Method and system for regularizing the optimization of application-specific semiconductor metrology system parameter settings

Abstract

A method and system for optimizing a semiconductor metrology recipe that is robust to geometric modeling errors and variations in hardware modeling parameters is described herein. The robust metrology recipe optimization minimizes a cost function that includes one or more regularization terms that constrain the process space, thereby significantly reducing the information processing effort required to optimize the metrology recipe. This reduces the total process time and improves wafer throughput. In certain examples, the optimization is performed based on metrology data for multiple instances of a semiconductor structure; each instance is characterized by differences in values ​​of one or more geometric parameters of interest. In certain examples, the search for the optimized metrology recipe is limited to a distinct set of metrology system parameter values ​​associated with the available metrology data set. In this manner, the performance of the distinct metrology recipe is verified using existing metrology data.

Description

[Technical field]

[0001] [CROSS-REFERENCE TO RELATED APPLICATIONS] This patent application claims priority under 35 U.S.C. § 119 to U.S. Provisional Patent Application No. 63 / 294,841, filed December 29, 2021, entitled “Methods for using regularization to increase time efficiency of metrology,” the subject matter of which is incorporated herein by reference in its entirety.

[0002] The described embodiments relate to metrology systems and methods, and more particularly to methods and systems for improving metrology of semiconductor structures. [Background technology]

[0003] Semiconductor devices, such as logic and memory devices, are typically fabricated by applying a series of processing steps to a specimen. The various features and multiple structural levels of the semiconductor devices are formed by the processing steps. For example, lithography is a semiconductor manufacturing process that involves creating patterns 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 may be created on a semiconductor wafer and then separated into individual semiconductor devices.

[0004] Metrology processes are used at various steps during the semiconductor manufacturing process to detect defects on the wafers and facilitate improved yield. A number of metrology-based techniques, such as scatterometry and reflectometry implementations and their associated analysis algorithms, are widely used to characterize the critical dimensions, film thickness, composition and other parameters of nanoscale structures.

[0005] Traditionally, scatterometry critical dimension (SCD) metrology has been performed on targets composed of thin films and / or repeating periodic structures. During device fabrication, these films and periodic structures typically represent the actual device geometry and material structure or intermediate design. As devices (e.g., logic and memory devices) move to smaller nanometer-scale dimensions, they become more difficult to characterize. This is exacerbated by the incorporation of complex 3D geometries and materials with diverse physical properties into devices. For example, modern memory structures often have high aspect ratio 3D structures that limit the penetration of optical radiation into underlying layers. Optical metrology tools that use infrared-visible light can penetrate many semi-transparent material layers, but the longer wavelengths that provide good penetration depths do not provide sufficient sensitivity to small anomalies. Additionally, a larger number of parameters are required to characterize complex structures (e.g., FinFETs), leading to increased parameter correlation. As a result, it is often not possible to reliably separate the parameters that characterize the target.

[0006] As an example, longer wavelengths (e.g., near infrared) are being attempted to overcome the penetration problem in 3D FLASH devices that utilize polysilicon as one of the alternating materials in the stack. However, such mirror-like structures of 3D FLASH inherently experience a drop in light intensity as the illumination propagates deeper into the film stack. This creates sensitivity loss and correlation problems at depth. In this scenario, SCDs can only successfully extract a small set of metric dimensions with high sensitivity and low correlation.

[0007] As another example, opaque high-k materials are increasingly being employed in modern semiconductor structures. Optical radiation is often unable to penetrate layers composed of such materials. As a result, measurements with thin film scatterometry tools, such as ellipsometers or reflectometers, become increasingly challenging.

[0008] In response to these challenges, more sophisticated optical metrology tools have been developed, including those with multiple illumination angles, shorter illumination wavelengths, wider illumination wavelength ranges, and more complete information acquisition from the reflected signal (e.g., measuring multiple Mueller matrix elements in addition to more traditional reflectance or ellipsometry signals). In addition, X-ray scatterometry systems, such as transmission small-angle X-ray scatterometry (T-SAXS) systems, have shown promise in addressing challenging metrology applications. These X-ray based scatterometry systems also offer a wide range of illumination angles and a wide illumination wavelength range. Although state-of-the-art optical and X-ray scatterometry systems can address challenging metrology applications, timely metrology recipe generation is emerging as a performance-limiting issue.

[0009] Metrology recipe optimization is a key aspect of scatterometry. A metrology recipe specifies a set of metrology system settings (e.g. specific wavelengths, angles of incidence, azimuth angles, exposure times, etc.) that are used to estimate the structural parameters of interest (e.g. critical dimensions, film thickness, material composition, etc.). Ideally, a metrology recipe should contain the minimum number of separate measurements required to estimate the parameters of interest, thus maximizing metrology throughput. Modern scatterometry tools offer a wide range of metrology system parameters (e.g. angles of incidence, wavelengths, etc.). This complicates recipe generation due to the large variety of metrology system parameter values ​​available. Furthermore, there is a limited time to perform useful measurements; it is essential to be able to generate metrology recipes for each individual metrology application in that time alone.

[0010] The time to generate a metrology recipe is critical, especially for metrology technologies where a relatively long time period is required for each measurement. For example, some T-SAXS measurements suffer from low brightness and small scattering cross sections, which in turn lead to long acquisition times for those measurements. In some instances, the metrology models for T-SAXS measurements can be complex, requiring long computational times to solve the models.

[0011] An ideal semiconductor structure metrology would be one that is performed over the full range of available metrology system settings (e.g., incidence angle, azimuth angle, beam divergence, wavelength, exposure time, etc.). Data from the semiconductor structure metrology at each combination of available metrology system settings would be collected and analyzed over relatively long exposure times to arrive at an estimate of the parameters of interest that characterize the structure under measurement. Such ideal metrology is impractical with modern scatterometry tools because the time required to perform measurements of metrology targets over the full range of metrology options is impractically long. Furthermore, the photon dose required to perform such an exhaustive set of measurements threatens the integrity of the structures under measurement.

[0012] Currently, at the beginning of metrology recipe generation, a relatively large number of separate measurements for each metrology application are identified, all of the measurements are performed, and an improved metrology recipe is then generated. For example, a relatively large set of measurements with each separate system setting (i.e., separate system parameter values) is identified. Then, measurements of one or more structures are performed with each of the separate defined metrology system settings. The metrology data for all of the measurements is collected and analyzed to generate an improved metrology recipe (i.e., a subset or separate set of measurements).

[0013] This approach is applied iteratively to arrive at a satisfactory metrology recipe. In each iteration a new set of measurements is applied to a different lot of wafers. If a given metrology recipe is inappropriate, an improved metrology recipe is applied to the next lot of wafers. As a result, a process shift is triggered to trigger an iterative recipe optimization over a long period (e.g. several weeks) before values ​​can be obtained from the metrology system. For slower tools (e.g. photon-starved tools) this recipe optimization approach introduces unacceptable delays.

[0014] In some examples, a relatively large number of separate measurements for each individual metrology application are simulated, and a metrology recipe is generated that takes into account the tradeoff between metrology performance and acquisition time. Examples of implementing an automatic tradeoff between performance and acquisition time are described in U.S. Pat. No. 6,393,313 and U.S. Pat. No. 6,393,326, each of which is incorporated herein by reference in its entirety.

[0015] In conventional metrology recipe optimization based on metrology performance index, an optimal metrology recipe is identified for a single simulated target geometry given predefined assumptions about parameter errors, such as errors in system parameters, such as hardware tolerances, and errors in geometric parameters used to characterize the geometry under measurement.

[0016] Unfortunately, conventional metrology recipe optimization suffers from a lack of robustness: for example, when the range of the real structures being measured varies significantly from the simulated target structures used to generate the metrology recipe, the performance of the optimized metrology recipe degrades significantly. [Prior art documents] [Patent documents]

[0017] [Patent Document 1] US Patent Application Publication No. 2020 / 0025554 [Patent Document 2] US Patent Application Publication No. 2019 / 0293578 [Patent Document 3] U.S. Patent No. 7,929,667 [Patent Document 4] US Patent Application Publication No. 2015 / 0110249 [Patent Document 5] U.S. Patent No. 7,826,071 [Patent Document 6] U.S. Patent No. 7,478,019 Summary of the Invention [Problem to be solved by the invention]

[0018] Future metrology applications will face metrology challenges due to ever finer resolution requirements, multi-parameter correlation, more complex geometries, and the increasing use of opaque materials, therefore improved metrology recipe generation methods and systems are desired. [Means for solving the problem]

[0019] A method and system for optimizing a semiconductor metrology recipe that is robust to geometric modeling errors and variations in hardware modeling parameters is described herein. The robust metrology recipe identifies a minimum set of metrology system settings that meets wafer throughput and measurement uncertainty requirements, regardless of the metrology system error uncertainty, the geometric modeling errors, and the underlying geometry of the structures being measured.

[0020] Robust metrology recipe optimization minimizes a cost function that not only includes terms characterizing metrology performance and exposure time, but also includes one or more regularization terms that constrain the process space explored during the optimization. By using regularization as described herein to increase optimization robustness and reduce bias for individual sets of simulated model parameter values, fewer sets of simulated model parameter values ​​are required. This significantly reduces the information processing effort required to optimize the metrology recipe.

[0021] In general, the regularized metrology recipe optimization described herein can incorporate any performance estimation method, including error propagation, machine learning, regression, etc. By introducing a cost into the evaluation of available points in the process space, the regularization described herein increases metrology recipe robustness and reduces the total metrology process time.

[0022] An optimized set of metrology system parameter values ​​describes a sequence of measurements of semiconductor structures by the metrology system at each of one or more metrology sites. Each measurement in the sequence is characterized by different values ​​of one or more metrology system parameters that define a configuration of the metrology system. In other words, the metrology system configuration (e.g., incidence angle, divergence, azimuth angle, beam energy, integration time, etc.) varies for each measurement in the sequence. In one aspect, a regularized metrology recipe optimization cost function incorporates a regularization term that characterizes the roughness of a curve that describes exposure time as a function of incidence angle.

[0023] In another aspect, a regularized metrology recipe optimization cost function incorporates a regularization term that characterizes the degree of asymmetry of the curve representing exposure time as a function of incidence angle.

[0024] In another aspect, a regularization term that characterizes the difference between the current metrology recipe and the reference metrology recipe is incorporated into the regularized metrology recipe optimization cost function.

[0025] In another aspect, a regularized metrology recipe optimization cost function incorporates a regularization term that characterizes the difference between the current value of the metrology system parameter as specified by the current metrology recipe and a reference metrology system parameter value.

[0026] In general, the regularization cost function may incorporate any number of regularization terms, including any combination of the regularization terms described herein.

[0027] In a further aspect, the regularized metrology recipe optimization is performed based on metrology data for multiple instances of a semiconductor structure, each instance being characterized by different values ​​of one or more geometric parameters of interest, where the metrology data includes measurements of the semiconductor structure at multiple distinct nominal values ​​of the geometric parameters characterizing the geometry of the structure.

[0028] In certain embodiments, a value of a regularized cost function for optimizing a metrology recipe is determined for each instance of the semiconductor structure. The resulting values ​​of the regularized cost function are averaged, and the average value of the regularized cost function is used to drive the next iteration of the metrology recipe. Averaging the values ​​of the regularized cost function for many different instances of semiconductor structure performance makes the optimized metrology recipe more robust to geometric variations in the structure under measurement.

[0029] In general, regularization terms can be synthesized and employed as a component of the metrology recipe optimization cost function based on any known characteristic of the structure under measurement, including but not limited to the structure's symmetry, optical density, height, and class. In addition, regularization terms can be synthesized and employed as a component of the metrology recipe optimization cost function based on individual parameters of interest, such as CD, tilt, etc.

[0030] In a further aspect, the search for the optimized metrology recipe is limited to a distinct set of metrology system parameter values ​​associated with the available metrology data set, i.e., the optimized metrology recipe is a distinct subset of the metrology system parameter values ​​associated with the available metrology data set, such that the performance of each individual metrology recipe is verified using existing metrology data.

[0031] The foregoing is a summary, and as such contains various simplifications, generalizations, and omissions of detail; as such, those skilled in the art will appreciate that this summary is illustrative only and is not intended to be in any way limiting. Other aspects, novel features, and advantages of the devices and / or processes described herein will become apparent in the non-limiting detailed description set forth herein. [Brief description of the drawings]

[0032] [Figure 1] FIG. 1 illustrates an example metrology system 100 configured to measure properties of a sample in accordance with the methods described herein. [Diagram 2] FIG. 2 illustrates another embodiment of a metrology tool 200 configured to measure properties of a specimen in accordance with the methods presented herein. [Diagram 3] 1 depicts an X-ray illumination beam 117 incident on a wafer 101 at a particular orientation described by angles φ and θ. [Figure 4] 3 is a flow chart illustrating an example metrology recipe optimization method 300 described herein. [Diagram 5] FIG. 1 illustrates an example model building and analysis engine 150 configured to elucidate sample parameter values ​​based on X-ray scatterometry data in accordance with the methods described herein. [Figure 6] 1 illustrates another embodiment of a trench structure measured by a transmission small angle X-ray scattering (T-SAXS) tool, such as a metrology system 100. [Figure 7] 18 is a plot 180 illustrating exposure time as a function of incidence angle for a metrology recipe. [Figure 8] FIG. 1 illustrates elements of metrology systems 100 and 200 that are contained in a vacuum environment isolated from the sample 101. [Figure 9A] FIG. 1 is an isometric view of a typical 3D FLASH memory device 190 subjected to metrology in the manner described herein. [Figure 9B]FIG. 1 is a top view of a typical 3D FLASH memory device 190 subjected to metrology as described herein. [Figure 9C] FIG. 1 is a cross-sectional view of an exemplary 3D FLASH memory device 190 subjected to metrology as described herein. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0033] Reference will now be made in detail to background and certain embodiments of the present invention, examples of which are illustrated in the accompanying drawings.

[0034] Described herein are methods and systems for selecting a subset of available semiconductor metrology system configurations that are optimized for a particular metrology application and are robust to geometric modeling errors and variations in hardware modeling parameters (e.g., beam flux, beam center, etc.).

[0035] Metrology tools have a wide variety of metrology options. Measurement performance varies for each metrology option and metrology application. A robust metrology recipe specifies a minimal set of metrology system settings, specifically, a minimal set for which wafer throughput and measurement uncertainty are met regardless of metrology system error uncertainty, geometric modeling error, and the underlying geometry of the structure under measurement.

[0036] Robust metrology recipe optimization minimizes a cost function that includes terms characterizing metrology performance and exposure time, as well as one or more regularization terms that constrain the process space explored during the optimization. The regularization terms are formulated to incorporate prior knowledge about the metrology application to facilitate robust metrology recipe optimization. Furthermore, regularization reduces the bias of the recipe optimization to individual nominal parameter values, thereby reducing the uncertainty across the entire space of potential geometric variations. By using regularization as described herein to increase optimization robustness and reduce bias to individual sets of simulated model parameter values, fewer sets of simulated derived model parameter values ​​are required. This significantly reduces the information processing effort required to optimize the metrology recipe.

[0037] The total metrology process time includes both the metrology time and the metrology recipe optimization time. The recipe optimization time increases dramatically if all potential metrology system parameter settings are considered in the optimization. Furthermore, the metrology time increases dramatically if long exposure times are required across many different metrology system parameter settings. Regularizing the recipe optimization to incorporate prior knowledge about the structure under measurement reduces bias in the optimized recipe, which in turn leads to better system parameter selection with shorter metrology times. This reduces both the metrology time and the recipe optimization time.

[0038] In general, the regularized metrology recipe optimization described herein can incorporate any performance estimation method, including error propagation, machine learning, regression, etc. By introducing a cost into the evaluation of available points in the process space, the regularization described herein increases metrology recipe robustness and reduces the total metrology process time.

[0039] One embodiment of a metrology tool 100 for measuring properties of a specimen in accordance with example methods presented herein is depicted in Figure 1. As shown in Figure 1, the system 100 may be used to perform X-ray scatterometry measurements over an inspection area 102 of a specimen 101 positioned on a specimen positioning system 140.

[0040] In the illustrated embodiment, the metrology tool 100 includes an X-ray illumination source 110 configured to generate X-ray radiation suitable for X-ray scatterometry metrology. In certain embodiments, the X-ray illumination system 110 is configured to generate wavelengths between 0.01 nanometers and 1 nanometer. An X-ray beam 117 generated by the X-ray illumination source 110 is incident on the inspection area 102 of the sample 101.

[0041] In general, any suitable high brightness X-ray illumination source capable of producing high brightness X-rays at flux levels sufficient to enable high throughput in-line metrology can be envisioned for providing X-ray illumination for X-ray scatterometry. According to certain embodiments, the X-ray source can incorporate a tunable monochromator to enable different selectable wavelengths of X-ray radiation delivered by the X-ray source.

[0042] In certain embodiments, one or more x-ray sources that emit radiation at photon energies greater than 15 keV can be utilized to ensure that the x-ray source provides light at a wavelength sufficient to propagate through the entire device and wafer substrate. By way of non-limiting example, any of particle accelerator sources, liquid anode sources, rotating anode sources, stationary solid anode sources, microfocus sources, microfocus rotating anode sources, and inverse Compton sources can be employed as the x-ray source 110. As an example, an inverse Compton source available from Lyncean Technologies, Inc., Palo Alto, Calif., USA, may be considered. An inverse Compton source has the added advantage of being capable of producing x-rays over a wide range of photon energies, thus allowing for a wide selection of wavelengths of x-ray radiation delivered by the x-ray source.

[0043] An example of an X-ray source includes an electron beam source configured to bombard a solid or liquid target to stimulate emission of X-ray radiation. FIG. 2 illustrates a metrology tool 200 for measuring properties of a specimen according to example methods presented herein. Like numbered elements of metrology tools 100 and 200 are similar. However, in the embodiment illustrated in FIG. 2, the X-ray illumination source 110 is a liquid metal X-ray illumination system. A liquid metal jet 119 is provided from a liquid metal container 111 and collected in a liquid metal collector 112. A liquid metal circulation system (not shown) returns the liquid metal collected by the collector 112 back to the liquid metal container 111. The liquid metal jet 119 contains one or more elements. By way of non-limiting example, the liquid metal jet 119 contains any of aluminum, gallium, indium, tin, thallium, and bismuth. In this way, the liquid metal jet 119 produces X-ray lines corresponding to its constituent elements. In some embodiments, the liquid metal jet comprises an alloy of gallium and indium. In certain embodiments, the x-ray illumination system 110 is configured to produce wavelengths between 0.01 nanometers and 1 nanometer. An electron beam source 113 (e.g., an electron gun) generates an electron stream 118 that is directed toward the liquid metal jet 119 by electron-optics 114. Suitable electron-optics 114 include electromagnets, permanent magnets, or a combination of electromagnets and permanent magnets to focus the electron beam and direct it toward the liquid metal jet. The encounter between the liquid metal jet 119 and the electron stream 118 produces an x-ray beam 117 that is incident on the inspection area 102 of the sample 101.

[0044] A method and system for producing high brightness liquid metal x-ray illumination is described in US Pat. No. 6,399,434, issued Apr. 19, 2011 to KLA-Tencor Corp., the entire contents of which are incorporated herein by reference.

[0045] In one embodiment, the incident X-ray beam 117 is at the 24.2 keV Indium kα line. The X-ray beam is collimated down to a divergence of less than 1 milliradian using multi-layer X-ray optics for X-ray scatterometry measurements.

[0046] In certain embodiments, the X-ray scattering measurements described herein are accomplished without the use of a screen between the X-ray source and the sample under measurement. In these embodiments, the measured intensity of the incident beam over a range of angles of incidence, multiple wavelengths, or a combination of both, provides sufficient information to resolve a distribution map (i.e., image) of the desired material property (e.g., complex refractive index, electron density, or absorption) of the measured structure. In other examples, a pinhole or other aperture can be placed on an otherwise opaque screen between the X-ray source and the measured sample to improve the collimation of the X-ray beam. The intensity of the diffraction pattern is measured for several aperture positions. In other embodiments, a screen with a pseudorandom aperture pattern is used, and the diffraction pattern is measured for several screens. These techniques can also be considered to provide additional information to resolve the three-dimensional distribution of the desired material property of the measured structure.

[0047] In certain embodiments, the profile of the incident X-ray beam is controlled by two or more apertures, slits, or a combination thereof, and in further embodiments, the apertures, slits, or both are configured to rotate in lockstep with the orientation of the sample, such that the incident beam profile is optimized for a particular angle of incidence, azimuth angle, or both.

[0048] As depicted in FIG. 1, the X-ray optics 115 shapes and directs the incident X-ray beam 117 onto the sample 101. In certain examples, the X-ray optics 115 may incorporate an X-ray monochromator to monochromatize the X-ray beam incident on the sample 101. In certain examples, a crystal monochromator, such as a Loxley-Tanner-Bowen monochromator, may be used to monochromatize the X-ray radiation beam. In certain examples, the X-ray optics 115 collimates or focuses the X-ray beam 117 onto the inspection area 102 of the sample 101 using multi-layer X-ray optics to a divergence of less than 1 milliradian. In certain embodiments, the X-ray optics 115 comprises one or more X-ray collimating mirrors, X-ray apertures, X-ray beam stops, refractive X-ray optics, diffractive optics such as zone plates, specular X-ray optics such as grazing incidence ellipsoidal mirrors, polycapillary optics such as hollow capillary X-ray waveguides, multi-layer optics or systems, or any combination thereof. Further details are described in U.S. Patent No. 6,399,633, which is incorporated herein by reference in its entirety.

[0049] Typically, the focal plane of the illumination optical system is optimized for each metrology application. By configuring system 100 in this manner, the focal plane can be located at various depths within the sample depending on the metrology application.

[0050] X-ray detector 116 collects X-ray radiation 125 scattered from sample 101 in accordance with an X-ray scatterometry metrology technique and generates an output signal 126 indicative of a property of sample 101 that is sensitive to the incident X-ray radiation. In certain embodiments, sample positioning system 140 positions and orients sample 101 so that angle-resolved scattered X-rays are generated as scattered X-rays 125 are collected by X-ray detector 116.

[0051] In certain embodiments, the X-ray scatterometry system has a wide dynamic range (e.g., 10 5The system includes one or more photon-counting detectors having a thickness greater than 100 nm and a thick highly absorbing crystal substrate that absorbs the direct beam (i.e., the zeroth order beam) without damage and with minimal parasitic backscatter. In certain embodiments, a single photon-counting detector detects the location and number of detected photons.

[0052] Full-beam X-ray scatterometry requires collection of the higher diffracted orders in addition to collection of the zeroth order beam. The zeroth order is several orders of magnitude more intense than the other orders. If the zeroth order beam is not fully absorbed by the X-ray sensitive section of the detector, it will be scattered and generate parasitic signals. The strength of these parasitic signals limits the dynamic range of the measurement. For example, if the parasitic signals are less than 10 times the maximum flux signal (i.e. the zeroth order signal), -4 Therefore, in order to extend the effective dynamic range of full-beam metrology, it is essential that the detector (e.g., detector 116) has a high conversion efficiency from X-rays to electron-hole pairs and a strong X-ray absorption.

[0053] Examples of detector materials suitable for full-beam x-ray scatterometry include cadmium telluride (CdTe), germanium (Ge), and gallium arsenide (GaAs) crystals, etc. In certain embodiments, a detector material is selected that provides high conversion efficiency over a narrow energy band corresponding to the source energy.

[0054] In certain embodiments, the thickness of the detector material is selected to achieve a desired absorption of the incoming x-rays. According to certain embodiments, the detector can be tilted with respect to the incoming x-ray beam (various diffraction orders) to increase the path length of the x-ray beam in the detector material, thus increasing the total absorption.

[0055] In certain embodiments, a dual threshold detector is employed to improve the SNR.

[0056] In certain embodiments, the X-ray detector 116 resolves one or more X-ray photon energies and generates X-ray energy components signals indicative of a characteristic of the sample. In certain embodiments, the X-ray detector 116 comprises a CCD array, a microchannel plate, a photodiode array, a microstrip proportional counter, a gas-filled proportional counter, a scintillator, and a phosphor material.

[0057] In this way, X-ray photon interactions in the detector are discriminated by energy in addition to pixel location and count number. In certain embodiments, the discrimination is performed by comparing the energy of the X-ray photon interaction with a predetermined upper threshold and a predetermined lower threshold. In some embodiments, the information is sent via output signal 126 to information processing system 130 for further processing and storage.

[0058] In certain embodiments, the detector is moved in a scanning motion relative to the incoming x-rays to reduce damage and excess charging from the incident zeroth order beam. In some of these embodiments, the detector is moved in a continuous scanning motion relative to the incoming x-rays to avoid the zeroth order beam staying at a specific location on the detector surface for a long period of time. In certain other embodiments, the detector is moved in a periodic motion relative to the incoming x-rays to avoid the zeroth order beam staying at a specific location on the detector surface for a long period of time. In certain embodiments, the scanning or periodic motion is approximately perpendicular to the incoming x-rays. In some embodiments, the motion is rotational (e.g., the detector is rotated so that the specific location on the detector surface traces a circle in space). In some embodiments, the motion is a combination of translational motions that move the point of incidence of the zeroth order beam to various different locations on the detector surface.

[0059] In X-ray scatterometry, a collimated X-ray beam is diffracted by a structure (e.g. a high aspect ratio vertical fabrication structure) resulting in multiple diffracted orders. Each diffracted order travels in a specific, predictable direction. The angular spacing of the diffracted orders is inversely proportional to the lattice constant of the sample divided by the wavelength. The diffracted orders are detected by a detector array placed some distance from the wafer. Each pixel of the detector outputs a signal indicative of the number of photons that struck that pixel.

[0060] The intensities of the diffracted orders have the form I(m,n,θ,φ,λ), where {m,n} are integer exponents indicating the diffraction order, {θ,φ} are the elevation and azimuth angles of the incident beam (i.e., the polar coordinate values ​​of the incident chief ray with respect to a coordinate system fixed on the wafer), and λ is the wavelength of the incident X-ray.

[0061] Several noise sources perturb the illumination light on its way from the illumination source to the sample, such as electron beam current wander, temperature-induced optics drift, etc. The perturbed incident flux is denoted as F0(1+n1).

[0062] The scattering form of the incident radiation at the target depends on the azimuth angle and elevation angle of the incident beam. The light scattering efficiency into orders (m,n) is S mn (θ,φ). As the diffracted light propagates from the sample to the detector, it passes through other scattering media, where all orders are equally affected and some variance (1+n2) and parasitic noise (n3) are added. In this case, the total intensity I mn can be expressed by equation (1). I mn =S mn (θ,φ)(1+n2)(1+n1)F0t+n3(1)

[0063] According to certain embodiments, measurements can be desirably performed at a variety of orientations; these orientations are described by rotations about the x and y axes as illustrated by coordinate system 146 in FIG. 1. This increases the number and variety of data sets available for analysis, incorporating a variety of large angle out-of-plane orientations, thereby increasing the precision and accuracy of the measurement parameters and reducing inter-parameter correlation. Measuring sample parameters with deeper and more diverse data sets also reduces inter-parameter correlation and improves measurement accuracy. For example, x-ray scatterometry at orthogonal orientations can resolve the critical dimensions of a feature, but is largely insensitive to the sidewall angle and height of the feature. In contrast, measurement data collected over a wide range of out-of-plane angle positions can resolve the sidewall angle and height of the feature.

[0064] As depicted in FIG. 1 , the metrology tool 100 includes a sample positioning system 140 configured to align and orient the sample 101 over a wide range of out-of-plane angular orientations relative to the scatterometer. In other words, the sample positioning system 140 is configured to rotate the sample 101 over a large angular range about one or more rotation axes that are in-plane aligned with respect to the surface of the sample 101. In certain embodiments, the sample positioning system 140 is configured to rotate the sample 101 over a range of at least 90 degrees about one or more rotation axes that are in-plane aligned with respect to the surface of the sample 101. In certain embodiments, the sample positioning system is configured to rotate the sample 101 over a range of at least 120 degrees about one or more rotation axes that are in-plane aligned with respect to the surface of the sample 101. In certain other embodiments, the sample positioning system is configured to rotate the sample 101 within a range of at least 1 degree about one or more pivot axes that are in-plane aligned with the surface of the sample 101. In this way, angle resolved measurements of the sample 101 are collected by the metrology system 100 across several locations on the surface of the sample 101. In one example, the information processing system 130 sends command signals indicative of a desired position of the sample 101 to a motion controller 145 of the sample positioning system 140. In response, the motion controller 145 generates command signals for various actuators of the sample positioning system 140 to achieve the desired position of the sample 101.

[0065] By way of non-limiting example, as depicted in FIG. 1, the specimen positioning system 140 includes an edge grip chuck 141 that can fixedly mount the specimen 101 to the specimen positioning system 140. A rotation actuator 142 is configured to rotate the edge grip chuck 141 and the mounted specimen 101 relative to a perimeter frame 143. In the illustrated embodiment, the rotation actuator 142 is configured to rotate the specimen 101 about the x-axis of a coordinate system 146 depicted in FIG. 1. As depicted in FIG. 1, rotation of the specimen 101 about the z-axis is rotation within the plane of the specimen 101. Rotation about the x- and y-axes (not shown) is rotation out of the plane of the specimen 101, effectively tilting the surface of the specimen relative to the metrology elements of the metrology system 100. Although not depicted, a second rotation actuator is configured to rotate the specimen 101 about the y-axis. A linear actuator 144 is configured to translate the perimeter frame 143 along the x-direction. Another linear actuator (not shown) is configured to translate the perimeter frame 143 along the y-direction. In this way, each location on the surface of the sample 101 is available for measurement over a range of out-of-plane angular positions. For example, in one embodiment, locations on the sample 101 are measured over several angular increments within a range of -45 degrees to +45 degrees relative to an orientation perpendicular to the sample 101.

[0066] In general, the sample positioning system 140 may incorporate any combination of mechanical elements suitable to achieve the desired linear and angular positioning performance, including, but not limited to, goniometer stages, hexapod stages, angular stages, and linear stages.

[0067] The X-ray scatterometry metrology described herein is performed with multiple orientations of the illuminating X-ray beam relative to the surface normal of the semiconductor wafer. Each orientation is described by two angular rotations of the wafer 101 relative to the X-ray illumination beam or vice versa. According to an example, the orientation can be described with reference to a coordinate system fixed relative to the wafer. FIG. 3 illustrates an X-ray illumination beam 117 incident on the wafer 101 at a specific orientation described by angles θ and φ. The coordinate system XYZ is fixed to the metrology system, and the coordinate system X'Y'Z' is fixed to the wafer 101. Z is aligned with an axis perpendicular to the surface of the wafer 101. X and Y lie in a plane aligned with the surface of the wafer 101. Similarly, Z' is aligned with an axis perpendicular to the surface of the wafer 101, and X' and Y' lie in a plane aligned with the surface of the wafer 101. As illustrated in FIG. 3, the X-ray illumination beam 117 lies in the X'Z' plane. The angle φ describes the orientation of the X-ray illumination beam 117 in the X'Z' plane relative to the surface normal of the wafer. Additionally, the angle θ describes the orientation of the X'Z' plane relative to the XZ plane. Together, θ and φ uniquely define the orientation of the X-ray illumination beam 117 relative to the surface of the wafer 101. In this example, the orientation of the X-ray illumination beam relative to the surface of the wafer 101 is described by a rotation about an axis perpendicular to the surface of the wafer 101 (i.e., the Z axis) and a rotation about an axis aligned with the surface of the wafer 101 (i.e., the Y' axis). In certain other examples, as described with reference to FIG. 1, the orientation of the X-ray illumination beam relative to the surface of the wafer 101 is described by a rotation about a first axis aligned with the surface of the wafer 101 and a rotation about another axis perpendicular to the first axis and aligned with the surface of the wafer 101.

[0068] In a further aspect, an X-ray scatterometry system is used to determine a property (e.g., a structural parameter value) of the specimen based on one or more diffracted order measurements. As depicted in FIG. 1, an information processing system 130 included in the metrology tool 100 can be used to acquire signals 126 generated by the detector 116 according to a robust metrology recipe and to determine a property of the specimen based at least in part on the acquired signals.

[0069] 4 depicts a method 300 suitable for implementation by the metering systems 100 and 200 of the present invention. According to certain embodiments, as can be appreciated, the data processing blocks of the method 300 can be implemented through execution of pre-programmed algorithms by one or more processors of the information processing system 130. Although the following description is presented in the context of the metering systems 100 and 200, it is recognized herein that the specific structural aspects of the metering systems 100 and 200 should be taken as illustrative only and not limiting.

[0070] In block 301, metrology data is generated for at least one semiconductor structure having known values ​​for one or more parameters of interest, for a first plurality of measurements, each of which has a distinct value for one or more metrology system parameters.

[0071] In preferred embodiments, the metrology signal is predicted by electromagnetic simulation, in which a simulated metrology signal is generated based on a geometric model of the measured structure, characterized by one or more parameters of interest, such as critical dimensions, height, etc.

[0072] In certain examples, the measurement system parameters may include different illumination angles (e.g., angles of incidence and azimuth), different detector resolutions, different exposure times, different target sizes, different source sizes, different collection energies, or any combination thereof.

[0073] In block 302, values ​​of the one or more parameters of interest for the at least one semiconductor structure are estimated given the metrology data and the metrology model.

[0074] In certain embodiments, values ​​of parameters of interest (e.g., critical dimensions, sidewall angles, height, overlay, etc.) are estimated based on the metrology data using inverse solution techniques, such as model-based regression, ptychography, tomography, one or more machine learning models, or a combination thereof.

[0075] In some of these embodiments, values ​​of the one or more parameters of interest are determined by inverse solution of a predetermined metrology model with the metrology data. The metrology model includes a small number of adjustable parameters (e.g., on the order of 10) that represent the geometric and optical properties of the sample and the optical properties of the metrology system. Target profile parameters are then estimated by solving for the parameterized metrology model values ​​that minimize the error between the measured scattered x-ray intensity and the modeled results.

[0076] In a further aspect, the information processing system 130 is configured to generate a structural model (e.g., a geometric model, a material model, or a combined geometric-material model) of the measured structure of the specimen, generate an X-ray scatterometry response model including at least one geometric parameter derived from the structural model, and perform a fitting analysis of the X-ray scatterometry measurement data with the X-ray scatterometry response model to resolve at least one specimen parameter value. The analysis engine can be used to compare the simulated X-ray scatterometry signal to the measured data to determine geometric and material properties of the specimen, such as electron density. In the embodiment depicted in FIG. 1, the information processing system 130 is configured as a model building and analysis engine, and the engine is configured to perform the model building and analysis functions as described herein.

[0077] FIG. 5 illustrates an example model building and analysis engine 150 implemented by information processing system 130. As illustrated in FIG. 5, model building and analysis engine 150 includes a structural model building module 151 that generates a structural model 152 of a measured structure of a sample. In certain embodiments, structural model 152 also incorporates material properties of the sample. The structural model 152 is received as an input to an X-ray scatterometry response function building module 153. X-ray scatterometry response function building module 153 generates an X-ray scatterometry response function model 155 based at least in part on the structural model 152. In certain examples, the X-ray scatterometry response function model 155 is based on an X-ray form factor.

number

number

[0078] In some cases, the fit of the modeled data to the experimental data is accomplished by minimizing the chi-squared value. For example, in X-ray scatterometry measurements, the chi-squared value is

number

[0079] However, S j SAXS experimentis the X-ray scatterometry signal 126 measured in "channel" j, where the index j is an index describing a set of system parameters, e.g., diffraction order, energy, angular coordinate, etc. j SAXS model (v1,…,v L ) is the modeled X-ray scatterometry signal S associated with “channel” j. j Let v1,…,v be a set of structural (target) parameters. L The parameters are geometric (CD, sidewall angle, overlay, etc.) and material (electron density, etc.) parameters. SAXS,j is the uncertainty associated with the jth channel. N SAXS is the total number of channels in the X-ray metrology. L is the number of parameters characterizing the metrology target.

[0080] In equation (4), it is assumed that the uncertainties for the different channels are uncorrelated. In instances where the uncertainties for the different channels are correlated, the covariance between the uncertainties can be calculated. In those instances, the chi-squared value for the x-ray scatterometry measurements is

number

[0081] However, V SAXS is the covariance matrix of the SAXS channel uncertainties, and T denotes its transpose.

[0082] In certain examples, a fitting analysis module 157 performs a fitting analysis on the x-ray scatterometry metrology data 126 with the x-ray scatterometry response model 155 to resolve at least one sample parameter value. SAXS 2 is optimized.

[0083] As previously described herein, the fitting of the x-ray scatterometry data is accomplished by minimizing the chi-squared value, although in general the fitting of the x-ray scatterometry data can be accomplished by other functions.

[0084] Fitting of X-ray scatterometry metrology data can be useful for any type of X-ray scatterometry technology that is sensitive to the geometric and / or material parameters of interest. The sample parameters can be either deterministic (e.g. CD, SWA, etc.) or statistical (e.g. rms sidewall roughness, roughness correlation length, etc.) as long as an appropriate model is used that describes the X-ray scatterometry beam interaction with the sample.

[0085] Typically, the information processing system 130 is configured to utilize real-time critical dimensioning (RTCD) to access model parameters in real time, or may access a library of pre-calculated models to determine values ​​for at least one specimen parameter associated with the specimen 101. Typically, some form of CD engine can be used to estimate the difference between a specified CD parameter of the specimen and a CD parameter associated with the measured specimen. An example of a specimen parameter value calculation method and system is described in U.S. Patent Application Publication No. 2010 / 0133994, issued Nov. 2, 2010 to KLA-Tencor Corp., which is incorporated herein by reference in its entirety.

[0086] In certain examples, the model building and analysis engine 150 improves the accuracy of parameter measurements through some combination of feed-sideway analysis, feed-forward analysis, and parallel analysis. Feed-sideway analysis involves taking multiple data sets on separate areas of the same sample and passing common parameters from the first data set to the second data set for analysis. Feed-forward analysis involves taking data sets on separate samples and forwarding common parameters for subsequent analysis using a stepwise copy exact parameter feed-forward technique. Parallel analysis involves the parallel or simultaneous application of a nonlinear fitting methodology to multiple data sets, where at least one common parameter is combined during the fitting.

[0087] Multi-tool and structural analysis refers to feed-forward, feed-sideway, or parallel analysis that relies on regression, look-up tables (i.e., "library" matching), or other multiple data set fitting procedures. An example of a multi-tool and structural analysis method and system is described in U.S. Patent Application Publication No. 2009 / 0133634, issued to KLA-Tencor Corp. on January 13, 2009, which is incorporated herein by reference in its entirety.

[0088] In block 303, at each distinct value of the one or more system parameters, the sensitivity of the value of each of the one or more parameters of interest to changes in the value of each of the one or more measured system parameters is determined.

[0089] In certain embodiments, the Jacobian matrix quantifies the sensitivity of the estimate of the parameter of interest to different measurement system parameter values, such as measurement time, angle of incidence, azimuth angle, etc.

[0090] In block 304, a set of metrology system parameter values ​​is determined based on optimizing a regularized cost function that includes the determined sensitivities.

[0091] An optimized set of metrology system parameter values ​​describes a sequence of semiconductor structure measurements to be performed by the metrology system at each of the one or more metrology sites. Each measurement in the sequence is characterized by different values ​​of one or more metrology system parameters that define a configuration of the metrology system. In other words, the configuration of the metrology system (e.g., angle of incidence, divergence, azimuth angle, beam energy, integration time, etc.) is different for each measurement in the sequence.

[0092] The search for available metrology configurations may use nonlinear least squares, nonlinear integer optimization, exhaustive search, simulated annealing, L1 norm regression, genetic search, pre-trained models, etc. The pre-trained models may be based on the methods listed above, synthetic training sets, or decisions based on actual results. In certain embodiments, the Jacobian matrix is ​​taken as part of the optimization to optimize the regularized metrology performance index by selecting a set of metrology system parameter values ​​and associated measurement times. In general, the metrology recipe is iteratively updated until a final metrology recipe is reached that minimizes the regularized metrology performance index, or until the maximum time allowed for metrology recipe generation has expired.

[0093] In certain embodiments, the optimization cost function is regularized to ensure measurement robustness to outliers and process excursions while trading off some combination of measurement uncertainty, measurement time, travel time, exposure time, exposure dose, etc.

[0094] In one embodiment, a regularization term is incorporated into the regularized metrology recipe optimization cost function to characterize the roughness of the curve representing the exposure time as a function of the angle of incidence. Experiments have shown that the curve representing the process variation, e.g., exposure time T, as a function of the angle of incidence AOI, e.g., T(AOI), should be smooth, i.e., with negligible roughness. In one example, the roughness is characterized by the normalized standard deviation of the second derivative of the exposure time as a function of the angle of incidence T(AOI), as expressed by Equation (6). Roughness = stdev(d2 T(AOI) / dAOI 2 ) / mean(T(AOI)) (6)

[0095] In another embodiment, a regularization term is incorporated into the regularization metrology recipe optimization cost function to characterize the asymmetry of the curve representing the exposure time as a function of the incidence angle. In CD-SAXS metrology, the resulting scattering intensity is highest when the incidence angle of the incident metrology beam is aligned with the tilt angle of the measured structure. At this incidence angle, the contribution of the measured signal to the total metrology precision and accuracy is maximized. Furthermore, process variations in tilt or overlay tend to be equally present on both sides of the average tilt or overlay, respectively. Therefore, it is beneficial to prefer metrology recipes that exhibit a symmetric exposure time distribution around an average geometry, e.g., average tilt angle, average overlay, etc. In such an example, the curve representing the process variation, e.g., exposure time T, as a function of the incidence angle AOI, e.g., T(AOI), should be symmetric. In one example, the regularization term characterizing the asymmetry of the exposure time as a function of the difference between the incidence angle and the average tilt or overlay is represented by equation (7); where x is the average value of the tilt or overlay. Typically, the average value of tilt or overlay is known to the user of the metrology system based on process knowledge. Symmetry = Σ AOI |T(AOI+x)-T(-AOI+x)| / mean(T) (7)

[0096] 6 is an example diagram illustrating a cross-sectional view of a trench structure 170 measured by a transmission small-angle X-ray scattering (T-SAXS) tool, e.g., metrology system 100. As depicted in FIG. 6, trench structure 170 is fabricated with a tilt angle α relative to a surface normal 171 of a semiconductor wafer 172. In one example, the average tilt angle of multiple samples is set to +1 degree. In this example, a regularization using the asymmetry term represented by equation (7) is performed during metrology recipe optimization, such that the optimization favors metrology recipes that exhibit exposure time symmetry around the +1 degree incidence angle.

[0097] 7 is a plot 180 illustrating exposure time as a function of incidence angle for a metrology recipe. As depicted in FIG. 7, the metrology recipe exhibits symmetry in exposure time around an incidence angle of +1 degree.

[0098] In another example, the average tilt angle over a large number of samples is taken to be 0 degrees. In this example, there is no expected tilt, and regularization using the asymmetry term described by equation (7) is performed during metrology recipe optimization, which results in the optimization favoring metrology recipes that exhibit exposure time symmetry around a 0 degree incidence angle.

[0099] In another aspect, a regularization term that characterizes the difference between the current metrology recipe and the reference metrology recipe is incorporated into the regularized metrology recipe optimization cost function. In one example, the regularization term that characterizes the difference between the current metrology recipe and the reference metrology recipe is expressed by equation (8); where T(AOI) is the exposure time as a function of the angle of incidence for the current metrology recipe, and T ref where (AOI) is the exposure time as a function of the angle of incidence for the reference metrology recipe. Thus, the regularization term expressed by equation (8) penalizes the cost function based on how much the current metrology recipe differs from the reference recipe. Variance from reference recipe = Σ AOI |T(AOI)-T ref (AOI)| / mean(T(AOI)) (8)

[0100] In certain instances, a reference metrology recipe is a metrology recipe that has worked well in the past for measuring similar geometries with a similar metrology system, such as channel holes, word line cuts, DRAMs, etc. Reasonably, an optimized metrology recipe for measuring similar geometries with a similar metrology system should not be significantly different from the reference metrology recipe.

[0101] In certain examples, a reference metrology recipe is synthesized by analyzing the sensitivity of one or more metrology system parameters to an estimated value of the parameter of interest, and in certain examples, values ​​of the incidence angle, azimuth angle, or both that are less sensitive to the parameter of interest are excluded from the reference metrology recipe.

[0102] In certain other examples, a reference metrology recipe is synthesized by analyzing the correlation of an estimated parameter of interest across a range of metrology system parameters and eliminating a subset of the range of metrology system parameters that are strongly correlated. Strongly correlated signals are unlikely to contribute to minimizing a performance cost function metric, e.g., precision or accuracy. Thus, excluding the subset reduces the space of metrology system parameters sampled by the reference metrology recipe.

[0103] In certain other examples, a reference metrology recipe is synthesized by analyzing the correlation of the metrology system parameters to other metrology system parameters and constraining a subset of the metrology system parameters that are strongly correlated. Because strongly correlated metrology system parameters tend to be redundant, their values ​​should be absolutely fixed or constrained to the values ​​of other metrology system parameter values ​​in order to reduce the space of metrology system parameters sampled by the reference metrology recipe.

[0104] In certain other examples, a reference metrology recipe is synthesized by running metrology optimization without regularization over a range of distinct value pairs of metrology system parameters, such as incidence angle and azimuth angle.

[0105] In certain other instances, a reference metrology recipe is synthesized based on existing metrology process knowledge. For example, the desired azimuth angle for measuring a line cut feature is that perpendicular to the cut, which may better capture the shape of the channel sidewalls. In this instance, the space of metrology system parameters sampled by the reference metrology recipe can be reduced by excluding all other azimuth angles.

[0106] In another aspect, the regularized metrology recipe optimization cost function incorporates a regularization term that characterizes the difference between the current value of the metrology system parameter prescribed by the current metrology recipe and the reference metrology system parameter value. For example, as is known, x-ray scatterometry-based metrology of relatively low-profile structures is more sensitive at angles of incidence away from orthogonal incidence. For relatively low-profile structures, the amount of material exposed to x-ray penetration, and therefore the scattering intensity, increases significantly when moving away from orthogonal incidence. Conversely, x-ray scatterometry-based metrology of relatively high-profile structures is more sensitive at angles of incidence closer to orthogonal incidence.

[0107] In one example, the regularization term characterizing the distance from zero incidence angle is expressed by equation (9); where C is a positive constant provided by the user. The larger the value of the constant C, the stronger the regularization. The value of C is selected to be relatively large for tall structures and relatively small or zero for short structures. In this way, the regularization term expressed by equation (9) penalizes the cost function based on how much the current incidence angle prescribed by the current metrology recipe differs from zero, or orthogonal incidence. Distance from zero = Σ AOI {CT(AOI)abs(AOI)} / mean(T(AOI)) (9)

[0108] In one example, the cost function is regularized by minimizing the asymmetry and roughness of the exposure time vs. AOI curve. The optimization penalizes the cost function by the amount of roughness and asymmetry at each iteration of the metrology recipe. A smooth and symmetric distribution of exposure time as a function of incidence angle is appropriate for a large metrology sample and reduces overemphasis of certain metrology sites relative to other sites during recipe optimization.

[0109] In certain examples, each regularization component is weighted and added to the unregularized cost function components as represented by equation (8); where w1 and w2 are weights. Regularized cost function = Unregularized cost function + w1 · Roughness + w2 · Asymmetry (8)

[0110] These weights are typically selected by the user. The unregularized cost function typically represents a performance metric that quantifies measurement precision, accuracy, etc.

[0111] In general, the regularization cost function may incorporate any number of regularization terms, including any combination of the regularization terms described herein.

[0112] In a further aspect, the regularized metrology recipe optimization is performed based on metrology data for a plurality of instances of a semiconductor structure, each instance characterized by different values ​​of one or more geometric parameters of interest, where the metrology data includes measurements of the semiconductor structure at a plurality of distinct nominal values ​​of the geometric parameters characterizing a geometry of the structure.

[0113] In certain embodiments, a value of a regularized cost function for optimizing a metrology recipe is determined for each instance of the semiconductor structure. The resulting values ​​of the regularized cost function are averaged, and the average value of the regularized cost function is used to drive the next iteration of the metrology recipe. By averaging the values ​​of the regularized cost function for many different instances of semiconductor structure performance, the optimized metrology recipe becomes more robust to geometric variations in the structure under measurement.

[0114] In general, regularization terms can be synthesized and employed as a component of the metrology recipe optimization cost function based on any known characteristic of the structure under measurement, including but not limited to the structure's symmetry, optical density, height, and class. In addition, regularization terms can be synthesized and employed as a component of the metrology recipe optimization cost function based on specific parameters of interest, such as CD, tilt, etc.

[0115] In a further aspect, the search for an optimized metrology recipe is limited to a distinct set of metrology system parameter values ​​associated with the available metrology data set, i.e., the optimized metrology recipe is a distinct subset of the metrology system parameter values ​​associated with the available metrology data set. In this way, the performance of a particular metrology recipe can be verified using existing metrology data. In certain embodiments, the metrology recipe optimization is performed using nonlinear integer optimization rather than sequential optimization, and runs directly on the distinct set of metrology system parameter values.

[0116] In certain embodiments, the optimized metrology recipe is synthesized without any adjustment of the exposure times associated with each measurement in the available metrology data set. In these embodiments, a particular combination of metrology system parameters, e.g., AOI, AZ, etc., is either considered part of the optimized metrology recipe at all exposure times considered in the metrology data set or is never considered part of the optimized metrology recipe. In other words, the exposure times associated with a particular measurement included in the metrology recipe are not altered compared to the exposure times associated with a particular measurement in the available metrology data set. In these embodiments, the optimized metrology recipe is verified by completely removing the metrology signals from the available metrology data set, performing a regression against the metrology model with the metrology data associated with the optimized recipe, and verifying the resulting metrology performance, e.g., measurement precision, accuracy, etc.

[0117] In certain other embodiments, an optimized metrology recipe is synthesized with individual adjustments to the exposure times for each measurement in the available metrology data set. In these embodiments, the exposure times for specific measurements included in the metrology recipe may be individual subsets of the exposure times for specific measurements in the available metrology data set. In one example, each specific measurement is performed as a sequence of frames, e.g., a sequence of several frames of 3 seconds each. In this example, the optimized metrology recipe may include a subset of the available frames for each measurement in the available metrology data set. In these embodiments, the optimized metrology recipe is verified by removing specific frames from the metrology signals of the available metrology data set, running a regression against the metrology model with the metrology data associated with the optimized recipe, and verifying the resulting metrology performance, e.g., measurement precision, accuracy, etc.

[0118] In yet another aspect, an optimized metrology recipe is determined based on a search of a library of candidate metrology recipes.

[0119] In one example, a value of a regularized cost function described herein is evaluated for each metrology recipe in a library of historical metrology recipes, and the metrology recipe associated with the minimum value of the regularized cost function is selected as the optimal metrology recipe or as an initial metrology recipe that is further optimized in an iterative manner using the regularized cost function.

[0120] In yet another aspect, an optimized metrology recipe is validated by evaluating the measurement uncertainties associated with measurements of one or more parameters of interest (i.e., the set of metrology system settings defined by the optimized metrology recipe). In general, an optimized metrology recipe can be validated based on metrology data, simulated derived data, or both.

[0121] In certain examples, the Jacobian matrix quantifies the change in the parameter estimate of interest in response to random or systematic measurement system errors. In these examples, the Jacobian matrix is ​​used to estimate achievable measurement precision, accuracy, or both, given expected measurement system errors.

[0122] In certain other examples, a machine learning based model is utilized to estimate measurement uncertainties associated with measurements of one or more parameters of interest associated with an optimized metrology recipe.

[0123] In certain other examples, model-based regression is used to estimate measurement uncertainties associated with measurements of one or more parameters of interest associated with an optimized metrology recipe.

[0124] In some examples, a set of metrology results for a semiconductor structure from a metrology system may include measurements of one or more separate target parameters (e.g., MCD, BCD, OVL, SWA, etc.) such that optimization of the metrology recipe may involve selection of one or more target parameters that provide a better estimate of the parameter of interest (e.g., CD) for a particular semiconductor structure.

[0125] The regularized metrology recipe optimization described herein can be performed on several separate metrology systems, such as, but not limited to, X-ray transmission tools, X-ray reflectance tools, infrared transmission tools, etc.

[0126] In a further aspect, X-ray scatterometry measurements are performed according to a metrology recipe optimized as described herein over a range of incidence angles that provide sufficient resolution and penetration depth to characterize high aspect ratio structures through their full depth.

[0127] In a further aspect, the optimized metrology recipe is implemented on the metrology system by sending control commands that cause changes in the state of one or more components of the metrology system to implement the optimized metrology recipe.

[0128] In some examples, the control commands are provided to an illumination source, which in turn adjusts its electrical conditions to change the scanning spot size and shape, illumination power, spot offset, angle of incidence, etc.

[0129] In some examples, the control commands are provided to one or more positioning devices that control the location of one or more optical elements in the metrology system, which in turn change the position / orientation of the optical element or elements to adjust the angle of incidence, focal length between the illumination source and the illumination optics, beam geometry, beam spot location on the optics to minimize effects of surface roughness, etc.

[0130] Metrology systems and techniques can be used to measure structure and material properties associated with various semiconductor manufacturing processes. In certain examples, optimized metrology recipes are used for X-ray scatterometry metrology of critical dimensions, thickness, overlay and material properties of high aspect ratio semiconductor structures, including but not limited to spin transfer torque random access memory (STT-RAM), three dimensional NAND memory (3D-NAND) or volumetric NAND memory (V-NAND®), dynamic random access memory (DRAM), three dimensional FLASH memory (3D-FLASH), resistive random access memory (Re-RAM) and phase change random access memory (PC-RAM).

[0131] In certain embodiments, the X-ray detectors 116 are maintained in the same ambient environment (e.g., gas purged environment) as that of the sample 101. However, in some embodiments, the distance between the sample 101 and the X-ray detectors 116 is so long that environmental disturbances (e.g., air disturbances) introduce noise into the detected signal. Therefore, in some embodiments, one or more of the X-ray detectors are maintained in a local vacuum environment separated from the sample (e.g., sample 101) by a vacuum window.

[0132] Similarly, in certain embodiments, the X-ray illumination source 110, the illumination optics 115, or both are maintained in the same ambient environment (e.g., a gas purged environment) as that of the sample 101. However, in some embodiments, the optical path lengths between the X-ray illumination source 110 and the illumination optics 115 and between the illumination optics 115 and the sample 101 are long enough that environmental disturbances (e.g., air disturbances) introduce noise into the illumination beam. Therefore, in some embodiments, the X-ray illumination source, the illumination optics 115, or both are maintained in a local vacuum environment separated from the sample (e.g., sample 101) by a vacuum window.

[0133] FIG. 8 illustrates an embodiment of a vacuum chamber 160 containing the X-ray illumination source 110 and illumination optics 115, and a vacuum chamber 160 containing the X-ray detector 116. In a preferred embodiment, a significant portion of the optical path between the X-ray illumination source 110 and the sample 101 is provided within the vacuum chamber 160, and a significant portion of the optical path between the sample 101 and the X-ray detector 116 is provided within the vacuum chamber 163. The openings of the vacuum chamber 160 and the vacuum chamber 163 are covered by vacuum windows 161 and 164, respectively. The vacuum windows 161 and 164 may be made of any suitable material that is substantially transparent to X-ray radiation, e.g., beryllium. The illumination beam 117 propagates through the vacuum window 161 toward the sample 101. After interacting with the sample 101, the scattered X-ray radiation 125 passes through the vacuum window 164 into the vacuum chamber 160 and is incident on the X-ray detector 116. A suitable vacuum environment 162 can be maintained within vacuum chamber 160 to minimize disturbances to illumination beam 117, and a suitable vacuum environment 165 can be maintained within vacuum chamber 163 to minimize disturbances to scattered x-ray radiation 125. Suitable vacuum environments can include any suitable level of vacuum, any suitable purged environment with an inert gas (e.g., helium), or any combination thereof. Having as much of the beam path as possible in a vacuum thus maximizes light flux and minimizes disturbances.

[0134] In certain embodiments, the entire optical system is kept in vacuum, including the sample 101. However, there are generally high costs associated with keeping the sample 101 in vacuum due to the complexity involved in constructing the sample positioning system 140.

[0135] In certain embodiments, a metrology target characterized by the X-ray scatterometry metrology described herein is placed within a scribe line of the wafer under measurement. In these embodiments, the metrology target is sized to fit within the width of the scribe line. In certain examples, the scribe line width is less than 80 microns. In certain examples, the scribe line width is less than 50 microns. In general, there is a trend toward smaller scribe line widths employed in semiconductor manufacturing.

[0136] In certain embodiments, a metrology target characterized by the X-ray scatterometry metrology described herein is located within the active die area of ​​the wafer under measurement and is part of a functional integrated circuit (e.g., memory, image sensor, logic device, etc.).

[0137] Generally, the aspect ratio characterizing a metrology target is defined as the maximum height dimension of the metrology target (i.e., the dimension perpendicular to the wafer surface) divided by the maximum lateral dimension (i.e., the dimension aligned to the wafer surface). In certain embodiments, the aspect ratio of the metrology target under measurement is at least 20. In certain embodiments, the aspect ratio of the metrology target is at least 40.

[0138] 9A-9C respectively show an isometric view, a top view and a cross-sectional view of a typical 3D FLASH memory device 190 that is subject to measurement as described herein. The total height (equivalent to the depth) of the memory device 190 is in the range of one to several micrometers. The memory device 190 is a vertically manufactured device. A vertically manufactured device, such as the memory device 190, is essentially a conventional planar memory device rotated 90 degrees with its bit lines and cell strings oriented vertically (perpendicular to the wafer surface). To provide sufficient memory capacity, multiple alternating layers of different materials are deposited on the wafer. This requires that the patterning process be well performed down to a depth of several micrometers for structures with a maximum lateral extent of 100 nanometers or less. As a result, aspect ratios of 25:1 or 50:1 are not uncommon.

[0139] In general, the use of high brightness X-ray scatterometry allows for high flux X-ray radiation penetration into opaque areas of the target. Examples of geometric parameters that can be measured using X-ray scatterometry include pore size, hole density, line edge roughness, line width roughness, sidewall angle, profile, critical dimension, overlay, edge placement error, and pitch. An example of a material parameter that can be measured is electron density. According to certain examples, X-ray scatterometry can measure sub-10 nm features and advanced semiconductor structures such as STT-RAM, V-NAND, DRAM, PC-RAM, and Re-RAM when measurements of geometric and material parameters are required.

[0140] It should be appreciated that the various steps described throughout this disclosure may be performed by a single computer system 130 or, alternatively, by multiple computer systems 130. Additionally, various subsystems included in the system 100, such as the sample positioning system 140, may incorporate computer systems suitable for performing at least a portion of the steps described herein. Thus, the above description should be taken as merely illustrative and not limiting on the present invention. Additionally, the information processing system or systems 130 may be configured to perform any other step(s) of any method embodiment described herein.

[0141] Additionally, computer system 130 may be communicatively coupled to detector 116 and illumination optics 115 in any manner known in the art. For example, one or more information processing systems 130 may be coupled to an information processing system associated with detector 116 and an information processing system associated with illumination optics 115. Also for example, both detector 116 and illumination optics 115 may be directly controlled by a single computer system coupled to computer system 130.

[0142] Computer system 130 may be configured to receive and / or acquire data or information from its own subsystems (e.g., detector 116 and illumination optics 115, etc.) through a transmission medium, such as a wired and / or wireless section, which may then serve as a data link between computer system 130 and other subsystems of system 100.

[0143] The computer system 130 of the metrology system 100 may be configured to receive and / or acquire data or information (e.g., measurement results, modeling inputs, modeling results, etc.) from other systems via a transmission medium, such as a wired and / or wireless section. In this case, the transmission medium may act as a data link between the computer system 130 and the other system (e.g., the on-board memory of the metrology system 100, an external memory, or an external system). For example, the information processing system 130 may be configured to receive measurement data (e.g., signal 126) from a storage medium (i.e., memory 132 or 180) via a data link. For example, spectroscopy results obtained using a spectrometer of any of the detectors 116 may be stored in a permanent or semi-permanent memory device (e.g., memory 132 or 180). Thus, the measurement results may be imported from the on-board memory or from an external memory system. Furthermore, data may be sent from the computer system 130 to other systems via a transmission medium. For example, the sample parameter values ​​170 determined by the computer system 130 can be stored in a permanent or semi-permanent memory device (e.g., memory 180) such that the measurement results can be exported to other systems.

[0144] Information handling system 130 may include, but is not limited to, a personal computer system, a mainframe computer system, a workstation, an image computer, a parallel processor, or any other device known in the art. In general, the term "information handling system" may be broadly defined to encompass any device having one or more processors that execute instructions obtained from a memory medium.

[0145] Program instructions 134 implementing methods such as those described herein may be transmitted over a transmission medium such as a wire, cable or wireless transmission link. For example, as depicted in Figure 1, program instructions stored in memory 132 are transmitted over bus 133 to processor 131. Program instructions 134 are stored in a computer readable medium (e.g., memory 132). Examples of computer readable media include read only memory, random access memory, magnetic or disks and magnetic tape.

[0146] In certain embodiments, the optimized metrology recipe described herein is implemented as part of a manufacturing process tool. Examples of manufacturing process tools include, but are not limited to, lithography exposure tools, film deposition tools, implant tools, and etch tools. The results of the optimized metrology recipe can then be used to control the manufacturing process. For example, x-ray scatterometry metrology data collected from one or more targets is sent to the manufacturing process tool. The x-ray scatterometry metrology data is analyzed as described herein, and the results are used to adjust the operation of the manufacturing process tool.

[0147] The scatterometry metrology described herein can be used to characterize a variety of semiconductor structures, including but not limited to FinFETs, low dimensional structures such as nanowires or graphene, sub-10 nm structures, lithographic structures, through substrate vias (TSVs), memory structures such as DRAM, DRAM4F2, FLASH, MRAM, and high aspect ratio memory structures. Examples of structural properties include but are not limited to geometric parameters such as line edge roughness, line width roughness, hole size, hole density, sidewall angle, profile, critical dimension, pitch, and material parameters such as electron density, composition, grain structure, morphology, stress, strain, and elemental type.

[0148] The term "critical dimension" as used herein includes any critical dimension of a structure (e.g., bottom critical dimension, middle critical dimension, top critical dimension, sidewall angle, grid height, etc.), the critical dimension between any two or more structures (e.g., the distance between two structures), and the misalignment between two or more structures (e.g., the overlay misalignment between overlapping grid structures, etc.) Structures may include three-dimensional structures, patterned structures, overlay structures, etc.

[0149] As used herein, the terms "critical dimension application" and "critical dimension metrology application" are intended to encompass any critical dimension metrology application.

[0150] The term "metrology system" as used herein includes any system that is employed at least in part to characterize a specimen in any manner, including metrology applications such as critical dimension metrology, overlay metrology, focus / dose metrology, and composition metrology. However, these technical terms do not limit the scope of the term "metrology system" as used herein. Additionally, the system 100 can be configured for metrology of patterned and / or unpatterned wafers. The metrology system can be configured as an LED inspection tool, an edge inspection tool, a backside inspection tool, a macro inspection tool, or a multi-mode inspection tool (with simultaneous data acquisition from one or more platforms), or any other metrology or inspection tool that benefits from calibration of system parameters based on critical dimension data.

[0151] Various embodiments are described herein in terms of a semiconductor metrology system that may be used to measure a specimen within any semiconductor processing tool (e.g., an inspection system or a lithography system). The term "specimen" as used herein refers to any wafer, reticle, or other specimen that may be processed (e.g., printed or inspected for defects) by means known in the art.

[0152] The term "wafer" as used herein generally refers to a substrate formed of a semiconductor or non-semiconductor material. Examples include, but are not limited to, monocrystalline silicon, gallium arsenide, and indium phosphide. Such substrates are commonly found and / or processed in semiconductor manufacturing facilities. In some cases, a wafer may consist of only a substrate (i.e., a bare wafer). Alternatively, a wafer may have one or more layers of dissimilar materials formed on a substrate. One or more layers formed on a wafer may be "patterned" or "unpatterned." For example, a wafer may have multiple dies with repeatable pattern features.

[0153] A "reticle" may be a reticle at any stage in the reticle manufacturing process or a finished reticle, which may or may not have been released for use in a semiconductor manufacturing facility. A reticle or "mask" is generally defined as a substantially transparent substrate having a pattern of substantially opaque areas formed thereon. The substrate may, for example, comprise a glass material, such as amorphous SiO2. The reticle may be placed over a resist-covered wafer during the exposure step of the lithography process, allowing the pattern on the reticle to be transferred into the resist.

[0154] One or more layers formed on a wafer may be patterned or unpatterned. For example, a wafer may have multiple dies, each having repeatable pattern features. The formation and processing of such layers of material may ultimately result in a completed device. A wide variety of devices may be formed on a wafer, and the use of the term wafer herein is intended to encompass wafers on which any type of device known in the art may be fabricated.

[0155] In accordance with one or more exemplary embodiments, the functions described above may be implemented in hardware, software, firmware, or any combination thereof. When implemented in software, the functions may be stored on or transmitted over a computer-readable medium as one or more instructions or code. Computer-readable media includes both computer storage media and communication media, including any media that facilitates the transfer of a computer program from one place to another. A storage medium is any available medium that can be accessed by a general purpose or special purpose computer. By way of example, and not limitation, such computer-readable media may comprise 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 carry or store desired program code means in the form of instructions or data structures and that can be accessed by a general purpose or special purpose computer or a general purpose or special purpose processor. Any connection may be referred to as a computer-readable medium. For example, if the software is transmitted from a website, server, or other remote source using coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technology such as infrared, radio frequency, or microwave, the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technology such as infrared, radio frequency, or microwave would fall within the definition of the medium. The term disk / disc in this application includes compact disks (CDs), laser disks, optical disks, digital versatile disks (DVDs), floppy disks, and Blu-ray disks, as well as disks on which data is typically reproduced magnetically and disks on which data is reproduced optically with a laser. Combinations of the above are also naturally included within the scope of computer readable media.

[0156] Although certain specific embodiments are described above for instructional purposes, the teachings in this patent application are of general applicability and are not limited to the specific embodiments described above. Thus, various modifications, adaptations and combinations of the various features of the above-described embodiments may be made without departing from the scope of the invention as set forth in the claims.

Claims

1. A method comprising: generating measurement data related to a plurality of measurements of at least one semiconductor structure having one or more target parameters of known values, wherein each of the plurality of measurements has one or more measurement system parameters of different values; estimating values of the one or more target parameters related to the at least one semiconductor structure based on the measurement data and a measurement model; determining, for each of the different values of the one or more measurement system parameters, the sensitivity of the value of each of the one or more target parameters to a change in the value of each of the one or more measurement system parameters; determining an optimized set of values of the measurement system parameters based on optimization of a regularization cost function including the determined sensitivity; A method.

2. The method according to claim 1, wherein the regularization cost function includes a constraint on measurement time.

3. The method according to claim 1, wherein the measurement data is simulation measurement data, actual measurement data, or both.

4. The method according to claim 1, wherein the measurement data includes a plurality of instances of the at least one semiconductor structure, each of the plurality of instances having the one or more target parameters of different known values.

5. The method according to claim 4, wherein the value of the regularization cost function related to a measurement recipe is an average of the values of the regularization cost function related to each of the plurality of instances of the at least one semiconductor structure.

6. The method according to claim 1, further comprising: determining a value of a measurement performance indicator based on the optimized set of values of the one or more measurement system parameters.

7. The method according to claim 1, wherein the one or more measurement system parameters include an azimuth angle, an incident angle, and an exposure time.

8. The method according to claim 1, wherein the optimized set of values of the one or more measurement system parameters is an individual subset of the one or more measurement system parameters of the different values.

9. The method according to claim 1, wherein the regularization cost function includes a feature description of the at least one semiconductor structure.

10. The method according to claim 9, wherein the feature description includes any one of the symmetry of the at least one semiconductor structure, the optical density of the at least one semiconductor structure, the height of the at least one semiconductor structure, the structural class of the at least one semiconductor structure, and any combination thereof.

11. The method according to claim 1, wherein the optimization of the regularization cost function involves a search through a library of candidate sets of measurement system parameters.

12. The method according to claim 1, wherein the optimization is non-linear integer optimization.

13. The method according to claim 1, further comprising a method for verifying measurement performance based on a regression test for synthetic measurement data or actual measurement data.

14. The method according to claim 13, wherein the verification is based on the measurement data related to the first plurality of measurements of the at least one semiconductor structure.

15. A system, a metrology tool having an illumination source and a detector, the detector being configured to collect a first amount of actual measurement data based on the measurement of one or more semiconductor structures disposed on a first wafer according to a set of optimized measurement system parameter values; an information processing system; comprising, the information processing system generating measurement data related to a first plurality of measurements of at least one semiconductor structure having one or more target parameters as known values, each of the first plurality of measurements having one or more measurement system parameters with different values; estimating the values of the one or more target parameters related to the at least one semiconductor structure based on the measurement data and a measurement model; determining the sensitivity of the values of each of the one or more target parameters to changes in the values of each of the one or more measurement system parameters at each of the different values of the one or more measurement system parameters, and determining an optimized set of values of the optimized measurement system parameters based on the optimization of a regularization cost function including the determined sensitivity. A configured system.

16. The system according to claim 15, wherein the measurement data includes a plurality of instances of the at least one semiconductor structure, and each of the plurality of instances has the one or more target parameters with different known values.

17. The system according to claim 16, wherein the value of the regularization cost function related to the measurement recipe is the average of the values of the regularization cost function related to each of the plurality of instances of the at least one semiconductor structure.

18. The system according to claim 15, wherein the set of optimized measurement system parameter values is an individual subset of one or more measurement system parameters with different values.

19. The system according to claim 18, wherein the optimization is non-linear integer optimization.

20. The system according to claim 15, wherein the regularization cost function includes a characterization of the at least one semiconductor structure.

21. The system according to claim 20, wherein the characterization includes any one of the degree of symmetry of the at least one semiconductor structure, the optical density of the at least one semiconductor structure, the height of the at least one semiconductor structure, the structural class of the at least one semiconductor structure, and any combination thereof.

22. The system according to claim 15, wherein the optimization of the regularization cost function involves a search through a library of candidate sets of measurement system parameters.

23. A system comprising: a metrology tool having an illumination source and a detector, the detector being configured to collect a first amount of actual measurement data based on the measurement of one or more semiconductor structures disposed on a first wafer according to a set of optimized measurement system parameter values; a non-transitory computer-readable medium containing a set of instructions; wherein when the instructions are executed by one or more processors provided in an information processing system, the information processing system generates measurement data related to a first plurality of measurements of at least one semiconductor structure having one or more target parameters as known values, provided that each of the first plurality of measurements has one or more measurement system parameters with different values. Based on the measurement data and the measurement model, values of the one or more target parameters related to the at least one semiconductor structure are estimated, for each respective different value of the one or more measurement system parameters, a sensitivity of the value of each of the one or more target parameters to a change in the value of each of the one or more measurement system parameters is determined, and based on an optimization of a regularization cost function including the determined sensitivity, an optimized set of values of optimized measurement system parameters is determined, System.

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