Patent Application
20150002852
Non-contact surface characterization techniques, such as coherence scanning interferometry (CSI), are useful tools for measuring shape and surface finishes, and are particularly relevant to manufacturing industries for process development, quality control and process control. Desirable attributes of a non-contact method are short measurement time, insensitivity to environmental perturbations (vibration, acoustic noise, etc.) and high-resolution.
An advantage of CSI is that it allows for measuring surface structures that are more than one half-wavelength in surface height difference from one imaging pixel to the next, without the so-called fringe ambiguity characteristic of phase shifting interferometry (PSI). However, CSI is limited in its data acquisition speed, its scanning range, and its ability to tolerate certain types of disturbances such as vibration, mechanical scanning errors and instrument noise.
The present disclosure relates to coherence scanning interferometry using phase shifted scanning interferometry signals. Various aspects of the disclosure are summarized as follows.
In general, in a first aspect, the subject matter of the disclosure can be embodied in a low-coherence scanning interferometry method, in which method includes: for each optical path length difference (OPD) of a sequence of OPDs between test light reflected from a test object and reference light in a scanning interferometer, simultaneously measuring two phase-shifted interferograms corresponding to intensity patterns produced by interfering the test light reflected from a test object with the reference light on respective first and second detectors, in which the test light and reference light are derived from a common source and wherein the sequence of OPDs spans a range larger than the coherence length of the common source. The interferograms measured by the first detector define a first set of scanning interferometry signals corresponding to multiple transverse locations on the test object, the interferograms measured by the second detector define a second set of interferometry signals corresponding to substantially the same multiple transverse locations on the test object, in which each interferometry signal in the second set is phase-shifted relative to a corresponding interferometry signal in the first set. Every interferometry signal includes a series of intensity values corresponding to the sequence of OPDs. The method further includes using an electronic processor to process the interferometry signals to determine information about the test object with reduced sensitivity to errors, in which the electronic processer performs operations includes: i) processing the first set of interferometry signals, independently from the second set of interferometry signals, to obtain first processed information about the test object over the multiple transverse locations; ii) processing the second set of interferometry signals, independently from the first set of interferometry signals, to obtain second processed information about the test object over the multiple transverse locations; and iii) combining the first processed information with the second processed information to determine the information about the test object with the reduced sensitivity to the errors.
Implementations of the method can include one or more of the following features and/or features of other aspects. For example, in some implementations, each of the first processed information and the second processed information is independent of the OPD. The first processed information may include multiple first data values corresponding to information about the test object at different transverse locations on the test object. The second processed information may include multiple second data values corresponding to information about the test object at the same transverse locations as the first data values.
In some implementations, the first processed information is any of a relative height map, a film thickness map, or surface profile. In some implementations, the second processed information is any of a relative height map, a film thickness map, or surface profile. In some implementations, the information about the test object is any of a relative height map, a film thickness map, or surface profile.
In some implementations, the only interferometry signals processed by electronic processor are those from the interferograms measured by the first and second detectors.
In certain implementations, the phase shift between each simultaneously measured interferogram is approximately 90°.
In some implementations, the phase shift between each simultaneously measured interferogram is approximately 180°.
In certain implementations, the method includes translating a measurement scan position of the test object or a reference object relative to one another to obtain the sequence of intensity values corresponding to the sequence of OPDs, each intensity value of every interferometry signal being measured at a different measurement scan position. The different measurement scan positions may be separated by uniform scan intervals. The different measurement scan positions may be separated by non-uniform scan intervals. Successive intensity values in each of the interferometry signals may be measured at measurement scan positions alternately separated by a first scan interval and a second scan interval, the first scan interval being less than the scan second interval. The multiple intensity values for each interferometry signal of the first set of scanning interferometry signals may be measured over multiple camera frames of the first detector, and the multiple intensity values for each interferometry signal of the second set of scanning interferometry signals may be measured over multiple camera frames of the second detector. An absolute range over which the sequence of OPDs are obtained may be at least about 25 microns. A scan interval between intensity values may be at least about 3 quarters of a wavelength of the interferometry signal. A measurement scan position may be translated at a scan rate of at least about 10 micron/sec.
The method may further include modulating the test light and reference light. Modulating the test light and reference light may include periodically switching the common source from a substantially off-state to an on-state, and simultaneously measuring two phase-shifted interferograms occurring during the on-state of the common source. The first detector may include a first camera shutter and the second detector may include a second camera shutter, in which modulating the test light and reference light comprises periodically opening and closing the first camera shutter and the second camera shutter at approximately the same times, and in which simultaneously measuring two phase-shifted interferograms occurs during the opening of the first camera shutter and the second camera shutter. A camera frame-time for each detector may be greater than a length of time over which each intensity value is measured.
In some implementations, the multiple intensity values for each interferometry signal are acquired at a rate that is less than a Nyquist rate of the interferometry signal.
In some implementations, using the electronic processor to process the first set of interferometry signals and to process the second set of interferometry signals includes fitting a function to each interferometry signal, the function being parameterized by one or more parameter values. The function may be expressible as including multiple intensity values for corresponding virtual scan positions, the virtual scan positions being defined relative to the measurement scan positions, and in which, for each interferometry signal, fitting the function includes: applying a series of shifts to the virtual scan positions relative to the measurement scan positions; evaluating the function for each of the series of shifts in the virtual scan positions; and comparing a degree of similarity between each evaluated function and the corresponding interferometry signal. Evaluating the function further may include varying one or more of the parameters for each of the series of shifts in the virtual scan positions, and calculating the intensity values of the function based on the one or more varied parameters. The one or more parameter values may include a phase value, an average magnitude value, and an offset value. Comparing a degree of similarity between each evaluated function and the corresponding interferometry signal may include determining which of the series of shifts in the virtual scan positions produce an optimum fit between the function and the corresponding interferometry signal. Determining which of the series of shifts in the virtual scan positions produces the optimum fit may include applying a window function to the different measurement and virtual scan positions being evaluated. The window function may be a tapered window function. The window function may include a raised cosine function. Comparing a degree of similarity between each evaluated function and the corresponding interferometry signal may include identifying the virtual scan position and parameters of the function that produce a minimum square of the difference between the function and the corresponding interferometry signal. Comparing a degree of similarity between each evaluated function and the corresponding interferometry signal may include calculating a merit function for each of the series of shifts in the virtual scan positions, the merit function being indicative of a degree of similarity between the evaluated function and the corresponding interferometry signal. The merit function may be proportional to the square of the magnitude of the function at the virtual positions. The merit function may be inversely proportional to the minimum square difference between the function and the corresponding interferometry signal at the virtual scan positions. The virtual scan positions may be separated by uniform increments, each increment being less than a spacing between the measurement scan positions. The virtual scan positions may be separated by uniform increments, each increment being greater than a spacing between the measurement scan positions.
In some implementations, combining the first processed information and the second processed information includes averaging the first processed information and the second processed information. The first processed information may include multiple first merit functions, each first merit function being indicative of a degree of similarity between a function fitted to a corresponding interferometry signal in the first set of interferometry signals, and the second processed information including multiple second merit functions, each second merit function being indicative of a degree of similarity between a function fitted to a corresponding interferometry signal in the second set of interferometry signals.
In some implementations, providing the light beam includes providing an input beam from the common source, and separating the input beam into the test light and the reference light. The method may include: directing the test light through a first polarization filter towards the test object, and transmitting the reference light through a second polarization filter toward a reference object, in which the test light and the reference light have approximately the same intensity and opposite polarizations prior to reaching the first polarization filter and the second polarization filter, respectively, the test light and the reference light being orthogonally polarized with respect to each other after passing through the first and second polarization filters, and the test light reflects off the test object and the reference light reflects off the reference object; combining the reflected test light and the reflected reference light to provide combined light; transmitting the combined light through an optical component, in which the optical element is configured to alter a polarization state of the combined light; and directing a first portion of the combined light through a third polarization filter toward the first detector to produce the first interferogram, and directing a second portion of the combined light through a fourth polarization filter toward the second detector to produce the second interferogram.
The test light and the reference light may have the same polarization state, in which the method may include: transmitting the test light through a first optical component and through a first polarization filter so as to reflect off the test object, and receiving the reflected test light back through the first optical component and the first polarization filter, in which the first optical component is configured to alter a polarization state of the test light; transmitting the reference light through a second optical component and a second polarization filter so as to reflect off the reference object, and receiving the reflected reference light back through the second optical component and the second polarization filter, in which the second optical component is configured to alter a polarization state of the reference light; combining the reflected test light and the reflected reference light to produce combined light; and directing a first portion of the combined light through a third polarization filter toward the first detector to produce the first interferogram, and directing a second portion of the combined light through a fourth polarization filter toward the second detector to produce the second interferogram.
The method may include: transmitting the test light through a first optical component so as to reflect off the test object, and receiving the reflected test light back through the first optical component, in which the first optical component is configured to alter a polarization state of the test light; transmitting the reference light through a second optical component so as to reflect off a reference object, and receiving the reflected reference light back through the second optical component, in which the second optical component is configured to alter a polarization state of the reference light; combining the reflected test light and the reflected reference light into combined light; and directing a first portion of the combined light through a first polarization filter to the first detector to produce the first interferogram, and directing a second portion of the combined light through a second polarization filter to the second detector to produce the second interferogram.
Separating the input beam into the test light and the reference light may include passing the input beam into a polarizing beam-splitter such that the test light and the reference light are orthogonally polarized with respect to one another, in which the method may include: transmitting the test light through a first optical component so as to reflect off the test object, and receiving the reflected test light back through the first optical component, in which the first optical component is configured to alter a polarization state of the test light; transmitting the reference light through a second optical component so as to reflect off a reference object, and receiving the reflected reference light back through the second optical component, in which the second optical component is configured to alter a polarization state of the reference light; combining the reflected test light and the reflected reference light into combined light; transmitting the combined light through a third optical component, in which the third optical component is configured to alter a polarization state of the combined light; and directing a first portion of the combined light through a first polarization filter to the first detector to produce the first interferogram, and directing a second portion of the combined light through a second polarization filter to the second detector to produce the second interferogram.
Separating the input beam into the test light and the reference light may include passing the input beam into a polarizing beam-splitter such that the test light and the reference light are orthogonally polarized with respect to one another, in which the method may further include: transmitting the test light through a first optical component so as to reflect off the test object, and receiving the reflected test light back through the first optical component, in which the first optical component is configured to alter a polarization state of the test light; transmitting the reference light through a second optical component so as to reflect off a reference object, and receiving the reflected reference light back through the second optical component, in which the second optical component is configured to alter a polarization state of the reference light; combining the reflected test light and the reflected reference light into combined light; and directing a first portion of the combined light through a first polarization filter to the first detector to produce the first interferogram, and directing a second portion of the combined light through a second polarization filter and through a third optical component to the second detector to produce the second interferogram, in which the third optical component is configured to alter a polarization state of the second portion.
Separating the input beam into the test light and the reference light may include passing the input beam into a polarizing beam-splitter such that the test light and the reference light are orthogonally polarized with respect to one another, in which the method may include: directing the test light toward the test object and directing the reference light towards the reference object, in which the test light reflects off the test object, and the reference light reflects off the reference object; combining the reflected test light and the reflected reference light in the polarizing beam-splitter to provide combined light; passing the combined light through an optical component configured to alter polarization state of the combined light; directing a first portion of the combined light through a first polarization filter to the first detector to provide the first interferogram; and directing a second portion of the combined light through a second polarization filter to the second detector to provide the second interferogram.
In general, in another aspect, the subject matter of the disclosure may be embodied in a low-coherence scanning interferometry method that includes: for each optical path length difference (OPD) of a sequence of OPDs between test light reflected from a test object and reference light in a scanning interferometer, simultaneously measuring two phase-shifted interferograms corresponding to intensity patterns produced by interfering the test light reflected from a test object with the reference light on respective first and second detectors, in which the test light and reference light are derived from a common source and in which the sequence of OPDs spans a range larger than the coherence length of the common source, the interferograms measured by the first detector defining a first set of scanning interferometry signals corresponding to multiple transverse locations on the test object, the interferograms measured by the second detector defining a second set of interferometry signals corresponding to the substantially the same multiple transverse locations on the test object, in which each interferometry signal in the second set is phase-shifted relative to a corresponding interferometry signal in the first set, in which every interferometry signal comprises a series of intensity values corresponding to the sequence of OPDs; and for each interferometry signal in the second set and the corresponding interferometry signal in the first set, using an electronic processor to apply a global least squares fit to the pair of interferometry signals to determine information about the test object with reduced sensitivity to errors.
Implementations of the method may include one or more of the following features and/or features of other aspects. For example, in some implementations, the information about the test object is any of a relative height map, film thickness map, or surface profile.
In some implementations, the phase shift between each simultaneously measured interferogram is approximately 90°.
In some implementations, the phase shift between each simultaneously measured interferogram is approximately 180°.
In some implementations, the method includes translating a measurement scan position of the test object or a reference object relative to one another to obtain the sequence of OPDs, each intensity value of every interferometer signal being measured at a different measurement scan position. The different measurement scan positions may be separated by uniform scan intervals. The different measurement scan positions may be separated by non-uniform scan intervals. Successive intensity values in each of the interferometry signals may be measured at measurement scan positions alternately separated by a first scan interval and a second scan interval, the first scan interval being less than the scan second interval. The multiple intensity values for each interferometry signal of the first set of scanning interferometry signals may be measured over multiple camera frames of the first detector, in which the multiple intensity values for each interferometry signal of the second set of scanning interferometry signals are measured over multiple camera frames of the second detector. The method may include modulating the test light and reference light. Modulating the test light and reference light may include periodically switching the common source from a substantially off-state to an on-state, and simultaneously measuring two phase-shifted interferograms occurring during the on-state of the common source. The first detector may include a first camera shutter and the second detector may include a second camera shutter, in which modulating the test light and reference light includes periodically opening and closing the first camera shutter and the second camera shutter at approximately the same times, and in which simultaneously measuring two phase-shifted interferograms occurs during the opening of the first camera shutter and the second camera shutter. A camera frame-time for each detector may be greater than a length of time over which each intensity value is measured.
In some implementations, the multiple intensity values for each interferometry signal are acquired at a rate that is less than a Nyquist rate of the interferometry signal.
In some implementations, the only interferometry signals processed by the electronic processor are those from the interferograms measured by the first and second detectors. Applying the global least squares fit for each pair of interferometry signals may include: fitting a first model function to the interferometry signal in the second set; fitting a second model function to the corresponding interferometry signal in the second set; combining the square of the difference between the first model function and the interferometry signal for a series of evaluation scan positions and the square of the difference between the second model function and the corresponding interferometry signal for the series of evaluation scan positions; and determining the evaluation scan position that results in a minimum value for the combination. The first model function and the second model function may be each expressible as including multiple intensity values for corresponding virtual scan positions, the virtual scan positions being defined relative to the measurement scan positions. The one or more parameter values may include a phase value, an average magnitude value, and an offset value.
In some implementations, providing the light beam includes: providing an input beam from the common source; separating, in a polarizing beam-splitter, the input beam into the test light and the reference light such that the test light and the reference light are orthogonally polarized with respect to one another, directing the test light toward the test object and directing the reference light towards the reference object, in which the test light reflects off the test object, and the reference light reflects off the reference object; combining the reflected test light and the reflected reference light in the polarizing beam-splitter to provide combined light; passing the combined light through an optical component configured to alter polarization state of the combined light; directing a first portion of the combined light through a first polarization filter to the first detector to provide the first interferogram; and directing a second portion of the combined light through a second polarization filter to the second detector to provide the second interferogram
In general, in another aspect, the subject matter of the disclosure may be embodied in a low-coherence scanning interferometry system that includes: an interferometry apparatus comprising a light source, an interferometer, a first detector, and a second detector, the apparatus configured to simultaneously measure, for each optical path length difference (OPD) of a sequence of OPDs between test light reflected from a test object and reference light, first and second phase-shifted interferograms corresponding to intensity patterns produced by interfering the test light reflected from a test object with the reference light on the first and second detectors, respectively, the test light and reference light being derived from the light source, each interferogram measured by the first detector defining a first set of scanning interferometry signals corresponding to multiple transverse locations on the test object, each interferogram measured by the second detector defining a second set of interferometry signals corresponding to the substantially the same multiple transverse locations on the test object, in which each interferometry signal in the second set if phase-shifted relative to a corresponding interferometry signal in the first set, every interferometry signal including a series of intensity values corresponding to the sequence of OPDs; and an electronic processor coupled to the interferometry apparatus, in which the electronic processor is configured to perform operations including, i) processing the first set of interferometry signals, independently from the second set of interferometry signals, to obtain first processed information about the test object over the multiple transverse locations, ii) processing the second set of interferometry signals, independently from the first set of interferometry signals, to obtain second processed information about the test object over the multiple transverse locations, and iii) combining the first processed information with the second processed information to determine the information about the test object with the reduced sensitivity to errors.
Implementations of the system may include one or more of the following features and/or features of other aspects. For example, in some implementations, the light source is configured to provide an input light beam, and the system further includes an objective assembly configured to convert the input light beam into the test beam and the reference beam, in which the test beam and the reference beam have orthogonal polarizations states with respect to one another. The objective assembly may be further configured to introduce a phase-shift between constituent components of the test beam and of the reference beam. The input beam may have a linearly polarization state or is unpolarized. Each pixel of the first detector may be aligned to substantially the same location on the test object as a corresponding pixel of the second detector.
In general, in another aspect, the subject matter of the disclosure may be embodied in a low-coherence scanning interferometry system that includes: an interferometry apparatus comprising a light source, an interferometer, a first detector, and a second detector, the apparatus configured to simultaneously measure, for each optical path length difference (OPD) of a sequence of OPDs between test light reflected from a test object and reference light, first and second phase-shifted interferograms corresponding to intensity patterns produced by interfering the test light reflected from a test object with the reference light on the first and second detectors, respectively, the test light and reference light being derived from the light source, each interferogram measured by the first detector defining a first set of scanning interferometry signals corresponding to multiple transverse locations on the test object, each interferogram measured by the second detector defining a second set of interferometry signals corresponding to substantially the same multiple transverse locations on the test object, in which each interferometry signal in the second set if phase-shifted relative to a corresponding interferometry signal in the first set, every interferometry signal comprising a series of intensity values corresponding to the sequence of OPDs; and an electronic processor coupled to the interferometry apparatus, in which the electronic processor is configured to perform operations comprising processing the interferometry signals to determine information about the test object with reduced sensitivity to errors, in which the only interferometry signals the electronic processor is configured to process are those from the interferograms measured by the first and second detectors.
Implementations of the system may include one or more of the following features and/or features of other aspects. For example, in some implementations, the light source is configured to provide an input light beam, and the system further includes an objective assembly configured to convert the input light beam into the test beam and the reference beam, in which the test beam and the reference beam have orthogonal polarizations states with respect to one another. The objective assembly is further configured to introduce a phase-shift between constituent components of the test beam and of the reference beam.
In some implementations, the input beam has a linearly polarization state or is unpolarized.
In some implementations, each pixel of the first detector is aligned to substantially the same location on the test object as a corresponding pixel of the second detector.
The details of one or more embodiments are set forth in the accompanying drawings and the description below. Other features will be apparent from the description, drawings, and claims.
a is a schematic diagram of a structure suitable for use in solder bump processing.
b is a schematic diagram of the structure in
Embodiments of coherence scanning interferometry and systems for performing the same are disclosed in which two detectors imaging the same surface simultaneously acquire interference information, where there is a relative phase shift between the information acquired by the first detector and the information acquired by the second detector. The information acquired by the two detectors is obtained over a scan range that is greater than a coherence length of the source light used for the scanning interferometry. An electronic processor coupled to the two detectors processes the interferometry signals from the two detectors to determine topography information about the surface being imaged. The electronic processor may be configured to process the interferometry signals from the first detector independently from the interferometry signals from the second detector, and then combine the independently processed signals to produce the topography information. Alternatively, or in addition, the electronic processor may be configured to process the interferometry signals from the two detectors together to produce the topography information, in which the interferometry signals from the two detectors are the only interferometry signals processed by the electronic processor. One or more embodiments of the coherence scanning interferometry technique may be useful for obtaining topography information about a surface while minimizing signal noise due to vibration errors and/or scan-related errors, and for enhancing data acquisition rates.
The following disclosure is divided into separate sections. First, examples of a scanning interferometer system for simultaneously acquiring phase-shifted interference signals at two detectors are described. Then, methods for acquiring interferometry signals in quadrature for vibration compensation and speed enhancement are discussed. The principles of sliding window least squares (LSQ) analysis utilizing discrete sampling of the phase-shifted interferometry signals obtained from the two detectors are then presented. Finally, exemplary applications for the coherence scanning methods are presented and examples of pattern matching to simulated phase-shifted interference signals for different acquisition techniques are described.
Referring to
Source 54 may be a spectrally-broadband source, such as a white-light lamp, or may include a plurality of different wavelengths, e.g., resulting from a plurality of light emitting diodes. As an alternative or in combination with a broadband source, the source 54 can include a narrow band or quasi-monochromatic source. The light emitted from source 54 can be polarized or unpolarized (i.e., randomly polarized).
First lens component 55, which may include, for example, an achromatic doublet, expands and transmits a beam emitted from source 54. A second lens component 56, which may also include an achromatic doublet, transmits a collimated beam to a beam-splitting element 57 that reflects the incident beam toward a polarized objective 58. The polarized objective 58 includes components arranged to separate the incident beam into a separate test beam and a reference beam having different polarizations. For example, polarized objective 58 may be a polarized Michelson objective that includes a third lens component 59 and a polarizing beam-splitter 60. Third lens component 59 may include, for example, an achromatic doublet or other objective lens to direct input light towards (and collect light from) the test and reference surfaces. Preferably, third lens component 59 has a numerical aperture suitable for resolving features on the surface of measurement object, while also allowing one to image a relatively large field of view. As an example, third lens component 59 may have a numerical aperture of about 0.2. Third lens component 59 transmits the incident beam from beam-splitting element 57 toward polarizing beam-splitter 60, which then separates the incident beam into a polarized test beam and a polarized reference beam. For example, polarizing beam-splitter 60 may transmit only portions of the incident beam having a first polarization, while reflecting only portions of the incident beam having a second polarization that is orthogonal to the first polarization, such that a linearly polarized test beam and a linearly polarized reference beam are formed. In the Michelson-type objective, the beam-splitting interface of beam-splitter 60 is oriented at an acute angle to the optical axis defined by third lens component 59 (e.g., at 45 degrees) to direct the reference beam to a side reference object 61 and to direct the test beam on measurement object 53.
In some implementations, reference object 61 is optically flat and includes only a single reflecting surface. For example, reference object 61 may be a reference mirror. In some implementations, reference object 61 exhibits a three-dimensional surface topography and/or includes more than one spaced-apart layer that reflects light. In the following discussion, it is assumed without limitation that reference object 61 is a reference mirror including a single reflective surface.
Polarizing beam-splitter 60 combines light reflected from reference mirror 61 and from measurement object 53. The combined light is directed back to third lens component 59, which collimates and transmits the combined light toward beam-splitting element 57. At least a portion of the combined light passes through beam-splitting element 57 and is incident on a detector assembly 62.
As explained above, the reference and test beam paths are encoded by polarization using beam-splitter 60. The polarization encoding allows controlled phase shifts to be introduced using both polarizers and waveplates elsewhere in interferometer 51. For example, detector assembly 62 includes a waveplate 63, a fourth optical component 64, a beam-splitting element 65, a first detector 66, a second detector 67, a first polarizer 68, and a second polarizer 69. The combined light first passes through waveplate 63, which shifts the phase between the polarized reference and test beam components of the combined light. For example, waveplate 63 may be a quarter-wave plate with its optical axis oriented at 45° with respect to the orthogonally polarized components of the combined beam. This waveplate converts the linearly polarized measurement and reference beams into circularly polarized light beams, where there is an approximately 90° phase shift between the constituent components of the reference and test beams (e.g., the constituent electric-field components Ey and Ex). Other phase shifts may be introduced as well. As noted further below, different optical elements within detector assembly 62 can produce different phase shifts so as to allow light to reach each detector.
The combined light having the reference and test beam components with their relative phase shifts is then transmitted by fourth optical component 64 to beam-splitting element 65. Fourth optical component 64 is an imaging lens and may be another achromatic doublet or other optical component arranged to focus the incoming beam. Beam-splitting element 65 is a non-polarizing beam-splitter that directs a first portion of the combined light toward first detector 66 and a second portion of the combined light toward second detector 67. Prior to reaching the detectors, however, each portion of the combined light derived by beam-splitting element 65 passes through a corresponding polarizer element. For example, the first portion of combined light passes through first polarizer 68 with its optical axis oriented at a first angle (e.g., 0°), and the second portion of the combined light passes through second polarizer 69 with its optical axis oriented at a second different angle (e.g., 45°). Each polarizer element blocks the components of light that are not aligned with the polarizer element's optical axis. Given that the reference and test beams are circularly polarized from waveplate 63, the first beam portion and second beam portion will each include part of the test beam component and reference beam component. However, the first beam portion and second beam portion will be phase-shifted relative to one another. The polarizer elements may be formed as thin films on faces of beam-splitting element 65 using fabrication techniques known in the art. Alternatively, the polarizer elements may be separate stand-alone components.
The first portion of the combined beam passing through first polarizer 68 is focused onto first detector 66. Similarly, the second portion of the combined light passing through second polarizer 69 is focused onto second detector 67. Since each portion of combined light includes a reflected test beam component and a reflected reference beam component, the two components interfere at each detector to produce a corresponding detector signal indicative of the resultant beam intensity.
Each detector typically includes a plurality of detector elements, e.g., pixels, arranged in at least one and more generally two dimensions. In the following discussion, it is assumed without limitation that each of first detector 66 and second detector 67 includes a two-dimensional array of detector elements. For example, the detectors may each be a CCD that includes multiple pixels. In the embodiment shown in
In the present embodiment, first detector 66 and second detector 67 are aligned such that the image points for each of the two detectors correspond to substantially the same points on the measurement object 53. For example, assume the pixels of first detector 66 are arranged in a two-dimensional array in the x and y directions, such that each pixel P1 of first detector 66 is located at a different coordinate, P1(x, y). Similarly, assume the pixels of second detector 67 are arranged in a two-dimensional array in the y and z directions, such that each pixel P2 of second detector is locate at a different coordinate, P2(y, z). The two detectors are then aligned so that the same image point Pm on the measurement object is imaged by a pair of pixels, i.e., P1(x, y) from first detector 66 and P2(y, z) from second detector 67. That is, each pixel of first detector 66 is aligned to record test beam and reference beam interference resulting from the substantially same image point as a corresponding pixel of second detector 67. Ideally, each pixel is aligned to exactly the same image point; however, a certain amount of misalignment is acceptable so long as the effect on the measurable spatial frequencies of the object under test is sufficiently small. For example, given that the measurable spatial frequency content is generally limited by system optical resolution and spatial sampling, an acceptable level of misalignment between pixels may be about 1/10th of a pixel. As explained above, the first portion of the combined beam and the second portion of the combined beam have a relative phase shift between them. Therefore, even though the pixels of the detectors are aligned to image the same points on measurement object 53, the interferograms recorded by first detector 66 and second detector 67, if recorded at substantially the same time, will be phase-shifted relative to one another. The phase-shift between the simultaneously acquired interferograms can be, for example, about 90°, about 180°, or any other phase-shift.
System 50 is typically configured to create an optical path length difference (OPD) between light directed to and reflected from reference object 61 and light directed to and reflected from measurement object 53. In some implementations, measurement object 53 can be displaced or actuated by an electromechanical transducer, such as a piezoelectric transducer (PZT), and associated drive electronics 70 controlled by computer control system 52 so as to effect precise scans along a direction that varies the OPD of the interferometer 51. In some implementations, system 50 is configured to modify the OPD by moving reference object 61; in other implementations, system 50 is configured to modify the OPD by moving measurement object 53. For example, as shown in
As the OPD is modified, such by scanning a position of measurement object 53 or a position of reference object 61, first detector 66 and second detector 67 simultaneously record a plurality of detector signals. For the purposes of this disclosure, simultaneous recording of detector signals means that, for a particular OPD, the exposure/integration time of first detector 66 and second detector 67 occur at the same time. The detector signals thus acquired can be stored in digital format as an array of interference signals, where each pixel acquires a corresponding interference signal, and each interference signal represents a variation in intensity as a function of OPD for a different location of measurement object 53 or reference object 61, depending on which object is translated. For example, if first detector 66 and second detector 67 each include a 128×128 array of pixels, and if 64 images are stored by each detector during a scan, then there will be approximately 32,000 interference signals (approximately 16,000 for each detector), each of which is 64 data points in length, recorded altogether by the two detectors. Furthermore, just as the interferograms recorded on first detector 66 and second detector 67 are phase shifted relative to one another for a particular OPD, each interference signal recorded by a pixel of first detector 66 for a range of OPD is phase-shifted relative to an interference signal recorded by a corresponding pixel of second detector 67 for the same range of OPD, if the pixels are aligned to image approximately the same point on measurement object 53. In embodiments using a broadband source 54, the interference signals may be referred to as scanning white light interferometry (SWLI) interference signals, more generally as low coherence length scanning interference signals.
After the data has been acquired, the computer 52 can process the interference signals from each detector to determine information about measurement object 53. For example, in some implementations, computer 52 can process the interference signals from first detector 66 independently from the interference signals from second detector 67 in accordance with, e.g., pattern fitting techniques. The information obtained by processing the interference signals from both the first and second detectors may be independent of the OPD. For example, electronic processor may independently obtain from each of the first detector 66 and the second detector 67 a corresponding map of data values that are representative of information about measurement object 53. Each map may include multiple data values, in which each data value of a particular map corresponds to a different transverse location (e.g., in the x- or y-direction) on measurement object. Because of the alignment of the first and second detectors, the data values in the map obtained from the first detector 66 correspond to the same transverse locations as the data values in the map obtained from the second detector 67. The data values may be representative of information such as a height of measurement object 53, a thickness of a film or films on measurement object, or a refractive index. The data values may be representative of other information about measurement object 53 as well.
Computer 52 then may combine the independently processed information to produce data about the measurement object 53. For example, the data from the combined information may be indicative of a surface topography of the measurement object. Alternatively, or in addition, the data may be indicative of a thickness profile for a film formed on measurement object. In some implementations, computer 52 processes the information from both detectors together to produce data about the measurement object 53. For example, computer 52 may apply a global fit to the information obtained from first detector 66 and second detector 67.
The embodiment shown in
Examples of different interference objectives include a Mirau-type interference objective. In the Mirau-type object, the beam-splitter is oriented to direct the reference light back along the optical axis to a small reference mirror in the path of the input light. The reference mirror can be small, and thereby not substantially affect the input light, because of the focusing by the objective lens). In a further embodiment, the interference objective can be of the Linnik-type, in which case the beam splitter is positioned prior to the objective lens for the test surface (with respect to the input light) and directs the test and reference light along different paths. A separate objective lens is used to focus the reference light to the reference lens. In other words, the beam splitter separates the input light into the test and reference light, and separate objective lenses then focus the test and reference light to respective test and reference surfaces. Ideally the two objective lenses are matched to one another so that the test and reference light have similar aberrations and optical paths. In some implementations, the system can be configured to collect test light that is transmitted through, rather than reflected by, the test sample and then subsequently combined with reference light. For such embodiments, for example, the system can implement a Mach-Zehnder interferometer with dual microscope objectives on each leg.
Light source 54 in the interferometer may be any of: an incandescent source, such as a halogen bulb or metal halide lamp, with or without spectral bandpass filters; a broadband laser diode; a light-emitting diode; a combination of several light sources of the same or different types; an arc lamp; any source in the visible spectral region (between about 390 nm and about 700 nm); any source in the near-infrared (IR) spectral region (between about 700 nm and 3 microns); and any source in the UV spectral region (between about 390 nm and about 10 nm). For broadband applications, the source preferably has a net spectral bandwidth broader than 5% of the mean wavelength, or more preferably greater than 10%, 20%, 30%, or even 50% of the mean wavelength. For tunable, narrow-band applications, the tuning range is preferably broad (e.g., greater than 50 nm, greater than 100 nm, or greater than even 200 nm, for visible light) to provide reflectivity information over a wide range of wavelengths, whereas the spectral width at any particular setting is preferable narrow, to optimize resolution, for example, as small as 10 nm, 2 nm, or 1 nm. Source 54 may also include one or more diffuser elements to increase the spatial extent of the input light being emitted from the source.
In some implementations, light source 54 may include the ability to modulate its output intensity. For example, light source 54 may be coupled to computer 52 or another controller that can modulate the intensity of light output by source 54. The source 54 may be modulated between being substantially off (e.g., no light or almost no light emitted by source 54, such that a detector measures zero intensity) to being substantially on (e.g., the source 54 emits light at full intensity or an intensity sufficient to be measured by a detector). In some implementations, the source 54 may be configured to provide polarized or non-polarized light. For example, the source 54 may include one or more optical elements to alter a polarization of the light emitted by source 54 so as to obtain a desired polarization such as linear or circular polarization.
Though not shown, interferometer 50 may also include one or more apertures such as, for example, an aperture located between first lens component 55 and second lens component 56 and/or between beam-splitting element 57 and detector assembly 62. Apertures can be placed in other suitable locations in interferometer 50, as well.
The electronic detectors can be any type of detector for measuring an optical interference pattern with spatial resolution, such as a multi-pixel CCD or CMOS camera capable of recording multiple frames per second. For example, the detector may have a camera frame rate of about 10 frames/sec, 25 frames/sec, 50 frames/sec, 75 frames/sec, or 100 frames/sec. Other frame rates are possible as well. Each detector may also include a shutter (mechanical or electrical) capable of blocking light incident on the detector's surface when the shutter is closed. Instead of altering light intensity output by source 54, light modulation can be achieved by opening and closing the shutters on the detectors. In some implementations, the detectors include or are electronically coupled to a controller that operates the shutter opening and closing. For example, in some cases, the controller for operating the shutters may be a part of computer 52.
Furthermore, the various translation stages in the system, such as translation stage 70, may be: driven by any of a piezo-electric device, a stepper motor, and a voice coil; implemented opto-mechanically or opto-electronically rather than by pure translation (e.g., by using any of liquid crystals, electro-optic effects, strained fibers, and rotating waveplates) to introduce an optical path length variation; any of a driver with a flexure mount and any driver with a mechanical stage, e.g. roller bearings or air bearings. The translation stages may allow variable scan speeds along the direction of translation of the measurement and/or reference object. For example, the scan speed may be about 0.5 micron/sec, 1 micron/sec, 10 micron/sec, 20 micron/sec, 30 micron/sec, 40 micron/sec, or 50 micron/sec. Other scan speeds are possible as well. The absolute scan range over which the translation stage moves may also vary. For example, the scan range may span a distance of about 5 microns, 10 microns, 20 microns, 25 microns, 30 microns, 40 microns, 50 microns. Other scan ranges are also possible.
In
The width of the coherence envelope 154 that modulates the amplitudes of fringes 152 corresponds generally to the coherence length of the detected light. Among the factors that determine the coherence length are temporal coherence phenomena related to, e.g., the spectral bandwidth of the source, and spatial coherence phenomena related to, e.g., the range of angles of incidence of light illuminating the object. Typically, the coherence length decreases as: (a) the spectral bandwidth of the source increases and/or (b) the range of angles of incidence increases. Depending upon the configuration of an interferometer used to acquire the data, one or the other of these coherence phenomena may dominate or they may both contribute substantially to the overall coherence length. The coherence length of an interferometer can be determined by obtaining an interference signal from an object having a single reflecting surface, e.g., not a thin film structure. The coherence length corresponds to the full width half maximum of the envelope modulating the observed interference pattern.
As can be seen from
A low coherence interferometer can be configured to detect an interference signal over a range of OPD's that is comparable to or greater than the coherence length of the interferometer. For example, the range of detected OPD's may be at least 2 times greater or at least 3 times greater than the coherence length. In some implementations, the coherence length of the detected light is at least greater than a nominal wavelength of the detected light.
As will be explained in further detail below, different approaches may be used to obtain the intensity values for the interferometry signals. For example, in some embodiments, a pixel acquires the intensity values of an interferometry signal at uniform intervals. That is, each intensity value of an interference signal is acquired over a range of OPD, where the difference between each successive OPD is the same. In some embodiments, the intensity values are acquired by each pixel of a detector at non-uniform intervals. For example, the intensity values of an interferometry signal may be acquired in a “punctuated” manner, such that intensity values are acquired in successive pairs, where the scan distance between intensity values in each pair is short (e.g., within the length of a single fringe) relative to the scan distance between pairs (e.g., over the length of multiple fringes).
In some embodiments, the data acquisition rate at which the intensity values are recorded may be sparse relative to the corresponding interference pattern being sampled. For example, referring to the interference signal 150 shown in
Just as the intervals between scan positions may be non-uniform, the rate at which intensity values are acquired may be non-uniform. In some embodiments, the velocity at which a measurement object or reference object is scanned may be increased in regions between positions at which data intensity values are acquired. For example, the scan velocity may be sped up when translating the measurement object or reference object over regions where no surface is known to exist or where data acquisition is not desired. Accordingly, in some implementations, the time taken for acquiring data over the length of a scan can be reduced.
In some implementations, the measurement object can include more than one reflective surface such as a substrate including one or more at least partially optically transmissive layers. A first reflective surface is defined by the interface between the outermost optically transmissive layer and the surrounding atmosphere (or vacuum). Additional reflective surfaces are defined by each interface between layers or between layers and the substrate. In such embodiments, the light reflected from the measurement object can include a contribution, e.g., a separate beam, reflected from each reflective surface or interface. Because each reflective surface or interface is generally spaced apart along the axis of beam propagation, each separate beam generates a different interference pattern when combined with light reflected from the measurement object. The interference pattern observed by the corresponding detector includes the sum of the interference patterns generated by each separate beam reflected from the measurement object. As the measurement object and/or reference object is scanned through the range of OPDs, and depending on the thickness of the later or layers, the interference signals produced from each interface may overlap.
Additional configurations of the interferometer described above are also possible. For example,
As explained in the previous section, the coherence scanning interferometry systems utilize two detectors aligned to simultaneous image the same surface of an object, in which there is a relative phase shift between the information acquired by the first detector and the information acquired by the second detector. While various phase shifts can be introduced between the interferometry signals recorded at the first detector relative to the second detector, there are benefits, in certain implementations, of acquiring the data from each detector in phase-quadrature. In phase-quadrature, simultaneously acquired interferograms obtained at the first detector and the second detector have a relative phase offset between them of about 90°.
For example, an advantage of acquiring the interferometry data in phase-quadrature is that it provides a straightforward technique for canceling periodically occurring vibrational errors in the interferometry system. In particular, certain vibrational errors in interferometry systems manifest themselves as surface profile ripples having a frequency that is about twice the frequency of the fringes of the interferometry signals themselves. These vibrational errors can arise for various reasons including, for example, unexpected scan-motion behavior or coupling of external vibrations into the interferometry system—such as those produced by motors, pumps, or other machinery. By creating two copies of the interferometry signal obtained for the same range of OPD, in which one copy is phase-shifted relative to the other by about 90°, the vibrational error may be canceled when information obtained from the two signals is combined, for example, by averaging topography information obtained from each interferometry signal. Similarly, other errors having frequencies that are multiples of twice the interferometry fringe frequency may also be canceled using this technique. Thus, simultaneously recording low coherence interferometry signals in phase-quadrature for the same image point may suppress deviations due to relatively high-frequency vibrational errors (e.g., about 10% or more of the frame rate for the detector) and other errors related to the scan increment. For cyclic errors occurring from other causes, different phase shifts may be applied between the simultaneously acquired interferograms. For example, certain types of cyclic errors related to variations in the light intensity (intensity offsets and amplitude errors) during the data acquisition scan may be canceled by introducing a phase shift of about 180° between the simultaneously acquired interference signals. Though adding particular phase shifts between simultaneously acquired interferograms may reduce particular error modes, a phase shift of 0° may also be used simply to reduce the presence of random noise.
The simultaneous acquisition of phase-shifted low coherence interference signals may be further modified to enhance the speed at which data is acquired by the interferometry system. For example, the two detectors in the interferometer may sample intensity values of the interference signals at a rate that is sparse compared to the rate at which fringes of the interference signals move, i.e., the rate of translation of the reference object or measurement object. In some implementations, sampling of the interference signals occurs at a sub-Nyquist rate. The Nyquist rate is understood as corresponding to the lower bound at which a signal may be sampled without aliasing. For the present disclosure, the Nyquist rate is equal to two camera frames per interference cycle. Examples of sub-Nyquist sampling include the acquisition of intensity values at scan intervals that are greater than one-quarter of a wavelength of the interference signals being sampled.
The scan intervals between acquisitions of the intensity values (i.e., distance between subsequent OPDs at which data intensity values are acquired) can be uniform or non-uniform. For example, in some implementations, the two detectors may be operable to simultaneously acquire a first pair of interferograms nominally in quadrature followed by a short scan interval (e.g., within the length of a single fringe) and then simultaneously acquire a second pair of interferograms also nominally in quadrature. Subsequently, a longer scan interval (e.g., over the length of multiple fringes) may take place prior to the next pair of simultaneous interferogram acquisitions. This technique is referred to as “punctuated” data acquisition. In some cases, the sequential pairs of interferograms acquired at each detector are obtained in neighboring camera frames of the detector. In such instances, the minimum separation time between each acquisition of the sequential pair is determined based on the shutter time of the detector and/or the modulation rate of the light source.
The shaded areas of the frames 802, 804, 806, and 808 in
Non-uniform or variable scan intervals also may be useful to enhance the speed of data acquisition by the interferometry system. For example, when performing metrology on wafer solder bumps, the solder bump structure may allow for a reduction in total time necessary to acquire the intensity values of these interference signals by spacing the sample steps according to the expected feature height. This is called a nonlinear scan because the sampling density changes across the scan. That is, the sampling density may be increased along scan regions where features of interest are expected to occur and decreased between regions of interest.
Once the intensity values are acquired by the two detectors of the interferometer, the computer control system that is coupled to the detectors analyzes the signals to reconstruct topography information about the measurement object. The analysis may be performed in two ways. The computer control system may process the interference signals obtained from the pixels of the first detector to produce first information about the measurement object, and independently process the interference signals obtained from the pixels of the second detector to produce second information about the measurement object. For example, the first and second information may include information such as a relative height map of the measurement object, a surface profile of the measurement object, or a film thickness map of one or more films on the measurement object. Alternatively, the first and second information can include a function indicative of how well a model signal matches the first or second interference signal. The first and second information then may be combined (e.g., averaged) to produce robust topography information about the measurement object, in which noise due to vibration errors or scan rate errors are suppressed.
Instead of analyzing the interference signals from the detectors separately, the computer control system may process the interferometry signals from the two detectors together to determine information about the measurement object, in which the only interferometry signals processed by the electronic processor are those from the interferograms measured by the first and second detectors. Further details on the different methods for processing the interference signals from the detectors are set forth below.
To accommodate the interferometer flexibility with scan increments (such as sub-Nyquist sampling, variable scan rates, and punctuated data acquisition) and to maximize the benefit of the phase quadrature information for improving resistance to vibration and scan-related errors, a modified least squares (LSQ) fitting of a model signal to the experimental CSI signals may be used. In some implementations, application of the LSQ fitting approach entails applying the fit to the interference signals measured by the first detector and the second detector to provide separate height information about the measurement object from each detector, and then averaging the independently calculated height information. Alternatively, in certain implementations, a global least-squares fit may applied to the interference signals to obtain the topography information about the measurement object.
Before discussing how LSQ may be modified to accommodate the non-uniform scan intervals and phase-quadrature information obtained from two detectors, it is beneficial to first review the basic principles of least-squares fitting method. Additional detail on LSQ may be found in U.S. Pat. No. 7,321,431, which is incorporated herein by reference in its entirety. In LSQ fitting, the experimental signal is compared with the real part of a complex phase-shifted model signal. An example of a model signal is a complex sine-cosine signal that allows for a variable carrier phase. The model signal may either be derived from first principles or determined empirically using a system characterization procedure. The system characterization method (about which further details also can be found in U.S. Pat. No. 7,321,431) allows for signals that may contain imperfections, distortions and offsets that are characteristic of the instrument, but can in principle account for the instrument interaction with a complex surface structure containing unresolved features or films too thin to be interpreted by envelope splitting.
ƒ(y,{circumflex over (ζ)})=C(y)+V(y)Re{T({circumflex over (ζ)})exp[iφ(y)]}. (1)
The complex or analytical model signal T is qualitatively characterized by interference fringes modulated by a coherence envelope, and has imaginary and real parts that are sine-cosine versions of the same signal. For simplicity, the fitting function employs a single lateral coordinate y to show a dependence on the location within the image; although for full imaging there would of course be two lateral coordinates x, y.
With the experimental interference signal expressed as I, the location of fitting function ƒ is adjusted and (C, V, φ) are allowed to vary with the scan position ζ as needed to optimize the fit of ƒ to the signal I:
ƒ(y,{circumflex over (ζ)},ζ)=C(y,ζ)+V(y,ζ)Re{T({circumflex over (ζ)})exp[iφ(y,ζ)]}. (2)
The LSQ method solves for the parameters (C, V, φ) by optimizing the fit within a tapered window w at each of the scan positions ζ. The optimization minimizes a square difference function at each ζ, in which the square difference function can be expressed as:
χ2(y,ζ)=∫w({circumflex over (ζ)})[I(y,ζ+{circumflex over (ζ)})−ƒ(y,ζ,{circumflex over (ζ)})]2d{circumflex over (ζ)}. (3)
The window w places range limits on the local scan {circumflex over (ζ)} and allows us to concentrate on certain features of the signal with few computations. A tapered window such as the raised cosine (see Eq. (14), further on) is more forgiving of imperfections in the scan ζ than a simple square window. See, e.g., P. de Groot, “Derivation of phase shift algorithms for interferometry using the concept of a data sampling window,” Appl. Opt. 34(22) 4723-4730 (1995), incorporated by reference herein in its entirety.
The best-fit solution for the signal strength V at each scan position ζ is expected to rise and fall according to the envelope of the experimental signal I, as illustrated in
In some implementations, a model signal may be representative of complex surface structures having multiple interfaces, in which a single merit function peak is generated as opposed to multiple merit function peaks. For example,
In an actual scanning interferometer system, the experimental interference signals are typically recorded by a detector (e.g., a CCD camera) configured to capture multiple images, or camera frames, each frame being recorded at a different scan position. Thus, the interference signals I are sampled at a total of Y discrete lateral field positions y across the detector, in which the discrete lateral positions are indexed by the detector pixel number j=0 . . . (Y−1). For full imaging, there would also be discrete lateral positions indexed along the x direction. These signals are also sampled at discrete scan positions. In some implementations, the sample intensity values are uniformly distributed in the scan direction (i.e., uniform scan intervals), and the model signal T is sampled in an identical way for a direct comparison. However, to provide greater flexibility and accommodate variable scan rates in the interferometer system, the scan intervals of the sampled intensity values and/or of the model signal may be irregularly spaced (i.e., non-uniform scan intervals).
After data acquisition, we have for each pixel j a vector of experimental signal data Ij,2 for corresponding scan positions ζz indexed by z=0, 1 . . . N−1. These scan positions may be irregularly spaced but are assumed to be known. The fitting function relies on a model signal T that is quantified for scan positions {circumflex over (ζ)}{circumflex over (z)} indexed by {circumflex over (z)}=0, 1 . . . {circumflex over (N)}−1. The {circumflex over (N)} value is the number of discrete data points over which the fitting function is compared to the experimental signal. Usually, {circumflex over (N)} is an odd number so that for uniform sampling, there is a model signal point at the center flanked by the same number of points to either side.
The flexible sampling strategy is to determine the fit quality over a series of virtual evaluation scan positions ζneval for indices n=0, 1 . . . Neval−1 that are disconnected from the acquisition scan. The evaluation scan can be a uniform grid with a sampling increment ζstepeval that is as small (or as large) as desired:
In traditional LSQ, this evaluation grid is tied to the experimental scan positions ζz. Here, evaluations are instead allowed to occur at scan positions other than those corresponding to the recorded intensity value data points.
To determine the quality of fit of the model signal to the experimental data for a specific evaluation scan position ζneval, the first step is to locate the experimental scan position that most closely matches the evaluation scan position:
z
center(n)=z index that minimizes (ζz−ζneval) for this n (5)
In some special cases such as punctuated acquisition, there may be an interest in making the central position zcenter coincident with specific data points, such as points where z is even or odd or restricted to some range. See, e.g., L. L. Deck and P. J. de Groot, “Punctuated quadrature phase-shifting interferometry,” Optics Letters 23(1), 19 (1998), incorporated herein by reference in its entirety. Once the position zcenter is identified, a portion of the intensity data may be extracted as follows:
Î
n,{circumflex over (z)}
=I
j,Z(n,{circumflex over (z)}) (6)
where
Z(n,{circumflex over (z)})=zcenter(n)+{circumflex over (z)}−Δ (7)
and where the j dependence of the subvector Î is dropped only to simplify the notation as viewed. The offset Δ is the number of points to the left or to the right of the center point in the evaluation, and may be given by
where “thin films” refers to thin layers of material formed on a substrate surface (See, e.g., U.S. Pat. No. 7,298,494, incorporated herein by reference in its entirety). An implicit assumption is that the experimental data are more or less evenly distributed to either side of the center of the scan. For many situations, it is useful although not essential to have N be an odd number. In other cases, for example when the data arrive in pairs (e.g., in punctuated data acquisition), {circumflex over (N)} is preferably an even number.
The model signal Tn,{circumflex over (z)} is calculated for the following scan positions:
{circumflex over (ζ)}n,{circumflex over (z)}=ζZ(n,{circumflex over (z)})−ζneval. (9)
Calculating the model signal values Tn,{circumflex over (z)} follows from a complex inverse Discrete Fourier Transform (DFT) of the frequency-domain version qvsys of the model signal
where Kv refers to the frequency values (e.g., in units of radians of phase per micron of scan) within a bandwidth defined by the index range v=vmin, . . . vmax. The variables vmin and vmax are determined for a region of interest (ROI) in the spectrum that one desires to include in the reconstruction of the model signal T. The qvsys values follow from either a theoretical model or a model based on characterization of the system as described in more detail later in this disclosure.
Using the discrete subvectors Î and T, the square difference function of Eq. (3) becomes
where
ƒn,{circumflex over (z)}=Cn+Re[VnTn,{circumflex over (z)}exp(iφn)]. (12)
The window function w for the χ2 can be any appropriate tapered weighting function. For example, a raised cosine window can be expressed as:
where the window width {circumflex over (ζ)}width is a bit wider than the total length of the model signal scan range
and the offset {circumflex over (ζ)}offset is used to shift the window to the right
u=ζ
step/ζstepeval. (16)
The top plot in
Note that in the example shown in
In punctuated acquisition of data intensity values, there is a pair of successive acquisitions rapidly following each other, followed by some delay until the next acquisition pair.
The experimental scan positions can be expressed as
where int( ) returns only the integer portion of the argument (i.e., the function always rounds down to the nearest integer value). Punctuated data sampling is a special case for which the equation for determining zcenter (Eq. (5)) requires using an even value for z and an even value for {circumflex over (N)} that represents an odd number of data pairs. Then the experimental scan position that most closely matches the evaluation scan position can be expressed as:
z
center(n)=even value for z index that minimizes (ζz−ζstepeval) for this n (18)
Regardless of the data sampling strategy (e.g., uniform, sub-Nyquist, punctuated, or variable), the discrete square-difference function of Eq. (11) after substituting Eq. (12) is
This expands to
Defining a solution vector
we rewrite Eq. (20) as
As a simplification, for the moment define
T
Re
=Re(Tn,{circumflex over (z)}). (23)
T
Im
=Im(Tn,{circumflex over (z)}) (24)
w=w
{circumflex over (z)} (25)
I=Î
n,{circumflex over (z)}. (26)
Then Eq. (22) takes on a more compact appearance as
χn3=Σ[I−(Λn)0−(Λn)1TRe+(Λn)2TIm]2w (27)
where it is understood that the quantities I, TRe, TIm, w all depend on {circumflex over (z)} and that the summation is over all {circumflex over (z)}=0 . . . {circumflex over (N)}−1.
Continuing with this abbreviated notation, we seek a minimum for the square difference function χ2 by setting to zero the partial derivatives
Setting Eqs. (28)-(30) to zero, we have
ΣIw=Σ[(Λn)0+(Λn)1TRe−TIm(Λn)2]w (31)
ΣITRew=Σ[(Λn)0TRe+(Λn)1TRe2−(Λn)2TReTIm]w (32)
−ΣITImw=Σ[−(Λn)0TIm−(Λn)1TReTIm+(Λn)2TIm2]w. (33)
These results lead to the matrix equation for the solution vector Λ:
Λn=ΞnDn (34)
for
The results for the key parameters are:
C
n=(Λn)0 (37)
V
n
2=(Λn)12+(Λn)22 (38)
φnm=arctan [(Λn)2/(Λn)1] (39)
where the triple prime on the phase φnm indicates that there is a three-fold uncertainty in the fringe order of the local phase φ, first across scan position, then from pixel to pixel, and finally overall with respect to an absolute starting position for the scan.
In principle, the matrix Ξn is a function of the evaluation scan position index n. However, since the matrix depends uniquely on the model signal Tn,{circumflex over (z)} and not on the experimental data, there are at most Neval distinct values Ξn calculated prior to the experimental data acquisition. In the limit case where the model signal Tn,{circumflex over (z)} is not a function of the evaluation position, then all of the Ξn are identical and need not be calculated as a function of n. An intermediate case is the punctuated data acquisition of
The discussion to this point covers the LSQ algorithm for both uniform and non-uniform sampling. Next, a merit function is defined that can be used for locating the signal and determining the surface profile to account for the difference in the definition of the signal strength.
The definition of the merit function for locating the signal and determining the surface profile may depend on what one is trying to achieve. For example, if it is sufficiently certain that the peak signal strength corresponds to the signal location, then the simplest merit function is proportional to the square of the signal magnitude V that follows from Eq. (38). This is the so-called robust merit mode and can be expressed as follows:
Πj,nrobust=Vj,n2. (40)
This is a reasonable general-purpose merit function.
Alternatively, and more consistent with the ideal pattern match concept, a “best-fit” merit function can be defined that represents the goodness of fit between the model function and the interferometer signal as quantified by the inverse of the χ2 minimization function of Eq. (20) after solving for the parameters (C, V, φ). In order to ensure that the signal magnitude V is still reasonably strong at the selected position, the signal magnitude is included in the definition for the best-fit merit function as follows:
The χmin2 value in the denominator prevents accidental division by zero although other numbers may be used as well. The foregoing equation is called the fine merit mode, which may be more sensitive to random noise.
The determination of the measurement object surface height hj amounts to locating the peaks of the merit function along the evaluation scan positions for each pixel of the detector. As in previous algorithms, several measurement modes may be utilized, each of which performs a different peak search. For example, when determining the top surface height profile of a test object, the rightmost or leftmost (depending on the scan direction) peak in the merit function along the direction of the scan is identified. If a fit based merit function is used, the location of the peak is the scan position corresponding to an optimum fit of the model function to the experimental signal. When determining film thickness, the strongest two peaks of the merit function may be used. For fit based merit functions, the location of each peak is a scan position corresponding to an optimum fit of the model function to the measurement signal.
Following identification of the peak or peaks (depending on the type of structure present, i.e., single or multi-interface), a quadratic interpolation is performed on three points centered around each peak value. Preferably, the points straddle the peak, but a user operating the interferometer may select different values. An alternative approach that is useful for opaque surfaces or other situations where multiple peaks are not expected is a centroiding method, in which the surface height hj may be expressed as follows:
This equation provides an example of information about the measurement object that is independent of OPD, and is also obtained by processing the interferometry signals from one detector separately from the other detector.
In practice, the range of n values in the sum of Eq. (42) need only be sufficient to cover the fringe contrast envelope, for example, to the 10% contrast level. The n values should be centered at the position of the peak in the merit function. Either the robust merit function or the fine merit function may be used in Eq. (42).
There are at least two ways to create the complex model signal T: from theory or from experiment. For model signals based on theory, it is sufficient in some cases to describe the signal theoretically as a carrier evolving at a frequency K0 modulated by a fringe contrast envelope V. A discretely-sampled complex model signal following this approach can be expressed as:
T
{circumflex over (z)}
=V
{circumflex over (z)}exp[−i{circumflex over (ζ)}{circumflex over (z)}K0]. (43)
A negative phase term in Eq. (43) indicates that an increasing scan corresponds to moving the interference objective away from the measurement object. This is opposite to an increase in surface height, which by definition corresponds to a positive change in phase. Eq. (43) is an idealized model of the kind of signal that might be expected in a scanning white light interferometry (SWLI) system.
For model signals based on experiment, empirical data acquired from the interferometry instrument itself may be used, in which case an inverse Discrete Fourier Transform (DFT) based on the frequency-domain representation qvsys of a typical signal:
The qn,vsys is the average over multiple pixels of data of the frequency-domain representation of a typical interference signal for the interferometer system, acquired using a standard artifact, such as, for example, a SiC flat or other reference material.
The model signal acquired in this manner may have a complicated envelope and nonlinear phase, depending on the actual instrument characteristics. The variables vmin,vmax define the range of positive frequencies K (e.g., in units of radians of phase per micron of scan) within a region of interest (ROI) in the spectrum that one desires to include in the reconstruction of the model signal T.
One approach to processing quadrature data acquisition with two detectors is to perform an LSQ analysis independently on the intensity signals Ij,za, Ij,zb that are obtained from two detectors labeled a and b The merit functions then are averaged or, alternatively, the final height data hja, hjb for each pixel of each detector are calculated and then averaged. The rational for averaging is that certain measurement errors (e.g., as a result of vibrations and/or scan motion) in CSI manifest dominantly as cyclic errors at twice the interference fringe frequency. Accordingly, two data sets acquired in phase quadrature will in principle cancel out the errors. An advantage of averaging the data in this manner is that, at a minimum, the final result obtained from the averaging is in no case worse, in terms of cyclic errors, than a single detector acquisition. Moreover, nearly complete cancelation of the errors may be possible even if the phase difference between the signals at the two detectors is not exactly 90°. The averaging approach has the additional benefit of not requiring precise calibration of the relative fringe contrast and intensity offsets for the two detectors.
A technique for processing the data from each detector that is an alternative to averaging the data includes applying a global fit to the data from each detector. For such a global fit, additional information regarding the interferometer operation may be supplied, including, for example, a determination of the nominal phase quadrature. For this quadrature LSQ method, let us assume that the phase difference θ between the two detectors is at least known, even if it is not exactly 90°, and let us assume further that the signals from the two detectors have been normalized with respect to each other on a pixel-by-pixel basis so that they have the same fringe visibility V and offset D. Then the two fitting functions corresponding to the signals Ij,za, Ij,zb are
ƒn,{circumflex over (z)}a=Cn+Re[VnTn,{circumflex over (z)}aexp(iφn)]. (45)
ƒn,{circumflex over (z)}b=Cn+Re[VnTn,{circumflex over (z)}bexp(iφn)] (46)
where
T
n,{circumflex over (z)}
b
=T
n,{circumflex over (z)}
aexp(iθ). (47)
A global least-squares fit is the simultaneous minimization
χn2=Σ[Ia−(Λn)0−(Λn)1TRea+(Λn)2TIma]2w+ . . . +Σ[Ib−(Λn)0−(Λn)1TReb+(Λn)2TImb]2w (48)
where the example of Eqs. (23)-(26) has been followed to simplify the notation. It should be noted that the solution vector Λ is common to both signals for this global optimization technique.
The calculation now closely parallels Eqs. (28)-(39) because the derivatives of Eq. (48) form linear sums, and leads to the following results:
Λn=ΞnDn (49)
for
In the limit case of perfect quadrature, θ=π/2, and Tn,{circumflex over (z)}b is the complex conjugate of Tn,{circumflex over (z)}a. Eq. (50) simplifies to
Further simplifications are also possible. For example, in some implementations, the real and imaginary parts of the model signal are contrived to be identical in magnitude, which would cause two other terms to drop out of Eq. (52), leading to a very compact calculation. Eq. (50) is nonetheless a more general and realistic formulation given that adjusting the instrument for exact phase quadrature is more difficult than simply evaluating the phase difference θ in a calibration step.
The low coherence interferometry methods and systems utilizing simultaneously acquired phase-shifted interference signals described above may be used for any of the following surface analysis problems: simple thin films; multilayer thin films; sharp edges and surface features that diffract or otherwise generate complex interference effects; unresolved surface roughness; unresolved surface features, for example, a sub-wavelength width groove on an otherwise smooth surface; dissimilar materials; polarization-dependent properties of the surface, such as birefringence; and deflections, vibrations or motions of the surface or deformable surface features that result in incident-angle dependent perturbations of the interference phenomenon. For the case of thin films, the parameter of interest may be the film thickness, the refractive index of the film, the refractive index of the substrate, or some combination thereof. Exemplary applications including objects and devices exhibit such features are discussed next.
Among other things, advances in chip scale packaging, wafer-level packaging, and 3D packaging for integrated circuits have led to shrinking feature sizes and large aspect ratios that create challenges for surface metrology applications, such as solder-bump metrology, through-silicon via (TSV) metrology, and re-distribution layer (RDL) metrology in terms of lateral feature resolution and efficiency. For example, although general coherence scanning interferometry (CSI) enables the measurement of surface structures having surface height differences between neighboring imaging pixels that are more than one-half wavelength without the fringe ambiguity of phase-shifting interferometry, CSI may be limited due to its speed and vibration tolerances. Use of the systems and methods discussed herein in solder-bump, TSV, and RDL metrology offers the benefits of coherence scanning interferometry while improving acquisition speed and reducing noise due to vibration and other scan-related errors.
Referring to
During processing a mass of solder 1604 is positioned in contact with wettable region 1603. Upon flowing the solder, the solder forms a secure contact with the wettable region 1603. Adjacent non-wettable regions 1602 act like a dam preventing the flowed solder from undesirable migration about the structure. It is desirable to know spatial properties of the structure including the relative heights of surfaces 1607, 1609 and the dimensions of solder 1604 relative to surface 1602. Structure 1650 includes a plurality of interfaces between regions that may each result in an interference pattern. As shown in
The interferometry systems and methods disclosed herein can be used to evaluate the surface topology of the solder bumps, including the interfaces between layers in a reproducible and relatively fast manner that is resistant to vibration and/or scan-related errors, offering increased sample evaluation throughput. Examples of interferometer parameters that may be used for the foregoing or other applications are as follows: each detector may have a frame rate of about 30 frames/sec, 40 frames/sec, 50 frames/sec, 60 frames/sec, 70 frames/sec, 80 frames/sec, 90 frames/sec, 100 frames/sec, 200 frames/sec, or 500 frames/sec; a scan increment may be at least about 0.1 micron/frame, at least about 0.5 micron/frame, at least about 1 micron/frame, at least about 2 micron/frame, at least about 5 micron/frame, or at least about 10 micron/frame; a scan speed (e.g., along the z-direction in
Depending on the parameters selected, the interferometer may be used to image multiple fields of view across whole wafers rapidly. For example, a dual-detector interferometer as described herein may image a 50 mm wafer, a 100 mm wafer, a 200 mm wafer, a 300 mm wafer, or a 450 mm wafer. Wafers may be imaged using the dual-detector interferometer at rates including, for example, at least about 10 wafers/hour, at least about 15 wafers/hour, at least about 20 wafers per hour, at least about 25 wafers/hour, at least about 30 wafers/hour, at least about 40 wafers/hour, at least about 50 wafers/hour, at least about 75 wafers/hour, or at least about 100 wafers/hour. The parameters set forth above and/or the processing algorithms used (e.g., height averaging or quadrature LSQ with or without merit function centroiding) may be further modified to balance desired noise reduction against a desired speed of data acquisition.
The systems and methods described above can be used in a semiconductor process for tool specific monitoring or for controlling the process flow itself. In the process monitoring application, single/multi-layer films are grown, deposited, polished, or etched away on unpatterned Si wafers (monitor wafers) by the corresponding process tool and subsequently the thickness and/or optical properties are measured using the dual-detector interferometry system disclosed herein. The average of thickness (and/or optical properties), as well as wafer uniformity, of these monitor wafers are used to determine whether the associated process tool is operating with targeted specification or should be retargeted, adjusted, or taken out of production use.
In the process control application, single/multi-layer films are grown, deposited, polished, or etched away on patterned Si, production wafers by the corresponding process tool and subsequently the thickness and/or optical properties are measured with the interferometry system employing the sliding window LSQ technique disclosed herein. Production measurements used for process control typically include a small measurement site and the ability to align the measurement tool to the sample region of interest. This site may consists of multi-layer film stack (that may itself be patterned) and thus requires complex mathematical modeling in order to extract the relevant physical parameters. Process control measurements determine the stability of the integrated process flow and determine whether the integrated processing should continue, be retargeted, redirected to other equipment, or shut down entirely.
Specifically, for example, the interferometry systems and methods disclosed herein can be used to monitor devices and materials fabricated using the following equipment: diffusion, rapid thermal anneal, chemical vapor deposition tools (both low pressure and high pressure), dielectric etch, chemical mechanical polishers, plasma deposition, plasma etch, lithography track, and lithography exposure tools. Additionally, the interferometry system disclosed herein can be used to monitor and control the following processes: trench and isolation, transistor formation, as well as interlayer dielectric formation (such as dual damascene).
Determining a spatial property of a measurement object using the coherence scanning interferometry systems and methods described herein is further described in the context of the following examples based on simulations of simultaneously measured phase-shifted interferometry signals. The simulations presented here were developed using the MathCad® computer simulation software from PTC of Needham, Mass. The measurement object was assumed to be a reference flat having an opaque single surface.
The following system parameters were assumed for the simulations: a center wavelength of the light source was set equal to 800 nm and a bandwidth of the illumination was set equal to 80 nm; the light was assumed to have a perfect Gaussian spectral profile in the wavenumber domain; the numerical aperture for the system was set equal to 0; the aggregate scanning distance over which the simulation operated was equal to 40 microns; the area of each detector (for a single detector arrangement and a dual-detector arrangement) was assumed to be equivalent to a mask that is 1 pixel long and 300 pixels wide; a signal width of the LSQ model signal was set equal to approximately 9 microns; the LSQ peak searches were implemented based on a quadratic interpolation of the merit function near the highest peak; the model signal was perfectly-known; the standard sampling rate was set equal to 100 nm/frame (i.e., four frames per fringe of the interference signal); a fringe visibility was assumed to be 100%; acquisition of the data was shuttered (i.e., there is no “bucket effect” such that the integration time is effectively zero); sampling of the data intensity values occurred at either the standard sampling rate or a sub-Nyquist rate, in which the sub-Nyquist multiplier is an integer times the standard sampling rate; for punctuated acquisition when using a dual detector system, phase opposition (i.e., adjacent intensity values) were phase-shifted by about 180 degrees and successive intensity values were acquired at a rate equal to twice the standard sampling rate; and the reference flat was assumed to be tilted in one direction to cover a height range of about 4 microns.
It is worth noting that at 11× sub-Nyquist sampling in
Simulations involving errors caused by pure sinusoidal variations also were evaluated at 101 different vibrational frequencies ranging from zero to the detector frame rate. The amplitude of the vibrational disturbances in the simulations was set to 10 nm. The results were the average of the sensitivities for vibrational phase offsets of 0 and 90°.
When switching to a dual-detector arrangement in which the height information from each detector is averaged,
Although the transfer function curves for pure sinusoidal vibrations of
If the actual scan positions ζz can be monitored or otherwise communicated to the LSQ algorithm, the flexible-scan formalism allows for complete correction of the height errors. This method is only effective if we include the χ2 in the merit function calculation, as in Eq. (41). The scan information may be obtained, for example, by using a separate sensor dedicated to measuring scan position.
One concern when using LSQ, particularly for sub-Nyquist scans, is that the effective scan rate, as determined by the rate at which the interference fringes pass by, differs with respect to the model signal, or the effective scan rate is distorted by numerical aperture effects or surface slopes. Such variations can lead quite rapidly to errors. For example,
To address the increased error, additional processing may be employed to infer the correct fringe rate with high accuracy by averaging the fringe rate over the field of view. The mean fringe rate could then be employed to revise the model signal. Alternatively, or in addition, the dual-detector arrangement may be employed to correct the increased error due to the scan mismatch.
For example,
Depending on the embodiment, the techniques and analyses described herein for processing simultaneously acquired phase-shifted interference signals, in which each interference signal is from a separate different detector, can be implemented using control electronics in an interferometer system, in which the control electronics are implemented through hardware or software, or a combination of both. The techniques can be implemented in computer programs using standard programming techniques following the methods and figures described herein. Program code is applied to input data to perform the functions described herein and generate output information. The output information (e.g., position information related to a relative position of a target object to the optical assembly) is applied to one or more output devices such as a display device. Each program may be implemented in a high level procedural or object oriented programming language to communicate with a computer system, or the programs can be implemented in assembly or machine language, if desired. In any case, the language can be a compiled or interpreted language. Moreover, the program can run on dedicated integrated circuits preprogrammed for that purpose.
Each such computer program may be stored on a storage medium or device (e.g., ROM, magnetic diskette, FLASH drive, among others) readable by a general or special purpose programmable computer, for configuring and operating the computer when the storage media or device is read by the computer to perform the procedures described herein. The computer program can also reside in cache or main memory during program execution. The analyses described herein can also be implemented as a computer-readable storage medium, configured with a computer program, where the storage medium so configured causes a computer to operate in a specific and predefined manner to perform the functions described herein.
Embodiments relate to interferometry systems and methods for determining information about a test object. Additional information about suitable low-coherence interferometry systems, electronic processing systems, software, and related processing algorithms is disclosed in commonly owned U.S. Pat. Nos. 5,600,441, 6,195,168, 7,321,431, 7,796,273, and U.S. patent applications published as US-2005-0078318-A1, US-2004-0189999-A1, and US-2004-0085544-A1, the contents of each of which are incorporated herein by reference in their entirety.
A number of embodiments have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the invention. Accordingly, other embodiments are within the scope of the following claims.
This application claims benefit to Provisional Patent Application No. 61/839,448, filed on Jun. 26, 2013. The entire content of the provisional application is incorporated herein by reference.
| Number | Date | Country | |
|---|---|---|---|
| 61839448 | Jun 2013 | US |
