect of serrated apertures and also soft apertures in general. Therefore, in determining the serration width, a good compromise between the two effects needs to be practiced.
  • Fig. 46e shows the radial distributions of the first order light for different numbers of serrations around the aperture circumference.
  • Curve 4601 corresponds to 10 serrations around the aperture circumference
  • curve 4602 corresponds to 100 serrations
  • curve 4603 corresponds to 1000 serrations
  • curve 4604 to 10,000 serrations. This analysis indicates the following:
  • the radius of the no-first-order-light zone is approximately proportional to the number of serrations. This is especially true for a N larger than 1000.
  • the serrated aperture does not work well when the number of serrations is less than 100 because of the fast shrinkage of the no-first-order-light zone with the decrease of the number of serrations.
  • Equation (103) can be used to determine the number of serrations or an equivalent serration pitch required to put the first and all higher diffraction orders outside the image sensor [00464]
  • Equation (107) is identical to the diffraction angle expression for the serrations on linear edges.
  • the diffraction angle expression for the serrations on linear edges is identical to that for periodical structures like gratings. This means that if the pitch of the serration teeth is much smaller than the radius of curvature of the edge, the curvature of the edge can be ignored and the serrations on curved edges can be treated like those on straight edges.
  • edge serration technique can be applied to any edge of any shape as long as the edge does not have sharp corners and the pitch of the serrations is much smaller than the radius of curvature of the edge. For example, consider an aperture of irregular shape. In this case, the curvature of the aperture edge varies along the edge. However, as long as the aperture does not have sharp corners, we can make the serration pitch to satisfy equation (107).
  • the serration pitch does not need to be the same everywhere. As long as the pitch is varied slowly along the edges, the serration technique disclosed herein is expected to work at least to some degree. [00468] The advantages of a serrated aperture are summarized below.
  • the first and higher diffraction orders can be kept away from the image sensor.
  • Such advantages include: high defect signal; high defect detection sensitivity; less false defect detections; less sample pattern noise, ability to catch different kinds of defects at a time; ability to distinguish between voids and particles or a mesa and a valley; more accurate and reliable defect classification; improved detection consistency; improved illumination uniformity across the field leading to more effective utilization of image sensor dynamic range for the amplification of defect signals; fast setup of operational modes; the use of a mode-locked laser rather than a CW laser thereby lowering cost; avoidance of the need for speckle busting leading to lower cost; ability to use flood illumination thereby decreasing the chance of wafer damage; ability to use coherent illumination leading to well-defined diffraction orders, thereby providing for straightforward Fourier filtering; simple system configuration leading to lower cost; elimination of pupil or aperture stop relay leading to lower cost and decreasing energy loss; and efficient energy use.

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Abstract

L'invention concerne des systèmes et des procédés d'imagerie par interférométrie à cheminement commun pour la détection et la classification de défauts. Une source d'éclairement produit et dirige une lumière cohérente vers l'échantillon. Un système d'imagerie optique recueille la lumière réfléchie ou transmise par l'échantillon, y compris une composante dispersée et une composante spéculaire, qui n'est pas diffractée par l'échantillon de manière prédominante. Un système de commande à phase variable est utilisé pour ajuster la phase relative de la composante dispersée et de la composante spéculaire afin de modifier la manière dont elles interfèrent dans le plan de l'image. Le signal obtenu est comparé à un signal de référence pour la même position sur  l'échantillon et une différence dépassant un seuil est considérée comme constituant un défaut. Le processus est répété de multiples fois, à chaque fois avec un décalage de phase relative différent et chaque position des défauts et les signaux de différence sont stockés dans une mémoire. Ces données sont ensuite utilisées pour calculer l’amplitude et la phase de chaque défaut, ce qui peut être utilisé pour la détection et la classification des défauts. On s’attend à ce que ce procédé détecte des défauts beaucoup plus petits que les systèmes actuels d'inspection et trouve des défauts qui sont transparents pour ces systèmes.
PCT/US2009/045999 2008-06-03 2009-06-02 Détection et classification par interférométrie de défauts WO2009149103A1 (fr)

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CN200980121352.XA CN102089616B (zh) 2008-06-03 2009-06-02 干涉缺陷检测和分类
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