JP2009516171A - Interferometer and method for measuring properties of optically unprocessed surface features - Google Patents

Abstract

Comparing information derivable from a plurality of interference spectroscopic signals corresponding to different surface locations of a test object with information corresponding to a plurality of models of the test object, Comparing and outputting information about surface features that are not fully resolved based on the comparison, parameterized by a set of characteristics associated with one or more sufficiently unresolvable lateral features Interferometric spectroscopy is disclosed.

Description

    The present invention relates to measuring surface topography and / or other properties of objects having complex surface structures using scanning interferometry. Complex surface structures include, for example, thin films, separate structures of different materials, or separate structures that cannot be resolved sufficiently with the optical resolution of an interference microscope. Such measurements are related to the characterization of flat panel display components, semiconductor wafer metrology, and in-situ thin film and foreign material analysis.

  Interferometry techniques are widely used to measure the surface profile of an object. In order to perform the measurement, the interferometer generates an interferogram by combining the measurement wavefront reflected from the target surface and the reference wavefront reflected from the reference surface. The fringe in the interferogram indicates a spatial change between the target surface and the reference surface.

  Typically, a scanning interferometer has an optical path length difference (OPD) between the reference and measurement legs of the interferometer that is comparable to or longer than the coherence length of the interference wavefront. Scanning to generate a scanning interferometry signal for each camera pixel used to measure the interferogram. If a white light source is used, a limited coherence length can be generated. This is referred to as scanning white light interferometry (SWLI). A typical scanning white light interferometry (SWLI) signal is a small number of fringes localized near the zero optical path difference (OPD) position. Signal characteristics are typically sinusoidal carrier modulation ("fringe") with a bell-shaped fringe contrast envelope. The traditional idea underlying SWLI metrology is to measure the surface profile using localized fringes.

  There are two principal trends in SWLI processing technology. The first approach is to find the position of the peak or center of the envelope. In this case, it is assumed that this position corresponds to the zero optical path difference (OPD) of the two beam interferometer. One beam of the two-beam interferometer reflects from the object surface. The second approach is to convert the signal to the frequency domain and calculate the phase change rate with respect to wavelength. In this case, it is assumed that the gradient that is basically linear is directly proportional to the object position. See, for example, US Pat. No. 1,398,113 (Peter de Grot). This latter approach is referred to as frequency domain analysis (FDA).

  Unfortunately, such assumptions may not work when applied to a test object provided with a thin film. The reason is that reflection occurs not only at the top surface but also at the underlying film / substrate interface. Recently, US Pat. No. 6,545,763 (SW Kim and GH Kim) disclosed a method for dealing with such structures. In this method, the frequency domain phase profile of the SWLI signal for the thin film structure is matched to the estimated frequency domain phase profile for various film thicknesses and surface heights. The exact film thickness and surface height were determined by performing optimization simultaneously.

Complex surface structures such as patterned semiconductor wafers consist of features of different materials of various sizes, such as sizes from a few millimeters to tens of nanometers.
Currently, the quantitative measurement of surface topography is of considerable interest, especially in various industries, including the semiconductor industry. Due to the small size of typical chip features, the equipment used to make these measurements typically must have a high spatial resolution both parallel and perpendicular to the chip surface. Engineers and scientists use surface topography measurement systems to control processes and detect defects that occur during manufacturing, particularly defects that result from processes such as etching, polishing, cleaning, and patterning.

  In the semiconductor industry, non-optical measurement tools such as a top-down critical dimension (CD) scanning electron microscope (SEM) and an atomic force microscope (AFM) are widely used to acquire pattern and topography information. Both of these techniques have the required horizontal resolution, but have the disadvantage that they are very slow and require a significant amount of time to collect data over a large area of the wafer. This is particularly seen with AFM. A top-down CD SEM can be programmed to automatically collect data from a specific region of a set of wafers, but the time required to collect complete wafer data, even with this feature Is very long.

  Conventional optical surface profilers such as confocal, interference, or gradient sensors overcome some of the problems described above, but at very close intervals where the surface features are very small to be accurately resolved. Some, or both, are generally unusable if they result in inaccurate surface height changes.

  Conventional interference microscopes measure the surface profile by directly relating the interference phase to the optical path difference between the reference surface and the measurement surface. The microscope is typically limited in lateral resolution to about one wavelength of illumination of the light source.

  Scanning white light interference microscopes, also known as probe microscopes, laser radars, and vertical scanning interferometers that measure surface profiles, use the limited coherence of white light (more commonly broadband) illumination. It helps individual surface features, rough surface structure, and narrow line surface profiling. The microscope is typically limited in lateral resolution to about one wavelength of illumination of the light source. Some of these systems may be arranged to measure the thickness of the membrane.

  The scatterometer determines surface characteristics by matching the distribution of scattered or diffracted light to a pre-calculated library of scattered or diffracted light from a nominal structure. Scatterometers, unlike interferometers, do not directly measure the surface profile relative to a reference. Scatterometers generally operate only with a limited set of 2D structures.

A confocal microscope partitions a target object in a vertical direction using a limited depth of focus to determine a surface profile or the like.
Nomarski microscopes and other differential techniques measure differences in surface height by comparing with each other.

  Ellipsometers measure thin films of objects and different material structures using polarized light and Fresnel reflection coefficient at high angles of incidence. In general, the feature of interest is large compared to the wavelength of the light source, and the ellipsometer does not provide surface profile information.

  The inventor has found that there is a large amount of information in the scanning interferometry signal. This information is almost ignored in conventional processing. In the case of complex surface structures, for example, in the case of thin films or surface features that cannot be sufficiently resolved (ie, lateral surface features that are smaller than the spatial resolution of an interference microscope), the performance of conventional processing techniques may be reduced. . Prior art is based on identifying the peak location in the fringe contrast envelope or calculating the slope for the frequency domain phase profile. However, according to the novel processing technique disclosed herein, surface height information and / or information about its complex surface structure can be extracted.

  For example, if it is not assumed that the surface height information is directly related to the peak in the fringe contrast envelope, in some embodiments of the present invention, the surface height changes to If the scanning interferometry signal changes, otherwise, the shape of the scanning interferometry signal is maintained. In particular, when characterizing complex surface structures, the shape of the scanning interferometry signal is useful. This is because the shape of the signal is independent of the surface height. Similarly, in the frequency domain, it is assumed in some embodiments that a linear term is introduced into the frequency domain phase profile by changing the surface height. This is assumed even if the frequency domain profile itself is not linear. However, the frequency domain amplitude profile does not change when the surface height changes. Thus, frequency domain amplitude profiles are particularly useful in characterizing complex surface structures.

  If complex surface structures are characterized, the surface height can be determined efficiently. For example, a peak can be generated at the scan coordinates corresponding to the surface height by cross-correlation between the scanning interferometry signal and a model signal having a shape corresponding to a complex surface structure. Similarly, in the frequency domain, phase effects due to complex surface structures can be subtracted from the frequency domain phase profile. The surface height can also be extracted using conventional FDA analysis.

  Examples of complex surface structures include the following. Simple thin film (in this case, for example, the variable parameter of interest may be film thickness, film refractive index, substrate refractive index, or some combination thereof); multilayer thin film; diffracted or otherwise Sharp edges and surface features that generate complex interference effects; untreated surface roughness; untreated surface features, eg sub-wavelength grooves on otherwise smooth surfaces; different materials (eg, surface May contain a combination of thin film and solid metal, in which case the library will include both surface structure types and automatically identify the thin film or solid metal by matching against the corresponding frequency domain spectrum. Optical activity such as surface structures that produce fluorescence; surface spectroscopic properties such as color and wavelength dependent reflectivity; surface polarization Presence of characteristic, distortion of the surface or deformable surface features leading to disturbance of the interference signal, vibration or movement.

  In some embodiments, the limited coherence length of the light used to generate the scanning interferometry signal is based on a white light source, more generally a broadband light source. In other embodiments, the light source may be monochromatic and the limited coherence length uses a high numerical aperture (NA) to send light to and / or receive light from the test object. Can be generated. Due to the high NA, the light ray contacts the test surface over a range of angles and various spatial frequency components are generated in the recorded signal when the OPD is scanned. In further embodiments, limited coherence can be generated from a combination of both effects.

  The cause of the limited coherence length is also the physical basis for the presence of information in the scanning interferometry signal. That is, the scanning interferometry signal includes information about a complex surface structure. The reason is that this signal is generated by contacting the test surface with many different wavelengths and / or many different angles.

  In the processing techniques described herein, information that can be derived from the scanning interference spectral signal for the first surface location of the test object (including the scanning interference spectral signal itself) corresponds to multiple models of the test object. Compare with the information you want. The multiple models are parameterized by a series of characteristics for the test object. For example, the test object can be modeled as a thin film, and the set of properties can be a set of values for the thickness of the thin film. The information being compared may include, for example, information about the frequency domain phase profile, and may further include information about the shape of the scanning interferometry data and / or information about the frequency domain amplitude profile. In addition, all the models correspond to a fixed surface height at the first surface location of the test object in order to focus the comparison on a complex surface structure rather than a surface height at the first surface location. can do. The comparison itself can be based on the calculation of a merit function that indicates the similarity between the information from the actual scanning interferometry signal and the information from each model. For example, a merit function may indicate a fit between information derivable from scanning interferometry data and a function parameterized by a set of characteristics.

  Further, in some embodiments, the set of characteristics corresponds to the characteristics of the test object at a second location that is different from the first location. Examples of such a test object include a diffractive surface structure that affects an interface signal with respect to the first surface portion. Therefore, in many cases, the complex surface structure is anything other than the surface height at the first surface location corresponding to the scanning interference spectral signal, but the complicated surface structure corresponds to the scanning interference spectral signal. It may correspond to a surface height feature that is spaced from the first surface location.

  In a further embodiment, the information derivable from the scanning interferometry signal is an estimate for the relative surface height at the first location. This information is the apparent height at the first surface location when the interferometry system measures different values of the actual surface height profile (considering the effects of features that cannot be fully resolved at multiple surface locations). Compared to the model that calculates Based on the comparison, the accuracy of the surface height measurement is increased, such as by selecting the actual surface height used in the model that produced the apparent height most similar to the actual measurement.

  More generally, the information is derived from scanning interferometry signals at multiple surface locations (assuming that at least some of the surface features present at that location cannot be sufficiently resolved), and the information is sufficient to be of interest. Compared to a model that calculates how the information looks as a function of different values that parameterize features that cannot be decomposed into For example, the derivable information may correspond to an observation surface profile determined using a conventional scanning interference spectroscopy algorithm. The features that are not sufficiently resolved that are of interest affect the observed surface profile that is obscured by this surface profile, and the information about the features that cannot be fully resolved is compared to various models. It can be extracted from the profile.

  For example, individual lines of a grating structure that cannot be sufficiently resolved are not evident in the surface profile observed from conventional processing of interferometric signals at multiple surface locations. Nevertheless, the inventor has shown that the actual modulation depth of the grating structure can be correlated with the surface height of a well-defined collection of grating structures in the surface profile obtained from a conventional processed scanning interferometry signal. I found it.

  The observed surface height of the collection of lattice structures is an example of the “apparent” property of the test surface. In other words, it is an example of a property that relates to how the test surface appears to the measuring instrument because it includes features that the test surface cannot sufficiently decompose. Such apparent characteristics are compared with various models of the expected response of the instrument that are parameterized by different values that characterize incompletely resolved features of the test surface. The comparison shows which of the different values gives the expected response that most closely resembles the observed response, and for the incompletely resolved features of the test object based on the apparent characteristics obtained from the scanning interferometry signal Providing information.

  The measurement techniques and later analysis approaches described herein are applicable to several semiconductor processing stages. Through the use of optical proximity correction and / or a phase shift mask, the size of the patterned object may be smaller than the wavelength used by the optical lithography tool. For example, 193 nm lithography tools routinely pattern 65 nm objects in today's high-capacity manufacturing facilities, and the lower limit is expanded to 45 nm or less through the use of etch bias steps and hard mask structures. With the ability to print subwavelength features, there is a need to monitor these features and the associated etching and deposition steps. Embodiments of the present disclosure allow for the measurement of nested patterned structures, where nesting is defined as a repetitive surface structure of known shape whose periodicity is comparable to the lateral dimensions of the structure. . In particular, the nested structure is a process step for isolation patterning and etching, polysilicon gate electrode patterning and etching, source / drain etching and deposition, and multiple front end metallization patterning, etching and polishing processes. Can be used for monitoring. Further applications include measuring resistance on certain films / substrates. The exposure and focus curves are characterized by changes in line width and depth that can be measured using the apparatus and method of the present invention.

  As an example of such in-process metrology measurements of semiconductor chips, scanning interferometry measurements can be applied to non-contact surface topography measurement semiconductor wafers during chemical mechanical polishing (CMP) of the dielectric layer on the wafer. It is mentioned to use. CMP is used to form a smooth surface for the dielectric layer. A smooth surface is suitable for precision photolithography. Based on the results of the interferometric topography method, process conditions for CMP (eg, pad pressure, polishing slurry composition, etc.) can be adjusted to keep the surface non-uniformity within acceptable limits.

The various aspects and features of the invention will now be summarized.
In general, in one aspect, (i) comparing information derivable from a plurality of scanning interferometry signals corresponding to different surface locations of the test object and information corresponding to a plurality of models of the test object. Where the models are parameterized by a set of characteristics associated with one or more sufficiently unresolved lateral features of the test object, and (ii) cannot be sufficiently resolved based on the comparison A method comprising outputting information about surface features is disclosed.

Embodiments of the method may include any of the following features.
One or more sufficiently unresolved lateral features of the test object are one of pitch, modulation depth, and element width for a patterned lateral structure that is not fully resolved on the test object. Or you may respond | correspond to two or more. For example, the series of characteristics may include different values for the modulation depth. In addition, multiple models are represented by correlations that map possible results for information derivable from multiple interferometric spectral signals to one corresponding value of different values for modulation depth, and comparing Determining which of the different values for depth corresponds best to information derivable from a plurality of interferometric spectral signals may be included.

The modulation depth may be expressed relative to the bias offset value.
At least some interferometric signals may be obtained from illumination of the test object that is directed against the lateral structure of the patterned element. For example, the polarized light may be linearly polarized light (referred to herein as x-polarized light) that is aligned perpendicular to the length of the individual elements that form the patterned lateral structure.

  One or more sufficiently unresolvable lateral features of the test object may correspond to one or more of the step height and position of the test object. For example, the set of characteristics may include different values for the step height or position.

  Information derivable from a plurality of interferometry signals may include one or more values extracted from a height profile for a test object derived from the plurality of interferometry signals, and surface features that cannot be sufficiently resolved are The extracted height profile is ambiguous or does not appear. For example, the test object may include a patterned lateral structure that is unclear or does not appear in the height profile from which the individual elements are extracted.

  The information derivable from the plurality of interferometry signals may be a height value for a collection of elements that cannot be fully resolved in a patterned lateral structure extracted from a height profile. Information about surface features that cannot be fully resolved may correspond to one or more of the modulation depth and element width for the patterned lateral structure.

  The different surface locations for the interferometry signal may include a reference portion of the test object that provides a reference height value for the extracted height profile. For example, the test object may be etched to form a patterned structure, and the reference portion of the test object may be part of a test object that is known not to be etched.

  At least some interferometric spectral signals from which the height profile is determined may be obtained from illumination of the test object that is directed against the lateral structure of the patterned element. For example, the polarized light may be linearly polarized light (x-polarized light) that is aligned perpendicular to the length of the individual elements that form the patterned lateral structure.

  The height profile may be obtained from a frequency domain analysis of the interferometry signal. Alternatively, the height profile may be obtained from the relative position of the coherence peak in each interferometry signal. The height profile may be obtained using other methods.

Lateral features that cannot be fully resolved of the test object may include feature sizes of less than 400 nm, less than 200 nm, and even less than 100 nm.
The model may be generated computationally using rigorous coupled wave analysis (RCWA).

The model may be generated experimentally from a test object with known properties.
Information about surface features that cannot be sufficiently resolved may be output to the user.
Information about surface features that cannot be fully resolved may be output to an automated process control system for semiconductor manufacturing.

  The interference spectral signal may be a scanning interference spectral signal. For example, the test light generated from the test object is imaged and interfered with the reference light on the detector, and the optical path length from the common light source to the detector between the interference part of the test light and the interference part of the reference light The scanning interference spectral signal is generated by changing the difference, the test light and the reference light are extracted from a common light source, and the scanning interference spectral signal is measured by the detector when the optical path length difference is changed. Corresponding to The method further includes generating a scanning interferometry signal.

  Such a scanning interference spectral signal may be a low coherence scanning interference spectral signal. For example, the test light and the reference light may have a spectral bandwidth greater than 5% of the center frequency for the test light and the reference light, and the optical path length difference is greater than the spectral coherence length corresponding to the bandwidth. Changing over a long range, a scanning interferometry signal is generated. Low coherence is obtained by defining the numerical aperture for the test light to a value greater than 0.8 using an optical component that sends the test light onto the test object and images it onto the detector. Also good. In order to reduce the coherence length, the common light source may be a spatially extended light source.

  In another related aspect, a processor in a computer compares information derivable from a plurality of interferometric signals corresponding to different surface locations of the test object with information corresponding to a plurality of models of the test object, Here, the multiple models are parameterized by a set of characteristics associated with one or more sufficiently unresolved lateral features of the test object, and based on comparisons, the surface features for the unresolved surface features An apparatus comprising a computer readable medium having a program for outputting information is disclosed.

  In another related aspect, (i) an interferometry system configured to generate a plurality of interferometry signals corresponding to different surface locations of the test object; and (ii) connected to the interferometry system and interferometry An electronic processor for receiving signals, comparing information derivable from a plurality of interferometric spectral signals with information corresponding to a plurality of models of the test object, wherein the models are An electronic processor programmed to output information about surface features that are parameterized by a set of characteristics associated with one or more insufficiently resolvable lateral features and that are not sufficiently resolvable based on the comparison; An apparatus comprising: is disclosed.

These two device embodiments may include any of the features described above for the corresponding method.
In another aspect, a method for determining one or more spatial properties of a grating structure on a test object, wherein the grating element comprises a line element having a width of less than 400 nm, so that the line element is completely removed by an interference microscope. A method is disclosed that cannot be decomposed. The method includes: (i) determining an apparent height for a collection of at least some grid lines from interference signals at different locations of the test object measured by an interference microscope; (ii) to the characteristics of the grid structure Providing the expected response of the interference microscope for different possible values, the expected response includes the effects from line elements that cannot fully resolve the lattice structure, and (iii) the apparent height is the expected response for the different possible values Comparing to determine information about the spatial properties of the lattice structure, and (iv) outputting the determined information about the spatial properties of the lattice structure.

In addition to the above features, embodiments of the method may include any of the following features.
The apparent height may be determined with reference to a reference portion of the test object.
The interference microscope may illuminate the grating structure with light that is polarized perpendicular to the length of the individual grating lines (x-polarized light) when determining the apparent height.

The determined information about the spatial properties of the lattice structure may correspond to the modulation depth for the lattice structure.
The lattice structure may be a series of periodically spaced lines formed at least partially by etching portions between lines of the test object.

  The interference signal forms an image of the test light generated from the test object and causes it to interfere with the reference light on the detector. From the common light source to the detector between the interference part of the test light and the interference part of the reference light, It may be a scanning interference spectral signal generated by changing the optical path length difference, and the test light and the reference light are extracted from a common light source, and each scanning interference spectral signal is measured by the detector when the optical path length difference is changed. Corresponding to the interference intensity. For example, the optical path length difference may be changed over a range longer than the coherence length of the interference microscope.

  In a related aspect, an apparatus for determining one or more spatial properties of a grating structure on a test object, the grating structure comprising line elements having a width of less than 400 nm, so that the line elements are detected by an interference microscope. In an apparatus that cannot be fully resolved, a processor in a computer 1) determines the apparent height for at least some collection of grid lines from interference signals at different locations of the test object measured by an interference microscope, 2 ) Provide the expected response of the interference microscope for different possible values to the properties of the lattice structure, where the expected response includes the effects from line elements that cannot be fully resolved of the lattice structure, and 3) the apparent height, 4) determining the information about the spatial properties of the lattice structure by comparison with the expected response for different possible values; Apparatus comprising a computer-readable medium having a program for outputting information determined on the properties is disclosed.

  In another related aspect, an apparatus for determining one or more spatial characteristics of a grating structure on a test object, the line element comprising a line element having a width of less than 400 nm, so that the line element is an interference microscope In an apparatus that cannot be completely resolved by an interference microscope and an electronic processor connected to the interference microscope, 1) of at least some grid lines from interference signals at different points of the test object measured by the interference microscope Determining the apparent height for the cluster, 2) providing the expected response of the interference microscope for different possible values to the properties of the grating structure, where the expected response is from line elements that are not sufficiently resolvable of the grating structure 3) The apparent height is compared with the expected response to different possible values to determine information about the spatial properties of the lattice structure. And, 4) device and a programmed electronic processor to output the information determined about the spatial properties of the grating structure is disclosed.

These two device embodiments may include any of the features described above for the corresponding method.
In another aspect, (i) determining one or more apparent characteristics of the test surface from an interferometric signal generated by the interferometric system; (ii) an apparent characteristic determined from the interferometric signal; Comparing to the expected response of the interferometry system for different possible values to one or more sufficiently unresolvable features of the test surface; (ii) one or more sufficiently unresolved of the test surface based on the comparison A method comprising outputting information about a feature is disclosed.

In addition to the above features, embodiments of the method may include any of the following features.
The interferometry system may be a scanning interferometry system.
The apparent characteristics of the test surface may be determined from the interference spectroscopic signal based on changes in any of the interference phase, interference contrast, and surface reflectivity.

Expected responses may be calculated for changes in one or more of surface height and surface composition.
The test surface has a patterned structure with modulation depth, periodicity, and wide elements, and the expected response is calculated for changes in one or more of the modulation depth, periodicity, and element width. May be. For example, the expected response may be calculated for changes in modulation depth.

  The correspondence between the actual modulation depth and the apparent modulation calculated for the expected response is in the positive correlation over the first range of actual modulation depth and the second range of actual modulation depth. It may include negative correlations over time.

  Information about one or more unresolvable features includes isolation patterning and etching, polysilicon gate electrode patterning and etching, source / drain etching and deposition, and metallization patterning, etching, and It may be used to monitor one or more semiconductor processing steps, such as a polishing process.

  In another related aspect, a processor in a computer 1) determines one or more apparent characteristics of a test surface from an interferometry signal generated by an interferometry system, and 2) is determined from the interferometry signal. Comparing the apparent properties with the expected response of the interferometry system to different possible values for one or more well-resolved features of the test surface, 3) based on the comparison, one or more of the test surface An apparatus is disclosed that comprises a computer-readable medium having a program that outputs information about features that cannot be sufficiently resolved.

  In another related aspect, an interferometry system configured to generate a plurality of interferometry signals corresponding to different surface locations of a test object, and an electronic processor connected to the interferometry system and receiving the interferometry signals 1) determining one or more apparent characteristics of the test surface from the interferometry signal, and 2) apparent characteristics determined from the interference spectroscopic signal and one or more fully resolved test surfaces. Programmed to output the information about the one or more unresolvable features of the test surface based on the comparison, comparing the expected response of the interferometry system to different possible values for the impossible feature An apparatus comprising an electronic processor is disclosed.

These two device embodiments may include any of the features described above for the corresponding method.
In another aspect, (i) determining one or more apparent properties of the test surface from an interferometry signal (eg, an operational interferometry signal) generated by the interferometry system, (ii) a test surface (eg, Providing the expected response of the interferometric microscope to different possible values for the properties of the surface height and the change in surface composition (s), where the expected response is from a sufficiently unresolvable feature of the test surface A method is disclosed that includes affecting and (iii) improving the accuracy of the determined characteristic compared to the apparent characteristic determined from the interferometric spectral signal and an expected response to different values of the characteristic.

Embodiments of the method may include any of the following features.
The apparent characteristics of the test surface may be determined from the interference spectroscopic signal based on changes in any of the interference phase, interference contrast, and surface reflectivity.

  Expected responses may be calculated for changes in one or more of surface height and surface composition. For example, the test surface has a patterned structure (eg, a grating) with modulation depth, periodicity, and width elements, and the expected response is that of modulation depth, periodicity, and element width. It may be calculated for changes in one or more.

  The correspondence between the actual characteristic associated with the interferometric signal and the actual value of the characteristic used to generate the model is the result of the positive correlation and the actual modulation over the first range of actual modulation depths. It may include a negative correlation across the second range of depths. For example, in a specific embodiment, the expected response may be calculated for changes in modulation depth. In such a case, the correspondence between the actual modulation depth and the apparent modulation calculated for the expected response is the positive correlation over the first range of actual modulation depth and the actual modulation depth. A negative correlation over the second range may be included.

  In further embodiments, a feature that cannot be fully resolved may be a single trench, step, or protrusion, rather than a series of elements as in a patterned structure. In such an example, the information from the actual signal and the information for the model may correspond to any of the feature depth (in the case of steps or protrusions) and location or width.

  The method further includes monitoring the semiconductor processing stage using the measured properties of the test surface with improved accuracy. For example, processing steps may include any of isolation patterning and etching, polysilicon gate electrode patterning and etching, source / drain etching and deposition, metallization patterning, etching, and polishing processes, etc. .

  In another aspect, a processor in a computer can cause the apparent characteristics of the test surface determined from the interferometry signal generated by the interferometry system and the expected response of the interference microscope to different possible values for the test surface characteristics. A method is disclosed comprising a computer readable medium having a program that includes a program for improving the accuracy of a characteristic determined based on the comparison, wherein the expected response includes effects from features that are not sufficiently resolved of the test surface. .

  In yet another aspect, an interferometry system configured to generate interferometry and an electronic processor coupled to the interferometry system and receiving the interferometry signal, the interferometry signal generated by the interferometry system Compare the apparent properties of the test surface determined from the interference microscope's expected response to different possible values for the test surface properties, where the expected response is an effect from the incompletely resolved characteristics of the test surface And an electronic processor programmed to improve the accuracy of the characteristic determined based on the comparison.

  Embodiments of such devices may include any of the features described above along with corresponding methods. In general, in another aspect, features of the present invention compare information derivable from scanning interferometry signals for a first surface location of a test object with information corresponding to multiple models of the test object. The plurality of models is a method that is parameterized by a set of characteristics for the test object.

Embodiments of the invention may include any of the following features.
The method may further include determining an exact characteristic for the test object based on the comparison.

  The method may further include determining a relative surface height relative to the first surface location based on the comparison. Determining the relative surface height is based on a comparison that determines which model corresponds to the exact one of the properties for the test object, using a model that corresponds to the exact property. It may include calculating the relative surface height.

  For example, using a model corresponding to the exact characteristic may include correcting data from the scanning interferometry signal to reduce the effects resulting from the exact characteristic. Correcting the data includes extracting the phase effect resulting from the exact characteristic from the phase component of the transform of the scanning interferometry signal on the test object, and using the model corresponding to the exact characteristic further It may include calculating the relative surface height from the phase component of the transformation after removing the phase effect resulting from the exact characteristic.

  In another example, calculating the relative surface height using a model corresponding to the exact property is used to compare information for the test object with information for the model corresponding to the exact property. Determining the position of the peak in the correlation function.

  The method may further include comparing information derivable from the scanning interferometry signal for additional surface locations with information corresponding to the plurality of models. The method may also further include determining a surface height profile for the test object based on the comparison.

Comparing may include calculating one or more merit functions that indicate the similarity between information derivable from the scanning interferometry signal and information corresponding to each model.
Comparing may include fitting information derivable from the scanning interferometry signal into a representation for the information corresponding to the model.

  The information corresponding to the plurality of models may include information on at least one amplitude component of the converted part (for example, Fourier transform part) of the scanning interference spectral signal corresponding to each model of the test object. Similarly, information derivable from the scanning interference spectral signal may include information on at least one amplitude component of the converted scanning interference spectral signal for the test object.

Comparing may include comparing the relative strength of the at least one amplitude component for the test object with the relative strength of the at least one amplitude component for each model.
The information corresponding to the plurality of models may be a function of coordinates with respect to the converted amount. For example, the information corresponding to a plurality of models may include a converted amplitude profile for each model. Further, the comparing may include comparing the amplitude profile of the converted scanning interference spectral signal for the test object with each amplitude profile for the model.

  Comparing may further include comparing information in the phase profile of the conversion of the scanning interferometry signal for the test object with information in the phase profile of the conversion for each model. For example, the information in the phase profile may include information about the non-linearity of the phase profile with respect to the transformed coordinates and / or information about the phase shift value.

  The information that can be derived and compared from the scanning interferometry signal may be a number. Alternatively, the information that can be derived and compared from the scanning interferometry signal may be a function. For example, the function may be a scan position function or a spatial frequency function.

  Information about the test object may be obtained by transforming the scanning interference spectral signal for the test object into the spatial frequency domain (eg, Fourier transform). The information on the test object may include information on the converted amplitude profile and / or the converted phase profile.

  Information about the test object may relate to the shape of the scanning interferometry signal at the first location of the test object. For example, the information for the test object may relate to the fringe contrast amplitude in the shape of the scanning interferometry signal. It may also relate to the relative spacing between zero crossings in the shape of the scanning interferometry signal. Alternatively, it may be expressed as a function of the scanning position, and the function may be obtained from the shape of the scanning interference spectral signal.

  Comparing may include calculating a correlation function (eg, a complex correlation function) between information for the test object and information for each model. Comparing may further include determining one or more peak values in each correlation function. And the method may further comprise determining an exact characteristic for the test object based on the parameterization of the model corresponding to the maximum peak value. Alternatively or additionally, the method further includes determining a relative surface height at the first surface location of the test object based on coordinates for at least one peak value in the correlation function. Also good.

The plurality of models may correspond to a fixed surface height at the first location of the test object.
The set of characteristics may include a set of values for at least one physical parameter of the test object. For example, the test object may include a thin film layer having a thickness, and the physical parameter may be the thickness of the thin film at the first location.

  The set of properties may include a set of properties of the test object at a second surface location that is different from the first surface location. For example, the test object may include a structure at a second surface location that diffracts light and affects a scanning interference spectral signal for the first surface location. In one example, the set of characteristics at the second surface location may include a substitution of the amplitude for the step height at the second location and the position for the second location. In another example, the series of characteristics at the second surface location may include permutation of the modulation depth relative to the grating and the offset position of the grating, and the grating may extend across the second location.

  Furthermore, the information derivable from the interference spectroscopic signal may correspond to an estimate for the relative surface height of the first surface location. For example, the relative estimate of the first surface location may be based on a frequency domain analysis of the interference spectroscopic signal, or the relative surface height estimate of the first surface location is a coherence in the interferometry signal. -It may be based on the relative position of the peak.

  The method compares information derivable from interference spectroscopy signals for one or more additional surface locations of the test object, including the second surface location, with information corresponding to multiple models of the test object. Further comprising.

  Information derivable from the interferometry signal for the first and further surface locations may correspond to a surface height profile for the test object over a range of surface locations including the first and further surface locations. Furthermore, the information corresponding to the plurality of models is determined by the interference spectroscopy system used to generate the interference spectroscopy signal when using conventional processing of the interference spectroscopy signal for each of the plurality of models of the test object. The expected surface height profile may be generated, the expected surface height profile including the effects from features that cannot be sufficiently resolved to produce an interference signal for the first surface location, and the second surface. Includes effects related to the test object at the location. For example, the test object may include a structure at a second surface location that diffracts light and affects a scanning interference spectral signal for the first surface location.

  In one example, the test object includes a patterned structure extending across the first and further surface locations, and the information derivable from the scanning interferometry signal for the first and further surface locations is the pattern May include an estimate for at least one of a modulation depth for the patterned structure, a periodicity for the patterned structure, and a width for each element of the patterned structure.

  Similarly, as an example of a patterned structure, the set of characteristics at the second surface location is the modulation depth for the patterned structure, the periodicity for the patterned structure, and the first surface location. Different values for at least one of the widths for each element of the patterned structure may be included.

  In further embodiments, a feature that cannot be fully resolved may be a single trench, step, or protrusion, rather than a series of elements as in a patterned structure. In such an example, the information from the actual signal and the information for the model may correspond to any of the feature depth (in the case of steps or protrusions) and location or width.

  Information derivable from the interferometry signal may correspond to an estimate for the relative surface height of the first surface location, and the set of characteristics at the second surface location is relative to the second surface location. A series of values for different surface heights may be supported.

  For example, the test object may include a patterned structure that spans first and second surface locations, and an estimate for the relative surface height of the first surface location is a modulation of the patterned structure. Corresponding to an estimate for depth, a series of values for relative surface height at the second surface location corresponds to the modulation depth for the patterned structure. The multiple models may improve the estimation for the modulation depth by correlating different estimates for the modulation depth with a corresponding one value.

  In some embodiments, the plurality of models correlate information derivable from the interferometry signal with corresponding values for information for the plurality of models, the correspondence changing from a positive correlation to a negative correlation.

  For example, in the case of a patterned structure, the correlation between the different estimate for the modulation depth and the corresponding value for the modulation depth from the model changes from a positive correlation to a negative correlation.

  The method may include determining an accurate characteristic for the test object, such as a relative surface height relative to the first surface location, based on the comparison. For example, determining the relative surface height can be based on a comparison to determine which model corresponds to the exact one of the properties for the test object, and the model corresponding to the exact property. May be used to determine relative surface height. The series of properties may be a series of surface materials for the test object.

The series of properties may be a series of surface layer configurations for the test object.
The scanning interferometry signal may be generated by the scanning interferometry system and comparing may include defining systematic effects on the scanning interferometry signal that results from the scanning interferometry system. For example, the systematic effects may include information about the dispersion of phase changes upon reflection from components of the scanning interferometry system. The method may further include comparing information derivable from the scanning interferometry signal for additional surface locations with information corresponding to the plurality of models. In this case, systematic influences may be analyzed for a plurality of surface locations. The method may further include calibrating the systematic effects of the scanning interferometry system with other test objects of known characteristics.

  The generation of the scanning interferometry signal is formed by imaging the test light emerging from the test object and causing it to interfere with the reference light on the detector, and a common light source between the interference part of the test light and the interference part of the reference light The scanning interferometry signal changes the optical path length difference by extracting the test light and the reference light from a common light source (eg, a spatially extended light source) by changing the optical path length difference from the sensor to the detector. May correspond to the interference intensity measured by the detector.

The test light and the reference light may have a spectral bandwidth greater than 5% of the center frequency for the test light and the reference light.
The common light source may have a spectral coherence length, and the optical path length difference may be changed over a range longer than the spectral coherence length to generate the scanning interference spectral signal.

The numerical aperture for the test light may be defined to a value greater than 0.8, depending on the optical components used to send the test light onto the test object and image it on the detector.
The method may further include generating a scanning interferometry signal.

  In another aspect, the invention features a processor in a computer that can derive information from a scanning interferometry signal for a first surface location of a test object and information corresponding to a plurality of models of the test object. An apparatus including a computer readable medium having a program for comparing the plurality of models, wherein the plurality of models are parameterized by a series of characteristics for the test object.

The apparatus may include any of the features described above in connection with the method.
In another aspect, the invention features a scanning interferometry system configured to generate a scanning interferometry signal and an electronic processor coupled to the scanning interferometry system to receive the scanning interferometry signal, An apparatus comprising: an electronic processor programmed to compare information derivable from scanning interferometry signals for a first surface location of a test object with information corresponding to a plurality of models of the test object. Thus, the multiple models are devices that are parameterized by a series of characteristics for the test object.

The apparatus may include any of the features described above in connection with the method.
In general, in another aspect, features of the present invention include chemical mechanical polishing of a test object, collecting scanning interferometry data for the surface topography of the test object, and scanning interferometry data Adjusting the process conditions for chemical mechanical polishing of the test object based on the information obtained from the method. For example, the process conditions may be pad pressure and / or polishing slurry composition. In a preferred embodiment, adjusting the process conditions based on information obtained from scanning interferometry data includes information derivable from scanning interferometry signals for at least a first surface location of the test object, and the test object. The plurality of models may be parameterized by a series of characteristics for the test object. The analysis of the scanning interferometry signal may further include any of the features described above in conjunction with the first described method.

  Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. In case of conflict with publications, patent applications, patents, and other references mentioned and incorporated herein by reference, the specification, including definitions, will be reviewed.

  For example, as used herein, a scanning interferometer involves a mechanical scan of the relative optical path length between a reference leg and a measurement leg, but a scanning interferometer is an additional technique that changes the relative optical path length. Intended to include non-mechanical means. For example, the interferometric spectral signal can be generated by changing the center frequency of the light source over a range of wavelengths in an interferometer with unequal path lengths (ie, different nominal optical path lengths for the reference and measurement paths). . Since different wavelengths have different optical path lengths, different phase shifts occur with respect to the reference path and the measurement path, and the phase shift is changed between the paths.

  Further, it is understood that the term “light” may be limited to electromagnetic radiation in the visible spectrum, but as used herein, the term “light” includes ultraviolet, visible, near infrared, And is intended to include electromagnetic radiation in all infrared spectral regions.

  Other features, objects, and advantages of the present invention will become apparent from the following detailed description.

FIG. 1 is a flow chart that schematically illustrates one embodiment of the present invention in which scanning interferometry data is analyzed in the spatial frequency domain.
Referring to FIG. 1, to measure data from the surface of a test object, an optical path difference (OPD) between a reference path and a measurement path is mechanically or electro-optically scanned using an interferometer. To do. The measurement path is directed to the object surface. The OPD is a function of the local height of the object surface at the start of the scan. A plurality of camera pixels correspond to different surface locations on the surface of the object, and the computer records an interference intensity signal during OPD scanning for each camera pixel. Next, after storing the interference intensity signal as a function of the OPD scan position for each of the different surface locations, the computer performs a transform (eg, a Fourier transform) to generate a frequency domain spectrum of the signal. The spectrum includes both amplitude information and phase information as a function of the spatial frequency of the signal in the scan range. For example, a suitable frequency domain analysis (FDA) for generating such a spectrum is disclosed in the following document. Commonly owned US Pat. No. 5,398,113 (Pita de Groot), title of invention “Method and apparatus for surface topography measurement by spatial frequency analysis of interferogram”. The contents of this document are incorporated herein by reference.

  In separate steps, the computer generates a theoretical prediction library for the frequency domain spectrum for various surface parameters and a model for the interferometer. These spectra may cover a range of possible thin film thicknesses, surface materials, and surface textures, for example. In a preferred embodiment, the computer generates a library spectrum for a constant surface height, eg height = zero. Thus, in such an embodiment, the information contained in the library has nothing to do with surface topography. The information included is only about the type of surface structure and the interaction of the surface structure, optical system, illumination, and detection system in generating the characteristic features of the frequency domain spectrum. As an alternative, the prediction library may be generated empirically using sample artifacts. As another alternative, the library may receive information from prior supplementary measurements of the object surface provided by other equipment, such as an ellipsometer, and any other input from the user regarding known characteristics of the object surface. It may be used to reduce the number of unknown surface parameters. Any of these approaches to library formation augmented by supplementary measurements, theoretical modeling, empirical data, or theory can be extended by interpolation to provide intermediate values as part of library formation or during library search. It may be generated in real time.

In the next step, the experimental data and the prediction library are compared using a library search that provides surface structure parameters. In the case of a film of unknown thickness, a library for a single surface type, eg SiO ₂ on Si, spans many film thicknesses where the top surface height may always be equal to zero. Another example is surface roughness. In this case, the adjustable parameter may be roughness depth and / or spatial frequency. Library searching provides a match for FDA spectral characteristics that are independent of surface height. Such characteristics are related to, for example, the average value of the amplitude spectrum (related to the overall reflectivity of the surface) or the change in amplitude as a function of spatial frequency (in a monochromatic high NA system, the scattering angle of the reflected light). ).

  The analysis may also include system characterization. System characterization includes, for example, measuring one or more reference workpieces with known surface structure and surface topography to determine system wavefront error, variance, and efficiency (cannot be included in the theoretical model) And determining parameters such as

  Furthermore, the analysis may include an overall calibration. The overall calibration includes, for example, measuring one or more reference workpieces, and measuring these surface parameters, eg, film thickness determined by library search, and those determined independently, eg, by ellipsometry. Determining the correlation between values for parameters.

  Based on the comparison of the experimental data with the prediction library, the computer identifies the surface model that corresponds to the best match. The computer may then display or send the surface parameter results numerically or graphically to a user or host system for further analysis or data storage. Using the surface parameter results, the computer may then determine surface height information in addition to the characteristics specified by the library search. In some embodiments, the computer generates a corrected phase spectrum. This is done, for example, by subtracting the corresponding theoretical phase spectrum directly from the experimental phase spectrum. The computer then determines a local surface height for the one or more surface points. This is done by analyzing the corrected phase as a function of spatial frequency, for example by analyzing the coefficients generated by a linear fit. The computer then generates a complete three-dimensional image constructed from the height data and the corresponding image plane coordinates, along with a graphical or numerical display of the surface characteristics determined by the library search.

  In some cases, library searching and data collection can be performed iteratively to further improve the results. Specifically, the library search can be refined on a pixel-by-pixel basis or on a region basis. This is done by forming a refined library in relation to the local surface type. For example, if during a preliminary library search it is found that there is a thin film of approximately 1 micron on the surface, the computer generates a fine-grained library of example values close to 1 micron to further search. Make it elaborate.

  In further embodiments, the user's interest may be only the surface characteristics modeled by the prediction library, not the surface height. In this case, the step of determining the surface height is not performed. Conversely, the user's interest may be just the surface height, not the surface characteristics that are modeled in the prediction library. In this case, the computer uses a comparison between the experimental data and the prediction library to correct the experimental data for surface property effects. As a result, the surface height is determined more accurately. However, there is no need to determine the surface characteristics clearly or display the characteristics.

  This analysis may be applied to the following various surface analysis problems. The surface analysis task is, for example, a simple thin film (in this case, for example, the variable parameter of interest may be film thickness, film refractive index, substrate refractive index, or some combination thereof); Multilayer thin film; sharp edges and surface features that diffract or otherwise create complex interference effects; untreated surface roughness; untreated surface features, eg, subwavelength widths on otherwise smooth surfaces Different materials (eg, the surface may contain a combination of thin film and solid metal. In this case, the library will include both surface structure types, and the thin film or solid metal may be included in the corresponding frequency domain spectrum. May be automatically identified by matching); optical activity such as fluorescence; surface spectroscopic properties such as color and wavelength dependent reflection ; Including and data distortion associated with the data acquisition procedure; polarization dependence of the properties of the surface; surface distortion or deformable surface features leading to disturbance of the interference signal, vibration or movement. The data acquisition procedure includes, for example, a data acquisition window that does not completely contain interference intensity data.

  The interferometer may include any of the following features. A spectrally narrowband light source having a high numerical aperture (NA) objective lens; a spectrally broadband light source; a combination of a high NA objective lens and a spectrally broadband light source; Objective lenses including, for example, oil / water immersion and solid immersion formats, eg, in Michelson, Mirau, or Linnik geometry; a series of measurements at multiple wavelengths; unpolarized Light: polarized light, eg, linear, circular, or structured polarized light. For example, structured polarized light requires, for example, a polarization mask and produces different polarizations for separate segments of the illumination pupil or imaging pupil, resulting in polarization-dependent optical due to surface properties. You may clarify the effect. The interferometer may also include the overall system calibration described above.

  When comparing theoretical and experimental data, the library search may be based on any of the following: Product or difference between amplitude and / or phase data in the frequency spectrum, eg, average amplitude and average phase, average amplitude itself, and average phase itself product or difference; amplitude spectrum slope, width and / or high Interference contrast; data in frequency spectrum at DC or zero spatial frequency; nonlinearity or shape of amplitude spectrum; zero frequency cutoff of phase; nonlinearity or shape of phase spectrum; and any combination of these criteria. As used herein, amplitude and wave height are used interchangeably.

  Shown in FIG. 2 is a flow chart generally illustrating another embodiment for analysis of scanning interferometry data. The analysis is similar to that described in FIG. 1 except that the comparison between the experimental data and the prediction library is based on information in the scan coordinate domain. The experimental signal feature may be a quasi-periodic carrier vibration modulated in amplitude by an envelope function with respect to the scan coordinate. When comparing theoretical and experimental data, the library search may be based on any of the following: Average signal strength; shape of signal envelope, eg deviation from some ideal or reference shape, eg Gaussian; phase of carrier signal for envelope function; zero crossing and / or signal maximum and minimum relative spacing; maximum and The values for the minimum and their ordering; the peak value of the correlation between the library signal and the measurement signal after adjustment for the optimal relative scan position; and any combination of these criteria.

  In further embodiments, for a library model, information can be derived from experimental signals from multiple surface locations. This is particularly useful when the test object contains surface features that cannot be fully resolved because the experimental information can correspond to the overall surface response of the test surface to interferometry measurements compared to the library model. . For example, the information derived from experimental signals from a plurality of surface locations is the surface profile of the test surface obtained from conventional processing of interference spectroscopy signals, information derived from the surface profile, or the like. Such a treatment provides only the apparent properties of the test surface, since features that cannot be sufficiently resolved are ambiguous. Nevertheless, by comparing the apparent characteristics and the corresponding model of the test object parameterized by values characterizing features that cannot be fully resolved, features that cannot be sufficiently resolved are those that cannot be fully resolved. Properties that are correlated with more accurate information can be left in the apparent surface profile.

  In addition, the test object may include certain reference structures associated with comparing the apparent features with the library model. For example, when comparing various models to the apparent surface height profile of an etched grid pattern where individual lines cannot be sufficiently resolved, some of the test objects that are known not to be etched are This is a reference point for the apparent surface height in the lattice portion.

  Thus, in one embodiment, an interferometric profiler, such as a broadband or low coherence interferometer, that includes both a measurement beam and a reference beam is a complex, uncomplicated product as seen on patterned semiconductor wafers. Used to measure the surface structure characteristics of the treatment. The profiler views changes in interference phase, contrast, and / or surface reflectivity as changes in apparent measured surface height. In a separate step, the data processing means calculates the expected response of the profile to possible changes in the actual surface height and / or surface composition of the surface including the untreated surface structure. The data processing means then compares the apparent measured surface height to the profiler's expected response to possible changes in actual surface height, untreated surface structure, and / or surface composition. Determine true surface properties.

  Prior to, during, or after data acquisition as described above, the data processor will provide the expected response of the instrument to the actual surface height and / or possible changes in surface composition of the surface, including the raw surface structure. calculate. FIG. 25 shows an example of an object having untreated surface features for visible spectroscopy (400-700 nm wavelength) interferometry. Specifically, FIG. 25 shows an arrangement of elements (also referred to herein as patterned structures or lattice structures). The untreated surface feature has a height H, a separation l, and a width d from the adjacent surface S. The height H is also referred to herein as the modulation depth for the patterned structure. “Unprocessed” means that due to the limited lateral resolution of the device, individual features are not well spaced in the surface profile image, have an incorrect profile, and / or have a height H of Means an error.

  FIG. 26 illustrates the unwavelength on the object of FIG. 25 for a visible wavelength interferometer (center wavelength 560 nm, full width half maximum 110 nm bandwidth) and objective lens NA 0.8 using the Rayleigh hypothesis technique (described in detail below). The expected response to the processing feature is shown. Since the surface features are unprocessed, the result is an apparent measured surface profile that is not at all similar to the actual surface structure. In this calculation, height H = 20 nm, separation l = 200 nm, and width d = 120 nm. FIG. 27 shows the raw measured profile of FIG. 26 as a function of the actual height H of the feature. Note that the relationship between measured height and true height is complex and is negatively correlated beyond 40 nm. The latter phenomenon is explained as the difficulty of coupling light into narrow sub-wavelength trenches.

  After obtaining the data and calculating the expected system response, the data processor is responsible for the apparent measured surface height and the actual surface height, raw surface structure, and / or possible changes in surface composition. True surface features are determined by comparing the expected response of the device of the present invention. This is because, based on the example of FIGS. 25 to 27, the relationship between the actual height H and the apparent measured height is determined as shown in FIG. Involves determining the actual height from Alternative forms of measurement include determining the width d and separation l, etc. As described further below, the sensitivity to specific parameters such as etch depth is achieved by polarizing the objective lens, as is done by adjusting the sensitivity range using an alternative light source to change the illumination wavelength. Can be increased.

  A number of processing techniques are used to extract the apparent characteristic or characteristics (eg, apparent surface profile) from the scanning interferometry data. For example, conventional techniques include identifying the position corresponding to the peak or center of the fringe contrast envelope for each pixel, or using frequency domain analysis (FDA) for each pixel, directly with the surface height. Including associating a phase change rate with a proportional wavelength (see, eg, US Pat. No. 5,398,113). Further, US Patent Application Publication No. 2005/0078318 by Peter de Grotto, the title of the invention “Method for interference spectroscopy analysis of surfaces and Application methods related to the system (METHODS AND SYSTEMS FOR INTERFROMETRIA ANALYSIS OF SURFACES AND RELATED APPLICATIONS), and commonly owned US Patent Application No. 11 / 437,002, filed May 18, 2006 Method and system for analyzing low coherence interferometry signals for structural information (METHOD AND SYSTEM FOR ANALYZ) It is also possible to use more advanced processing techniques that attempt to eliminate thin film effects from interferometric spectral signals, as disclosed in ING LOW-COHERENCE INTERROMETREY SIGNALS FOR INFORMATION ABOUT THIN FILM STRUCTURES). Of course, the model library used for comparison should also consider the processing techniques used to extract the experimentally derived information.

  In the following, a detailed mathematical description of the analysis is given and examples are given. First, a typical scanning interferometer will be described. Second, the determination of a mathematical model for the scanning interferometry data will be described. Third, the optical characteristics of the surface and a method for generating an accurate model of scanning interference spectral data for various surface characteristics using such information will be described. Fourth, how to obtain information about the test object by comparing experimental interference spectroscopy data with the prediction library will be described. First, thin film applications will be described, and then other complex surface structures, specifically, step heights and lattice patterns that cannot be optically sufficiently resolved will be described. First, the analysis will be focused on the analysis in the spatial frequency domain, and then the analysis in the scanning coordinate domain will be described. Further examples of techniques for extracting information about surface features that cannot be sufficiently resolved from interference spectral signals, such as the examples of FIGS. 25 to 27 described above, will be described later.

  FIG. 3 shows a linic type scanning interferometer. Illumination light 102 from a light source (not shown) is partially transmitted by beam splitter 104 to form reference light 106 and partially reflected by beam splitter 104 to form measurement light 108. To do. Measurement light is focused by a measurement objective 110 onto a test sample 112 (eg, a sample comprising a thin single film or multiple films of one or more different materials). Similarly, the reference light is focused on the reference mirror 116 by the reference objective lens 114. Preferably, the measurement and reference objectives have common optical properties (eg, numerical apertures are matched). Measurement light reflected (or scattered or diffracted) from the test sample 112 propagates backward through the measurement objective 110, is transmitted by the beam splitter 104, and is detected by the imaging lens 118. The image is formed on the device 120. Similarly, the reference light reflected from the reference mirror 116 propagates backward through the reference objective lens 114, is reflected by the beam splitter 104, and is imaged on the detector 120 by the imaging lens 118, There it interferes with the measurement light.

  For ease of explanation, the measurement and reference light shown in FIG. 3 is focused to a specific point on the test sample and reference mirror, respectively, and then interferes on the corresponding point on the detector. Such light corresponds to the portion of the illumination light that propagates perpendicular to the pupil plane relative to the measurement and reference legs of the interferometer. The other part of the illumination light eventually illuminates the test sample and other points on the reference mirror. These points are then imaged at corresponding points on the detector. In FIG. 3, this is illustrated by the dashed line 122. Dashed lines 122 correspond to chief rays that emerge from different points on the test sample and are imaged at corresponding points on the detector. The chief rays intersect at the center of the pupil plane 124 of the measurement leg. The pupil plane 124 is a rear focal plane of the measurement objective lens 110. Of the light that emerges from the test sample, those that appear at an angle different from the principal ray intersect at different locations on the pupil plane 124.

  In a preferred embodiment, detector 12Q is a multi-element (ie, multi-pixel) camera that independently measures interference between measurement light and reference light corresponding to different points on the test sample and reference mirror. (Ie give spatial resolution for the interference pattern).

  A scanning stage 126 coupled to the test sample 112 scans the position of the test sample relative to the measurement objective lens 110. This is indicated by the scan coordinates in FIG. For example, the scanning stage can be based on a piezoelectric transducer (PZT). Detector 120 measures the intensity of optical interference at one or more pixels of the detector as the relative position of the test sample is being scanned, and the information is analyzed by computer 128 for analysis. Send to.

  Since the region where scanning is performed is a region where the measurement light is focused on the test sample, the optical path length of the measurement light from the light source to the detector is changed by scanning. This change depends on the angle at which the measurement light is incident on the test sample and emerges from the test sample. As a result, the optical path difference (OPD) from the light source to the detector between the interference portion of the measurement light and the reference light interference portion is increased or decreased by the scanning coordinate ζ, while the measurement light is incident on the test sample, Depending on the angle emerging from the test sample. In other embodiments of the invention, the same result is achieved by scanning the position of the reference mirror 116 relative to the reference objective lens 114 (instead of scanning the test sample 112 relative to the measurement objective lens 110). Can do.

Since there is a difference in how the OPD changes with the scanning coordinate ζ, the coherence length is limited in the interference signal measured in each pixel of the detector. For example, the interference signal (which is a function of the scan coordinate) is typically modulated by an envelope on the order of spatial coherence length λ / 2 (NA) ² . Here, λ is the nominal wavelength of the illumination light, and NA is the numerical aperture of the measurement and reference objective lenses. As described further below, the modulation of the interference signal provides angle dependent information about the reflectivity of the test sample. In order to increase the limited spatial coherence, the numerical aperture defined by the objective lens in the scanning interferometer is preferably large. For example, greater than about 0.7 (or more preferably, greater than about 0.8 or greater than about 0.9). The interference signal can also be modulated by a limited temporal coherence length associated with the spectral bandwidth of the illumination source. Depending on the configuration of the interferometer, either one of these limited coherence length effects may dominate, or both may substantially affect the overall coherence length.

Another example of the scanning interferometer is the Mirau interferometer shown in FIG.
Referring to FIG. 4, illumination light 206 is supplied to beam splitter 208 by light source module 205. Beam splitter 208 sends illumination light 206 to Mirau interferometry objective assembly 210. The assembly 210 includes an objective lens 211, a reference plane 212 (having a reflective coating on its small central portion to define a reference mirror 215), and a beam splitter 213. In operation, illumination light is focused through the reference plane 212 toward the test sample 220 by the objective lens 211. The beam splitter 213 reflects the first portion of the focus light to the reference mirror 215 to define the reference light 222, and the second portion of the focus light is transmitted to the test sample 220 so that the measurement light 224 is It is formed. The beam splitter 213 then recombines the measurement light reflected (or scattered) from the test sample 220 with the reference light reflected from the reference mirror 215. The objective lens 211 and the imaging lens 230 form an image of the combined light and cause it to interfere on the detector (for example, a multi-pixel camera) 240. As with the system of FIG. 3, the measurement signal from the detector is sent to a computer (not shown).

  In the scan in the embodiment of FIG. 4, a piezoelectric transducer (PZT) 260 is coupled to the Mirau interferometry objective lens assembly 210. The piezoelectric transducer (PZT) 260 scans the entire assembly 210 with respect to the test sample 220 along the optical axis of the objective lens 211 to obtain scanning interference spectral data I (ζ, h) at each pixel of the camera. It is configured to be. Alternatively, the PZT may be coupled to the test sample rather than the assembly 210 to provide relative motion between them. This is illustrated by the PZT actuator 270. In still other embodiments, scanning may be performed by moving one or both of the reference mirror 215 and the beam splitter 213 relative to the objective lens 211 along the optical axis of the objective lens 211.

  The light source module 205 includes a spatially expanded light source 201, a telescope (formed by the lenses 202 and 203), a diaphragm disposed in the front focal plane of the lens 202 (coincident with the rear focal plane of the lens 203). 204. With this arrangement, a spatially expanded light source is imaged onto the pupil plane 245 of the Mirau interferometry objective lens assembly 210. This is an example of Koehler imaging. The size of the aperture controls the size of the illumination field on the test sample 220. The system includes an aperture stop (not shown) disposed between the beam splitter 208 and the interferometric spectroscopic objective lens assembly 210. In other embodiments, the light source module may include an apparatus for imaging a spatially extended light source directly onto the test sample, known as critical imaging. Any type of light source module may be used with the linic scanning interference system of FIG.

  In a further embodiment of the invention, a scanning interferometry system may be used to determine angle-dependent scatter or diffraction information for a test sample, ie for light wave scatterometry. For example, using a scanning interferometry system, the test sample is illuminated by a test incidence over only a very narrow range of incidence angles (eg, substantially normal incidence or otherwise collimated). Also good. The incident is then scattered or diffracted by the test sample. The light emerging from the sample is imaged on the camera and interferes with the reference light. This is as described above. The spatial frequency of each component in the scanning interference spectroscopic signal varies depending on the angle of the test light emerging from the test sample. Therefore, performing a Fourier analysis after a vertical scan (ie, scanning along the optical axis of the objective lens) does not directly access or image the back focal plane of the objective lens. In addition, measurements of diffracted light and / or scattered light can be made as a function of appearance angle. In order to obtain substantially normal incidence illumination, for example, the configuration of the light source module is such that the point light source is imaged on the pupil plane, otherwise the illumination light is set to the numerical aperture of the measuring objective lens. This can be done to reduce the degree of filling. Lightwave scatterometry techniques are for analysis of discrete structures within a sample surface, such as grating lines, edges, or general surface roughness, which can diffract and / or scatter light to higher angles. Can be useful.

  It is assumed in most of the analysis herein that the polarization state of the light in the pupil plane is random, that is, approximately equal amounts of s-polarized light (perpendicular to the incident plane) and p (incident plane). (Both orthogonally polarized). Alternative polarizations are possible, such as pure s-polarized light. For example, a radial polarizer in the pupil plane (for example, in the back focal plane of the object to be measured in the case of a linic interferometer and in the back focal plane of a common objective lens in the Mirau interferometer) You may implement | achieve by arrange | positioning. Other possible polarizations include radial p-polarization, circular polarization, and modulated (eg, two states, one following the other) polarization for polarization measurements. In other words, the analysis of the optical properties of the test samples can be done not only for their angle or wavelength dependence, but also for their polarization dependence or for selected polarizations. Such information may also be used to improve the characterization accuracy of the thin film structure.

  In order to implement such ellipsometric measurements, the scanning interferometry system may include a fixed or variable polarizer in the pupil plane. Referring again to FIG. 4, for example, the Mirau interferometry system includes a polarizing optic 280 in the pupil plane to select the desired polarization for light incident on and emerging from the test sample. It has become. Furthermore, the polarization optics may be reconfigurable to change the selected polarization. The polarizing optical component may include one or more elements including a polarizer, a waveplate, an apodization aperture, and / or a modulation element for selecting a predetermined polarization. Further, the polarization optics may be fixed, structured, or reconfigurable to generate data similar to ellipsometer data. For example, after a first measurement using a radially polarized pupil for s-polarization, a radially polarized pupil for p-polarization may be used. In other examples, an apodized pupil plane may be used with linearly polarized light, such as a slit or wedge. The slit or wedge is a screen that can be rotated or reconfigurable in the pupil plane to send any desired linear polarization state to the object, such as a liquid crystal display.

  In addition, polarization optics may provide variable polarization across the entire pupil plane (eg, by including multiple polarizers or spatial modulators). In this way, the polarization state can be “tagged” according to the spatial frequency. This is done, for example, by providing a different polarization from a shallow angle for a high angle of incidence.

  In still other embodiments, selectable polarization may be combined with phase shift as a function of polarization. For example, a polarizing optical component includes a linear polarizer placed in the pupil plane, after which two wave plates (eg, 1/8 wave plates) are placed in opposing quadrants of the pupil plane. Also good. As a result of the linear polarization, the polarization angle covers the entire range with respect to the entrance surface of the objective lens. For example, if the wave plates are aligned so that the phase shift of the dominant s-polarized light is fixed, both radial s-polarized light and p-polarized light are present at the same time, but the phase is only π, for example, from each other Due to the shift, the interferometer effectively detects the difference between these two polarization states as a fundamental signal.

In further embodiments, the polarizing optics may be located elsewhere in the device. For example, linear polarization can be realized anywhere in the system.
Next, a physical model for the scanning interference spectral signal will be described.

Suppose that the object surface has a height feature h and that it is desired to profile the height feature h over the region indicated by the lateral coordinates x, y. By means of the stage, a smooth continuous scan ζ is realized for the interference objective lens or the object itself as shown. During the scan, intensity data I _{ζ, h} for each image point or camera pixel is recorded by the computer in successive camera frames. The main dependence of the intensity I _{ζ, h} on the scanning position and the surface height is indicated by a subscript. This subscript is a notation used throughout.

  Appropriate physical models of optical components can be very elaborate. This reduces the partial coherence of the light source, polarization mixing within the interferometer, the imaging properties of high NA objectives, and the interaction of electric field vectors at high angles of incidence and in the presence of discontinuous surface features. Made by considering.

  For example, to accurately predict the interferometric signal from a given structure, it is necessary to solve the Maxwell equation for that structure. White light interferometry techniques require a sufficiently dense set of wavelengths to cover the illumination bandwidth. There are a number of approaches to solving the Maxwell equation in 2D. In 2D, one particularly simple approach is based on the Rayleigh hypothesis. In this approach, the structure is treated as a thin film stack, and the interface between each layer in the stack has a specific topography. The Rayleigh hypothesis states that in each layer, the electromagnetic field is expanded into upper and lower propagating plane waves, and the solution can be obtained by selecting coefficients so that the electromagnetic field satisfies the standard boundary conditions at the interface. This approach is simple to perform and is relatively fast and can obtain a complete optical transfer function or scattering matrix of a surface at one wavelength and for one polarization with a single calculation. The limitation is that an effective solution can be obtained only if the topography of each interface covers less than about half the wavelength in the layer that bounds the interface. High refractive materials such as silicon limit topography at visible wavelengths much less than 100 nm.

  3D modeling techniques include finite difference time domain method (FDTD), finite element and rigorous coupled wave analysis (RCWA) and the like. For example, M. Gee. Morum and Tee. Kay. "Diffraction analysis of dielectric surface-relief gratings" by TK Gaylord. Opt. Soc. Am. , 72, 1385-1392 (1982) and Em. "Numerical simulation of high-NA quantitative polarization microscopy and corresponding near-field (Numerical simulation of high-NA quantitative and microscoping and corresponding near-field 1)" refer. Furthermore, Institute of Technical Optics (ITO) of Stuttgart University Based on the work of M. Totzek, software was developed to run RCWA called Microsim. These techniques are often limited to small volumes, i.e., one-sided wavelengths, but are useful for properly maintaining both memory requirements and runtime. Nevertheless, because such techniques can be used in advance to generate a suitable library, the large amount of computation time used to generate the library hinders the in-process application of the technique disclosed herein. There is nothing.

  For convenience and to demonstrate certain curved surfaces of the present invention, the model is simplified by assuming a randomly polarized and diffuse, low coherence extended light source. The interference signal modeling makes it easy to examine the effects of all the light bundles (shown in FIG. 5) that are reflected from the object surface at the incident angle Ψ after passing through the pupil plane of the objective lens.

  The effect of interference on a single beam bundle through the optical system is proportional to:

ここでＺ_β，ｋは、有効な対象物強度反射率であり、たとえばビーム・スプリッタの効果を含む。Ｒ_β，ｋは、有効な基準反射率であり、ビーム・スプリッタおよび基準ミラーの両方を含む。周囲媒体の屈折率はｎ_０であり、入射角Ψに対する方向余弦は、以下の通りである。

Here, Z _{β, k} is an effective object intensity reflectance, and includes, for example, the effect of a beam splitter. R _{β, k} is an effective reference reflectivity and includes both a beam splitter and a reference mirror. The refractive index of the surrounding medium is n ₀ , and the direction cosine with respect to the incident angle Ψ is as follows.

また光源照明に対する波数は、以下の通りである。

The wave numbers for the light source illumination are as follows.

位相に対する記号の取り決めによって、表面高さの増加を、位相の正の変化に対応させる。位相項は、干渉計内の対象物経路に対する影響ω_β，ｋ、たとえば対象物表面からの薄膜効果と、基準経路に対する影響ν_β，ｋ、たとえば基準ミラーおよび対物レンズ内の他の光学部品とを有する。

The symbol convention for phase allows the increase in surface height to correspond to a positive change in phase. The phase term has an effect on the object path in the interferometer ω _{β, k} , eg a thin film effect from the object surface, and an influence on the reference path ν _{β, k} , eg on the reference mirror and other optical components in the objective lens Have

  The total interference signal integrated on the pupil plane is proportional to:

ここで、Ｕ_βは瞳平面の光分散であり、Ｖ_ｋは光学的なスペクトル分散である。方程式（４）における重み付け係数βは、投影角度に起因するｃｏｓ（Ψ）項と、瞳平面内の幅ｄΨの環の直径に対するｓｉｎ（Ψ）項とから得られる。

Here, U _β is the light dispersion in the pupil plane, and V _k is the optical spectral dispersion. The weighting factor β in equation (4) is obtained from the cos (ψ) term due to the projection angle and the sin (ψ) term for the diameter of the ring of width dψ in the pupil plane.

ここで、図５に図示したように、対物レンズはアッベの正弦条件に従うと仮定する。このような比較的簡単な重み付けは、ランダムに偏光された、空間的にインコヒーレントな照明（すべての光線束が互いに無関係である）の場合に可能である。最後に、すべての入射角に亘る積分範囲は、０≦ｐ≦１を意味し、すべての波数に亘るスペクトル積分は、０≦ｋ≦∞である。

Here, as shown in FIG. 5, it is assumed that the objective lens obeys Abbe's sine condition. Such a relatively simple weighting is possible in the case of randomly polarized, spatially incoherent illumination (all beam bundles are independent of each other). Finally, the integration range over all incident angles means 0 ≦ p ≦ 1, and the spectral integration over all wave numbers is 0 ≦ k ≦ ∞.

In the frequency domain analysis (FDA), first, Fourier transform of the interference intensity signal I _{ζ, h} is calculated. Use non-standardized Fourier integrals for literal (non-numeric) analysis.

ここで、Ｋは空間周波数であり、たとえば、単位は周期／ミクロンである。周波数ドメイン値ｑ_Ｋ，ｈの単位は、波数の逆であり、たとえばμｍである。これから、パワー・スペクトルと、

Here, K is a spatial frequency. For example, the unit is a period / micron. The unit of the frequency domain value q _{K, h} is the inverse of the wave number, for example, μm. From now on, the power spectrum,

位相スペクトルとが得られる。

And a phase spectrum.

φ”_Ｋ，ｈに対するダブル・プライムの意味は、フリンジのオーダに２倍の不確かさがあるということである。すなわち画素ごとのものと、走査の出発点に対する全体的なものとの両方である。そのため、従来のＦＤＡでは、パワー・スペクトルＱ_Ｋ，ｈによって重み付けされた位相スペクトルφ”_Ｋ，ｈに対する線形フィットによって表面トポグラフィを決定することに、直接進む。フィットによって、各画素に対して、勾配と、

The meaning of double prime for φ ″ _{K, h} is that there is twice the uncertainty in the fringe order, both pixel-by-pixel and global to the starting point of the scan. Therefore, conventional FDA goes directly to determining the surface topography by a linear fit to the phase spectrum φ ″ _{K, h} weighted by the power spectrum Q _{K, h} . By fitting, for each pixel, a gradient,

切片とが得られる。

Sections are obtained.

なお、切片または「位相ずれ」Ａ”は、高さｈとは無関係であるが、位相データのフリンジのオーダの不確かさから引き継いだダブル・プライムを備える。勾配σには、この不確かさはない。切片Ａ”および傾斜σ_ｈから、特定の平均または公称上の空間周波数Ｋ０に対して、「コヒーレンス・プロファイル」と、

Note that the intercept or “phase shift” A ″ is independent of the height h, but comprises a double prime inherited from the fringe order uncertainty of the phase data. The slope σ does not have this uncertainty. From the intercept A ″ and the slope σ _h , for a specific average or nominal spatial frequency K 0, a “coherence profile”;

「位相プロファイル」とを規定することができる。

A “phase profile” can be defined.

単純で理想的な場合、すなわち誘電体表面が完全に均一、均質で、薄膜および異なる材料の影響がなく、ならびに光学システムが分散に対して完全に平衡状態である場合には、位相およびコヒーレンス・プロファイルは、表面高さに直線的に比例する。

In simple and ideal cases, i.e. where the dielectric surface is perfectly uniform and homogeneous, without the influence of thin films and different materials, and the optical system is perfectly balanced with respect to dispersion, the phase and coherence The profile is linearly proportional to the surface height.

２つの高さ計算のうち、位相に基づく高さ値ｈ”_θの方が正確である。しかし、この値は、単色の干渉分光法のフリンジのオーダの特性に不確かさがある。高分解能を得るために、コヒーレンスに基づく明瞭であるが正確さに劣る値ｈ_Θを用いることで、この不確かさを取り除き、最終的な値ｈ_θを得る。

Of the two height calculations, the phase-based height value h ″ _θ is more accurate. However, this value is uncertain in the fringe order characteristics of monochromatic interferometry. In order to obtain this, the uncertainties are removed by using a clear but inaccurate value h _Θ based on coherence, and a final value h _θ is obtained.

Conventional FDA assumes that the interference phase φ ″ _{K, h} is still a nearly linear function of spatial frequency _, even in less ideal situations. However, in this embodiment, the main parameter of the surface structure, for example, the film thickness is determined by comparing the experimental data with the theoretical prediction. Such predictions can include a highly nonlinear phase spectrum and the accompanying modulation of the power spectrum.

  To do this, the equation (6), which is the definition of the Fourier transform, is combined with the interference signal equation (4) into the following equation for the predicted FDA spectrum:

計算の効率を向上させるために、方程式（１５）における３重積分の部分的な文字上の評価を行なうことができる。

In order to improve the computational efficiency, a partial character evaluation of the triple integral in equation (15) can be performed.

The lexical analysis of equation (15) begins by changing the order of integration, and first the values of the individual interference signals g _{β, k, ζ, h} are over all scanning positions ζ, Determined with β and k fixed.

余弦項ｇ_{β，ｋ，ζ，ｈ}を、以下の式を用いて通常の方法で展開した後、

After expanding the cosine terms g _{β, k, ζ, h} in the usual way using the following formula:

ζについての内部の積分を以下のように求める。

The internal integral for ζ is determined as follows:

ここで、以下の式を用いた。

Here, the following formula was used.

δ関数は、引数の逆の物理単位、この場合には逆の波数を有する。

The δ function has the opposite physical unit of the argument, in this case the opposite wavenumber.

These δ functions confirm the equivalence between the spatial frequency K and the product 2βkn ₀ .
The theoretical variation of the variable for the next integral is thus

ここで、κ＾は、空間周波数Ｋと同じ意味であるが、積分の自由変数として使用される。方程式（１８）は、以下のように書くことができる。

Here, κ ^ has the same meaning as the spatial frequency K, but is used as a free variable of integration. Equation (18) can be written as:

ここで、

here,

なお、変数を変えることによって、方程式（２３）におけるＲ、Ｚ、ν、ω項に対するβ依存性は、κ＾およびｋに対する依存性となる。

Note that by changing the variables, the β dependence on the R, Z, ν, and ω terms in equation (23) becomes dependence on κ ^ and k.

  As the next step, the following will be described first.

ここで、Ｈは、以下にように定義される無単位のヘビサイドのステップ関数である。

Here, H is a unitless snake-side step function defined as follows.

ｆは、Ｋおよびｋの任意の関数である。方程式（２５）〜（２７）を用いて、方程式（２３）は以下のようになる。

f is an arbitrary function of K and k. Using equations (25)-(27), equation (23) becomes:

ここで以下の式を用いると、

Here, using the following formula,

最終的に以下のような結果となる。

The final result is as follows.

方程式（３３）は、積分の数が少ないので、当初の式（１５）の三重積分と比べて著しく能率的な計算となる。

Since the number of integrals is small in the equation (33), the calculation is significantly more efficient than the triple integral of the original equation (15).

There are some extreme cases that are interesting to solve analytically. For example, when the influence of the phase (ν _{K, k} −ω _{K, k} ) = 0 and the reflectances R and Z are independent of the incident angle and the wavelength, the equation (33) is as follows: It will be easy.

したがって、方程式（２４）において定義される重み付け係数Γ_Ｋ，ｋを伴う積分のみを取り扱えばよい。この理想的なケースでは、方程式（３４）に対してさらに２つの極限的なケースを評価することが簡単になる。すなわち、高ＮＡ対物レンズを有する準単色の照明、および低ＮＡを有する広帯域の照明である。

Therefore, only the integration with the weighting coefficients Γ _{K, k} defined in equation (24) need be handled. In this ideal case, it becomes easier to evaluate two more extreme cases for equation (34). That is, quasi-monochromatic illumination with a high NA objective lens and broadband illumination with a low NA.

In the case of a quasi-monochromatic light source having a narrow spectral bandwidth _kΔ , the spectrum is normalized as follows.

ここで、ｋ_０は、公称上の光源波数である。方程式（３４）における積分は、以下のような形となる。

Here, k ₀ is a light source wavenumber nominal. The integral in equation (34) takes the form:

Ｕ_Ｋ，ｋは、小さい帯域幅ｋ_Δ上で本質的に一定であると仮定すると、以下の式が得られる。

Assuming U _{K, k} is essentially constant over a small bandwidth k _Δ , the following equation is obtained:

ここで、積分の値を求める際に、以下の関係を用いた。

Here, the following relationship was used when calculating the value of integration.

これは、狭帯域幅ｋ_Δ≪ｋ０に対しては有効である。特に、スペクトルの正の非ゼロ部分は、以下のようになる。

This is effective for a narrow bandwidth k _Δ << k0. In particular, the positive non-zero part of the spectrum is

結果として、光源のスペクトル帯域幅が狭く、反射率Ｒ、Ｚが一定で、位相の影響ωがないこの特別な場合には、以下のようになる。

As a result, in this special case where the spectral bandwidth of the light source is narrow, the reflectivities R and Z are constant, and there is no phase effect ω:

この特別な場合には、位相は、表面高さに直線的に比例し、従来のＦＤＡと一致する。また空間周波数は、方向余弦に直接対応する。

In this special case, the phase is linearly proportional to the surface height and is consistent with conventional FDA. The spatial frequency directly corresponds to the direction cosine.

したがって、ＦＤＡスペクトルの空間周波数座標と入射角との間には、１対１の関係がある。さらに、フーリエ振幅√Ｑ_ＫにおけるＫ重み付けは、方程式（４１）から計算されることに注意されたい。このことは、図６（ａ）の例示スペクトルにおいて明らかである。同図では、垂直入射から、対物レンズＮＡによって課される方向余弦限界までの範囲に亘って、瞳平面を完全に均一に充填する場合に対する理論的な予測を示す。

Therefore, there is a one-to-one relationship between the spatial frequency coordinates of the FDA spectrum and the incident angle. Furthermore, note that the K weighting at the Fourier amplitude √Q _K is calculated from equation (41). This is evident in the exemplary spectrum of FIG. The figure shows a theoretical prediction for the case where the pupil plane is filled completely uniformly over the range from normal incidence to the direction cosine limit imposed by the objective lens NA.

第２の例として、垂直入射付近の方向余弦の狭い範囲β_Δに限定された均一な照明を伴う広帯域の照明の場合を考える。したがって、規格化された瞳平面分散は以下のようになる。

As a second example, consider the case of broadband illumination with uniform illumination limited to a narrow range β _Δ of the direction cosine near normal incidence. Therefore, the normalized pupil plane dispersion is as follows:

変数を変えた後、

After changing the variable

方程式（３４）における定積分は、この場合には以下の形となる。

The definite integral in equation (34) takes the following form in this case:

これは以下の値となる。

This is the following value:

ここで、以下の関係を用いた。

Here, the following relationship was used.

スペクトルの正の非ゼロ部分は、この広帯域の光源照明用であり、したがって、垂直入射付近は、以下のようになる。

The positive non-zero part of the spectrum is for this broadband light source illumination, so near normal incidence is:

これは、フーリエ振幅（√Ｑ_Ｋ）が光源スペクトル分散Ｖ_{Ｋ／２ｎ０}に比例するという熟知結果に密接に対応する。このことはたとえば、図６（ｂ）において、公称上または平均の波長ｋ_０の中心に置かれたガウシアン・スペクトルに対して示されている。なお方程式（５２）は、以下の線形的な位相の展開が、

This closely corresponds to the familiar result that the Fourier amplitude (√Q _K ) is proportional to the light source spectral dispersion V _{K / 2n0} . This is for example, in FIG. 6 (b), are shown for Gaussian spectra placed nominally or average of the center wavelength k _0. Equation (52) has the following linear phase expansion:

従来のＦＤＡと一致するという仮定にも適合する。

It also meets the assumption that it is consistent with conventional FDA.

Since the Fourier amplitude √Q _{K, h} = | q _{K, h} | and the phase φ ″ _{K, h} = arg (q _{K, h} ) are obtained from the Fourier transform of the interference intensity I _{ζ, h} , Return to the interference signal domain.

ここで、もう一度、κ＾を空間周波数に対して用いて、これが方程式（５４）における積分の自由変数であることを強調した。したがって、強度信号を計算する１つの方法は、方程式（３３）によってフーリエ成分ｑ_Ｋ，ｈを生成し、方程式（５４）を用いてＩ_ζ，ｈに変換することである。

Here again, κ ^ is used for the spatial frequency to emphasize that this is a free variable of integration in equation (54). Thus, one way to calculate the intensity signal is to generate a Fourier component q _{K, h} by equation (33) and convert it to I _{ζ, h} using equation (54).

  In this model, it is assumed that the light source light is randomly polarized. However, this does not mean that the polarization effect should be ignored. Rather, the above calculations assume an incoherent superposition that is the result of being equally weighted from two orthogonal polarization states s and p defined by the entrance plane of the illumination. For polarization, superscript notation is used.

したがって、このβ、ｋにおける未偏光光に対する平均の位相角度は、以下のようになる。

Therefore, the average phase angle with respect to unpolarized light at β and k is as follows.

なお、２つの偏光の影響に対して振幅が同一である場合を除いて、ほとんどの場合、以下のようになる。

In most cases, except when the amplitude is the same for the two polarization effects,

また、ｑ^ｓ _β，ｋおよびｑ^ｐ _β，ｋが、複素平面において完全に平行である場合を除いて、以下のようになる。

Further, except for the case where q ^s _{β, k} and q ^p _{β, k} are completely parallel in the complex plane, they are as follows.

同じ所見を、システムおよび対象物反射率であるＲ^ｓ _β，ｋ、Ｒ^ｐ _β，ｋ、およびＺ^ｓ _β，ｋ、Ｚ^ｐ _β，ｋに、それぞれ適用する。これらは、位相が同一である場合を除いて、直接足し合わせることはできない。

The same observations apply to the system and object reflectivity R ^s _{β, k} , R ^p _{β, k} and Z ^s _{β, k} , Z ^p _{β, k} respectively. They cannot be added directly, except when the phases are the same.

  If the polarization effect is properly taken into account in the calculation of the object surface reflectivity, the modeling is fairly simple and quite adaptable, and can handle the more interesting cases of polarized light.

The next step is to convert it into a separate numeric expression, taking into account software development. The relationship between the interference signal I _{ζ, h} and the Fourier spectrum q _{K, h} is redefined using a separate Fourier transform as follows:

ここで、ｑ~_Ｋ^，ｈは、ｑ_Ｋ^，ｈの複素共役であり、干渉信号にはＮ個の別個のサンプルが存在する。方程式（６０）および後述の式において、導出時には重要であったが空間周波数Ｋに対する代わりとしてはもはや必要ではない自由変数Ｋを用いることは、やめている。したがって、予測される正の周波数ＦＤＡ複素スペクトルは、以下のようになる。

Here, q ~ _{K ^, h} is a complex conjugate of qK _{^, h} , and there are N separate samples in the interference signal. In equation (60) and the equations described below, the use of free variable K, which was important at the time of derivation but is no longer necessary as a substitute for spatial frequency K, is ceased. Thus, the predicted positive frequency FDA complex spectrum is:

ここで、規格化された、高さに無関係な係数は、以下のようになる。

Here, the normalized coefficient independent of the height is as follows.

ここで、積分範囲に対する規格化は、以下のようになる。

Here, normalization with respect to the integration range is as follows.

方程式（６２）におけるヘビサイドのステップ関数Ｈによって、足し合わせに対する不必要な影響が防止されている。重み付け因子Γ_Ｋ，ｋは、方程式（２４）において定義される通りである。

The snake side step function H in equation (62) prevents unwanted effects on summing. The weighting factor Γ _{K, k} is as defined in equation (24).

To compare the experiment with theory, an equation (61) is used to generate an experimental FDA spectrum, and equation (62) is used to convert back to the space domain to obtain the theory of I _{ζ, h} . Predictive. This is most efficiently done when fast Fourier transform (FFT) is used. The range of the K value is determined by the characteristics of the FFT. If N separate samples for I _{ζ, h} are spaced apart by an increment ζ _step , start from zero and increase to N / 2 periods per data trace (N / 2) +1 positive There is a spatial frequency. They are spaced apart by the following increments:

周波数ドメインにおける位相アンラッピングを容易にするために、走査に対するゼロ位置の調整を試みて、その位置が信号ピーク付近にくるようにすることで、周波数ドメインにおける位相勾配が小さくなる。ＦＦＴでは、走査における最初のデータ点がゼロにあることが常に仮定されているため、信号を適切にオフセットしなければならない。

In order to facilitate phase unwrapping in the frequency domain, attempting to adjust the zero position relative to the scan so that the position is near the signal peak reduces the phase gradient in the frequency domain. In FFT, it is always assumed that the first data point in the scan is at zero, so the signal must be offset appropriately.

Focus on modeling of sample surfaces with thin films.
Shown in FIG. 7 are two surface types with and without thin films. In both cases, the effective amplitude reflectivity Z _{β, k} is defined according to:

ここで、Ｚ_β，ｋは強度反射率であり、ω_β，ｋは反射時の位相変化である。添え字β、ｋは、照明の方向余弦への依存性を強調するものである。

Here, Z _{β, k} is the intensity reflectance, and ω _{β, k} is the phase change during reflection. The subscripts β and k emphasize the dependence of the illumination on the direction cosine.

ここで、Ψ_０は入射角であり、波数については以下のようになる。

Here, Ψ ₀ is an incident angle, and the wave number is as follows.

ここで、λは光源の波長である。添え字βは、第１の入射方向余弦β_０を指すものと理解される。

Here, λ is the wavelength of the light source. The subscript β is understood to refer to the first incident direction cosine β ₀ .

The surface is characterized, in part, by its refractive index. The refractive index of the surrounding medium (usually air) is n _0. In the case of a simple surface in FIG. 7 (a), only one refractive index n _1. In the case of the thin film FIG. 7B, there are two surface refractive indexes. That is, n ₁ for a transparent or partially transparent film and n ₂ for a substrate. Most commonly, these refractive indices are complex numbers characterized by real and imaginary parts. For example, a typical refractive index is n ₁ = 3.18 + 4.41i at λ = 550 nm, for example in the case of chromium. Here, the convention that the imaginary part is defined as positive is adopted.

The refractive index of the material depends on the wavelength. The dispersion of the refractive index n ₀ with respect to air is not very large, but is important for many sample surfaces, especially metals. At small wavelength changes near the nominal k0, most materials depend almost linearly on wavenumber. So we can write:

ここで、ｖ^（０） _１、ｖ^（１） _１はそれぞれ、屈折率ｎ_１に対して公称上の波数ｋ０における、切片および勾配である。

Here, v ⁽⁰⁾ ₁ and v ⁽¹⁾ ₁ are an intercept and a gradient at a nominal wavenumber k0 with respect to the refractive index n ₁ , respectively.

  The most common use of refractive index is Snell's law. Referring to FIG. 7B, the refractive beam angle inside the film is as follows.

ここで、Ψ_０は、屈折率ｎ_０の媒体内の角度であり、これが屈折率ｎ_１の媒体の最上面に入射する。また、Ψ_{１，β，ｋ}は、屈折角である。これらの角度は、屈折率が複素数である場合には、複素数値を取ることができ、部分的にエバネッセントな伝搬を示す。

Here, Ψ ₀ is an angle in the medium having the refractive index n ₀ , and this is incident on the top surface of the medium having the refractive index n ₁ . Moreover, Ψ _{1, β, k} is a refraction angle. These angles can be complex values when the index of refraction is complex, and show partially evanescent propagation.

  The complex amplitude reflectivity at the boundary between the two media depends on the polarization, wavelength, incident angle, and refractive index. The s- and p-polarized reflectivities of the top surface of the film of Fig. 7 (b) are given by the Fresnel equation as follows:

β、ｋに対する依存性は、角度Ψ_０、Ψ_{１，β，ｋ}から生じる。出口角Ψ_{１，β，ｋ}によって、屈折率ｎ_１，ｋを介したｋ依存関係が導入される。同様に、基板−膜界面の反射率は、以下の通りである。

The dependence on _{β, k} arises from the angles Ψ ₀ , Ψ _{1, β, k} . The exit angle Ψ _{1, β, k} introduces a k dependence via the refractive index n _{1, k} . Similarly, the reflectance at the substrate-film interface is as follows.

なお、フレネル方程式において、入射角および屈折角が同じ場合には、両方の偏光に対する反射率はゼロになる。

In the Fresnel equation, when the incident angle and the refraction angle are the same, the reflectivity for both polarized lights is zero.

  In the case of a simple surface (no thin film), the reflectance of the sample surface is the same as that of the top surface.

その結果、表面反射によって引き起こされる反射時の位相変化（ＰＣＯＲ）は、以下のようになる。

As a result, the phase change (PCOR) during reflection caused by surface reflection is as follows.

なお、境界条件を満たすために、ｓ−偏光は、反射時に「反転する」（＝誘電体の場合のπ位相シフト）が、ｐ−偏光は反転しない。正確に垂直入射の場合には偏光状態間の区別は意味がなくなる。すなわち、どんな場合でもフレネル方程式においてゼロ除算となるため、この極限的なケースを取り扱う式は異なるものとなる。

In order to satisfy the boundary condition, s-polarized light is “inverted” upon reflection (= π phase shift in the case of a dielectric), but p-polarized light is not inverted. In the case of exactly normal incidence, the distinction between polarization states is meaningless. In other words, since the Fresnel equation is divided by zero in any case, the formula for handling this extreme case is different.

When the plus sign convention is used for the complex part of the refractive index, the greater the absorption (complex part), the greater the PCORωβ _{, k} . In other words, increasing the absorption coefficient is equivalent to reducing the effective surface height. This can be understood intuitively. That is, absorption is envisioned as the light beam penetrates into the material before reflection, rather than the precise reflection and transmission that occurs exactly at the boundary. The normal surface, i.e. the increase in surface height, corresponds to a positive change in the phase difference between the reference surface and the measurement surface, subtracting the positive surface PCOR from the interferometer phase.

  A thin film is a special case of parallel plate reflection. The light is partially reflected as it passes through the top surface (see FIG. 7) and travels to the substrate surface. Second reflection occurs on the substrate surface. This reflection is delayed in phase with respect to the first reflection. But that doesn't end there. The light reflected from the substrate is partially reflected again when it passes back through the top surface. The result is a further reflected beam that faces down again to the substrate. This continues in principle forever, and each further reflection is slightly weaker than the previous one. Assuming all these multiple reflections persist and affect the final surface reflectance, the infinite set has the following values:

説明の備考として、β_{１，β，ｋ}のβ依存関係が、屈折率ｎ_０の周囲媒体中の入射方向余弦β_０への依存関係を指すことを、思い起こされたい。同じ方程式（７７）が、対応する単一の表面反射率を有する両方の偏光状態に適用される。

As a remark of explanation, recall that the β dependence of β _{1, β, k} refers to the dependence of the refractive index n ₀ on the incident cosine β _{0 in} the surrounding medium. The same equation (77) applies to both polarization states with a corresponding single surface reflectance.

  Examining these equations shows why conventional FDA processing fails in the presence of thin films. In conventional FDA, the surface height is determined by a linear fit to the Fourier phase spectrum weighted by the Fourier power spectrum, and a broad band (white) light is used to form the spread of the Fourier spatial frequency. . The idea is that the phase expansion is brought about by the expected linear phase dependence on the surface height. Any other constant offset or linear factor (eg, “dispersion”) associated with the surface characteristics is removed by characterization of the system or by simply ignoring phase effects that do not vary with field position.

  This works perfectly accurately for simple surfaces. In the case of unpolarized light, and perhaps circularly polarized light, the wavelength dependence of PCOR is approximately linear with wavenumber and constant for a given material. However, if a thin film is present, conventional analysis will not work. The phase is non-linear and the phase gradient is sensitive to film thickness and may vary across the field of view. Therefore, in this analysis, the determination of the main parameters of the surface structure, such as the film thickness, is made by comparing experimental data with theoretical predictions, for example how the thin film modulates the reflectivity of the surface. Knowledge is used.

Next, it will be described how surface structure parameters such as film thickness and phase change (PCOR) during reflection are obtained by comparing experimental data with a library of theoretical predictions. For films of unknown thickness, a library for a single surface type, eg, SiO ₂ on Si, spans many possible film thicknesses. In the frequency domain embodiment, the idea is to search this library for a match to the FDA spectral characteristics that are independent of surface topography, for example a unique structure for the amplitude spectrum due to thin film interference effects. The library spectrum is then used in the computer to correct the FDA data to allow an accurate surface topography map.

In one embodiment, the library contains exemplary FDA spectra for surface structures. Each spectrum provides a series of complex coefficients ρ _K that represent the Fourier coefficients as a function of the spatial frequency K. These spectra are Fourier transforms of the intensity data I _{ζ, h} acquired during the optical path length scan ζ of the interferometer. The spatial frequency K is proportional to the angular wave number k = 2π / λ for the segment of the light source light spectrum, the refractive index n ₀ of the surrounding medium, and the direction cosine β = cos (ψ). Here, Ψ is an incident angle with respect to a light beam transmitted to the surface of the object.

予測ライブラリに対するρ_Ｋ係数は、ＦＤＡスペクトルの外観に影響を与える可能性がある表面の光学特性（表面高さを除く）を含む。

The ρ _K coefficient for the prediction library includes surface optical properties (excluding surface height) that can affect the appearance of the FDA spectrum.

In order to predict the FDA spectrum, it is necessary to perform an integration representing the incoherent sum of the light bundles over the range of the incident angle Ψ and the angular wave number k with respect to the light source light. As described above, the numerical integration can be a single sum over N angular wave numbers K (weighted by factors Γ _{K, k} ) that make the calculation efficient.

重み付け因子は、以下の通りである。

The weighting factors are as follows.

ここで、Ｖ_Ｋは、光源スペクトルであり、Ｕ_Ｋ、ｋは、瞳平面の光分散である。対応する規格化γは、重み付け因子のすべての空間周波数に亘る合計である。

Here, V _K is the light source spectrum, and U _{K, k} is the light dispersion in the pupil plane. The corresponding normalization γ is the sum of all weighting factors over all spatial frequencies.

ここで、γは、簡潔に規定されるべき規格化であり、Ｈは、ヘビサイドのステップ関数である。

Here, γ is a normalization to be succinctly defined, and H is a snake side step function.

The surface structure of the object, in particular the unique properties of the thin film, becomes part of the spectrum ρ _K through the object-path phase ω _{K, k} and the reflectivity Z _{K, k} . This has already been described in detail. Equally important are the reference-path phase ν _{K, k} and the reflectivity R _{K, k} . These depend on the scanning interferometer itself. Such factors can be determined by theoretically modeling a scanning interferometer or by calibrating it with a test sample of known characteristics. This will be further described later.

A typical prediction library for a thin film is a series of spectra ρ _K indexed by film thickness L. The range of spectra stored is only a narrow spatial frequency region of interest (ROI), typically 15 or 16 values for 256 frames of intensity data acquisition. The remaining value outside this ROI is zero. The ROI range is derived from the definition of spatial frequency.

１００Ｘのミラウ対物レンズおよび狭帯域幅、５００ｎｍ光源に基づく走査型干渉計に対する空間周波数の典型的な範囲は、２．７μｍ^−１〜４．０μｍ^−１である。計算を能率的に行なうために、数式（８０）〜（８３）を用いて各画素に対して複数回再計算することを伴う解析的な検索ルーチンではなく、サンプル・スペクトル間の０．５〜５ｎｍによってインデックスされる高密度なルック・アップ・テーブルを用いることができる。

100X of Mirau objective and narrow bandwidth, the typical range of spatial frequency for scanning interferometer-based 500nm light source is 2.7μm ^-1 ~4.0μm ^-1. In order to perform the calculation efficiently, it is not an analytical search routine involving recalculation for each pixel by using the equations (80) to (83), but 0.5 to 0.5 between the sample spectra. A dense look-up table indexed by 5 nm can be used.

  Library searching involves the following steps: (1) Select a predicted FDA spectrum from a library corresponding to a particular surface type. (2) Calculate how closely this spectrum matches the experimental data using the merit function. And (3) iterate through some or all library data sets to determine from which theoretical spectrum the best match is obtained. What we are looking for are “discriminating characteristics” in the frequency domain that are uniquely related to the surface characteristics. Surface properties are, for example, thin films, foreign materials, step structures, roughness, and their interaction with the interferometer optical system. Thus, such a comparison clearly removes the linear rate of phase change with respect to spatial frequency. This is a property of the FDA spectrum that varies directly with surface topography and is therefore not relevant for library searching.

  In the comparative spectrum, it is beneficial to separate the phase effect and the amplitude effect on the calculation. Therefore, with respect to the theory:

ここで、ｃｏｎｎｅｃｔ_Ｋは、φ_Ｋ，ｈの空間周波数依存性における２−πステップを取り除く関数である。実験データに対しては、以下のようになる。

Here, connect _K is a function that removes the 2-π step in the spatial frequency dependence of φK _{, h} . The experimental data is as follows.

φ”^ｅｘ _Ｋに対するダブル・プライムは、走査における出発点に対する画素間および全体の両方からのフリンジのオーダにおける不確かさを示す。実験データは必然的に、局所的な表面高さに関係する勾配項を含む。これが、ｐ符号の代わりにｑ符号を用いる理由である。

The double prime for φ ″ ^ex _K shows the uncertainty in the order of fringes from both the inter-pixel and the whole relative to the starting point in the scan. The experimental data necessarily inevitably has a gradient term related to the local surface height. This is why the q code is used instead of the p code.

  The phase difference can be calculated for a particular set of trial surface parameters.

トライアルなパラメータは正確であると仮定して、位相差ζ”_Ｋ，ｈは、補正されたＦＤＡ位相である。理論が実験に良好にマッチングすることにより、原理的には切片がゼロ（すなわちゼロ位相ずれ）の空間周波数Ｋの単純な線形関数である位相ζ”_Ｋ，ｈが得られる。したがって、先を見越すと、成功裏に補正された位相ζ”_Ｋ，ｈは、最終的には従来のＦＤＡ解析へと下流に供給されるものである。従来のＦＤＡ解析では、周波数空間における位相の勾配は、表面高さに正比例していると仮定している。

Assuming that the trial parameters are correct, the phase difference ζ ″ _{K, h} is the corrected FDA phase. In principle, the intercept is zero (ie, zero because the theory matches well with the experiment. A phase ζ ″ _{K, h} which is a simple linear function of the spatial frequency K of (phase shift) is obtained. Therefore, in anticipation, the successfully corrected phase ζ ″ _{K, h} is ultimately supplied downstream to the conventional FDA analysis. In the conventional FDA analysis, the phase in the frequency space is Is assumed to be directly proportional to the surface height.

Based on the findings in the previous paragraph, the corrected phase ζ ″ _{K, h} has two features of interest that allow the evaluation of matching theory against experiments independent of surface height. The first is the phase shift A ″ or the intercept value ζ ″ _{K = 0, h} of _{K = 0} , which is obtained by a linear fit. The second is the remaining nonlinearity with respect to the wavenumber after the linear fit. The corresponding merit function is, for example:

ここで、σ_ｈは、補正された位相ζ”_Ｋ，ｈに対する（振幅が重み付けされた）線形フィットの勾配である。方程式（９１）におけるｒｏｕｎｄ（）関数によって、位相ずれＡ”が範囲±πに制限される。

Where σ _h is the slope of the linear fit (amplitude weighted) with respect to the corrected phase ζ ″ _{K, h} . The round () function in equation (91) causes the phase shift A ″ to be in the range ± π. Limited to

A library search can proceed using phase information alone, ie, minimizing one or both of the merit function values χ _φ and / or χ _φnon , but important and useful discriminating properties are Fourier transforms. It also exists in amplitude. The amplitude is particularly interesting in that it is inherently independent of the surface height. Therefore, for example, the following amplitude merit function can be defined almost the same as the phase merit.

ここで、Ωは経験的なスケーリング因子である。

Where Ω is an empirical scaling factor.

メリットχ_Ｐは、対象物表面の全反射率に最も密接に関係しており、空間周波数依存性とは無関係である。一方で、χ_Ｐｎｏｎは、理論および実験的な振幅プロットが、形状においてどの程度良好にマッチングするかを表現する。

The merit χ _P is most closely related to the total reflectance of the object surface, and is independent of the spatial frequency dependence. On the other hand, χ _Pnon represents how well the theoretical and experimental amplitude plots match in shape.

The amplitude merit function χ _P and / or χ _Pnon is separate from or even in place of the phase merit χ _φ and / or χ _φnon . Therefore, a general library search merit function is as follows.

ここで、ｗは重み付け因子である。原理的には、種々のパラメータに対する標準偏差を知ることで、方程式（９６）における重みを決定することができる。より経験的なアプローチは、実際のデータおよびシミュレートされたデータに対して種々の重みを試して、それらがどの程度良好に機能するかを調べることである。以下の例では、すべてのメリットの影響に対して、等しい重みｗ_φ＝ｗ_φｎｏｎ＝ｗ_Ｐ＝ｗ_Ｐｎｏｎ＝１を選択する。

Here, w is a weighting factor. In principle, knowing the standard deviation for various parameters, the weight in equation (96) can be determined. A more empirical approach is to try different weights on the actual and simulated data to see how well they work. In the following example, an equal weight w _φ = w _φnon = w _P = w _Pnon = 1 is selected for all merit effects.

In the examples of FIGS. 8 to 13, the merit function search procedure is shown for six film thicknesses of SiO ₂ on Si: 0, 50, 100, 300, 600, and 1200 nm, respectively. The single library for all examples contains the range 0-1500 nm with 2 nm spacing. The data is a simulation and there is no noise. As with all examples described herein, the scanning step is 40 nm, the source wavelength is 498 nm, and the source Gaussian FWHM is 30 nm (pseudo-monochromatic).

The most interesting aspect of these simulated searches is the behavior of the four merit functions. It is generally accepted that the inclusion of these four functions reduces the ambiguity in the final merit value and there is a strong periodicity as a function of film thickness for each merit value. Another common finding is that the benefits based on non-linearity are most effective at 300 nm and above, both in phase and amplitude, but the phase shift and average amplitude are dominant at film thicknesses below 300 nm. ,That's what it means. This shows that χ _φ , χ _P merit functions are particularly useful for true thin films, where system characterization is important and directly combines to result in phase shifts and amplitudes That is.

Once the film thickness is determined (or other usage for the material or algorithm is specified), the FDA process proceeds in the usual way. However, instead of the original experimental phase data, the corrected FDA phase ζ ″ _{K, h} is used. In principle, if modeling is successful, ζ ″ _{K, h} has no nonlinearity. The phase shift should be zero. The next step is therefore a linear fit to the phase spectrum ζ ″ _{K, h} . It appears that using the amplitude spectrum P _K instead of the square of the amplitude is more effective for high NA FDA. What is obtained for each pixel by the fit is the gradient,

切片（位相ずれ）とである。

It is an intercept (phase shift).

なお、位相ずれＡ”は、位相データのフリンジのオーダの不確かさから引き継いだダブル・プライムを有する。傾斜σ_ｈには、この不確かさはない。切片Ａ”および傾斜σ_ｈから、特定の平均または公称上の空間周波数Ｋ０に対して、以下のように「コヒーレンス・プロファイル」と、

Note that the phase shift A ″ has a double prime inherited from the fringe order uncertainty of the phase data. The slope σ _h does not have this uncertainty. From the intercept A ″ and the slope σ _h , a specific average Or, for the nominal spatial frequency K0, “coherence profile” as follows:

「位相プロファイル」とを定義する。

Define a “phase profile”.

次に、位相θ”_ｈにおける画素間のフリンジのオーダの不確かさを取り除く。

Next, the uncertainty of the fringe order between pixels in the phase θ ″ _h is removed.

ここで、α’は、画素間２πステップがない本来の位相ずれＡ”に対する近似である。

Here, α ′ is an approximation to the original phase shift A ″ with no 2π step between pixels.

  Finally, the height profile is obtained from:

なお、位相オフセットγを差し引く必要はない。その理由は、補正された位相ζ_Ｋ，ｈを生成する際に、差し引くことはすでに行なわれているからである。

It is not necessary to subtract the phase offset γ. This is because the subtraction has already been performed when the corrected phase ζ _{K, h} is generated.

  The first example of surface topography measurement (FIG. 14) is a pure simulation. The surface topography is zero everywhere. However, the underlying film layer increases from 0 to 1500 nm in 10 nm increments. Using the same prediction library as in FIGS. 8-13, this test demonstrates that the film thickness is clearly determined over the entire range of the prediction library, albeit with perfect noise-free data. Yes.

Although the next example (FIG. 15) is also a simulation, noise is added. The random additive noise is Gaussian, the standard deviation is 2 bits, and the average is 128 intensity bits. This seems to be typical of actual data. Although there is a significant difference in reflectance between the SiO ₂ and Si (4% ~45%), the result is to go unequivocally satisfactory.

Next, system characterization will be described.
Data collected during the system characterization procedure is used to define the phase offset γ _sys and the linear variance τ _sys . To include system characterization data, the Fourier transformed experimental data is corrected using the following before library search and before any other inter-pixel based FDA processing.

ここで、Ｋ０は公称上の空間周波数であり、ＦＤＡデータ・セットに対する公称上のスペクトルの周波数を表わす。これは、たとえば、ＲＯＩの中心点を位置決めすることによって特定される。なお、理論的なライブラリは変わってはいない。スケーリング係数Ｍ（ギリシャ語大文字の「Ｍ」）は、対象物の表面反射率をライブラリ検索におけるパラメータとして使用することを可能にする新しいシステム特徴付けである。

Where K0 is the nominal spatial frequency and represents the nominal spectral frequency for the FDA data set. This is specified, for example, by positioning the center point of the ROI. The theoretical library has not changed. The scaling factor M (Greek capital letter “M”) is a new system characterization that allows the surface reflectance of an object to be used as a parameter in a library search.

The phase offset γ _sys and system phase shift A _sys as a function of field position can be stored as a function of field position, and the true system variance can be calculated according to the following equation:

振幅係数Ｍも、フィールド依存性である。

The amplitude coefficient M is also field dependent.

  The generation of system characterization data proceeds in a similar manner as described above for the object sample. The features are transferred to a known workpiece and measured to determine the system characterization. This decision is made by looking at how the results differ from what is expected for a complete system. Specifically, using a known sample whose exact library entry is predetermined, the phase shift A "as in equation (98) and the final height h as in equation (102). Next, assuming a perfectly flat workpiece, the system phase offset and

システム位相ずれとを計算する。

Calculate system phase shift.

ここで、ｃｏｎｎｅｃｔ_ｘｙ（）は、画素間位相アンラッピングである。振幅マップは、以下の通りである。

Here, connect _xy () is inter-pixel phase unwrapping. The amplitude map is as follows.

種々の実施形態においては、複数のシステム特徴付けを平均化することができる。これはおそらく、ある範囲のサンプル形式に亘る最終的な応用例（たとえばＳｉ上のＳｉＯ_２）と同様の表面構造を有する加工品を用いることによって、行なわれる。

In various embodiments, multiple system characterizations can be averaged. This is probably done by using a workpiece with a surface structure similar to the final application (eg SiO ₂ on Si) over a range of sample formats.

  Although most of the foregoing description and simulation has focused on thin film surface structures, the analysis is applicable to other types of complex surface structures. In the following, it will be shown how the scanning interferometry data can be analyzed to reveal surface structures that are smaller than the optical resolution of the scanning interferometer microscope. The optical resolution is ultimately limited by the wavelength of the light source and the NA of the collection optics.

  FIG. 16a shows a height profile determined from actual scanning interference spectroscopy data. In this case, with a grating of 2400 lines / mm (lpmm), the peak-valley (PV) modulation depth is 120 nm, and the light source used has a nominal wavelength of 500 nm. The upper profile of FIG. 16a shows the height profile determined using conventional FDA analysis. The PV modulation depth shown by the conventional analysis is only about 10 nm, and the actual modulation depth is extremely underestimated. The reason for this inaccuracy is that the grating features exist at the limits of the optical resolution of the 500 nm instrument. This is true even if the pixel resolution of the camera in the device is high enough to accurately resolve the grid.

  One way to consider this effect is that the scanning interferometry signal for the first camera pixel that generally corresponds to the first surface location may also include the effects from adjacent surface locations, and this occurs because The surface feature of the further surface location is when it is sufficiently sharp with respect to the light wavelength to diffract the light into the first pixel. These surface height features from adjacent surface locations impair conventional analysis of the scanning interferometry signal corresponding to the first surface location.

  At the same time, however, this means that the scanning interferometry signal corresponding to the first surface location contains information about nearby complex surface features. This is shown in FIG. In the figure, scanning interference spectral signals from pixels corresponding to various locations around this step height feature are shown. In the signal in (a), the step height is on the right side of the pixel and is higher. In the signal in (b), the step passes directly through the pixel. In the signal in (c), the step is on the left side of the pixel and is lower. One of the discriminating characteristics immediately apparent in the signal is that the fringe contrast in (b) is lower than in (a) and (c). For example, if the step height is equal to a quarter of the wavelength and the pixel location corresponds exactly to the position of the step height, the fringe contrast in (b) is completely extinguished. The reason is that the interference from the two sides of the step cancels each other exactly. There is a lot of information in the signals shown in (a) and (c). For example, FIG. 18 shows nonlinear distortion in the frequency domain phase spectrum for signals (a) and (c) of FIG. 17, respectively. This distortion is due to the nearby step height. These spectra are shown in FIG. 18 as (a) and (b), respectively. In the absence of a step height, the frequency domain phase spectrum is linear. That is, the non-linear feature in the frequency domain phase spectrum for the pixel corresponding to the surface location adjacent to the step height includes information about the step height.

  In order to more accurately measure the surface profile of the test surface when there are surface features that cannot be sufficiently resolved in this way, the library search technique described above for thin films can be used. For example, for a test surface with a grid that cannot be sufficiently resolved, a series of model FDA spectra are generated for different values of PV modulation depth and offset position. As with the thin film example, the surface height for the model spectrum remains fixed. The analysis is then continued as in the thin film example described above, except that the model spectrum is not parameterized by the thin film thickness but by the modulation depth and offset position. Matching can then be determined using a comparison between the identification characteristics of the FDA spectrum for the actual test surface and the identification characteristics of the various model spectra. Based on the matching, the distortion in the actual FDA spectrum for each pixel caused by the presence of the grid is removed so that the surface height for each pixel can be determined using conventional processing. Figures 16b and 19b show the results of such an analysis using the same merit function as described above for the thin film.

  FIG. 16b shows the height profile determined using library search analysis for the 2400 line / mm grid described above with reference to FIG. 16a. The same data was used in FIGS. 16a and 16b. However, by library search analysis, the PV modulation depth for the grating was determined to be 100 nm. This is much closer to the actual modulation depth of 120 nm than the 10 nm result determined by the conventional FDA process of FIG. 16a. Shown in FIGS. 19a and 19b is a similar analysis for a simulation with a discrete step height and assuming a nominal 500 nm light source. FIG. 19a shows a comparison between a height profile (solid line) determined using conventional FDA processing and an actual height profile (broken line) for the simulation. FIG. 19b shows a comparison between the height profile (solid line) determined using the library search method and the actual height profile (broken line) for the simulation. The parameters for the model spectrum in the library search were location and step height amplitude. As illustrated, the library search analysis improves the lateral resolution from about 0.5 microns to about 0.3 microns.

  In the example of FIGS. 19a-19b, the library was theoretically generated for a thin film using an equation similar to equation (77), but in this case the denominator is set to 1 (multiplication from the underlying layer). Because there is no reflection), the first and second terms of the molecule are weighted according to the lateral distance of the measurement point from the actual step height position, and the parameter L is the step height rather than the film thickness. Corresponds to itself. This theoretical model is therefore based on a complex addition of rays originating from both sides of the step height. Since the distance in the horizontal direction of the pixel under inspection increases from the position of the step height, the signal tends to be a simple plane.

  In the example of FIGS. 16a-16b, a library is created experimentally by observing the signal generated by the interferometer for a 2400 line grating. Based on this experimental data, the characteristics in the scanning interferometry data are associated with the corresponding lateral positions in the grating period, and a library is constructed. The experimental data for each pixel of the test sample (in this case the same 2400 line grid) is then compared to the library to determine the best lateral position in the period for that pixel.

  In the detailed analysis described above, a comparison between information in actual data and information corresponding to various models was made in the frequency domain. In other embodiments, the comparison can be made in the scan coordinate domain. For example, a change in the absolute position of the fringe contrast envelope generally indicates a change in surface height at the first surface location corresponding to the signal of interest, but the shape of the signal (regardless of its absolute position) is complex. Information on the surface structure at the first surface location, such as the underlying layer at the first surface location and / or the adjacent location.

  One simple case is to consider the amplitude of the fringe contrast envelope itself. For example, if the thickness of the thin film is very small compared to the wavelength range generated by the light source, the interference effect generated by the thin film becomes independent of the wavelength. In this case, the amplitude of the fringe contrast envelope is directly modulated by the thin film thickness. Thus, in general, the fringe contrast amplitude can be compared with the fringe contrast amplitude for models corresponding to various thin film thicknesses to identify a match for a particular thin film thickness (from the interferometer itself). Systematic impacts of

  Another simple case is to look at the relative spacing of the fringe zero crossing below the fringe contrast envelope. When a simple surface structure is illuminated with symmetric frequency dispersion, the relative spacing between the various zero crossings should nominally be the same. Thus, the change in relative spacing indicates a complex surface structure (when considering systematic effects from the interferometer itself). The change in relative spacing can also be compared to models for various complex surface structures to identify a match for a particular surface structure.

  In other cases, look at the correlation between the scan domain signal and the scan domain signal corresponding to the various models of the test surface. Matching generally corresponds to the correlation with the highest peak value. The highest peak value indicates a model in which the shape of the scan domain signal is most similar to the shape of the actual signal. Such an analysis is generally independent of the surface height. The reason is that the difference between the actual sample surface height and the surface height of each model only shifts the peak location in the correlation function, and generally does not affect the peak value itself. is there. On the other hand, once an accurate model is identified, the peak location in the correlation function of the accurate model provides the surface height for the test sample without the need for further analysis (eg, conventional FDA).

  Similar to analysis in the spatial frequency domain, analysis in the scan coordinate domain can be used for many different types of complex surfaces. Such surfaces include not only thin films, but also other complex surface structures such as the surface height features that cannot be fully resolved as described above.

The scanning coordinate library search analysis with correlation between the signal for the test sample and the corresponding signal for the various models of the test sample will now be described in detail.
This approach excludes any assumptions about the interference pattern except as described below. That is, in a data set corresponding to surface locations having the same complex surface characteristics, all pixels contain the same basic localized interference pattern, which is simply a location for each pixel. Is only shifted (or rescaled). It doesn't matter what the signal really looks like, whether it is a Gaussian envelope or a linear phase behavior in the frequency domain. The idea is to generate a sample signal or template that represents this local interference pattern for various models of complex surface structures for the test object, and for each pixel the local interference pattern is the actual local pattern. Find a model that best matches the shape of the interference pattern and, for that model, determine the scan position in the data set that gives the best match between the interference pattern template and the observation signal that gives the surface height. To find. Several techniques are available for pattern matching. One approach is to mathematically correlate each template with the data. For each model, two profiles are reproduced by using a complex (ie real part plus imaginary part) template function. One is closely related to the signal envelope and the other is related to the phase of the underlying carrier signal.

  In one embodiment, for example, the analysis for each pixel includes: (1) select a test template from a library of tunable parameters, eg calculated or recorded for a specific value of film thickness, (2) using the selected test template and correlation technique Find the local surface height (examples will be described later), (3) record the peak merit function value for the test template selected based on the correlation technique, (4) all of the templates in the library or Repeat steps 1-3 for the subset, (5) determine which test template gives the best match (= highest peak merit function value), (6) tunable for best matched template Record values for various parameters (eg thin film thickness), (7) Data Call the height values that gave peak matching position in the race.

  Next, a suitable correlation technique based on complex correlation will be described. A template interference pattern is generated for each model of the test surface.

ここで、屈折率ｊは、テンプレート・パターンに対する特定のモデルを示す。関数ｍ^ｊ _ｔｅｍｐ（ζ）およびφ^ｊ _ｔｅｍｐ（ζ）によって、複雑な表面構造が特徴付けられる。しかしこれらの関数は、信号に対応する箇所における表面高さには無関係である。表面高さはゼロに設定される。好ましい実施形態においては、関数ｍ^ｊ _ｔｅｍｐ（ζ）およびφ^ｊ _ｔｅｍｐ（ζ）によって、干渉計からの系統的な影響も明らかになる。そして、テンプレート・パターンに対する複素数表現を用いる。

Here, the refractive index j indicates a specific model for the template pattern. The functions m ^j _temp (ζ) and φ ^j _temp (ζ) characterize complex surface structures. However, these functions are independent of the surface height at the location corresponding to the signal. The surface height is set to zero. In the preferred embodiment, the functions m ^j _temp (ζ) and φ ^j _temp (ζ) also reveal the systematic effects from the interferometer. Then, a complex number expression for the template pattern is used.

さらにウィンドウ関数を用いて、複素テンプレート関数の特定の部分を選択する。

Further, a specific part of the complex template function is selected using a window function.

たとえば、適切なウィンドウは、以下のようであってもよい。

For example, a suitable window may be as follows:

ここで、ウィンドウ幅Δζは、手入力で設定することができる。

Here, the window width Δζ can be set manually.

Since there is an interference pattern template I ^ ^j _pat , it can be used to compare with the actual data set. In preparing this, it is convenient to generate a complex signal I ^ _ex starting from the actual experimental data set.

この信号のフーリエ変換は、以下の通りである。

The Fourier transform of this signal is as follows.

ここで、

here,

そして、スペクトルの正の周波数部分から部分的なスペクトルを構築する。

A partial spectrum is then constructed from the positive frequency portion of the spectrum.

そして逆変換は、以下の通りである。

The inverse transformation is as follows.

ここで、この複素関数Ｉ＾_ｅｘの実部は、当初の実験データＩ_ｅｘである。さらに、位相および包絡線は、簡単な操作によって分離することができる。たとえば、複素関数Ｉ＾_ｅｘの振幅を用いて、信号強さＡＣ_ｅｘ（ｘ）および包絡線ｍ_ｅｘの積を利用することができる。

Here, the real part of this complex function I ^ _ex is the original experimental data _Iex . Furthermore, the phase and envelope can be separated by a simple operation. For example, the product of the signal strength AC _ex (x) and the envelope m _ex can be utilized using the amplitude of the complex function I ^ _ex .

技術の基礎となる理論にしたがって、ｍ_ｅｘの少なくとも有意義な部分が、正確なモデルに対するｍ^ｊ _ｔｅｍｐと同じ一般的な形状を有し、唯一の違いは、線形のオフセットｈ_ｅｘおよびスケーリング因子ＡＣ_ｅｘ（ｘ）であると予想される。また実験および干渉パターン・テンプレート位相オフセットφ_ｅｘ、φ^ｊ _ｐａｔ間の差が、正確なモデルに対する高さｈ_ｅｘに直線的に比例していると予想される。

According to the underlying theory of the technology, at least a significant part of m _ex has the same general shape as m ^j _temp for the exact model, the only difference being the linear offset h _ex and the scaling factor AC _ex Expected to be (x). It is also expected that the difference between the experimental and interference pattern template phase offsets φ _ex , φ ^j _pat is linearly proportional to the height h _ex for the exact model.

The challenge for the time being is to place a specific signal pattern represented by the interference pattern template I ^ ^j _pat in the experimental data I ^ _ex to determine how good a matching exists for each of the different models j It is to be. In the following, it is described that the refractive index j is omitted and the matching analysis proceeds for each model.

The first step is to find the scan position ζ _best where the shapes of the envelopes m _ex , m _pat and φ _ex , φ _pat are best matched. A feasible approach is a merit function based on a normalized correlation between the interference pattern template and the signal in the segment of the scan defined by the window w.

ここで、

here,

は、複素相関関数であり、および

Is the complex correlation function, and

は、メリット関数Πを信号強さとは無関係にする規格化である。テンプレートの複素共役Ｉ＾^＊ _ｐａｔを用いることによって、同位相の線形の位相項Ｋ_０ζが打ち消され、φ_ｅｘ、φ_ｐｌａｔがマッチングするときにΠが最大になる。相関関係の絶対値によって、残りのわずかな複素位相も取り除かれる。

Is a standardization that makes the merit function Π independent of signal strength. By using the complex conjugate I ^ ^* _pat of the template, the linear phase term K ₀ ζ of the same phase is canceled, and Π is maximized when φ _ex and φ _plate match. The absolute value of the correlation also removes the remaining few complex phases.

  Carefully add a minimum value to the denominator so that ζ (ζ) does not yield false high values or encounter singularities at low signal levels. For example:

ここで、ｍａｘ（）関数は、全走査長さζにおける信号強さ｜Ｉ＾_ｅｘ｜の最大値を戻す。ＭｉｎＤｅｎｏｍは、メリット関数検索において有効であると考えられる最小の相対信号強さである。ＭｉｎＤｅｎｏｍの値は、５％または他の何らかの小さい値においてハード・コードすることもできるし、調整可能なパラメータのままにしておくこともできる。

Here, the max () function returns the maximum value of the signal strength | I ^ _ex | for the entire scanning length ζ. MinDenom is the minimum relative signal strength that is considered to be effective in the merit function search. The value of MinDenom can be hard coded at 5% or some other small value, or it can be left as an adjustable parameter.

  The correlation integral I ^ can also be performed in the frequency domain using the correlation theorem.

ここで、Ｉは以下の関係を用いた。

Here, I used the following relationship.

ここで、

here,

Πを通して検索してピーク値を見出すことによって、最良のマッチング位置ζ_ｂｅｓｔが得られる。Πの値は、マッチングの品質の測定値であり、ゼロから１の範囲である。なお１は、完全なマッチングに対応する。メリット関数のピーク値を、種々のモデルのそれぞれに対して計算して、どのモデルが最良のマッチングであるかを決定する。そしてそのモデルに対する最良のマッチング位置ζ_ｂｅｓｔによって、表面高さが与えられる。

The best matching position ζ _best is obtained by searching through Π to find the peak value. The value of Π is a measure of the quality of matching and ranges from zero to one. Note that 1 corresponds to perfect matching. The peak value of the merit function is calculated for each of the various models to determine which model is the best match. The surface height is then given by the _best matching position ζ _best for that model.

Examples of the present technology are illustrated in FIGS. FIG. 20 shows an actual scanning interference spectral signal of a base Si substrate without a thin film. Shown in FIGS. 21 and 22 are interference template patterns for a bare Si substrate and a thin film structure with 1 micron SiO ₂ formed on Si, respectively. Shown in FIGS. 23 and 24 are merit functions as a function of scan position for the template functions of FIGS. 21 and 22, respectively. The merit function shows that the matching of the interference template pattern to the bare substrate (peak value 0.92) is much better than the matching to the thin film template pattern (peak value 0.76). . Therefore, the merit function indicates that the test sample is a bare substrate. Furthermore, the position of the peak in the merit function for the correct template pattern gives the relative surface height position for the test sample.

In particular, specific examples of techniques related to surface features that cannot be sufficiently resolved, such as patterned structures in the front-end semiconductor manufacturing process, are described.
Although patterned by optical lithography, the front-end or transistor-level semiconductor manufacturing process involves features that are well below the resolution limit of visible wavelength microscopy. While the minimum features such as transistor gates are on the order of 40 nm wide, the transfer function of a typical scanning interferometer instrument is zero for a 400 nm periodic structure. For example, FIG. 28 shows the theoretical and experimental instrument transfer functions for a white light interference microscope using a 100 × 0.8 NA Mirau objective and non-coherent illumination. This lower limit often corresponds to gate, shallow trench isolation (STI), interconnect, and via isolation, and some, but not all, surface structures can be seen. Therefore, these characteristics that cannot be sufficiently resolved cannot be directly measured as a height object by a normal method using a white light interference microscope. However, if it is possible to understand how changes in height below resolution can adversely affect the generation of scanning interferometry data, it is still possible to parameter monitor (eg depth and width). It is.

  FIG. 29a shows a simple cross-sectional model of a symmetric grid with unpatterned regions on both sides. The y coordinate is parallel to the line and oriented in the direction of the drawing, and the x coordinate is in the left-right direction. The vertical position at z = 0 corresponds to the top of the line. With a simple scalar diffraction model and Abbe's principle, when the grating line width L and spacing W are below the resolution limit shown in FIG. 28, the grating lines are blurred together and the new view (NewView) has a lateral dimension L and It is confirmed that W and height H cannot be directly measured. However, this same scalar analysis shows that although the gate line itself is not distinguishable, the apparent height of the etched region actually depends on the line height, width, and spacing. The exact dependence can be predicted to some extent by modeling and is refined by experimental evidence.

  As described above, certain embodiments disclosed herein utilize observations that the apparent height of the patterned area is related to the feature parameter of interest. An apparent surface height profile is generated using conventional processing interferometry techniques such as FDA. If the pitch is less than half-wave, these profiles are at the overall “averaged” height H ′, as shown in FIG. 29b, which shows a simulated measured surface profile superimposed on the grating structure. Show no grid lines, or at most only some echoes of the lines. Therefore, the height H 'between the area on the line and the area on the unpatterned exposed substrate is measured. This result is referred to as the zero etch height by subtracting the etch depth E to obtain E '= H'-E. Alternatively, if a measured profile of zero etch is available as shown in FIG. 29c (also showing a simulated measured surface profile superimposed on the grating structure), the measured etch is measured. Depth E ′ is directly referenced as the zero etch height (this is a more common measurement scenario). Assuming that the lateral dimensions L and W are known in advance, the exact line height H follows the sensitivity of the entire measurement procedure to the parameter of interest by modeling. Alternatively, if H and L are known, other parameters such as W or line shape can be inferred.

  When more rigorous modeling is used in view of the polarization effect, the simulated profile shown in FIGS. 29b and 29c quantifies the behavior when the polarization is orthogonal to the gate line (defined as the x direction). Is shown. Conversely, parallel or y-polarized light is more strongly affected by the top of the line, and in some cases occurs as if there is no spacing between the lines. This makes physical sense in that the polarization aligned with the gate line at the expense of the area between the lines produces a current that enhances the effect of the top of the line. Since measurement sensitivity for various structural parameters varies with polarization, it is possible to isolate specific parameters such as etch depth to minimize sensitivity to other parameters such as line width.

  Thus, embodiments of the measurement technique are: 1) Step height between the use of a standard interference microscope with circular polarization and neighboring unpatterned regions in a known height field of view for pre-etched silicon. 2) Use of x (orthogonal to line) polarized light to improve sensitivity to deep (> 20 nm) trenches as described above; 3) Use of linearly polarized light and neighboring regions of orthogonally arranged grating lines A comparison of heights between; 4) a comparison of measured heights for each of the x and y polarization states in the same field of view for a common reference that is not polarization dependent, such as smooth and flat areas; Measured for each of the x and y polarization states in the same field of view by acquiring data for two polarizations simultaneously or by directly interfering the polarization states Comparison with each other in height, including. This approach eliminates all the need to provide a separate reference on the object surface.

Note that the basic measurement principle is not limited to gratings but can be extended to other structures.
Although the scalar or Abbe model presents some important insights into basic measurement problems, quantitative analysis of complex (multi-material) well-resolved surface structures is a 2D approach based on the Rayleigh hypothesis described above. Alternatively, the Maxwell equation can be solved over a range of bandwidths and angles of incidence, such as a more rigorous RCWA approach, to benefit from a more rigorous modeling of the interferometric signal.

  For example, the 2D Rayleigh approach describes the inversion result shown in FIG. 27 for circularly polarized light incident on a patterned structure sample wafer. Specifically, for unpolarized or circularly polarized light, there is a competition between the x and y polarization states that cause the inverse correlation. Since the inversion is due to the high sensitivity of the x-polarized reflection intensity to the etching depth, the contribution of x-polarized light is modulated compared to y-polarized light. Since the two polarizations exhibit different depths, the balance between their respective reflection intensities creates a non-linear correlation between the apparent and actual grating modulation depths. 2D Rayleigh calculations show that such inversion can occur on lattice lines that cannot be resolved.

  In another embodiment, a rigorous RCWA approach is used to model a pure silicon 5-line lattice without an overlayer, where the lines are W = 120 nm wide and the pitch L = 320 nm. A schematic representation of the grid is shown in FIG. 30a. The output of the simulation shown in FIG. 30b is a simulated SWLI signal (z direction) for each series of pixels (x direction). FIG. 30b shows only the results for y-polarization parallel to the line, which is more sensitive to the top of the line than to the region or trench between the lines. A familiar white, approximated by a carrier fringe pattern modulated by an envelope or fringe contrast function when looking at the output for a single pixel for x and y polarization, respectively, as in FIGS. 31a and 31b A light interference pattern can be recognized. Here, some distorted x indicating competition between the raw top of the grid line and the trench in between, leading to an attenuated signal with an envelope structure and a general shift to the left corresponding to a lower height Note the polarization signal (FIG. 31a).

  FDA analysis of these signals yields the apparent surface profiles shown in FIGS. 32a and 32b for x-polarized light (orthogonal to the grating line) and y-polarized light (parallel to the grating line), respectively. To correlate with the step height measurement, the central pixel is compared with the edge pixel to determine H ', where the edge pixel is assumed to indicate the true etch depth E of the substrate. The measured etching depth of the substrate is E ′ = H′−E. This value is a value measured when referring to an unetched substrate region. Modeling or experimental data is used to change the apparent etch depth to the actual depth.

  Figures 33a and 33b are extracted from simulated scanning interferometry data as a function of different actual etch depths E for y-polarization (parallel to the grating line) and x-polarization (perpendicular to the grating line), respectively. The RCWA analysis result with respect to the apparent etching depth E ′ = H′−E is shown. The E ′ = E line is for reference. Figures 34a and 34b show the corresponding signal intensities for different actual etch depths E for y-polarized light (parallel to the grating line) and x (perpendicular to the grating line), respectively. The result shows the expected behavior for the two polarization states. Clearly, assuming that the reflection intensity is minimal at an etching depth of 145 nm as shown in FIG. 34b, the preferred form for the sensitivity of the etching depth is x-polarized light.

  The difference between the measured height E 'and the etched height E is, in a sense, a bias or offset resulting from an unprocessed grid line containing the overlayer. In the ideal case, the instrument simply ignores the presence of the line, assuming that the substrate etch depth is the only parameter of interest. FIG. 35 is a graph for the same data as FIG. 33b, and shows that for x-polarized light, the bias is moderate and does not change rapidly with etch depth. Specifically, for a silicon grating, the measurement bias or offset E-E 'is shown as a function of the measured step height -E'.

  FIG. 36 shows the expected RCWA results for circularly polarized light for a pure Si grating. Specifically, the RCWA prediction for the measured etching depth E ′ = H′−E by circularly polarized light when compared to the one-to-one corresponding line as a function of the actual etching depth E for the silicon lattice. Show. Here, it is noted that the system response is generally poor, and in particular, the inverse correlation between the measured etch depth and the actual etch depth is 60 nm and 170 nm. This is expected from the Rayleigh hypothesis and is the same as the phenomenon shown in FIG. 27 and described above. For etching above 100 nm, the measured depth is negative, i.e., the etched silicon rises above the unetched silicon. The area appears as a protrusion rather than a depression.

  37a and 37b show the RCWA prediction of the measured (apparent) etch depth E ′ = H′−E for a 5-line silicon grating for y and x polarization, respectively, with etch depth E = 100 nm and pitch L = As a function of feature width W for 320 nm. In each graph, the solid line marks the reference etching depth. These graphs show several interesting behaviors, including relative insensitivity over a wide range of line widths. These results show that, for example, for line widths of 100 nm to 180 nm, at least for this parameter combination (compared to FIG. 33) x-polarization measurements are much more sensitive to etch width than line width. Yes. However, y-polarized light is less sensitive in each case, but is more sensitive to line width than etching depth.

  Quantitatively, the minimum reflectivity in FIG. 33b and the inverse correlation in FIG. 36 are the result from a state where the corresponding grating depth causes a phase flip associated with the quarter-wave antireflection state. Understood. Thus, if it is desired to move to a more linear part of the correlation curve, the wavelength of light used in the interferometer is adjusted for the quarter-wave state, where the quarter-wave state is The product of the grating depth and the material refractive index between lines (for example, n = 1 for air in this structure) is the sum of a quarter of the optical wavelength and an integer multiple of half the optical wavelength (including zero) Is satisfied when equal to. On the other hand, the presence of a minimum value of reflectivity (more generally, reflectivity information derived from interferometric spectral signal intensity) is useful for different models of samples to determine information about surface features that cannot be fully resolved. As information to be compared with expected information, it may be used alone or with an apparent surface profile.

  The above example is particularly concerned with one-dimensional patterned structures, but the general principles of the technique are other types of fully resolved such as discrete step heights and two-dimensional patterned structures. It can be extended to surface patterns that cannot. The underlying principle is that even if the surface features cannot be sufficiently resolved, they affect both the interference spectral signal for individual pixels and the collective information extracted from the interference spectral signals from multiple pixels. . Thus, the experimentally derived information can be compared to a model parameterized with different values for the features that are of interest and cannot be resolved, and the best comparison yields corresponding values for the features of interest.

  Further, in other examples, different portions of the grating may have different modulation depths and may be formed on different material compositions. For example, the lattice structure is formed on a silicon substrate that includes regions of silicon dioxide. Furthermore, the area of the lattice between silicon dioxide is etched to different depths. In such an embodiment, the information compared to the model is the apparent surface height difference between the various resolved regions of the grid. That is, the portion of the lattice formed on the silicon dioxide can be distinguished from the other portions of the lattice without the individual lattice lines being decomposed.

  FIG. 38 is a diagram illustrating how components of an interferometry system 900 used to generate an interferometry signal under control of the electronic processor 970 are automated, and in an embodiment of the present disclosure The electronic processor includes an analysis processor 972 that performs mathematical analysis (eg, comparison with a model library), a device controller 974 that controls various components of the interferometry system, and a user interface 976 (eg, a keyboard). And a display) and a storage medium 978 that stores information (eg, library model and calibration information), data files, and / or automated protocols. The interferometry system 900 generally directs test light 922 to a test object 926 that is secured to a mount 940 on a stage 950.

  Initially, the system includes a motorized turret 910 configured to support a plurality of objective lenses 912 and guide the selected objective lens into the path of input light. One or more objective lenses may be interference objective lenses, and different interference objective lenses provide different magnifications. Further, in some embodiments, the interferometric objective lens is attached (eg, to illuminate the grating pattern with light polarized perpendicular to the grating lines) (eg, a linear polarization element). Child). In such a case, the orientation of the polarizer may be under automatic control, for example, to align the polarization of the illumination light with respect to the grating lines of the patterned structure. In addition, the objective lens or lenses may be non-interfering spectroscopic objectives (ie, without a reference leg), each having a different magnification, so that the system 900 collects a light image of the test surface in a conventional microscope mode. Can also work. The turret 910 is under the control of an electronic processor 970 that selects the desired objective lens in response to user input or some automatic protocol.

  The system includes a motorized stage 920 (eg, a lens barrel holder) that supports relay lenses 936 and 938. Such a stage can be used to select between the profiling mode generally intended in this application and the ellipsometry or reflectometry mode in which the pupil plane is imaged on the detector, as referenced herein. US Patent Application Publication No. 2006/0158659 by Colonna de Lega et al., Entitled “Interferometer for determining characteristics of object surface”, incorporated by reference. Is disclosed. The motorized stage 920 is under the control of an electronic processor 970 that selects the desired relay lens in response to user input or some automated protocol. In other embodiments where the translation stage is moved to adjust the position of the detector to switch between the first and second modes, the translation is under the control of an electronic processor. Further, in embodiments with multiple detection channels, each detector is connected to an electronic processor 970 for analysis.

  In addition, the system includes apertures 930 and 932 that are under the control of electronic processor 970 to control the dimensions of the field stop and aperture stop, respectively. Again, the motorized aperture is under the control of an electronic processor 970 that selects the desired setting in response to user input or some automatic protocol.

  The translation stage 980 used to change the relative optical path length between the interferometer test leg and the reference leg is under the control of the electronic processor 970. The translation stage is connected to adjust the position of the interference objective relative to the mount 940 that supports the test object 926. Alternatively, in a further embodiment, the translation stage can adjust the position of the interferometry system as a whole with respect to the mount, or the translation stage may be connected to the mount, so that the mount has an optical path length difference. Moved to change.

  Further, a lateral translation stage 950 under the control of the electronic processor 970 is connected to a mount 940 that supports the test object for lateral translation across the region of the test surface being optically inspected. In certain embodiments, the translation stage 950 can orient the mount 940 (eg, tilt and tilt) to align the test surface perpendicular to the optical axis of the interfering objective.

  Finally, an object processing station 960 under the control of the electronic processor 970 is connected to the mount 940 to automatically guide and remove test samples from the system 900 for measurement. For example, automated wafer processing systems known in the art may be used for this purpose. Further, the system 900 and object processing system may be housed under vacuum or under a sterile room, if necessary, to minimize contamination of the test object.

  The resulting system is flexible in providing a variety of measurement methods and procedures. For example, the system may be initially configured in a microscope mode with one or more selected magnifications to capture light images of the test object for various lateral positions of the object. Such images are analyzed by the user or by the electronic processor 970 (using machine vision technology) and certain areas in the object (eg, specific structures or features, landmarks, fiducial markers, defects, etc.) Is identified. Based on this identification, selected regions of the sample are analyzed in ellipsometry mode to determine sample properties (eg, refractive index, underlying film thickness, material identification, etc.).

  When used in conjunction with the automatic object handling system 960, the measurement procedure is automatically repeated for a series of samples. This is useful for various process control schemes such as monitoring, testing and / or optimizing one or more semiconductor processing stages.

  For example, the system may be used in semiconductor processing to control tool specific monitoring or the process flow itself. For process monitoring applications, single / multilayer films are grown, deposited, polished, or etched on Si wafers (monitoring wafers) that are not patterned by the corresponding processing tool, Thickness and / or optical properties are measured using the disclosed interferometry system. The average thickness (and / or optical properties) of the monitoring wafer and the wafer uniformity are operating at the specifications that the relevant processing tool is intended for, or directed to a new target, adjusted, or Used to determine if it should be removed from production use.

  For process control applications, the latter monolayer / multilayer film is grown, deposited, polished, or etched on a Si production wafer patterned with a corresponding processing tool, and then the interference disclosed herein. The thickness and / or optical properties (eg, using ellipsometry mode, profiling mode, or both) are measured using a spectroscopic system. Manufacturing measurements used for process control typically involve aligning a measurement tool with a small measurement site and a sample region of interest. Since the part consists of a multilayer stack (which may itself be patterned), it requires complex mathematical modeling to extract physical parameters. Process control measurements should determine the stability of the integrated process flow and continue the integrated process, be directed to a new target, redirected to other equipment, or completely shut down Determine whether.

  Specifically, for example, the interferometry system described herein includes diffusion, rapid thermal annealing, chemical vapor deposition tools (low pressure and high pressure), dielectric etching, chemical mechanical polishing, plasma deposition, plasma etching, lithography Can be used to monitor equipment such as tracks, lithography exposure tools, etc. Furthermore, the described interferometry system can be used to control processes such as trench and isolation, transistor formation, and interlayer dielectric formation (eg, dual damascene). The methods and systems described above can be particularly useful in semiconductor applications. Further embodiments of the present invention include applying any of the measurement techniques described above to address any of the semiconductor applications described below, and a system that performs both the measurement techniques and the semiconductor applications.

  Currently, the quantitative measurement of surface topography is of considerable interest in the semiconductor industry. Due to the small size of typical chip features, the equipment used to make these measurements typically must have a high spatial resolution both parallel and perpendicular to the chip surface. Engineers and scientists use surface topography measurement systems to control processes and detect defects that occur during manufacturing, particularly defects that result from processes such as etching, polishing, cleaning, and patterning.

  In order for process control and defect detection to be particularly useful, surface topography measurement systems have a minimum horizontal resolution that is comparable to the horizontal size of typical surface features and the vertical resolution is acceptable. The surface step height must be comparable. This usually requires that the lateral resolution is less than a micron and the vertical resolution is less than 1 nanometer. Such a system also makes its measurements without touching the chip surface, and without otherwise exerting potentially damaging forces on the surface to avoid surface modification or defect introduction. It is preferable. In addition, it is well known that the effects of many processes used in chip fabrication are strongly dependent on local factors such as pattern density and edge approximation, so that surface topography measurement systems can achieve high measurement throughput, It is also important to have the ability to sample densely over a large area in a region that may contain one or many surface features.

  It is becoming common among chip manufacturers to use the so-called “dual damascene copper” process to create electrical interconnects between various parts of a chip. This is an example of a process that can be effectively characterized using a suitable surface topography system. The dual damascene process can be considered to have five parts. (1) Interlayer dielectric (ILD) deposition in which a layer of dielectric material (eg, polymer or glass) is deposited on the surface of a wafer (containing a plurality of separate chips). (2) Chemical mechanical polishing (CMP) that polishes the dielectric layer to form a smooth surface suitable for precision photolithography. (3) Lithographic patterning and reaction in which a complex network is formed that includes narrow trenches that run parallel to the wafer surface and small vias that run from the bottom of the trench to the lower (pre-defined) conductive layer. A combination of reactive ion etching steps. (4) A combination of metal deposition steps resulting in trenches and vias that are overfilled with copper. (5) A final chemical mechanical polishing (CMP) step that removes excess copper and leaves a network of copper filled trenches (and / or vias) surrounded by dielectric material.

  Typically, the copper thickness (ie, trench depth) in the trench region and the surrounding dielectric thickness is in the range of 0.2 to 0.5 microns. The resulting trench width may be in the range of 100 to 100,000 nanometers. Also, the copper regions in each chip may form a regular pattern, such as an array of parallel lines, in certain regions and no obvious pattern in other regions. Similarly, in some areas, the surface may be densely covered with copper areas, and in other areas the copper areas may be sparse. It is important to understand the following: That is, the polishing rate, and hence the thickness of the remaining copper (and dielectric) after polishing, as well as the polishing conditions (eg, pad pressure and polishing slurry composition) as well as local details of the copper and surrounding dielectric regions. Depends on placement (ie, orientation, proximity, shape) in a strong and complex manner.

  This “position dependent polishing rate” is known to produce variable surface topography at many lateral length scales. For example, a chip located near the edge of the wafer on the assembly is polished more rapidly than a chip located near the center, so that the copper area formed is thinner than desired near the edge and desired at the center. May mean thicker. This is an example of "wafer scale" process non-uniformity, i.e. occurs on a length scale comparable to the wafer diameter. Further, it is known that the polishing rate in the region where the high-density copper trench is present is higher than that in the nearby region where the copper line density is low. This causes a phenomenon known as “CMP induced corrosion” in the high copper density region. This is an example of "chip scale" process non-uniformity, i.e. occurs on a length scale comparable to the length dimension of a single chip (which may be much smaller). Within a single copper-filled trench region (which tends to polish at a higher rate than the surrounding dielectric material), another type of chip-scale non-uniformity (known as “desching”) is present. Occur. It is dangerous if the trench is larger than a few microns in width dishing, and the electrical resistance of the affected line may later become excessive. This causes a chip failure.

  CMP-induced wafer and chip-scale process non-uniformity is inherently difficult to predict. They also change over time as the state in the CMP processing system evolves. To ensure that process conditions are effectively monitored and adjusted appropriately to ensure that any non-uniformity remains within acceptable limits, the process engineer must perform many non-contact surface topography measurements on the chip and It is important to do it frequently in a wide area. This is possible using the embodiment of the interference spectroscopy technique described above.

  The above-described interferometer embodiments include Mirau and linic interference objective lenses. In the Mirau type, the beam splitter of the interference objective lens directs the reference light back along the optical axis of the test light. In the linic type, the beam spirit is positioned in front of the objective lens (relative to the input light) with respect to the test surface and directs the test light and the reference light along different paths. A separate objective lens is used to focus the reference light on the reference lens. That is, the beam splitter separates input light into test light and reference light, and separate objective lenses focus the test light and reference light on the test surface and reference surface, respectively. Ideally, the two objective lenses are matched to each other so that the test light and the reference light have similar aberrations and optical paths.

  In other embodiments, the interferometry system may alternatively use a different type of interference objective, such as a Michelson objective, where the beam splitter directs the reference light away from the optical axis of the test light. (For example, the beam splitter is oriented at 45 degrees with respect to the input light so that the test light and the reference light travel at right angles to each other). In such a case, the reference surface is positioned outside the test light path.

  Further interferometer structures are possible. For example, the system may be configured to collect test light that is combined with the reference light after passing through the test sample. In such an embodiment, the system may implement a Mach-Tender interferometer with a dual microscope objective on each leg.

  Interferometer light sources include incandescent light sources such as halogen or metal halide lamps with or without spectral bandpass filters, broadband laser diodes, light emitting diodes, combinations of several light sources of the same or different types, visible spectrum All light sources in the region, in particular all light sources in the IR spectral region for viewing rough surfaces and applying phase profiling, and especially in the UV spectral region for increased lateral resolution Either is acceptable. For broadband applications, the light source preferably has a net spectral bandwidth longer than 5% of the average wavelength, more preferably longer than 10%, 20%, 30% and even 50% of the average wavelength. For adjustable narrowband applications, the adjustment region is preferably wide enough to provide information over a wide range of wavelengths (eg, greater than 50 nm, greater than 100 nm, or even 200 nm for visible light). On the other hand, the spectral width at any particular setting is preferably narrow to optimize resolution as small as 10 nm, 2 nm, or 1 nm. The light source may include one or more diffusing elements to increase the spatial extent of input light emitted from the light source.

  In addition, the various translation stages in the system, such as translation stage 150, are driven by either a piezoelectric device, a stepper motor, and a voice coil, and pure translation (e.g., liquid crystal, electro-optic effect, All drive and mechanical stages, eg rolling bearings or air bearings, which are carried out optomechanically or optoelectronically (rather than using strained fibers and rotating waveplates) All the drive units provided may be used. As mentioned above, phase shifting with respect to the scanning interferometry signal is often performed using a mechanical translation stage, but if there is a non-zero optical path length difference between the test leg and the reference leg, the wavelength of the light source is changed. Thus, it is possible to change the phase between the test leg and the reference leg of the interferometer.

The electronic detector may be any type of detector that measures an optical interference pattern with spatial resolution, such as a multi-element CCD or CMOS detector.
Any of the computer analysis methods described above can be implemented in hardware or software or a combination of both. The method can be implemented in a computer program using standard programming techniques in accordance with the methods and figures described herein. Program code is applied to input data to execute the functions described herein and generate output information. The output information is applied to one or more output devices such as a display monitor. Each program may be implemented in a high level procedural or object oriented programming language to communicate with a computer system. However, the program can be implemented in assembly or machine language as required. In any case, the language can be a compiled language or an interpreted language. Furthermore, the program can be executed on a dedicated integrated circuit preprogrammed for that purpose.

  Each such computer program is preferably stored on a storage medium or device (eg, ROM or magnetic disk) readable by a general or special purpose programmable computer such that the storage medium or device is a computer. Configure and operate the computer to perform the procedures described herein. The computer program can also reside in cache or main memory during program execution. The analysis method can be realized as a computer-readable storage medium and can be configured by a computer program. By configuring the storage medium as such, the functions described herein are performed by operating the computer in a specific and predetermined manner. The specific description above relates to a scanning interferometry signal in which the interference fringes are localized due to limited coherence in the interferometry system, but in many embodiments an interference spectroscopy signal in which the fringes are not localized. It is possible to extract information about complex surface features from

  For example, interferometry signals from different locations on the test object without fringe localization can be further used to generate an apparent surface profile for the test object, or derived therefrom. The information obtained is compared to a model of expected response to different values of the lateral surface features of the test object that are unprocessed or obscure in the apparent surface profile, as described above for the low coherence scanning interferometry signal. Information about features that cannot be sufficiently resolved in substantially the same way is determined. Techniques for extracting surface profile information from such “high” coherence interferometry signals are commonly referred to as phase shift interferometry (PSI) algorithms and are well known in the art. For example, US Pat. No. 6,359,692, incorporated herein by reference, is entitled “Method and System for Profiling Objects with Multiple Reflective Surfaces Using Wavelength Tuned Phase Shift Interferometry (METHOD). Reference is made to the background and content of "AND SYSTEM FOR PROFILING OBJECTS HAVING MULTIPLE REFLECTIVE SURFACES USING WAVELENGTH-TUNING PHASE-SHIFTING INTERFROMETRY". To generate interferometry data for PSI analysis, the interferometry signal for a given pixel can be generated by mechanically changing the optical path length difference between the reference leg and the measurement leg, or the reference leg and the measurement leg. Is generated by changing the wavelength of light for a fixed non-zero optical path length difference between and.

  While many embodiments of the invention have been described, it will be appreciated that various changes may be made without departing from the spirit and scope of the invention.

It is a flow chart of interferometry. 2 is a flow chart showing a modification of the interferometry method of FIG. It is the schematic of a linic type scanning interferometer. It is the schematic of a Mirau type scanning interferometer. 2 is a diagram illustrating illumination of a test sample through an objective lens. It is a figure which shows the theoretical Fourier amplitude spectrum with respect to the scanning interference spectroscopy data in two limits. It is a figure which shows two surface types with / without a thin film. It shows a merit function search procedure for a simulation of a SiO ₂ film on a Si substrate with a thin film thickness of 0. Film thickness is a diagram showing a merit function search procedure for simulation of a SiO ₂ film on the Si substrate of 50nm. Film thickness is a diagram showing a merit function search procedure for simulation of a SiO ₂ film on the Si substrate of 100 nm. Film thickness is a diagram showing a merit function search procedure for simulation of a SiO ₂ film on the Si substrate of 300 nm. Film thickness is a diagram showing a merit function search procedure for simulation of a SiO ₂ film on the Si substrate of 600 nm. Film thickness is a diagram showing a merit function search procedure for simulation of a SiO ₂ film on 1200nm of the Si substrate. FIG. 6 shows the surface and substrate profile determined for a simulation of a SiO ₂ thin film on Si with the top surface always zero and the film thickness varying uniformly in increments of 10 nm per pixel from 0 to 1500 nm. FIG. 15 is a diagram showing the surface and substrate profiles determined for the simulation of FIG. 14 and the same simulation except that random noise was added (2-bit root mean square from an average value of 128 intensity bits). A library search method described herein for a surface height profile determined using conventional FDA analysis (FIG. 16a) and a grid of 2400 lines per mm with an actual peak / valley modulation depth of 120 nm ( FIG. 16b) is a diagram. FIG. 6 is a diagram illustrating distortion caused by a step height that cannot be sufficiently resolved when scanning interference signals for pixels corresponding to various surface locations near the step height. FIG. 18 shows non-linear distortion in the frequency domain phase spectrum for pixels corresponding to surface locations for left (FIG. 18a) and right (FIG. 18b) step heights that cannot be sufficiently resolved in FIG. FIG. 19 shows a surface height profile determined using conventional FDA analysis (FIG. 19a) and using the library search method described herein (FIG. 19b) for step heights that cannot be fully resolved. . It is a figure which shows the actual scanning interference spectroscopy signal of the Si substrate used as a base without a thin film. It is a figure which shows the interference template pattern with respect to a bare Si substrate. FIG. 6 shows an interference template pattern for a thin film structure with 1 micron SiO ₂ formed on Si. It is a figure which shows the merit function as a function of the scanning position with respect to the template function in FIG. It is a figure which shows the merit function as a function of the scanning position with respect to the template function in FIG. 1 is a schematic illustration of an object having surface features (lattice pattern) that cannot be sufficiently resolved. FIG. 26 is a graph showing an expected surface profile of the lattice pattern of FIG. 25 based on conventional interference spectroscopy analysis. FIG. 26 is a graph showing the apparent modulation depth of the grating of FIG. 25 as a function of the actual modulation depth for conventional interference spectroscopy analysis. It is a graph which shows the transfer function of the theoretical and experimental apparatus of a white light scanning interferometer. FIG. 3 illustrates one embodiment of a grating structure and a technique for measuring a surface that cannot be fully resolved as disclosed herein. FIG. 3 illustrates one embodiment of a grating structure and a technique for measuring a surface that cannot be fully resolved as disclosed herein. FIG. 3 illustrates one embodiment of a grating structure and a technique for measuring a surface that cannot be fully resolved as disclosed herein. FIG. 5 is a schematic diagram of a model structure of 5 lattice lines (without an upper film layer) of pure Si, with W = 120 nm and pitch L = 320 nm. It is a figure which shows the exact coupling wave analysis (RCWA) which shows the scanning interference spectroscopy signal (z direction) with respect to a model structure. FIG. 6 is a diagram for y-polarized light parallel to the line, more sensitive to the top of the line than the region. It is a figure which shows the scanning interference spectroscopy signal with respect to the center pixel of FIG. 30 about the polarization | polarized-light of x. It is a figure which shows the scanning interference spectroscopy signal with respect to the center pixel of FIG. 30 about the polarization of y. 32a and 32b are diagrams showing surface height profiles derived from the FDA analysis of the signal in FIG. 30 for x (perpendicular to the grating line) and y-polarized light (parallel to the grating line), respectively. FIGS. 33a and 33b show the appearance extracted from simulated scanning interferometry data as a function of different actual etch depths E for y-polarization (parallel to the grating line) and x (orthogonal to the grating line), respectively. It is a graph which shows the result of the RCWA analysis with respect to the etching depth E '= H'-E. The E ′ = E line is for reference. FIGS. 34a and 34b are graphs showing corresponding signal intensities for different actual etch depths E for y-polarized light (parallel to the grating line) and x (perpendicular to the grating line), respectively. FIG. 35 is an alternative graph for the same data as FIG. 33b, showing the measured bias or offset E-E 'as a function of the measured surface height -E' for a silicon grating. FIG. 36 shows the RCWA prediction for the measured etch depth E ′ = H′−E with circularly polarized light as a function of the actual etch depth E for the silicon lattice, as compared to a one-to-one corresponding line. It is a graph. 37a and 37b show the RCWA prediction of the measured (apparent) etch depth E ′ = H′−E for a 5-line silicon grating for y and x polarization, respectively, with etch depth E = 100 nm and pitch L FIG. 6 is a graph showing the function width W as a function of 320 nm. 1 is a schematic diagram of an interferometry system showing how the various components of the system are under automatic control.

Claims (56)

A method,
Comparing information derivable from a plurality of scanning interferometry signals corresponding to different surface locations of the test object and information corresponding to a plurality of models of the test object, wherein the plurality of models are Comparing, parameterized by a series of characteristics associated with one or more sufficiently unresolvable lateral features of the test object;
Outputting information about the surface features that cannot be sufficiently resolved based on the comparison. 2. The method of claim 1, wherein the one or more unresolvable lateral features of the test object are a pitch relative to a patterned lateral structure on the test object that is not sufficiently resolvable. , Corresponding to one or more of modulation depth and element width. 2. The method of claim 1, wherein the one or more unresolvable lateral features of the test object are modulated on a patterned lateral structure that is not fully resolvable on the test object. A method that corresponds at least to depth. 4. The method of claim 3, wherein the set of characteristics is a different value for the modulation depth. 5. The method of claim 4, wherein the plurality of models map a correlation of possible results for information derivable from the plurality of interferometric spectral signals to a corresponding one value of the different values for the modulation depth. Represented by a relationship,
The comparing includes determining which of the different values for the modulation depth best corresponds to information derivable from the plurality of interferometric spectral signals. 4. The method of claim 3, wherein the modulation depth is expressed relative to a bias offset value. 3. The method of claim 2, wherein at least some of the interferometry signal is obtained from illumination of the test object whose polarization is directed relative to a lateral structure of the patterned element. 8. The method of claim 7, wherein the polarized light is linearly polarized light (x-polarized light) that is aligned perpendicular to the length of the individual elements that form the patterned lateral structure. Method. The method of claim 1, wherein the one or more unresolvable lateral features of the test object correspond to one or more of a step height and position of the test object. Method. 10. The method of claim 9, wherein the set of characteristics includes a different value for the height or the position of a step height. The method of claim 1, wherein
Information derivable from the plurality of interference spectroscopy signals includes one or more values extracted from a height profile for the test object obtained from the plurality of interference spectroscopy signals;
The method wherein the surface features that cannot be sufficiently resolved are obscured or do not appear in the extracted height profile. 12. The method of claim 11, wherein the test object comprises a patterned lateral structure in which individual elements are ambiguous or do not appear in the extracted height profile. 13. The method of claim 12, wherein information derivable from the plurality of interferometry signals is a height relative to a collection of elements that cannot be sufficiently resolved in the patterned lateral structure extracted from the height profile. Is the value of the method. 14. The method of claim 13, wherein the information about surface features that cannot be sufficiently resolved corresponds to one or more of modulation depth and element width for the patterned lateral structure. 14. The method of claim 13, wherein the different surface locations for the interferometry signal include a reference portion of the test object that provides a reference height value for the extracted height profile. The method of claim 15, wherein
The test object is etched to form a patterned structure;
The method wherein the reference portion of the test object is part of the test object that is known not to be etched. 13. The method of claim 12, wherein at least some of the interferometric spectral signals from which the height profile is determined are directed to the test object whose polarization is directed relative to a lateral structure of the patterned element. The method, derived from the lighting of the. 18. The method of claim 17, wherein the polarized light is linearly polarized light (x-polarized light) that is aligned perpendicular to the length of the individual elements that form the patterned lateral structure. Method. 12. The method of claim 11, wherein the height profile is obtained from a frequency domain analysis of the interferometric spectral signal. 12. The method of claim 11, wherein the height profile is obtained from the relative position of coherence peaks in each interferometry signal. The method of claim 1, wherein the sufficiently unresolved lateral features of the test object include feature sizes less than 400 nm. The method of claim 1, wherein the sufficiently unresolved lateral features of the test object include feature sizes less than 200 nm. The method of claim 1, wherein the sufficiently unresolved lateral features of the test object include feature sizes less than 100 nm. The method of claim 1, wherein the model is computationally generated using exact coupled wave analysis (RCWA). The method of claim 1, wherein the model is experimentally generated from a test object with known properties. The method of claim 1, wherein information about the surface features that cannot be sufficiently resolved is output to a user. 2. The method of claim 1, wherein information about the surface features that cannot be sufficiently resolved is output to an automated process control system for semiconductor manufacturing. The method of claim 1, wherein the interference spectroscopy signal is a scanning interference spectroscopy signal. The method of claim 28, wherein
The test light generated from the test object is imaged and interfered with the reference light on the detector, and the optical path length from the common light source to the detector between the interference part of the test light and the interference part of the reference light The scanning interference spectral signal is generated by changing the difference, the test light and the reference light are extracted from a common light source, and the scanning interference spectral signal is measured by the detector when the optical path length difference is changed. A method corresponding to the interference intensity to be applied. 30. The method of claim 29, further comprising generating the scanning interferometry signal. 30. The method of claim 29, wherein the test light and the reference light have a spectral bandwidth greater than 5% of a center frequency for the test light and the reference light. 32. The method of claim 31, wherein the common light source has a spectral coherence length, and the optical path length difference varies over a range longer than the spectral coherence length to generate the scanning interference spectral signal. The way. 30. The method of claim 29, wherein the numerical aperture for the test light is defined to be greater than 0.8 using an optical component for sending the test light onto the test object and imaging it on the detector. how to. 34. The method of claim 33, wherein the common light source is a spatially extended light source. A method for determining one or more spatial properties of a grating structure on a test object, wherein the line element cannot be completely resolved by an interference microscope because the grating structure comprises line elements having a width of less than 400 nm, In the method
Determining an apparent height for the collection of at least some of the grid lines from interference signals at different locations of the test object measured by the interference microscope;
Providing an expected response of the interference microscope for different possible values to the properties of the lattice structure, wherein the expected response includes an expected response from line elements that cannot be fully resolved of the lattice structure To do,
Comparing the apparent height with the expected response for the different possible values to determine information about the spatial properties of the lattice structure;
Outputting the determined information about the spatial properties of the lattice structure. 36. The method of claim 35, wherein the apparent height is determined with reference to a reference portion of the test object. 36. The method of claim 35, wherein the interference microscope illuminates the grating structure with light polarized perpendicular to the length of individual grating lines in determining the apparent height. 36. The method of claim 35, wherein the determined information about the spatial characteristics of the lattice structure corresponds to a modulation depth for the lattice structure. 36. The method of claim 35, wherein the lattice structure is a series of periodically spaced lines formed at least partially by etching portions between the lines of the test object. 36. The method according to claim 35, wherein the interference signal forms an image of test light generated from a test object and interferes with reference light on a detector, and the interference part of the test light and the interference part of the reference light A scanning interferometry signal generated by changing a difference in optical path length from a common light source to a detector between the test light and the reference light, and the scanning interference spectroscopy A method wherein the signal corresponds to the interference intensity measured by the detector when changing the optical path length difference. 41. The method of claim 40, wherein the optical path length difference is varied over a range that is longer than the coherence length of the interference microscope. A method,
Determining one or more apparent properties of the test surface from the interferometry signal generated by the interferometry system;
Comparing the apparent characteristic determined from the interferometry signal to an expected response of the interferometry system for different possible values to one or more sufficiently unresolvable features of the test surface;
Outputting information about the one or more unresolvable features of the test surface based on the comparison. 43. The method of claim 42, wherein the interferometry system is a scanning interferometry system. 43. The method of claim 42, wherein the apparent characteristic of the test surface is determined from the interference spectroscopic signal based on a change in any of interference phase, interference contrast, and surface reflectance. 43. The method of claim 42, wherein the expected response is calculated for changes in one or more of surface height and surface composition. 43. The method of claim 42, wherein the test surface has a patterned structure having elements with modulation depth, periodicity, and width;
The expected response is calculated for changes in one or more of the modulation depth, the periodicity, and element width. 47. The method of claim 46, wherein the expected response is calculated for changes in the modulation depth. 48. The method of claim 47, wherein the correspondence between the actual modulation depth and the apparent modulation calculated for the expected response is a positive correlation over a first range of actual modulation depths. And a negative correlation over a second range of actual modulation depths. 43. The method of claim 42, wherein the information about the one or more unresolvable features is used to monitor one or more semiconductor processing stages. 50. The method of claim 49, wherein the semiconductor processing steps include isolation patterning and etching, polysilicon gate electrode patterning and etching, source / drain etching and deposition, and metallization patterning, etching, and A method comprising any of polishing processes. A device,
A processor in a computer compares information derivable from a plurality of interference spectral signals corresponding to different surface locations of the test object with information corresponding to a plurality of models of the test object, wherein The model is parameterized by a set of characteristics associated with one or more sufficiently unresolved lateral features of the test object and outputs information about the unresolved surface features based on the comparison An apparatus comprising a computer-readable medium having a program to be executed. A device,
An interferometry system configured to generate a plurality of interferometry signals corresponding to different surface locations of the test object;
An electronic processor connected to the interference spectroscopy system and receiving the interference spectroscopy signal, and compares information derivable from the plurality of interference spectroscopy signals with information corresponding to a plurality of models of the test object. Wherein the plurality of models are parameterized by a set of characteristics associated with one or more sufficiently insoluble lateral features of the test object and cannot be sufficiently resolved based on the comparison An electronic processor programmed to output information about surface features. An apparatus for determining one or more spatial properties of a grating structure on a test object, wherein the line element cannot be completely resolved by an interference microscope because the grating structure comprises line elements having a width of less than 400 nm, In the device
To the processor in the computer,
1) determining an apparent height for a collection of at least some of the grid lines from interference signals at different locations of the test object measured by the interference microscope;
2) providing an expected response of the interference microscope for different possible values to the properties of the grating structure, wherein the expected response includes effects from line elements that cannot be fully resolved of the grating structure;
3) allowing the apparent height to be compared with the expected response for the different possible values to determine information about the spatial properties of the lattice structure;
4) An apparatus comprising a computer readable medium having a program for outputting the determined information about the spatial characteristics of the lattice structure. An apparatus for determining one or more spatial properties of a grating structure on a test object, wherein the line element cannot be completely resolved by an interference microscope because the grating structure comprises line elements having a width of less than 400 nm, In the device
An interference microscope,
An electronic processor connected to the interference microscope,
1) determining an apparent height for a collection of at least some of the grid lines from interference signals at different locations of the test object measured by the interference microscope;
2) providing an expected response of the interference microscope for different possible values to the properties of the grating structure, wherein the expected response includes effects from line elements that cannot be fully resolved of the grating structure;
3) comparing the apparent height with the expected response for the different possible values to determine information about the spatial properties of the lattice structure;
4) An electronic processor programmed to output the determined information about the spatial characteristics of the lattice structure. A device,
To the processor in the computer,
1) determining one or more apparent properties of the test surface from the interferometry signal generated by the interferometry system;
2) comparing the apparent characteristic determined from the interferometry signal with the expected response of the interferometry system for different possible values to one or more unresolvable features of the test surface;
3) An apparatus comprising a computer readable medium having a program for outputting information about the one or more unresolvable features of the test surface based on the comparison. A device,
An interferometry system configured to generate a plurality of interferometry signals corresponding to different surface locations of the test object;
An electronic processor connected to the interferometry system and receiving the interferometry signal,
1) determining one or more apparent properties of the test surface from the interference spectroscopy signal;
2) comparing the apparent characteristic determined from the interferometry signal with the expected response of the interferometry system for different possible values to one or more unresolvable features of the test surface;
3) an electronic processor programmed to output information about the one or more unresolvable features of the test surface based on the comparison.

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