DETECTION AND MEASUREMENT OF THE DIMENSIONS OF ASYMMETRIC STRUCTURES

Abstract

Metrology system (100) comprising: an illumination source (110) configured to generate an amount of broadband optical radiation (117); one or more optical elements directing the amount of broadband optical radiation (117) from the illumination source (110) to a measurement point (116) on a surface of a semiconductor wafer (120) at each of two or more azimuth angles (AZ); a spectrometer (126) configured to detect an amount of measurement light in response to the illumination of the semiconductor wafer (120) at each of the two or more azimuth angles (AZ) from the semiconductor wafer (120) and to determine a measured spectral response of a structure of interest to the illumination based on each detected amount of measurement light, wherein each measured spectral response includes spectra associated with multiple elements of a Müller matrix;and a computer system (130) configured to: estimate values ​​of one or more critical dimensional parameters that characterize the structure of interest, based on a fit of a modeled spectral response to the measured spectral responses associated with the two or more azimuth angles (AZ); select one or more subranges of wavelengths of at least one spectrum of one or more off-diagonal elements of the Müller matrix associated with each measured spectral response; integrate the at least one spectrum of the one or more off-diagonal elements of the Müller matrix over the selected one or more subranges of wavelengths to generate one or more spectral response metrics;and estimating the values ​​of one or more geometric parameters that describe an asymmetric feature of the structure of interest, based on the values ​​of one or more critical dimensional parameters and one or more spectral response metrics.

Description

CROSS-REFERENCE TO RELATED REGISTRATION The present patent application claims priority under 35 USC §119 from the preliminary US patent application with serial number 62 / 564,119 entitled “Detection And Measurement of Dimensions of Asymmetrie Structures”, filed on September 27, 2017, and from US patent application 16 / 138,813, filed on September 21, 2018, published as US 2019 / 0094711A1. TECHNICAL AREA The described embodiments relate to metrology systems and methods, and in particular methods and systems for improved measurement of semiconductor structures. BACKGROUND INFORMATION Semiconductor devices, such as logic and memory devices, are typically fabricated through a sequence of processing steps applied to a sample. The various features and multiple structural levels of the semiconductor devices are formed by these processing steps. For example, lithography is one of several semiconductor manufacturing processes that involves creating a pattern on a semiconductor wafer. Additional examples of semiconductor manufacturing processes include, but are not limited to, chemical-mechanical polishing, etching, deposition, and ion implantation. Multiple semiconductor devices can be fabricated on a single semiconductor wafer and then separated into individual semiconductor devices. Metrology processes are used at various steps during semiconductor manufacturing to detect defects on wafers and promote higher yields. Optical metrology techniques offer the potential for high throughput without the risk of sample destruction. A range of optical metrology-based techniques, including scatterometry and reflectometry implementations and associated analysis algorithms, are commonly used to characterize critical dimensions, layer thicknesses, composition, overlay, and other parameters of nanoscale structures. Many optical metrology systems measure the physical properties of a sample indirectly. In most cases, the measured optical signals cannot be used to directly determine the physical properties of interest. Traditionally, the measurement process consists of formulating a metrology model that attempts to predict the measured optical signals based on a model of the interaction between the target and the measurement system. The measurement model includes parameterizing the structure with respect to the physical properties of interest (e.g., layer thicknesses, critical dimensions, refractive indices, grating spacing, etc.). Furthermore, the measurement model includes parameterizing the measuring instrument itself (e.g., wavelengths, angle of incidence, polarization angle, etc.). For example, machine parameters are parameters used to characterize the measuring instrument itself. Examples of machine parameters include angle of incidence (AOI), analyzer angle (A0), polarizer angle (P0), illumination wavelength, numerical aperture (NA), etc.Sample parameters are parameters used to characterize the geometric and material properties of the sample. For a thin-film sample, examples of sample parameters include the refractive index, the tensor of the dielectric function, the nominal thickness of all layers, the layer sequence, etc. For measurement purposes, the machine parameters are treated as known, fixed parameters, and the sample parameters, or a subset of sample parameters, are treated as unknown, free parameters. The free parameters are determined through a fitting process (e.g., regression, library matching, etc.) that establishes the best fit between the theoretically predicted spectral data derived from the measurement model and the measured spectral data. The unknown sample parameters are varied, and the modeled spectra are iteratively calculated and compared with the measured spectral data until a set of sample parameter values ​​is found that shows a close agreement between the modeled and measured spectra. This traditional model-based measurement approach has been applied to estimate parameters describing asymmetric and symmetric structural features. In some examples, the estimation of parameters describing asymmetric structural features is improved by giving greater weight to the comparison of modeled and measured spectra associated with specific off-diagonal Müller elements. This approach is further described in US Patent US 8,525,993 B2 by Rabello et al. Unfortunately, in many cases, some parameters of interest, especially those describing asymmetric structural features, are only weakly correlated with the measured spectral response. In these cases, changes to the parameters describing an asymmetric structural feature do not lead to significant changes in the resulting spectra. This increases the uncertainty of the regressed values ​​of these parameters due to both measurement noise and errors in the measurement model. Furthermore, spectral fitting methods typically involve achieving the best fit for multiple model parameters. Several model parameters are varied while searching for the parameter set that provides the best match between the simulated and measured spectra. This increases the dimension of the search space for the best fit and often attenuates parameters that are weakly correlated with the measured spectral response, particularly parameters describing asymmetric structural features. Furthermore, model-based measurements of the parameters of interest are often based on measuring the structure of interest from a single plane of incidence. If the asymmetric feature lies along the plane of incidence, the resulting spectral signals (e.g., one or more off-diagonal Müller signals) may be insensitive to the asymmetry. As a result, it is often not possible to reliably determine parameters that describe asymmetric structural features by comparing modeled spectra with measured spectra using traditional techniques. US Patent 9,470,639 B1 discloses devices and methods for broadband spectroscopic metrology of periodic structures. A measurement model is used that depends on a series of system parameters. A subset of the available values ​​from this set of parameters is selected to reduce anomalies in the measurement of the periodic structures. A measurement protocol is then created based on this selected subset. US Patent 2016 / 0282282A1 describes a lithography system for producing periodic structures, in which an EUV light beam is focused onto a substrate. Radiation reflected from the substrate is spectrally decomposed, and a reference spectrum is also acquired; further spectra can be acquired as well. Properties of the structure, such as critical dimension and overlay, are calculated from the acquired spectra. In summary, the ongoing miniaturization and increasing depth of structural features place demanding requirements on optical metrology systems. These systems must meet high precision and accuracy requirements for increasingly complex targets at high throughput to remain cost-effective. Many structural features of interest exhibit asymmetry. In particular, deep holes, often asymmetry, are frequently found in the fabrication of advanced memory structures. In this context, the reliable measurement of asymmetric structural features has proven to be a critical factor in the effectiveness of optical metrology systems. Therefore, improved metrology systems and methods to overcome the limitations associated with measuring asymmetric structural features are highly desirable. OVERVIEW This paper presents methods and systems for performing spectroscopic measurements of asymmetric features in semiconductor structures. The measured spectra are processed to highlight the measurement of symmetry-breaking defects that arise during the fabrication of advanced semiconductor structures. In one aspect, the value of one or more geometric parameters describing an asymmetric feature of the structure of interest is determined based on the values ​​of one or more critical dimensional parameters, reliably estimated by spectral fitting, and one or more spectral response metrics. Spectral response metrics are scalar values ​​derived from spectra associated with one or more off-diagonal Müller matrix elements. Generally, the spectral response metrics depend on the asymmetric feature and other critical dimensions reliably determined by spectral fitting. In some embodiments, a trained linear model relates an asymmetry parameter to one or more spectral response metrics and one or more critical dimensions, which are reliably determined by spectral fitting. An estimate of the asymmetry parameter is determined by regression of the trained model. In some embodiments, a trained neural network model maps the measured spectral response metrics and critical dimensional parameters to the value of the asymmetry parameter. In some embodiments, a combination of models, such as a trained linear model and a trained neural network model, is used to estimate the value of one or more asymmetry parameters. In another aspect, spectral measurements of a structure of interest are performed at two or more different azimuth angles. The resulting measurements are used to estimate one or more geometric parameters that characterize an asymmetric feature of the structure. In a preferred embodiment, spectral measurements are performed at two mutually orthogonal azimuth angles. The combination of several orthogonal measurements enables a precise estimation of geometric parameters that characterize an asymmetric feature of the structure of interest and the axis along which the asymmetric feature lies. In another aspect, spectral response metrics are determined by integrating measured spectra associated with one or more off-diagonal elements of the Müller matrix. A spectral response metric is a scalar measure of the spectral response due to asymmetry. Integrating over the measured spectra reduces noise and increases the signal strength associated with the Müller matrix element or combination of Müller matrix elements. In another aspect, one or more wavelength subranges are selected that are associated with one or more off-diagonal elements of the Müller matrix. Furthermore, the spectral response metrics are determined by integrating the spectra associated with the one or more off-diagonal elements of the Müller matrix over the selected wavelength subranges. In some examples, determining a spectral response metric based on selected portions of the available measured spectrum increases the sensitivity of the spectral response metric to the parameter(s) that describe the asymmetry feature. This is achieved by highlighting wavelengths with the greatest sensitivity to the asymmetric feature and reducing the effects of random noise through integration. In another aspect, different spectral response metrics are weighted differently, for example by scaling each spectral response metric with a different constant. In this way, spectral response metrics that are more sensitive to certain asymmetry parameters are weighted more heavily than spectral response metrics that are less sensitive to those specific asymmetry parameters. In another aspect, the measurement results described here are provided as active feedback to a manufacturing tool (e.g. lithography tool, etching tool, deposition tool, etc.). The foregoing is an overview and therefore necessarily contains simplifications, generalizations, and omissions of details; consequently, those skilled in the art will recognize that the overview is for illustrative purposes only and is in no way limiting. Other aspects, inventive features, and advantages of the devices and / or methods described herein will become clear in the non-limiting, detailed description contained herein. BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 shows a metrology system 100 for performing spectroscopic measurements of asymmetric structural features in one embodiment. Fig. 2 shows a top view of the wafer 120 shown in Fig. 1 with a slant-hole feature 150. Fig. 3 shows a cross-sectional view of section A shown in Fig. 2. Fig. 4 shows a cross-sectional view of section A shown in Fig. 2, including several hole sections. Fig. 5 shows a representation of a spectral response 153 associated with the sum of the Müller matrix elements M02 and M20. Fig. 6 shows a representation of the simulated results, which represents a comparison between actual tilt angles associated with the simulation and regressed values ​​of the tilt angles estimated by a trained linear model described herein.Figure 7 shows a representation of simulated results illustrating a comparison between the actual orientation angles associated with the simulation shown in Figure 6 and the regressed values ​​of the orientation angles estimated by a trained linear model described herein. Figure 8 shows a representation of the simulated results illustrating a comparison between the actual tilt angles and the regressed values ​​of the tilt angles estimated by a combination of a neural network model and a trained linear model. Figure 9 shows a representation of the simulated results illustrating a comparison between the actual orientation angles and the regressed values ​​of the orientation angles estimated by a combination of a neural network model and a trained linear model.Figure 10 shows a representation of simulated results illustrating a comparison between the actual tilt angles and the regressed values ​​of the tilt angles estimated by a trained neural network model. Figure 11 shows an exemplary high-aspect-ratio NAND structure of interest. Figure 12 shows a method 200 for performing spectroscopic measurements of asymmetric structural features in at least one novel aspect. DETAILED DESCRIPTION The following section refers in detail to background examples and some embodiments of the invention, which are illustrated by way of example in the accompanying drawings. This paper presents methods and systems for performing spectroscopic measurements of asymmetric features in semiconductor structures. Measured spectra are processed to highlight the detection of symmetry-breaking defects that arise during the fabrication of advanced semiconductor structures. For example, controlling the deep hole etching process has proven to be a critical process requirement in the fabrication of high aspect ratio memory structures, such as three-dimensional NAND flash memory. Measurements of a structure of interest are performed at two or more azimuth angles to ensure sensitivity to an arbitrarily oriented asymmetric feature. Spectra associated with one or more off-diagonal Müller matrix elements sensitive to asymmetry are selected for further analysis.The selected spectra are further subdivided into one or more wavelength sub-ranges chosen to enhance the signal-to-noise ratio. These selected spectra are then integrated across the wavelength sub-ranges to generate spectral response metrics associated with the off-diagonal Müller matrix elements. Values ​​of parameters characterizing the geometry of an asymmetric feature are determined based on these spectral response metrics and critical dimensional parameters measured using traditional spectral-matching techniques. These features, individually or in combination, enable high-throughput, high-precision, and high-accuracy measurements of asymmetric features in high-aspect-ratio structures (e.g., structures with a depth of one micrometer or more). Fig. 1 shows an exemplary metrology system 100 for measuring asymmetric structural features of semiconductor structures. In some examples, the semiconductor structures contain at least one high aspect ratio (HAR) structure. As shown in Fig. 1, the metrology system 100 is configured as a broadband spectroscopic ellipsometer. In general, however, the metrology system 100 can be configured as a spectroscopic reflectometer, scatterometer, ellipsometer, or any combination thereof. The metrology system 100 comprises a light source 110 that generates a beam of illumination 117 which strikes a wafer 120. In some embodiments, the light source 110 is a broadband light source that emits illumination in the ultraviolet, visible, and infrared spectrum. In one embodiment, the light source 110 is a laser-assisted plasma light source (LSP) (also known as a laser-driven plasma source). The pump laser of the LSP light source can be continuous wave or pulsed. A laser-driven plasma source can generate significantly more photons than a xenon lamp over the entire wavelength range from 150 nanometers to 2000 nanometers. The light source 110 can be a single light source or a combination of several broadband light sources or light sources of discrete wavelengths.The light produced by the illumination source 110 comprises a continuous spectrum or parts of a continuous spectrum from ultraviolet to infrared (e.g., vacuum ultraviolet to mid-infrared). In general, the illumination light source 110 can be a super-continuum laser source, an infrared helium-neon laser source, an arc lamp, or any other suitable light source. In another aspect, the amount of illumination is broadband illumination, encompassing a wavelength range of at least 500 nanometers. For example, the broadband illumination includes wavelengths below 250 nanometers and wavelengths above 750 nanometers. Generally, broadband illumination covers wavelengths between 120 nanometers and 3,000 nanometers. In some embodiments, broadband illumination with wavelengths above 3,000 nanometers can be used. As shown in Fig. 1, the metrology system 100 includes an illumination subsystem configured to direct illumination light 117 onto one or more structures formed on the wafer 120. The illumination subsystem comprises the light source 110, one or more optical filters 111, the polarizing component 112, the field diaphragm 113, the aperture diaphragm 114, and the illumination optics 115. The one or more optical filters 111 are used to control the light level, the spectral power, or both from the illumination subsystem. In some examples, one or more multi-zone filters are used as the optical filters 111. The polarizing component 112 produces the desired polarization state at the output of the illumination subsystem. In some embodiments, the polarizing component is a polarizer, a compensator, or both, and may include any suitable commercially available polarizing component.The polarizing component can be fixed, rotatable to various fixed positions, or continuously rotating. Although the illumination subsystem shown in Fig. 1 contains one polarizing component, the illumination subsystem can contain more than one. The field diaphragm 113 controls the field of view (FOV) of the illumination subsystem and can contain any suitable commercially available field diaphragm. The aperture diaphragm 114 controls the numerical aperture (NA) of the illumination subsystem and can contain any suitable commercially available aperture diaphragm. Light from the illumination source 110 is guided through the illumination optics 115 to be focused onto one or more structures (not shown in Fig. 1) on the wafer 120.The illumination subsystem can comprise any type and arrangement of one or more optical filters 111, polarization component 112, field stop 113, aperture stop 114 and illumination optics 115 known in spectroscopic ellipsometry, reflectometry and scatterometry. As shown in Fig. 1, the beam of illumination light 117, as it propagates from the illumination source 110 to the wafer 120, passes through the optical filter(s) 111, the polarization component 112, the field stop 113, the aperture stop 114 and the illumination optics 115. The beam 117 illuminates a part of the wafer 120 via a measurement spot 116. The metrology system 100 also includes a collecting optics subsystem configured to collect light generated by the interaction between one or more structures and the incident illumination beam 117. A beam of collected light 127 is gathered from the measuring point 116 through the collecting optics 122. The collected light 127 passes through the collecting aperture 123, the polarizing element 124, and the field aperture 125 of the collecting optics subsystem. The collecting optics 122 contains any suitable optical elements to collect light from the one or more structures formed on the wafer 120. The collecting aperture 123 controls the neutral axis (NA) of the collecting optics subsystem. The polarizing element 124 analyzes the desired polarization state. The polarizing element 124 is a polarizer or a compensator. The polarizing element 124 can be fixed, rotatable to various fixed positions, or continuously rotatable. Although the collecting subsystem shown in Fig. 1 contains one polarizing element, the collecting subsystem can contain more than one. The collecting field stop 125 controls the field of view of the collecting subsystem. The collecting subsystem captures light from the wafer 120 and directs the light through the collecting optics 122 and the polarizing element 124 to focus it onto the collecting field stop 125.In some embodiments, the collecting field stop 125 is used as a spectrometer slit for the spectrometers of the detection subsystem. However, the collecting field stop 125 can be arranged at or near a spectrometer slit of the spectrometers of the detection subsystem. The collecting subsystem can include any type and arrangement of collecting optics 122, aperture diaphragm 123, polarizing element 124 and field diaphragm 125 known in spectroscopic ellipsometry, reflectometry and scatterometry. In the embodiment shown in Fig. 1, the collecting optics subsystem directs the light to the spectrometer 126. The spectrometer 126 generates an output depending on the light collected from the one or more structures illuminated by the illumination subsystem. In one example, the detectors of the spectrometer 126 are charge-coupled devices (CCDs) sensitive to ultraviolet and visible light (e.g., light with wavelengths between 190 nanometers and 860 nanometers). In other examples, one or more of the detectors of the spectrometer 126 are a photodetector array (PDA) sensitive to infrared light (e.g., light with wavelengths between 950 nanometers and 2500 nanometers). In general, however, other detector technologies can also be considered (e.g., a position-sensitive detector (PSD), an infrared detector, a photovoltaic detector, etc.).Each detector converts the incident light into electrical signals that indicate the spectral intensity of the incident light. In general, the spectrometer 126 generates output signals 170 that indicate the spectral response of the structure being measured to the illumination light. The metrology system 100 also includes the computer system 130, which is configured to receive the signals 170 indicating the measured spectral response of the structure of interest, and to estimate values ​​of one or more geometric parameters 171 describing an asymmetric feature of the measured structure(s) based on the measured spectral response. In general, the measured spectral response of the structure of interest comprises spectra associated with elements of a Müller matrix formulation used to characterize the measured response. The Stokes-Müller formalism describes the response of a medium to excitation by polarized light. Equation (1) shows a Müller matrix, M, that describes the relationship between the incident ray, characterized by the Stokes vector, SI, and the reflected ray, characterized by the Stokes vector, SR. In general, the Stokes vector represents the polarization state of a light wave. As an example, equation (2) shows a Stokes vector, S, where I is the total intensity, I0 is the intensity transmitted by a linear polarizer oriented at an angle of zero degrees to the P-polarization axis in a plane perpendicular to the direction of propagation, I45 is the intensity transmitted by a linear polarizer oriented at an angle of 45 degrees to the P-polarization axis in a plane perpendicular to the direction of propagation, I-45 is the intensity transmitted by a linear polarizer oriented at an angle of -45 degrees to the P-polarization axis in a plane perpendicular to the direction of propagation, IR is the intensity transmitted by a right-circular polarizer, and IL is the intensity transmitted by a left-circular polarizer.The values ​​in parentheses are spatially and temporally averaged. For a specific spectroscopic measurement, the illumination intensity and polarization properties of the incident beam are programmed. Thus, some or all elements of the Stokes vector associated with the incident beam, SI, are known a priori. Furthermore, the intensity and polarization properties of the reflected beam are measured with the spectrometer (i.e., spectrometer 126). Thus, some or all elements of the Stokes vector associated with the reflected beam, SR, are measured. As a result, some or all Müller matrix elements are determined based on the known and measured properties of the incident and reflected light, respectively. Equation [3] illustrates the elements of the Müller matrix and their relationship to the known and measured elements of the Stokes vectors SI and SR, respectively. Some or all elements of the Müller matrix can be determined directly from the known elements of the Stokes vectors, SI and SR, based on the linear relationship shown in equation [3]. Whether some or all elements of the Müller matrix are determined depends on the known intensity and polarization properties of the incident light and the measured intensity and polarization properties of the reflected light. For example, if polarizer 112 is configured as a rotating polarizer and polarizer 124 as a rotating analyzer, the element in the first three rows and the first three columns of the Müller matrix can be determined. If additional rotating compensators are used in the illumination path and in the collection path of metrology system 100, all elements of the 4x4 Müller matrix can be determined. In another aspect, values ​​of one or more critical dimensional parameters are determined based on a fit between a modeled spectral response and the measured spectral response associated with one or more elements of the Müller matrix. Typically, many critical dimensional parameters that do not describe asymmetric features of a structure under measurement are reliably estimated based on a spectral fit over one or more Müller matrix elements. However, geometric parameters that describe asymmetric features of a structure are typically not reliably estimated by spectral fit, even when a spectral fit is used in conjunction with certain off-diagonal elements of the Müller matrix. In one aspect, the value of one or more geometric parameters describing an asymmetric feature of the structure of interest is determined based on the values ​​of one or more critical dimension parameters, reliably estimated by spectral fitting, and one or more spectral response metrics. The spectral response metrics are scalar values ​​derived from spectra associated with one or more off-diagonal Müller matrix elements. Generally, the spectral response metrics depend on the asymmetric feature and other critical dimensions reliably determined by spectral fitting. The inventors found that decoupling the spectral fitting estimation of the critical dimension parameters from the estimation of asymmetry parameter values ​​improves the measurement of the asymmetry parameter values.In some embodiments, a trained linear model relates an asymmetry parameter to one or more spectral response metrics and one or more critical dimensions, which are reliably determined by spectral fitting. An estimate of the asymmetry parameter is determined by regression of the trained model. In some embodiments, a trained neural network model maps the measured spectral response metrics and critical dimension parameters to the value of the asymmetry parameter. In some embodiments, a combination of models, such as a trained linear model and a trained neural network model, is used to estimate the value of one or more asymmetry parameters. In general, any suitable modeling method can be used to estimate the value of one or more asymmetry parameters. Fig. 2 shows an asymmetrical hole feature 150 fabricated on wafer 120. As shown in Fig. 2, an XY coordinate system is connected to wafer 120. The X-axis of the XY coordinate system is aligned with the writing lines 154 of wafer 120. As shown in Fig. 2, the hole feature 150 is not perpendicular to the surface of wafer 120. The oblique orientation of the hole feature is oriented at an angle, OA, to the direction of the writing lines 154 of wafer 120. Similarly, the oblique orientation of the hole feature is oriented at an angle, OA, with respect to the X-direction of the XY coordinate frame connected to wafer 120. Fig. 3 shows the cross-section AA, aligned with the inclination of the hole feature 150 shown in Fig. 2. Fig. 3 shows an upper layer or a sequence of layers 120A immediately below the surface of the wafer 120. As shown in Fig. 3, the hole feature 150 is inclined at an angle TA with respect to a surface normal of the wafer 120. In the example shown in Fig. 2 and Fig. 3, the asymmetric hole feature 150 is described by two asymmetry parameters: orientation angle, OA, and inclination angle, TA. Fig. 4 shows the cross-section AA, aligned with the inclination of the hole feature 150 shown in Fig. 1. Fig. 4 shows, in particular, an upper layer or sequence of layers 120A directly below the surface of the wafer 120 and a buried layer or sequence of layers 120B directly below the layer(s) 120A. As shown in Fig. 4, the hole section 150 is inclined at an angle TA1 with respect to a surface normal of the wafer 120, and the hole section 152 is inclined at an angle TA2 with respect to the surface normal of the wafer 120. In addition, the hole section 152 is shifted horizontally (i.e., in a direction parallel to the surface of wafer 120) with respect to hole section 150 by an overlay offset, OL. In the example shown in Fig. 4, the asymmetrical hole sections 150 and 152 are described by four asymmetry parameters: orientation angle, OA, inclination angle, TA1 and TA2, and overlay offset, OL. The inclined hole sections 150 and 152 are given as a non-restrictive example. In general, many different structures can exhibit asymmetric features. Furthermore, the same asymmetric features can be described by different sets of asymmetry parameters. In one example, asymmetric hole features can also be parameterized by the elliptical shape of the holes. In another aspect, spectral measurements of a structure of interest are performed at two or more different azimuth angles. The resulting measurements are used to estimate one or more geometric parameters that characterize an asymmetric feature of the structure of interest, as described here. In a preferred embodiment, the spectral measurements are performed at two mutually orthogonal azimuth angles. The combination of several orthogonal measurements enables a precise estimation of the geometric parameters that characterize an asymmetric feature of the structure of interest and the axis along which the asymmetric feature lies. For example, if the asymmetric feature lies along the plane of incidence of a measurement, the orthogonal measurement is sensitive to the asymmetry. As shown in Fig. 1, the Z-axis is oriented perpendicular to the surface of the wafer 120. The X- and Y-axes are coplanar with the surface of the wafer 120 and thus perpendicular to the Z-axis. Likewise, the X' and Y'-axes are coplanar with the surface of the wafer 120 and thus perpendicular to the Z-axis. The X' and Y'-axes are rotated by an azimuth angle AZ with respect to the X and Y-axes. The azimuth angle specifies the orientation of the light source to the wafer 120 about the Z-axis. The principal ray 118 of the illuminating light beam 117 and the principal ray 121 of the collected light beam 127 define a plane of incidence. The X'-axis is aligned with the plane of incidence, and the Y'-axis is orthogonal to the plane of incidence. In this way, the plane of incidence lies in the X'-Z-plane. The beam of illumination light 117 strikes the surface of the wafer 120 at the angle of incidence α, relative to the Z-axis, and lies within the plane of incidence. In general, the orientation of an asymmetric feature with respect to the wafer being measured is unknown a priori. Measurements at multiple azimuth angles ensure that at least one of the measurements is sensitive to the asymmetric feature. Furthermore, performing measurements at two orthogonal azimuth angles increases the probability of accurately determining the axis of asymmetry. This is achieved, for example, by measuring the orientation angle of an asymmetric feature with respect to the plane of incidence of a first set of measurements and measuring the orientation angle of the asymmetric feature with respect to a second plane of incidence associated with a second set of measurements. Since the orientations of the planes of incidence associated with the two measurements are known with respect to the wafer, the orientation angle of the asymmetric feature with respect to the wafer is directly determined from both measurements.In many measurement scenarios, both measurements provide an independent estimate of the orientation angle with respect to the wafer. However, in some scenarios where the asymmetric feature is oriented towards the plane of incidence of a particular measurement, the measurement is insensitive to the asymmetry. In these scenarios, the orthogonal measurement is most sensitive to the same asymmetric feature and therefore provides the most reliable estimate of the asymmetric feature's orientation angle with respect to the wafer. In general, measurements at several different azimuth angles increase the available signal information and improve the measurement accuracy of asymmetric features. Although this document provides examples of measurements at two orthogonal angles, any number of measurements at different azimuth angles can generally be used to improve measurement accuracy in accordance with the methods described herein. In another aspect, one or more spectral response metrics, each associated with one or more off-diagonal elements of the Müller matrix, are determined by integrating measured spectra associated with these elements. A spectral response metric is a scalar measure of the spectral response due to asymmetry. Integrating over the measured spectra reduces noise and increases the signal strength associated with the Müller matrix element or combination of elements. In an example, represented by equation (4), the spectra associated with the Müller matrix element M30 are integrated over the wavelength. In some examples, integration is performed over the sum of several elements of the Müller matrix. Equation (5) illustrates a spectral response metric determined by integrating spectra associated with the sum of the Müller matrix elements M20 and M02. In a preferred embodiment, the sum of the off-diagonal Müller matrix elements M02 and M20 is used as the spectral response metric, since the sum M02 + M20 is zero in the absence of asymmetry. The degree of asymmetry is thus expressed by the deviation of SRMM02 + M20 from zero. Similarly, in a preferred embodiment, the off-diagonal Müller matrix element M30 is used as the spectral response metric, since M30 is zero in the absence of asymmetry. As such, the degree of asymmetry is expressed by the deviation of SRMM30 from zero. In another preferred embodiment, both the spectral response metric SRMM02 + M20 and SRMM30 are used to estimate the value of one or more geometric parameters that describe an asymmetric feature of a structure of interest as described herein. Although the spectral response metrics based on M30 and the sum (M02+M20) are specifically described here, spectral response metrics based on any suitable Müller matrix element or combination of Müller matrix elements can generally be considered within the scope of this patent document. For example, a spectral response metric based on M03, the sum (M12+M21), etc., can be determined. In another aspect, spectra associated with one or more off-diagonal elements of the Müller matrix are subdivided into one or more wavelength subranges. Furthermore, the spectral response metrics are determined by integrating the spectra associated with the one or more off-diagonal elements of the Müller matrix over the one or more wavelength subranges. In some examples, determining a spectral response metric based on selected portions of the available measured spectrum increases the sensitivity of the spectral response metric to the parameter(s) that describe the asymmetry feature. This is achieved by amplifying wavelengths with the greatest sensitivity to the asymmetric feature and reducing the effects of random noise through integration. Fig. 5 shows an exemplary spectral response 153 associated with the sum (M02+M20). As illustrated in Fig. 5, significant portions of the spectrum exhibit a signal response within the noise level of the measurement, while other portions show a signal response that significantly exceeds the noise level. In one example, the portions of the spectrum exceeding a predetermined threshold T are selected from the spectrum to identify the signal response that exceeds the noise level. In the illustrated example, the wavelength sub-ranges λ12 and λ34 are selected from the available spectrum. Furthermore, a spectral response metric associated with the sum (M02+M20) is determined by integrating the sum (M02+M20) over only the selected sub-ranges, as illustrated by equation (6). In the example shown in Figs. 2 and 3, the asymmetry of a slanted hole 150 is characterized by the inclination angle TA and the orientation angle OA. Furthermore, the slanted hole is characterized by other critical dimensions that do not describe the asymmetry of the hole feature, such as the height H of the hole and the diameter CD of the hole. The orientation angle, OA, is defined with respect to the positive direction of the X-axis shown in Fig. 1. When the orientation angle is zero, the asymmetric feature is distorted in the positive direction of the X-axis. Likewise, at an orientation angle of 90 degrees, the asymmetric feature is distorted in the positive direction of the Y-axis. The inclination angle, TA, is defined as zero when the central axis of the hole is normal to the wafer (i.e., no slant). In one example, the metrology system 100 is used to perform spectroscopic measurements of the inclined hole 150 at two orthogonal azimuth angles. In one measurement, the plane of incidence of the illumination light is aligned with the X-axis shown in Fig. 1. In another measurement, the plane of incidence of the illumination light is aligned with the Y-axis shown in Fig. 1. The measured spectra 170, associated with all available Müller matrix elements at both azimuth angles, are received by computer system 130. Computer system 130 determines several spectral response metrics based on the measured spectra. In one example, computer system 130 determines the spectral response metric by integrating selected contributions of Müller element M30 and the sum of the Müller matrix elements (M20+M02) for both azimuth angles. Equations (7) - (10) illustrate the spectral response metrics determined by integration over Nλ segments of the available spectrum of (M20+M02) measured at a 180-degree azimuth angle, Nλ segments of the available spectrum of M30 measured at a 180-degree azimuth angle, Nλ segments of the available spectrum of (M20+M02) measured at a 90-degree azimuth angle, and Nλ segments of the available spectrum of M30 measured at a 90-degree azimuth angle.The subscript a denotes the sum of the Müller matrix elements (M20+M02) and the subscript b denotes the Müller matrix element M30. Although the spectral response metrics represented by equations (7) - (10) are each determined by integration over Nλ segments of the available spectra, the wavelength segments selected for integration can generally be unique for each spectral response metric. The computer system 130 also estimates the values ​​of the hole height, H, hole diameter, CD, hole inclination angle, TA, and orientation angle, OA, by model-based spectral fitting with any combination of the available Müller matrix elements. As mentioned earlier, reliable estimates of H and CD are expected from the model-based spectral fitting, but the estimated values ​​of TA and OA are typically inaccurate. The computer system 130 estimates the values ​​of TA and OA based on the spectral response metrics described with reference to equations (7) - (10) and the values ​​of CD and H estimated by spectral fitting. In some examples, the computer system 130 generates a trained linear model, which is then used to estimate values ​​of TA and OA. The values ​​of the spectral response metric, SRM, are assumed to depend on CD, H, TA, and OA. It may be that the dependence on CD and H is generally not independent of the dependence on TA and OA. Equation (11) illustrates the assumption that a spectral response metric, SRM, depends on CD, H, TA, and OA, but the dependence can be expressed as a combination of a function, g, that depends on CD and H, and a function, h, that depends on TA and OA. It is assumed that the function h is directly proportional to the degree of inclination angle TA along the respective light axis, as shown in equations (12) - (13). The function g is assumed to be insensitive to TA and OA, and its consideration can be effectively decoupled from that of the function h. Additionally, the inventors discovered that the function g is approximately the same for each of the four spectral response metrics: SRMa,180, SRMb,180, SRMa,90, and SRMb,90. The relationship between function h and the parameters of interest OA and TA can be determined for nominal values ​​of CD and H, but the relationship does not hold for arbitrary CD and H. To solve this problem, the computer system 130 performs a linear least squares regression to map spectral response metrics, SRM, associated with general values ​​of CD and H to normalized spectral response metrics, SRM', associated with known nominal values ​​of CD and H, where SRM' is represented in equation (14). A spectral response metric, SRM, is related to the normalized spectral response metric, SRM', by the normalization factor g (CD, H) / g (CDNOM, HNOM), as illustrated by equation (15). Assuming nominal, non-trivial values ​​for TA and OA, the computer system 130 generates a set of spectral response metrics, SRM, associated with measurements of hole features with N different values ​​of CD and M different values ​​of H, as well as a set of spectral response metrics associated with the measurement of a hole feature at the chosen nominal values ​​for CD and H. The unknown coefficients (C0,...,CN) and (D0,...,DM) represented in equation (16) are determined by linear least squares regression to arrive at a model for the normalization factor g (CD, H) / g (CDNOM, HNOM). Assuming nominal values ​​of CD and H, the computer system 130 generates a series of normalized spectral response metrics, SRM', which are associated with different values ​​of TA and OA. The unknown coefficients A1 and A2 shown in equation (17) are determined by linear least squares regression. The unknown coefficients B1 and B2 shown in equation (18) are also determined by linear least squares regression. The results of equations (11) - (18) are combined to obtain a trained linear model that links the asymmetry parameters of interest, OA and TA, with spectral response metrics derived from measurements of asymmetric structures. The values ​​for the trained linear model are thus represented by equations (19) - (21). Fig. 6 shows a plot 155 of simulated results, comparing the actual tilt angles 156 associated with the simulation and regressed values ​​of the tilt angles 157 using the trained linear model described with reference to equations (11) - (21). Fig. 7 shows a plot 160 of simulated results, comparing the actual orientation angles 161 associated with the same simulation and regressed values ​​of the orientation angles 162 using the trained linear model described with reference to equations (11) - (21). In this example, CD and H of the inclined hole feature are randomly varied over a range of 5%, the tilt angle varies from 0° to 0.5°, and the orientation angle varies from 0° to 360°.The simulated measurement signals were subjected to random Gaussian noise, and a single wavelength subrange was used to determine the spectral response metrics. As shown in Fig. 6, the tilt angle estimates closely follow the actual tilt angle values. Similarly, as shown in Fig. 7, the orientation angle estimates closely follow the actual orientation angle values. In some examples, the computer system 130 generates a trained neural network model, which is then used to estimate the values ​​of TA and OA. In some examples, a neural network model is trained to map the previously described spectral response metrics and the reliably regressed critical dimensions to values ​​of one or more geometric parameters that characterize an asymmetric feature to be measured. In one example, the training input of a neural network model comprises the four spectral response metrics described with reference to equations (7) - (10), i.e., SRMa,180, SRMb,180, SRMa,90, and SRMb,90, and the reliably regressed values ​​of CD and height. The training output includes the normalization factor g(CD, H) / g(CDNOM,HNOM). In some examples, the linear least squares regression described here is applied with the normalization factor determined by the trained neural network. In one example, a neural network of 20 neurons with 2 hidden layers is trained to predict the normalization factor g(CD, H) / g(CDNOM, HNOM). Input data is generated from synthetic spectra linked with randomly varying values ​​of CD, height, TA, and OA in the same manner as described with reference to Figures 6 and 7. The nominal CD and height are selected from a single random profile in the training data. The linear least-squares regression described here is applied using the normalization factor determined by the trained neural network. Fig. 8 shows a diagram 165 of the simulated results, comparing the actual inclination angles, represented by triangular reference marks, with regressed inclination angle values, represented by square reference marks. The differences between the actual and regressed values ​​are represented by curve 166. In this example, the 3-sigma value (i.e., three times the standard deviation) of the difference between the actual and regressed inclination angle values ​​is 0.00298. Fig. 9 shows a diagram 175 with simulated results, comparing actual orientation angles represented by triangular reference marks with regressed orientation angle values ​​represented by square reference marks. The differences between the actual and regressed values ​​are represented by curve 176. In this example, the 3-sigma value (i.e., three times the standard deviation) of the difference between the actual and regressed orientation angle values ​​is 0.19000. In another example, instead of using linear regression to estimate the values ​​of the asymmetry parameters, another neural network model is trained to determine TA and OA based on the normalization factor and the measured inputs. In another example, the training input of a neural network model comprises the four spectral response metrics described with reference to equations (7) - (10), i.e., SRMa,180, SRMb,180, SRMa,90, and SRMb,90, and the reliably regressed values ​​of CD and height. The training output includes corresponding values ​​of TA and OA. Figure 10 shows a graph 180 with simulated results, where a trained neural network model is used to estimate TA and OA directly from the four spectral response metrics and the reliably regressed values ​​of CD and height. Figure 10 shows a comparison between the actual inclination angles, represented by triangular reference markers, and regressed inclination angle values, represented by square reference markers. The differences between the actual and regressed values ​​are represented by curve 181. In this example, the 3-sigma value (i.e., three times the standard deviation) of the difference between the actual and regressed inclination angle values ​​is 0.00783. In another example, the training input of a neural network model includes the four spectral response metrics described with reference to equations (7)-(10), but not the reliably regressed values ​​of CD and height. The training output contains corresponding values ​​of TA and OA. Simulation results validating this approach show that the 3-sigma value of the difference between actual and regressed values ​​of the inclination angle is 0.18000, which is not as effective as the approaches described previously. In general, the procedures described here for determining the values ​​of one or more geometric parameters that describe an asymmetric feature of a structure of interest are applied iteratively. In some examples, the estimated values ​​of the asymmetry parameters are fed to spectral fitting analysis to arrive at improved estimates of one or more critical dimensions. These improved estimates of the critical dimensions are used to update the spectral response metrics, which in turn are used to generate improved estimates of the asymmetric parameters. This iteration continues until convergence is reached with values ​​of the asymmetry parameters. The estimated values ​​of the asymmetry parameters are stored in memory (e.g., memory 132). In some embodiments, several different spectral response metrics are determined, each based on a different off-diagonal Müller matrix element or a different combination of Müller matrix elements (e.g., M30 and the sum (M20+M02)). In another aspect, different spectral response metrics are weighted differently, for example, by scaling each spectral response metric with a different constant. In this way, spectral response metrics that are more sensitive to certain asymmetry parameters are weighted more heavily than spectral response metrics that are less sensitive to the specific asymmetry parameters. Fig. 12 shows a method 200 for performing spectroscopic measurements of asymmetric parameters in at least one novel aspect. The method 200 is suitable for implementation by a metrology system such as the metrology system 100 shown in Fig. 1 of the present invention. It is recognized in one aspect that the data processing blocks of the method 200 can be executed via a pre-programmed algorithm that can be executed by one or more processors of the computer system 130 or any other general-purpose computer system. It is recognized here that the particular structural aspects of the metrology system 100 do not represent limitations and should only be interpreted as illustrative. In Block 201, a structure of interest fabricated on a semiconductor wafer is illuminated with a quantity of broadband optical radiation at two or more different azimuth angles. In block 202, in response to the illumination of the semiconductor wafer, a quantity of measurement light is detected from the semiconductor wafer at each of the two or more azimuth angles. In Block 203, a measured spectral response of the structure of interest to illumination at each of the two or more azimuth angles is determined based on each detected amount of measurement light. Each measured spectral response contains spectra that are associated with several elements of a Müller matrix. In Block 204, the values ​​of one or more critical dimensional parameters are estimated based on a fit of a modeled spectral response to the measured spectral responses associated with the two or more azimuth angles. In block 205, one or more sub-ranges of wavelengths of at least one spectrum of one or more non-diagonal elements of the Müller matrix are selected, which are assigned to each measured spectral response. In block 206, the at least one spectrum of the one or more non-diagonal elements of the Müller matrix is ​​integrated over the one or more selected sub-ranges of the wavelengths to generate one or more spectral response metrics. In Block 207, values ​​of one or more geometric parameters describing an asymmetric feature of the structure of interest are estimated based on the values ​​of one or more critical dimensional parameters and one or more spectral response metrics. Exemplary measurement techniques that can be configured as described here include spectroscopic ellipsometry (SE), including Müller matrix ellipsometry (MMSE), rotational polarizer SE (RPSE), rotational polarizer-rotational compensator SE (RPRC), rotational compensator-rotational compensator SE (RCRC), spectroscopic reflectometry (SR), including polarized SR, unpolarized SR, spectroscopic scatterometry, scatterometry overlay, beam profile reflectometry, both angle-resolved and polarization-resolved, beam profile ellipsometry, single or multiple discrete wavelength ellipsometry, etc. In general, any measurement technique that contains a wide range of angular information in the measurement signals can be considered individually or in any combination.For example, any SR or SE technique applicable to the characterization of semiconductor structures, including image-based measurement techniques, can be considered individually or in any combination. In a further embodiment, the system 100 comprises one or more computer systems 130, which serve to perform measurements on actual component structures based on spectroscopic measurement data acquired according to the methods described herein. The one or more computer systems 130 can be communicatively coupled to the spectrometer. In one aspect, the one or more computer systems 130 are configured to receive measurement data 170 associated with measurements of the structure of the sample 120. It should be acknowledged that one or more steps described throughout this disclosure can be performed by a single computer system 130 or, alternatively, by a multi-computer system 130. Furthermore, various subsystems of the system 100 can comprise a computer system capable of performing at least some of the steps described herein. The foregoing description is therefore not to be understood as limiting the present invention, but merely as illustrative. Furthermore, the computer system 130 can be communicatively coupled to the spectrometers in any manner known in engineering. For example, one or more computer systems 130 can be coupled to the computer systems associated with the spectrometers. In another example, the spectrometers can be directly controlled by a single computer system connected to the computer system 130. The computer system 130 of the metrology system 100 can be configured to receive and / or acquire data or information from the system's subsystems (e.g., spectrometers and the like) via a transmission medium that may include wired and / or wireless components. In this way, the transmission medium can serve as a data link between the computer system 130 and other subsystems of the system 100. The computer system 130 of the metrology system 100 can be configured to receive and / or acquire data or information (e.g., measurement results, modeling inputs, modeling results, reference measurement results, etc.) from other systems via a transmission medium that may include wired and / or wireless components. In this way, the transmission medium can serve as a data link between the computer system 130 and other systems (e.g., memory within the metrology system 100, external memory, or other external systems). For example, the computer system 130 can be configured to receive measurement data from a storage medium (e.g., memory 132 or external memory) via a data link. For instance, spectral results obtained with the spectrometers described herein can be stored in permanent or semi-permanent memory (e.g., memory 132 or external memory).The spectral results can be imported from the integrated memory or from an external storage system. Furthermore, the computer system 130 can send data to other systems via a transmission medium. For example, a measurement model determined by the computer system 130 or an estimated parameter value 171 can be transmitted and stored in external memory. Measurement results can also be exported to another system. The Computer System 130 can include, among other things, a personal computer system, a mainframe system, a workstation, an image processor, a parallel processor, or any other device known in technology. In general, the term "computer system" can be interpreted broadly and encompasses any device with one or more processors that execute instructions from a storage medium. Program instructions 134, which implement methods such as those described here, can be transmitted via a transmission medium such as a wired, cabled, or wireless transmission link. For example, as shown in Fig. 1, the program instructions 134 stored in memory 132 are transmitted to the processor 131 via bus 133. The program instructions 134 are stored on a computer-readable medium (e.g., memory 132). Examples of computer-readable media are read-only memory, random-access memory, a magnetic or optical disk, or a magnetic tape. In some examples, the measurement models described here are implemented as an element of an optical SpectraShape® measurement system for critical dimensions, available from KLA-Tencor Corporation, Milpitas, California, USA. In this way, the model is created immediately after the spectra are acquired by the system and is ready for immediate use. In some other examples, the measurement models described here are implemented offline, for example, by a computer system that implements the AcuShape® software from KLA-Tencor Corporation, Milpitas, California, USA. The resulting trained model can be included as an element of an AcuShape® library, which a metrology system performing measurements can access. In another aspect, the methods and systems described here for the spectroscopic metrology of semiconductor devices are applied to the measurement of asymmetric features of high-aspect-ratio (HAR) structures, large-lateral-dimension structures, or both. The described embodiments enable the metrology of asymmetric features of semiconductor devices, including three-dimensional NAND structures such as vertical NAND (V-NAND) structures, dynamic random-access memory (DRAM) structures, etc., manufactured by various semiconductor companies such as Samsung Inc. (South Korea), SK Hynix Inc. (South Korea), Toshiba Corporation (Japan), and Micron Technology, Inc. (United States), etc. Figure 11 shows an exemplary high-aspect-ratio NAND 190 structure that may contain asymmetric feature defects.A broadband spectroscopic ellipsometer with a wide azimuth range is suitable for measuring these high aspect ratio (HAR) structures. HAR structures often contain hard mask layers to facilitate etching processes. As described here, the term "HAR structure" refers to any structure characterized by an aspect ratio greater than 10:1, which can be up to 100:1 or higher. In another aspect, the measurement results described here are provided as active feedback to a tool in the manufacturing process (e.g., lithography tool, etching tool, deposition tool, etc.). For example, the values ​​of measurement parameters determined based on the measurement methods described here are transmitted to a lithography tool to adjust the lithography system to achieve a desired output (i.e., reduced asymmetry errors, etc.). Similarly, etching parameters (e.g., etching time, diffusivity, etc.) or deposition parameters (e.g., time, concentration, etc.) are adjusted to the etching or deposition tools based on the active feedback of the measured parameters. In some examples, corrections to process parameters determined based on measured asymmetric parameters are transmitted to a lithography tool, an etching tool, a deposition tool, etc.In response, a manufacturing tool adjusts a control parameter of the semiconductor manufacturing process to reduce structural defects characterized by the measured asymmetry. As described here, the term "critical dimension" encompasses any critical dimension of a structure (e.g., lower critical dimension, middle critical dimension, upper critical dimension, sidewall angle, lattice height, etc.), a critical dimension between two or more structures (e.g., distance between two structures), and a displacement between two or more structures (e.g., overlay displacement between superimposed lattice structures, etc.). The structures can include three-dimensional structures, patterned structures, superimposed structures, etc. As described here, the term “critical dimension application” or “critical dimension measurement application” includes any critical dimension measurement. As described herein, the term "metrology system" encompasses any system used, at least in part, to characterize a sample in any aspect, including measurement applications such as critical dimension measurement, overlay metrology, focus / dose metrology, and composition metrology. However, these technical terms do not limit the scope of the term "metrology system" as described herein. Furthermore, the Metrology System 100 can be configured for the measurement of structured and / or unstructured wafers. The metrology system can be configured as an LED inspection tool, edge inspection tool, backside inspection tool, macro inspection tool, or multi-mode inspection tool (with data from one or more platforms simultaneously), as well as any other measurement or inspection tool that benefits from the calibration of system parameters based on critical dimension data. This document describes various embodiments of a semiconductor measurement system that can be used to measure a sample within any semiconductor processing tool (e.g., an inspection system or a lithography system). The term "sample" here refers to a wafer, a reticle, or any other sample that can be processed (e.g., printed or inspected for defects) using methods known in the art. The term "wafer" as used here generally refers to substrates consisting of a semiconductor or non-semiconductor material. Examples include single-crystal silicon, gallium arsenide, and indium phosphide. Such substrates are commonly found and / or processed in semiconductor manufacturing equipment. In some cases, a wafer may consist only of the substrate (i.e., a bare wafer). Alternatively, a wafer may contain one or more layers of different materials formed on a substrate. One or more layers formed on a wafer may be patterned or unpatterned. For example, a wafer may contain a variety of dies with repeatable pattern features. A "reticule" can be a reticule at any stage of a reticule fabrication process, or a finished reticule that may or may not be ready for use in a semiconductor manufacturing system. A reticule, or "mask," is generally defined as an essentially transparent substrate with essentially opaque regions formed on it, configured in a pattern. The substrate may, for example, contain a glass material such as amorphous SiO2. A reticule can be positioned over a photoresist-coated wafer during an exposure step of a lithography process, allowing the pattern on the reticule to be transferred to the photoresist. One or more layers formed on a wafer can be patterned or unpatterned. For example, a wafer can contain a multitude of dies, each exhibiting repeatable pattern features. The formation and processing of such material layers can ultimately lead to finished electronic devices. Many different types of electronic devices can be formed on a wafer, and the term wafer, as used here, is intended to encompass any wafer on which any type of electronic device known in engineering is fabricated. In one or more exemplary embodiments, the described functions can be implemented in hardware, software, firmware, or any combination thereof. If implemented in software, the functions can be stored on a computer-readable medium or transmitted as one or more instructions or codes. Computer-readable media include both computer storage media and communication media, including all media that facilitate the transfer of a computer program from one location to another. A storage medium can be any available medium accessible to a general-purpose or specialized computer.As an example, and without limitation, such computer-readable media can include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to transmit or store desired program code means in the form of instructions or data structures and that can be accessed by a general-purpose or specialized computer or a general-purpose or specialized processor. Any connection is also correctly referred to as a computer-readable medium.If the software is transmitted from a website, server, or other remote source via coaxial cable, fiber optic cable, twisted-pair cable, digital subscriber line (DSL), or wireless technologies such as infrared, radio, and microwave, then these technologies are included in the definition of the medium. "Disc" and "disk," as used here, encompass compact discs (CDs), laserdiscs, optical discs, digital versatile discs (DVDs), floppy disks, and Blu-ray discs, with disks typically reproducing data magnetically, while discs reproducing data optically using lasers. Combinations of the above should also be included in the scope of computer-readable media.

Claims

Metrology system (100) comprising: an illumination source (110) configured to generate an amount of broadband optical radiation (117); one or more optical elements directing the amount of broadband optical radiation (117) from the illumination source (110) to a measurement point (116) on a surface of a semiconductor wafer (120) at each of two or more azimuth angles (AZ); a spectrometer (126) configured to detect an amount of measurement light in response to the illumination of the semiconductor wafer (120) at each of the two or more azimuth angles (AZ) from the semiconductor wafer (120) and to determine a measured spectral response of a structure of interest to the illumination based on each detected amount of measurement light, wherein each measured spectral response includes spectra associated with multiple elements of a Müller matrix;and a computer system (130) configured to: estimate values ​​of one or more critical dimensional parameters that characterize the structure of interest, based on a fit of a modeled spectral response to the measured spectral responses associated with the two or more azimuth angles (AZ); select one or more subranges of wavelengths of at least one spectrum of one or more non-diagonal elements of the Müller matrix associated with each measured spectral response; integrate the at least one spectrum of the one or more non-diagonal elements of the Müller matrix over the selected one or more subranges of wavelengths to generate one or more spectral response metrics;and estimating the values ​​of one or more geometric parameters that describe an asymmetric feature of the structure of interest, based on the values ​​of one or more critical dimensional parameters and one or more spectral response metrics. Metrology system (100) according to claim 1, wherein the computer system (130) is further configured to: transmit the values ​​of one or more geometric parameters to a semiconductor manufacturing tool, wherein the semiconductor manufacturing tool adjusts a control parameter of a semiconductor manufacturing process based on the values ​​of one or more geometric parameters to reduce structural defects characterized by the measured asymmetry. Metrology system (100) according to claim 1, wherein the two or more azimuth angles (AZ) comprise two mutually perpendicular azimuth angles (AZ). Metrology system (100) according to claim 1, wherein the one or more non-diagonal elements of the Müller matrix comprise the M30 element of the Müller matrix. Metrology system (100) according to claim 1, wherein one or more non-diagonal elements of the Müller matrix contain a sum of the M20 and M02 elements of the Müller matrix. Metrology system (100) according to claim 1, wherein the selection of one or more sub-ranges of wavelengths of at least one spectrum of one or more non-diagonal elements of the Müller matrix includes the selection of one or more sub-ranges of wavelengths with a spectral response that exceeds a predetermined threshold (T) within the one or more sub-ranges of wavelengths. Metrology system (100) according to claim 1, wherein the estimation of the values ​​of one or more geometric parameters is based on several spectral response metrics, each of the several spectral response metrics being weighted differently. Metrology system (100) according to claim 1, wherein one or more geometric parameters describing an asymmetric feature of the structure of interest comprise an inclination angle (TA) and / or an orientation angle (OA) of a hole feature (150). Metrology system (100) according to claim 1, wherein the structure of interest is a high aspect ratio storage structure. Metrology system (100) according to claim 1, wherein the estimation of the values ​​of one or more geometric parameters includes a trained neural network model that relates the values ​​of one or more critical dimensional parameters and one or more spectral response metrics to the values ​​of one or more geometric parameters. Metrology system (100) according to claim 1, wherein the estimation of the values ​​of one or more geometric parameters comprises a linear regression model that relates the values ​​of one or more critical dimensional parameters and one or more spectral response metrics to the one or more geometric parameters. Method comprising: Illuminating a structure of interest fabricated on a semiconductor wafer (120) with an amount of broadband optical radiation (117) at each of two or more azimuth angles (AZ); Detecting an amount of measurement light from the semiconductor wafer (120) in response to the illumination of the semiconductor wafer (120) at each of the two or more azimuth angles (AZ); Determining a measured spectral response of the structure of interest to the illumination provided at each of the two or more azimuth angles (AZ), based on each detected amount of measurement light, wherein each measured spectral response includes spectra that are assigned to multiple elements of a Müller matrix; Estimating values ​​of one or more critical dimensional parameters based on a fit of a modeled spectral response to the measured spectral responses that are assigned to the two or more azimuth angles (AZ);Selecting one or more wavelength subranges from at least one spectrum of one or more off-diagonal elements of the Müller matrix associated with each measured spectral response; integrating the at least one spectrum of the one or more off-diagonal elements of the Müller matrix over the one or more selected wavelength subranges to generate one or more spectral response metrics; and estimating values ​​of one or more geometric parameters describing an asymmetric feature of the structure of interest, based on the values ​​of the one or more critical dimensional parameters and the one or more spectral response metrics. The method of claim 12, further comprising: transmitting the values ​​of one or more geometric parameters to a semiconductor manufacturing tool, wherein the semiconductor manufacturing tool adjusts a control parameter of a semiconductor manufacturing process based on the values ​​of one or more geometric parameters in order to reduce structural defects characterized by the measured asymmetry. Method according to claim 12, wherein the two or more azimuth angles (AZ) comprise two mutually perpendicular azimuth angles (AZ). Method according to claim 12, wherein the selection of one or more sub-ranges of wavelengths of at least one spectrum of one or more non-diagonal elements of the Müller matrix includes the selection of one or more sub-ranges of wavelengths with a spectral response that exceeds a predetermined threshold (T) within the one or more sub-ranges of wavelengths. Method according to claim 12, wherein the one or more non-diagonal elements of the Müller matrix contain a sum of at least two elements of the Müller matrix. The method of claim 12, wherein the estimation of the values ​​of one or more geometric parameters includes a trained neural network model that relates the one or more geometric parameters to the values ​​of the one or more critical dimensional parameters and the one or more spectral response metrics. The method of claim 12, wherein the estimation of the values ​​of one or more geometric parameters includes a linear regression model that relates the one or more geometric parameters to the values ​​of the one or more critical dimensional parameters and the one or more spectral response metrics. Metrology system (100), comprising: one or more optical elements that direct a quantity of broadband optical radiation (117) from an illumination source (110) to a measurement point (116) on a surface of a semiconductor wafer (120); a spectrometer (126) configured to detect a quantity of measurement light from the semiconductor wafer (120) in response to illumination of the semiconductor wafer (120) and to determine a measured spectral response of a structure of interest based on the detected quantity of measurement light, wherein the measured spectral response includes spectra associated with multiple elements of a Müller matrix;and a computer-readable medium (132) containing instructions (134) which, when executed by one or more processors (131), cause the one or more processors (131) to: estimate values ​​of one or more critical dimensional parameters based on a fit of a modeled spectral response to the measured spectral response; select one or more subranges of wavelengths of at least one spectrum of one or more non-diagonal elements of the Müller matrix that are associated with the measured spectral response; integrate the at least one spectrum of the one or more non-diagonal elements of the Müller matrix over the one or more selected subranges of wavelengths to generate one or more spectral response metrics;and estimating the values ​​of one or more geometric parameters that describe an asymmetric feature of the structure of interest, based on the values ​​of one or more critical dimensional parameters and one or more spectral response metrics. Metrology system (100) according to claim 19, wherein the computer-readable medium (132) further comprises instructions which, when executed by the one or more processors (131), cause the one or more processors (131) to transmit the values ​​of the one or more geometric parameters to a semiconductor manufacturing tool, wherein the semiconductor manufacturing tool adjusts a control parameter of a semiconductor manufacturing process based on the values ​​of the one or more geometric parameters in order to reduce structural defects characterized by the measured asymmetry.

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