Evaluation of X-rays from perturbed objects

Abstract

The response to a perturbed object with a roughness comparable to the wavelength is evaluated using a model-based approach. [Solution] A detection signal is obtained indicating the X-ray signal received by a sensor from a perturbed object by irradiation of the perturbed object, which includes a perturbation (1103) on the order of wavelength of the X-ray signal. Based on the detection signal, at least one model-based evaluation of the perturbed object is performed. The execution of at least one model-based evaluation represents the perturbation of the perturbed object by a plurality of non-perturbed objects (1101(1)...1101(N)), calculates an estimated field for each of the plurality of non-perturbed objects, and evaluates the X-ray signal based on the fields of the plurality of non-perturbed objects.

Description

[Background technology]

[0001] (cross reference) This application claims priority from U.S. Provisional Patent Application 63 / 205,631 filed on 31 December 2021 and U.S. Provisional Patent Application 63 / 205,630 filed on 31 December 2021, both of which are incorporated herein by reference.

[0002] In the X-ray regime, the roughness size is comparable to the wavelength.

[0003] Figure 1 shows a typical line 11, with rough edges 12 and 13 and a critical dimension (the distance between edges 12 and 13) 15 (here, the length of the line).

[0004] Figure 2 shows an X-ray system having an X-ray source 21 and an optical system that focuses the X-ray beam 31 onto a small spot 33 on the sample 100, typically via a mirror symbolically represented as lens 22 in the figure. Reflected X-rays 32 from the sample are detected by a CCD camera 23 positioned in the far-field region. Figure 2 also shows the illumination angle 41 and the collection angle 32.

[0005] A conical illumination cone can differ from a conical collection cone, the latter typically being larger than the former (the primer) and enabling the detection of "scattered" X-rays. These are rays that are diffracted from the sample not into the specular direction.

[0006] In this scheme, multiple scattering directions are collected simultaneously by incident on different pixels of the CCD camera, thus reducing the need to scan the source / sample orientations of the sample / detector, or both.

[0007] However, this means that scattered light generated from one incident direction may interfere with scattered light generated from another incident direction in the detector.

[0008] When the coarseness is comparable to the wavelength, the impact of this coarseness on detection is significant and must be taken into consideration, especially when using a model-based approach to interpret the detected signal. [Overview of the Initiative]

[0009] A non-temporary computer-readable medium is provided for storing systems, methods, and instructions for evaluating X-ray signals from a perturbed object.

[0010] A method is provided for evaluating non-diffused x-ray signals received from a perturbed object by illumination of the perturbed object. The method includes calculating an estimated field for each of multiple non-perturbed objects, where the multiple non-perturbed objects represent perturbances of the perturbed object, the perturbances being on the order of the wavelength of the non-diffused x-ray signals, and evaluating the non-diffused x-ray signals based on the field of the multiple non-perturbed objects.

[0011] A method, system, and non-transitory computer-readable medium for estimating an x-ray signal are provided. The method includes estimating a field generated by a perturbation of a perturbed object that is on the order of the wavelength of the x-ray signal, the estimation including calculating a general function that responds to fields contributed by single perturbances of the perturbation of the perturbed object, the general function being applicable to a perturbed object of any shape, and evaluating the x-ray signal based on one or more statistical characteristics (properties) of the field and the perturbation.

[0012] To understand the present invention and to know how the present invention can actually be implemented, preferred embodiments will be described, by way of non-limiting examples only, with reference to the accompanying drawings.

Brief Description of the Drawings

[0013] [Figure 1] Shows a prior art line. [Figure 2] Shows a schematic operation of a prior art x-ray system. [Figure 3]An example of a perturbed object and its reflectance versus angular spectrum is shown. [Figure 4] An example of a structural element is shown. [Figure 5] This shows an example of a continuous perturbation on the surface. [Figure 6] This shows an example of an interface that can carry roughness. [Figure 7] An example of non-diffuse reflection at a wavelength of 4.47 nm is shown. [Figure 8] An example of a perturbed object and multiple non-perturbed objects is shown. [Figure 9] This shows an example of the simulation effect of roughness in a periodic structure. [Figure 10] Here is an example of the method. [Figure 11] Here is an example of the method. [Figure 12] An example of the signal-to-glazing angle is shown. [Figure 13] Here is an example of the method. [Figure 14] Examples of perturbed and unperturbed objects are shown. [Figure 15] Examples of perturbed and unperturbed objects are shown. [Figure 16] An example of the signal-to-glazing angle is shown. [Figure 17] An example of a non-perturbable object is shown. [Figure 18] An example of a non-perturbable object is shown. [Figure 19] An example of a non-perturbable object is shown. [Figure 20A] An example of the signal-to-glazing angle is shown. [Figure 20B] Here is an example of the method. [Figure 21] This shows a cross-sectional view of a periodic structure subjected to conventional scattering measurements using an incident beam with a single incidence angle. [Figure 22] This diagram shows a cross-sectional view of a periodic structure subjected to scattering measurements using incident beams with multiple incident angles, according to one embodiment of the present invention. [Figure 23]This shows a top view of a periodic structure subjected to conventional scattering measurements using an incident beam with a single azimuth angle. [Figure 24A] This is a top view of a periodic structure that has a central axis with zero azimuth and has undergone scattering measurements using incident beams with multiple azimuth angles, according to one embodiment of the present invention. [Figure 24B] This is a top view of a periodic structure that has a central axis with a non-zero azimuth angle and has undergone scattering measurements using incident beams with multiple azimuth angles, according to one embodiment of the present invention. [Figure 25] This shows a side view of an exemplary finFET device suitable for low-energy X-ray reflection scattering measurements, according to one embodiment of this invention. [Figure 26] One embodiment of this invention includes a plot of zero-order reflectivity versus scattering angle and a corresponding structure for a silicon (Si) fin having a periodic structure with a 10 nm / 20 nm line / space ratio. [Figure 27] One embodiment of this invention includes a plot of primary reflectance versus scattering angle and a corresponding structure for a silicon (Si) fin having a periodic structure with a 10 nm / 20 nm line / space ratio. [Figure 28] This is an explanatory diagram illustrating a periodic structure measurement system having X-ray reflectance scattering (XRS) functionality according to one embodiment of the present invention. [Figure 29] A block diagram of an exemplary computer system according to one embodiment of this invention is shown. [Examples]

[0014] In the following detailed description, several specific details are provided to give a full understanding of this invention. However, those skilled in the art will understand that this invention can be implemented even without these specific details. On the other hand, well-known methods, procedures, and components are not described in detail so as not to obscure this invention.

[0015] The subject matter of this invention is specifically pointed out and explicitly claimed in the concluding section of the specification. However, this invention, along with its purpose, features and advantages, as well as its uses and methods of operation, will be best understood by referring to the following detailed description, along with the accompanying drawings.

[0016] For the sake of simplification and clarity, please understand that the elements shown in the drawings are not necessarily drawn to scale. For example, the dimensions of some elements may be exaggerated relative to others for clarity. Furthermore, where appropriate, reference figures may be repeated between drawings to indicate corresponding or similar elements.

[0017] References in this specification to any one of a system, method, or non-temporary computer-readable medium should also apply mutatis mutandis to any other of a system, method, or non-temporary computer-readable medium. For example, references to a system should also apply mutatis mutandis to methods that can be executed by a system and non-temporary computer-readable medium capable of storing instructions that can be executed by a system.

[0018] Since at least one illustrated embodiment of this invention can be implemented for the most part using electronic components and circuits known to those skilled in the art, details will not be described beyond what is considered necessary for understanding the basic concepts of this invention and to avoid making the teachings of this invention difficult to understand or leading to departures from the teachings of this invention, as illustrated above.

[0019] The numbers and values ​​exemplified below should be considered non-exclusive examples.

[0020] The expression "A based on B" means that A is based solely on B, or that A is based on B and one or more other elements, and / or parameters, and / or information. "Based on" means that the calculation of A is influenced by B, and / or that the value of A is a function of the value of B.

[0021] The term "evaluation" can refer to measurement, estimation, simulation, calculation, approximation, verification, and model generation.

[0022] Evaluating X-ray signals may include performing an evaluation of the X-ray signals that should be detected as a result of the illumination of an object.

[0023] The term "obtaining" includes generating, receiving, and other similar actions. For example, receiving detection signals can include generating detection signals, generating detection signals by illuminating (shining light on) a perturbed object, or receiving or retrieving detection signals without generating them.

[0024] X-ray signals include diffused X-ray signals and non-diffused X-ray signals. Evaluation based on non-diffused X-ray signals (and evaluation not based on diffuse signals) is sometimes called non-diffused evaluation. Evaluation based on diffuse X-ray signals (and evaluation not based on non-diffused signals) is sometimes called diffuse evaluation.

[0025] A solid stack is a structure that consists of layers that are parallel to each other.

[0026] For simplicity, most examples refer to rough surfaces (which should be horizontal in their non-roughened state) and various non-perturbed surfaces. It should be noted that horizontal orientation is merely one example of orientation, and the rough and non-perturbed surfaces can be oriented in any way. The expressions up, upper, top, lower, lowest, and down should apply to any orientation.

[0027] The proposed solution is considered to be the first solution applicable to perturbed objects of any shape, and is not limited to solid stacks. This solution can be applied, for example, to perturbed periodic structures and / or perturbed pseudoperiodic structures (periodic structures up to a certain phase), or to perturbed aperiodic structures.

[0028] References to structure should be applied mutatis mutandis to structural elements, specimens, periodic structures, basic cells of periodic structures, and objects. The various objects, structural elements, specimens, or structures shown in the various drawings may form a grating or be arranged periodically. For example, structural element 61 may be a basic cell of a periodic structure.

[0029] A system, method, and non-temporary computer-readable medium for storing instructions for evaluating the emission of X-ray signals from perturbed objects of any shape can be provided.

[0030] The terms perturbations and roughness are used interchangeably. A perturbed object is an object that suffers from roughness.

[0031] A perturbed surface, or rough surface, exhibits roughness on the order of the X-ray wavelength (e.g., from 10% to 1000%). X-ray wavelengths range from 0.01 to 10 nanometers. Therefore, perturbed surfaces are on a nanometer scale, for example, between 0.01 and 80 nanometers, less than 0.01 nanometers, or greater than 80 nanometers. A single X-ray beam can form a spot capable of simultaneously illuminating multiple fundamental cells of a periodic structure.

[0032] The detector used to detect X-ray radiation can be a two-dimensional detector, and its pixels can be classified into diffuse pixels for detecting diffuse radiation and non-diffuse pixels for detecting non-diffuse radiation. This classification may be done per object, and / or per illumination, and / or per detection method.

[0033] Figure 3 includes a graph illustrating an example of a simulation showing how the X-ray reflectance (ratio of reflected intensity to incident intensity) from a solid-stack sample changes as the roughness is turned on (rough solid stack) or off (smooth solid stack) (see curves 51 and 52, respectively).

[0034] Figure 3 shows the reflectance as a function of elevation theta, assuming that both the light source and detector generate / capture light through very narrow illumination / focusing cones. Since this is a solid stack, the reflected signal is almost entirely in the specular direction, and therefore the reflection angle is equal to the illumination angle; thus, only a single angle theta is needed to parameterize the graph. The graph does not show reflectance in non-specular directions, although this would also be present if roughness is present.

[0035] There is also a need to characterize periodic (non-solid) structures that include roughness, and an algorithm is needed to evaluate the response of periodic samples with interface roughness to X-ray irradiation.

[0036] Derivation of the Scattered Electric Field for an Isolated Small Perturbation

[0037] First, the reflectance and inner field of a smooth (i.e., unperturbed) periodic sample are evaluated using a rigorous, known solution to the electromagnetic scattering problem. These are evaluated for two different directions of illumination and for the opposite polarization (of any incident ray) and any exit direction.

[0038] For lighting / collection with a finite cone (or other finite shape), superposition is employed, and the contributions from each single direction are added separately.

[0039] Given illumination direction k inc and input polarization state p inc Regarding a specific point within the structural element (r t The inner electric field vector at t) is given by the following:

[0040]

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[0041] It should be noted again that this field is evaluated for structural elements without perturbation. As shown below, two different internal electric fields are required to fully determine the effect of roughness, under the assumption that the perturbation is "small". a. The illumination (with unit amplitude and zero phase measured at the reference point O) is the inner field at the point (r inc and input polarization state p inc ), t) generated when arriving from the actual illumination direction k t : The format is as follows.

[0042]

Number

[0043] b. The illumination (with unit amplitude and zero phase measured at the reference point O) is the inner field at the point (r sc and output polarization state p sc ), t) generated when arriving from the opposite direction k of the collection direction t

[0044]

Number

[0045] To explain a method of determining the diffraction signal from the perturbation profile using these two fields (not necessarily probabilistic), first, it is explained how this is achieved for a profile perturbed by a small isolated volume.

[0046] Figure 4 shows a structural element made of a first material with little perturbation, and this structural element interfaces with a surrounding having a surrounding material (e.g., air) different from the first material. It is assumed that the object includes a repetition of the structural element. For example, it is a periodic repetition along the horizontal direction, and only a single period is shown in Figure 4.

[0047] ​The structural element 61 has a smooth outer surface which can be called a nominal surface 62 (shown as the top surface in Figure 4), the nominal surface 62 having a horizontal portion on the left end, followed by a positive inclined portion, followed by another (higher) horizontal portion, followed by a negative inclined portion, followed by a horizontal portion on the right end.

[0048] Figure 4 shows the coordinates (r) located on the negatively sloping portion. t This shows an example of a reference point (reference point) 65 in ,0). This has the following fields.

[0049]

number

[0050] The field at the above reference point is as described above. The first coordinate r t represents the position on the outer surface (for example, 2D coordinates), and the second coordinate t is point r t This is the distance from the surface at r. The second coordinate above is coordinate r t This is the distance along the normal to surface 65.

[0051] This structural element is slightly perturbed by adding a new element 63 with a smaller volume (relative to the volume of structural element 61).

[0052] The geometry of the new element 63 described above is determined by the nearest interface (coordinate r) of its "center of gravity" 64. t It is represented by specifying the projection onto ) and the distance of the center from that surface (indicated by 1D coordinate t). The new element 63 described above is d 2 r t It has a very small (difference) base area and a small (difference) height dt (measured in the direction normal to the surface), indicated by (the direction parallel to the inclined surface in Figure 4).

[0053] Instead of evaluating radiation emitted from structural elements that strike points on the detector, "inverse" radiation that substantially strikes (as shown in 33) the structural elements from the points on the detector and is substantially emitted (scattered) (as shown in 33) in the "reverse" direction from the structural elements toward the illumination light source is taken into consideration in the evaluation.

[0054] In Figure 4, radiation colliding with the structural element is shown by 31, and radiation emitted (e.g., scattered) from the structural element is shown by 32.

[0055] Using these notations, a unit amplitude zero-phase field component (measured at the same reference point O) is given the polarization state p inc Under direction k inc When the sample is irradiated from, the polarization state p is measured at the reference point O. sc Under direction k sc The Fourier components (amplitude and phase) of the complex-valued scattered field are given (under the "small" perturbation approximation) by the following equation:

[0056]

number

[0057] In this formula, E unperturbed This is the field that would be produced when the perturbation is absent. i is the unit imaginary complex number. k0 is the wave number and is related to the wavelength λ through the relationship k0 = 2π / λ. ε0 is the permittivity of vacuum. ε OldThis is the dielectric constant of the material in the volume where the perturbation is introduced, before the perturbation is introduced. ε New This is the dielectric constant of the material in the volume in which the perturbation is introduced, after the perturbation has been introduced.

[0058] In the following, we will use a shorthand notation for the difference between the two dielectric constants mentioned above. (4) Δε=ε New - ε Old

[0059] This difference is generally (r t It should be noted that this depends on t).

[0060] Equation (3), also known as the "Born first-order approximation," is valid when the perturbation is "sufficiently small." More precisely, its condition is given by the following equation:

[0061]

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[0062] Use of superposition to generalize for the case of a continuous perturbation.

[0063] As illustrated in Figure 5, consider the case where there is continuous perturbation on the surface.

[0064] The perturbed structural element 61 is perturbed, which is represented by the deviation (perturbation) from the (unperturbed) nominal surface 62 and such an unperturbed surface.

[0065] The above deviation includes, for example, perturbation 66 and another perturbation 66', where the other perturbation 66' includes multiple elements, represented by a centroid 64 and a reference point 65, such as the new element in Figure 4.

[0066] This can be divided into a collection of many non-overlapping "cubes" that constitute a continuous geometry in which the perturbation is completely covered. (1st order Born approximation) st In the Born approximation, in such cases, the individual scattering fields generated by each of these cubes can be superimposed (added) to obtain the resulting overall field.

[0067] This addition is, coordinate (r t It can be expressed mathematically by the integral of ,t), where the 2D coordinates r t The coordinates are integrated over the entire nominal surface 62 (the entire object, for example, if the object is a periodic structure, the coordinates are integrated over the entire periodic structure), on the other hand, the coordinate t (measured with respect to the nominal surface) is integrated with respect to the normal from the value at the surface (t=0) to the distance from the surface to which the perturbation occurs (for example, with respect to the reference point 65, the height h(r t )67 is equal to the distance from point 69 (the external point of the perturbation along the normal to the nominal surface 62 extending from the reference point 65).

[0068] The height above (positive value) / below (negative value) the nominal surface 62 is the nominal position r t Since it depends on r t It is a function of , and therefore h = h(r t Therefore, the overall field scattered by the perturbation profile is given by equation (6).

[0069]

number

[0070] Here, "Sur" is the surface of the perturbed object. In this equation, h(r t ) can take either a positive or negative value to represent perturbations above or below the nominal interface boundary. The value of Δε obtains an appropriate sign change to faithfully represent the difference in dielectric constants above / below the boundary.

[0071] Equation (6) calculates the field for a combination of a certain illumination angle and a single collection angle. Various combinations of collection and illumination angles can be calculated using equation (6). For example, assuming that the X-ray emission has a numerical aperture, the fields at a given collection angle are the sum of the electric fields contributed by various illumination angles within the numerical aperture of the X-ray emission.

[0072] Considering various combinations of illumination angle and focusing angle can be applied mutatis mutandis to all calculations (e.g., intensity calculations) in this specification.

[0073] Evaluating the intensity from the electric field, and applying randomness and ergodicity.

[0074] The intensity associated with the scattered electric field derived as described above can be evaluated by multiplying the field by its complex conjugate.

[0075]

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[0076] Here, the long notation of function arguments

[0077]

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[0078] The notation was changed to a shorter form (inc → sc). Therefore, for a given deterministic perturbation profile, there is an associated intensity.

[0079] If the area of ​​the irradiated sample is very large (for example, on a micron scale), then the spot can be thought of as "covering" many different profiles (on a nanometer scale) (each profile belonging to a different part of the sample, for example, a different pitch).

[0080] This variability in the profile can be considered as a random effect representing the probabilistic nature of the profile. Furthermore, because the spot size is large, the assumption that all possible random profiles derived from the given statistics exist within the illuminated area of ​​the sample is justified, and therefore the intensity actually measured can be assumed to be the average of the intensities of "all possible random profiles". This assumption, which introduces randomness into the analysis, is hereafter referred to as the ergodic assumption.

[0081] The following mathematical notation is used to represent this averaging.

[0082]

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[0083] Using this notation, the intensity under the ergodic assumption is given by the following:

[0084]

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[0085] The separation of intensity into a "diffuse" term and a "non-diffused" term, and their properties.

[0086] Therefore, it can be shown that the intensity is the average of the product of the electric fields. By adding or subtracting the product of the average electric fields, the above intensity formula can be reconstructed as the sum of the two terms shown in equation (10).

[0087]

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[0088] Therefore, the reflected signal in the presence of roughness can be decomposed into two additive terms. a. "Non-diffusive" intensity: This conveys only the effect of the roughness-related mean-field squared on the diffraction orders. b. "Diffusion" intensity: This describes the effect of roughness-related field-field covariance.

[0089] The conclusion is that the "diffusion" term depends only on the roughness statistic for each point along the boundary and not on the statistic for other points, whereas the "non-diffusion" term also depends on the correlation of roughness between any two points along the boundary.

[0090] The "non-diffusive" term is a sum of functions, and since each function depends on a perturbation at only one point along the boundary, the correlation between two perturbations along the surface is not considered in this term, and therefore this term can be calculated as if such two perturbations were perfectly correlated. This correlation dramatically simplifies the evaluation of this term because it allows us to assess the effect of roughness without releasing the periodicity assumption (without lifting), and therefore it only affects the intensity of the diffraction order, without any additional signals in directions that would otherwise not be included in the diffraction order. This property will be explained further below.

[0091] In contrast, the "diffusion" term is proportional to the field-field covariance mentioned above, and therefore includes correlation; further statistical analysis of random profiles is required to evaluate this term.

[0092] The difference between the two terms above also affects the angular dependence of the scattering intensity of each term with respect to a given incident direction. a. The "non-diffusive" term does not contribute to scattering directions other than the normal (unperturbed) diffraction order direction of the sample. b. The "diffusion" term generally contributes to scattering in any direction.

[0093] Expressing the intensity in terms of the statistical properties of the random profile.

[0094] Evaluation of the Non-Diffused Term

[0095] The expression for the non-diffused term requires the evaluation of the average of the electric field over all possible random profiles of deviations from the boundary.

[0096]

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[0097] This averaging can be evaluated based on the following field dependencies.

[0098]

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[0099] Each of these fields can be expanded as a Fourier series when viewed as a function of t, and their dot product (inner product) is...

[0100]

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[0101] This is essentially a term that falls into the perturbation of equation (6), and according to the convolution theorem, the amplitude and frequency of each frequency can be derived from the solution of the problem without perturbation, thus allowing it to be reconstructed in this form as well. Therefore, it is as follows:

[0102]

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[0103] Here, A n (r t(inc,sc) is defined as r along the boundary with respect to the given incident direction (inc) and scattering direction (sc). t This is the amplitude of the corresponding Fourier component. This value can be obtained by solving a problem without perturbation. k n (r t (inc, sc) is a point along the boundary with respect to a given incident direction (inc) and scattering direction (sc). t This is the frequency of the corresponding Fourier component. This value can also be obtained by solving a problem without perturbation.

[0104] In the case of a periodic structure, the field can be represented as a sum of discrete (rather than continuous) sets of frequencies. The index n is used to enumerate these discrete sets.

[0105] Equation (12) is still integrated over t (from 0 to h), and r t It is necessary to integrate over a certain distance and average the values ​​that h can take. If the probability density function of h is known and given by f(h), the average electric field (average E-Field) can be estimated by equation (13).

[0106]

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[0107] In general, integrals with respect to h can be evaluated numerically, but sometimes they can be evaluated analytically. For example, if f(h) is a Gaussian distribution function with mean 0 and standard deviation σ, the integrals with respect to t and h in Equation 10 can be evaluated analytically, and both can be found from the solution to the problem without perturbation. n (r t , inc, sc) and k n (r t It can be expressed as (inc, sc).

[0108] Evaluation of the Diffused Term

[0109] This term requires a more complex evaluation. Since it is proportional to the covariance of the field, it includes the correlation of perturbations between any two points along the boundary. Therefore, the function g(h, h';r t , r t '), point r on the boundary t The perturbation at point r is between h and h+dh, and at point r t We need to know the joint probability function where the perturbation at ' is between h' and h'+dh'. This is also a characteristic of a coarse boundary. Using this function, we can estimate the average of the field-field product (which is part of the definition of the field-field covariance) using equation (14).

[0110]

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[0111] Figure 6 shows examples of two possible interfaces that result in roughness. The first part 71 of the object has a first rough surface 73, and the second part 72 of the object has a second perturbation surface 74.

[0112] By superposition, the case of a structural element having roughness along both a vertical boundary (or several such boundaries) and a horizontal boundary (or several such boundaries) can be explained by separately adding the contributing strengths from each boundary (assuming that the roughness between two points belonging to two different boundaries is uncorrelated).

[0113] Figure 7 includes graphs 81–86, which show examples of non-diffuse reflectance at a wavelength of 4.47 nm from roughened samples consisting of oxide films of varying thicknesses deposited on silicon substrates. These graphs show both measured and simulated results, highlighting the need to introduce roughness in order to adequately model the observed effect of roughness.

[0114] Figure 8 shows the simulation effect of an example of roughness on a periodic structure (curve 91 represents a smooth top surface, and 94 represents a top surface with a roughness of 20 angstroms standard deviation). Structure 95 is made up of oxide lines etched onto a silicon substrate. Roughness is present at the uppermost interface of the above lines, and the effect of the non-diffusing portion of the signal on all diffraction orders is shown compared to the case without roughness.

[0115] Figure 9 shows an example of method 200.

[0116] Method 200 can be used to evaluate the X-ray signal received from a perturbed object by illuminating the perturbed object.

[0117] Models can be used for various purposes, such as determining the roughness of an object being perturbed.

[0118] For example, reference models can be generated for perturbed objects with various roughness values. Once an evaluated perturbed object is evaluated, the X-ray signal received from the evaluated object can be compared to the reference models to find one or more similar models. The roughness of the evaluated perturbed object can be determined based on the roughness of one or more reference models.

[0119] Method 200 starts in step 210 and estimates the field generated by the perturbations of the perturbed object. These perturbations are on the order of the wavelength of the X-ray signal.

[0120] Step 210 may include calculating a general function (Step 220) that responds to the field contributed by single perturbances of the perturbed object.

[0121] The general function described above can be applied to perturbed objects of various shapes, such as any shape. It is not limited to perturbed objects that contain multiple parallel layers.

[0122] Step 220 may include at least some of steps 221, 222, 223, and 224.

[0123] Step 221 involves calculating the general function by integrating a first integrable function that is independent of the shape of the perturbed object.

[0124] Step 221 involves integrating a first integrable function based on (a) the difference in dielectric constant coefficients (Δε) between the perturbed object and its surroundings at a location of one of the single perturbances, (b) the field contributing to the illumination of one of the single perturbances at a certain illumination angle (see equation (1)), and (c) the field contributing to the collection of illumination from the single perturbation at a certain collection angle (see equation (2)).

[0125] Referring to equation (6), the first integral addition function is as follows:

[0126]

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[0127] The field contributing to illumination collection at a given collection angle from a single perturbation is calculated by calculating the field contributing to the illumination of one of the single perturbations from an illumination angle that is opposite to the collection angle. For example, as follows:

[0128]

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[0129] Step 222 involves (a) computing the general function by first integrating the first integrable function over a height range representing one of the heights of a single perturbation in relation to the unperturbed version of the perturbed object, in order to provide a second integrable function. Equation (6) contains 0 and h(r t See the first integral between ).

[0130] Step 223 may include a third integrable function based on the second integrable function and the area of ​​a normal projection of one of the single perturbances on a non-perturbed version of the surface of the perturbed object. The area is given by d in equation (6). 2 r t It is represented by [this].

[0131] Step 224 involves performing a second integral of the third integrable function over one or more surfaces of the perturbed object to obtain a fourth function, and adding to the fourth function the field estimate resulting from illuminating the unperturbed version of the perturbed object. See the following double integral over the nominal interface surface in equation (6).

[0132]

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[0133] Step 220 is followed by Step 240, in which an assessment is performed based on one or more statistical properties of the field and perturbation.

[0134] Step 240 may include at least one of steps 241, 242, 243, 244, 245, 246, and 247.

[0135] Step 241 includes evaluating the roughness of the perturbed object.

[0136] Step 242 includes evaluating the X-ray signal generated from a perturbed object having a given roughness.

[0137] Step 243 involves determining one or more other properties (not roughness) of the perturbed object.

[0138] Step 244 includes verifying the roughness estimate.

[0139] Step 245 includes evaluating the intensity of the X-ray signal based on statistics of the field and the perturbation of the perturbed object.

[0140] Step 246 includes calculating the diffusion intensity and the non-diffusion intensity.

[0141] Step 247 is the step of calculating the non-diffusion intensity by averaging the field obtained over possible perturbed versions of the perturbed object. See, for example, below.

[0142]

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[0143] Step 247 involves calculating multiple integrals over various functions, the calculation of which includes calculating an initial integral between (a) the field contributing to the illumination of one of the single perturbations at a given illumination angle and (b) the field contributing to the collection of illumination from a single perturbation at a given collection angle.

[0144] Step 247 involves calculating the dot product by computing a Fourier series that represents the dot product.

[0145] The X-ray signal may be a diffuse X-ray signal, and step 240 may include calculating the intensity of the diffuse X-ray signal.

[0146] The X-ray signal may be a non-diffused X-ray signal, and step 240 may include calculating the intensity of the non-diffused X-ray signal.

[0147] Step 240 may include verifying or determining the intensity of the non-diffuse X-ray signal based on the intensity of the diffuse X-ray signal.

[0148] Step 240 may include verifying or determining the intensity of the diffuse X-ray signal based on the intensity of the non-diffusive X-ray signal.

[0149] Step 240 may include determining the properties of the perturbed object based on the intensity of the non-diffusive X-ray signal and the intensity of the diffuse X-ray signal.

[0150] Method 200 can be performed based on the actual lighting of the real perturbation object.

[0151] In addition to or instead of this, method 200 can be performed based on an illumination simulation of the perturbed object.

[0152] Method 200 can be performed multiple times on perturbed objects (simulated or actual) with varying roughness, and can provide estimates of the X-ray signals obtained when illuminating perturbed objects with varying roughness.

[0153] These estimates can be used to determine the roughness of the newly estimated perturbed object.

[0154] Figure 10 shows an example of a method for evaluating the non-diffusive X-ray signal received from a perturbed object by illuminating the perturbed object.

[0155] Method 300 includes step 310 of calculating multiple non-perturbed objects that represent perturbances of the perturbed object. The perturbations of the perturbed object are on the order of the wavelength of the non-diffusive X-ray signal.

[0156] Step 320, following step 310, calculates an estimated field for each of the multiple unperturbed objects that represent the perturbation of the perturbed object.

[0157] Step 330, following step 320, evaluates the non-diffusive X-ray signal based on the fields of multiple non-perturbed objects.

[0158] The interfaces between a perturbed object and multiple unperturbed objects can have a uniform dielectric constant.

[0159] The perturbation of the perturbed object may follow a perturbance distribution function. Step 310 may include calculating several unperturbed objects based on the above perturbance distribution function.

[0160] The above perturbation distribution function may also be a probability function of the height parameter of the perturbation of the perturbed object.

[0161] The height parameter of a given protrusion related to the interface of the perturbed object is the distance between the protrusion and the interface of the perturbed object, and the given protrusion belongs to the perturbation.

[0162] A perturbed object may have a single rough interface. Multiple unperturbed objects may have corresponding unperturbed interfaces, each of which has one corresponding unperturbed interface for each unperturbed body of the multiple unperturbed objects.

[0163] The perturbation distribution function of the height parameter of a perturbation at a single rough interface may be substantially equal to the perturbation distribution function of the height parameter at a given unperturbed interface.

[0164] A perturbed object may have multiple rough interfaces. In this case, multiple non-perturbed objects have corresponding non-perturbed interfaces, and each of the multiple non-perturbed objects has multiple corresponding non-perturbed interfaces. Multiple non-perturbed objects can have different non-perturbed surfaces that represent combinations of the perturbance distribution functions of the plurality of rough interfaces. Different combinations of locations of non-perturbed interfaces that represent different rough interfaces should be evaluated.

[0165] Figure 9 shows an example of multiple (N) non-perturbed objects 1101(1) to 1101(N) (one per non-perturbed object), each having a non-perturbed surface 110(1) to 1103(N), which represents a perturbed object 1100 having a perturbed surface 1103. The above multiple non-perturbed objects are illustrated to include a non-perturbed object 1101(M) having a non-perturbed surface 1101(M).

[0166] In Figure 9, points along the perturbed surface 1103 are distributed according to the height distribution (for example, they have a y-axis coordinate). The heights of the non-perturbed surfaces 1101(3) to 1103(N) follow the height distribution of the perturbed surface.

[0167] The height of the non-perturbed surface 1103(1) represents the highest point of the perturbed surface 1101.

[0168] The height of the non-perturbed surface 1103(N) represents the lowest point of the perturbed surface 1101.

[0169] The height of the non-perturbed surface 1103(M) represents the intermediate point of the perturbed surface.

[0170] In Figure 9, there is one instance at the highest point, one instance at the lowest point, and two instances at intermediate heights. This can be represented by the number of unperturbed objects assigned to each height, the weights related to calculations associated with each height, and so on.

[0171] Figure 9 also shows point 1104 and points 1104(1) to 1104(N) where the field is calculated. The field can be calculated at any reference point.

[0172] Figure 11 shows an example of a method 300 for evaluating non-diffusive X-ray signals received from a perturbed object due to illumination of the perturbed object.

[0173] Method 300 is initiated in step 310 by calculating a non-perturbed object that represents the perturbed object, the non-perturbed object including one or more regions of variable dielectric constant that represent one or more regions of the perturbed object with uniform dielectric constant.

[0174] In step 320, following step 310, the estimated field of the non-perturbed object is calculated.

[0175] In step 330, following step 320, the non-diffusive X-ray signal is evaluated based on the estimated field of the non-perturbed object.

[0176] The perturbation of the object being perturbed may follow a perturbance distribution function, and the variable dielectric constant in one or more regions is calculated based on the above perturbance distribution function.

[0177] Within the variable dielectric constant region, the dielectric constant may change arbitrarily, such as continuously, discontinuously, stepwise, or in a stepped manner. To simplify the explanation, the following examples show sub-regions (partial regions) within the variable dielectric constant region that form a stepwise change in dielectric constant.

[0178] Step 310 includes replacing the perturbed object region with sub-regions of multiple non-perturbed objects having different dielectric constants. These sub-regions of multiple non-perturbed objects may be multiple layers or may have other shapes.

[0179] The above-mentioned sub-regions of non-perturbed objects may include (a) an upper perturbed sub-region located above the nominal plane of the perturbed object region, and (b) a lower perturbed sub-region located below the nominal plane of the perturbed object region.

[0180] The perturbed object described above has a perturbed region with a nominal surface. The nominal surface of the perturbed region is the non-perturbed version of the perturbed region.

[0181] The upper and lower perturbation sub-regions may have a thickness equal to a coefficient obtained by multiplying the perturbance distribution function of the perturbances of the perturbed object by the standard deviation of that coefficient.

[0182] The dielectric constant of the upper perturbation sub-region may be different from that of the lower perturbation sub-region. The dielectric constants of the upper and lower perturbation sub-regions are the weighted sums of (a) the dielectric constant (ε1) of the perturbed object region and (b) the dielectric constant (ε2) of other regions that interfere with the perturbed object region.

[0183] The following diagram illustrates an example of calculating the field of a non-perturbed object instead of the field of a perturbed object.

[0184] Figure 12 shows an example of a signal versus grazing angle. Curve 111 shows this relationship for a smooth grating (object), curve 112 shows this relationship for a perturbed object, and point 113 shows the evaluation relationship based on N=100 unperturbed objects representing the perturbed object.

[0185] Figure 13 shows an example of Method 400.

[0186] Method 410 begins with a step 410 of calculating an unperturbed object representing a perturbed object, where the unperturbed object includes one or more regions of variable dielectric constant representing one or more regions of perturbed objects with uniform dielectric constant.

[0187] In step 420, following step 410, the estimated field of the non-perturbed object is calculated.

[0188] In step 430, following step 420, the non-diffusive X-ray signal is evaluated based on the estimated field of the non-perturbed object.

[0189] Figure 14 shows a perturbed object 120 and a non-perturbed object 126 having a non-perturbed region 127 of variable dielectric constant.

[0190] The perturbed object 120 includes a perturbed region 121 (with a uniform dielectric constant ε1) having a rough surface 123. The reflected field, averaged across many profiles and characterized by having a typical perturbation distribution function (Gaussian in the example shown in the figure), is equivalent to the field obtained from an unperturbed object 126 having an unperturbed region 127 with a variable dielectric constant, for example, a field with a graduated-perturbed object orthogonal to the plane of the rough surface 123 of the perturbed object 120. The graduated permittivity is a weighted sum that varies along the normal according to a cumulative distribution function (in the case of Figure 14, the error function and complementary error function).

[0191] The perturbed object 120 includes a perturbed region 121 having a rough surface 123 (with a uniform dielectric constant ε1), and also includes other regions 122. The perturbed object interfaces with its surroundings 124 (air or another object) having a different dielectric constant (ε2).

[0192] The non-perturbed object 126 has a non-perturbed region 127 and other regions 122 of variable dielectric constant. The dielectric constant value at each point in the non-perturbed region 127 of variable dielectric constant is represented by the grayscale at that point.

[0193]

number

[0194] A method is provided that requires the profile of an object to be decomposed along the axial direction (vertical direction) in order to form a layer with a uniform dielectric constant.

[0195] Figure 15 shows an example of a perturbed object 170 having an upper region with dielectric constant ε1 and a rough interface 171. The height distribution of the rough surface has a standard deviation σ.

[0196] The perturbed object 170 is represented by the unperturbed object 173, and the rough interface is represented by multiple (R) upper layers 174(1) to 174(R) and multiple (R) lower layers 175(1) to 175(R). The dielectric constant of the upper layer is determined by the cumulative distribution function and the distance of this layer from a plane that represents the rough interface.

[0197] The sum of the heights of all upper levels is h up This is shown by.

[0198] The sum of the heights of all lower levels is h down This is shown by.

[0199] The effective dielectric constant of all layers is given by ε, which is a function of the variable t, where t represents the position relative to the nominal top surface (smooth surface).

[0200]

number

[0201] By changing the number of layers selected, the graded-index profile can be approximated more accurately.

[0202] Figure 16 shows an example of the signal versus grazing angle in a zero-order field. a. Non-perturbed object - Curve 181 Object with bR=1 - Curve 182 Object with cR=2 - Curve 183 Object with dR=5 - Curve 184 Object with eR=10 - Curve 185 f. Rough object - Curve 186

[0203] Figure 16 shows that the more layers used, the more accurately the graded index is approximated. The graph on the right of Figure 16 focuses on a specific angle of incidence and shows that increasing the number of layers (curve 182) brings the rigorous result (curve 181) closer to a better result. For reference, curve 181 represents an unperturbed object.

[0204] Since the computation time for evaluating the field scales with the number of layers, it is sometimes desirable to reduce the number of layers in order to shorten the computation time.

[0205] To do this without sacrificing accuracy in the case of rough interfaces, the layer thickness and dielectric constant must be optimized so that they best match the effect of the perturbation up to a given order of the normal distance from the interface.

[0206] To best match to second order in the above field, it was found that using single layers with a specific thickness (proportional to roughness) and a specific dielectric constant (a constant weighted sum of the dielectric constants of the upper and lower layers of the smooth interface) is sufficient.

[0207] Each of the two layers can contain two segments, one to the right and one to the left of the object's center (for example, S in Figure 17).

[0208] Figure 17 shows an example of a non-perturbed object 130, including a bottom region 133 (having an inverted T-shape), a lower layer 131, an upper layer 132, and other regions 122. The lower layer 131 and the upper layer 132 represent a single perturbed region (indicated by reference numeral 121 in Figure 14). The interface between the lower layer and the upper layer 132 is located on a surface 125, which represents a nominal surface of the perturbed region.

[0209] Let heff1 be the height of the upper layer 132, heff2 be the height of the lower layer 132, εeff1 be the dielectric constant of the upper layer, and εeff2 be the dielectric constant of the lower layer.

[0210]

number

[0211] To optimally adapt to fields up to the fourth order, two upper layers and two more upper layers are required, as shown in Figure 18.

[0212] Figure 18 shows an example of a non-perturbed object 140, including a bottom region 145 (having an inverted T-shape), the lowest layer 142, the lower layer 144, the top layer 141, the upper layer 143, and other regions 122. The lowest layer 142, the lower layer 144, the top layer 141, and the upper layer 143 are a single perturbed region (reference numeral 121 in Figure 14). It represents.

[0213] Let the height of the uppermost layer 141 be heff1, the height of the lowermost layer 142 be heff2, the height of the upper layer 143 be heff3, and the height of the lower layer 144 be heff4.

[0214] Let the dielectric constant of the uppermost layer 141 be εeff1, the dielectric constant of the lowermost layer 142 be εeff2, the dielectric constant of the upper layer 143 be εeff3, and the dielectric constant of the lower layer 144 be εeff4.

[0215]

Number

[0216] To optimally fit the field up to the sixth order, as shown in FIG. 19, three upper layers and three upper layers are required.

[0217] FIG. 19 shows an example of the object 150 without perturbation, including a bottom region 159 (having an inverted T shape), a lowermost layer 152, an intermediate lower layer 154, a lower layer 156, an uppermost layer 151, an intermediate upper layer 153, an upper layer 155, and another region 122. The lowermost layer 152, the intermediate lower layer 154, the lower layer 156, the uppermost layer 151, the intermediate upper layer 153, and the upper layer 155 represent a single perturbation region (reference numeral 121 in FIG. 14).

[0218] Let the height of the uppermost layer 151 be heff1, the height of the lowermost layer 152 be heff2, the height of the intermediate upper layer 153 be heff3, the height of the intermediate lower layer 154 be heff4, the height of the upper layer 155 be heff5, and the height of the lower layer 156 be heff6.

[0219] Let the dielectric constant of the uppermost layer 151 be εeff1, the dielectric constant of the lowermost layer 152 be εeff2, the dielectric constant of the intermediate upper layer 153 be εeff3, the dielectric constant of the intermediate lower layer 154 be εeff4, the dielectric constant of the upper layer 155 be εeff5, and the dielectric constant of the lower layer 156 be εeff6.

[0220]

Number

[0221] Figure 20A shows an example of the signal-to-glazing angle of a non-perturbed object (curve 161), curve 162 shows the case using the graded permittivity approach (representing a perturbed region with a layer thickness between zero and 4σ), curve 163 shows the case where the object is rough, and curve 164 shows the case with an optimal layer.

[0222] Figure 20B shows an example of method 601.

[0223] Method 601 includes steps 610, 620, and 630.

[0224] Step 610 includes illuminating the perturbed object to obtain a detection signal indicating an X-ray signal received by the sensor from the perturbed object.

[0225] The above acquisitions include generating detections from sensors, simulating detection signals, or receiving detection signals from storage devices or other sources.

[0226] In step 620, following step 610, at least one model-based evaluation related to the perturbed object based on the detection signals is performed.

[0227] Step 620 includes comparing the detection signal with reference detection signals associated with reference models of reference perturbed objects associated with one or more reference parameters, as described in Step 622.

[0228] The above reference model can be calculated using any of the steps in methods 200, 300, and 400.

[0229] In step 624, following step 622, one or more selected reference models for the reference perturbation object are selected, and the parameters of the perturbation object are determined based on the parameters of one or more selected reference models for the reference perturbation object. The selected parameters can be any type, such as best matching or distance-based selection.

[0230] In step 626, following step 624, one or more parameters of the perturbed object are set to one or more parameters of the selected reference perturbed object modeled by the selected reference model. This may include applying interpolation, interpolation, weighted sum, or use of statistical functions of any other function, if there is one or more selected reference models.

[0231] One or more parameters of the perturbed object may relate to roughness, dimensions, or other factors.

[0232] The reference model can be computed in any way, for example, by applying any step of methods 200, 300, and 400.

[0233] Step 620 may include at least one of the following: a. Measurement of the roughness of the perturbed object. b. Measure the roughness of the perturbed object and perform additional evaluations of the perturbed object. c. Perform additional evaluations based on the roughness of the perturbed object. d. Measurement of dimensions of the perturbed object. e. Determination of the standard deviation of the roughness of the perturbed object and the correlation length of the above roughness based on the diffusion signal. f. Determination of a non-spreading-based model of perturbation signals based on correlation. g. Obtaining a model of the perturbation object and subsequently correcting the model. The model is determined based on one or more statistical characteristics of the field and the perturbation. h. Obtaining a model of the perturbation object and subsequently correcting the model. The model is based on additional information regarding the perturbation model. The additional information is not based on a detection signal indicating an X-ray signal. i. Evaluating the diffusion-based roughness of the perturbation object. j. Correcting the non-diffusion-based model of the perturbation object.

[0234] U.S. Patent No. 9,588,066, which is incorporated herein by reference, shows a system for measuring a periodic structure. The periodic structure includes a repetition of a basic cell. Examples of the basic cell are shown in the above-mentioned drawings and text, and also in the following text and drawings.

[0235] The system illustrated in U.S. Patent No. 9,588,066 can be modified to apply any of the above-described methods. In addition or alternatively, measurements by the system described in the specification of U.S. Patent No. 9,588,066 can also be used as inputs to the above method.

[0236] Embodiments relate to methods and systems for measuring a periodic structure using multi-angle X-ray reflectance scatterometry (XRS).

[0237] In one embodiment, a method for measuring a sample by X-ray reflectance scatterometry includes colliding an incident X-ray beam with a sample having a periodic structure to generate a scattered X-ray beam, the incident X-ray beam providing a plurality of incident angles and a plurality of azimuth angles simultaneously. This method also includes collecting (condensing) at least a part of the scattered X-ray beam.

[0238] In another embodiment, a system for measuring a sample by X-ray reflectivity scattering includes an X-ray source for generating an X-ray beam having an energy of approximately 1 keV or less. The system also includes a sample holder for positioning a sample having a periodic structure. The system also includes a monochromator positioned between the X-ray source and the sample holder. The monochromator is for focusing the X-ray beam and supplying the incident X-ray beam to the sample holder. The incident X-ray beam has multiple incidence angles and multiple azimuthal angles simultaneously. The system also includes a detector for collecting at least a portion of the scattered X-ray beam from the sample.

[0239] This paper describes a method and system for measuring periodic structures using multi-angle X-ray reflectivity scattering (XRS). The following description specifies numerous specific details, such as X-ray beam parameters and energies, to provide a complete understanding of the embodiments of this invention. It will be apparent to those skilled in the art that embodiments of this invention can be implemented without these specific details. In other examples, well-known features, such as entire semiconductor device stacks, are not described in detail to avoid unnecessarily obscuring the embodiments of this invention. Furthermore, it should be understood that the various embodiments shown in the figures are illustrative and not necessarily drawn to scale.

[0240] One or more embodiments described in this specification are directed toward the use of an X-ray source configured to simultaneously utilize multiple incident beam angles incident on a periodic (lattice) structure for X-ray reflectance scattering measurements. The embodiments enable the detection of scattered light in two angular directions, as well as the use of reflected X-ray intensity to infer the shape and pitch of the periodic structure. The embodiments can provide appropriate accuracy and stable measurement of the shape and size of complex two-dimensional (2D) and three-dimensional (3D) periodic structures in a production fab semiconductor environment. Such measurements include the shape profile of the periodic structure, and dimensions such as the width, height, and sidewall angles of the periodic structure.

[0241] To explain the background, state-of-the-art shape measurement solutions utilize optical techniques with single-wavelength or spectral light sources with nominal wavelengths of 150 nanometers or greater. Spectral solutions are typically single-wavelength light sources with a fixed wavelength and variable incident angle. Such solutions exist in the wavelength / energy regime of λ > d (where λ is the incident light source and d is the fundamental dimension of the periodic structure). However, light scattering measurements are approaching their fundamental sensitivity limits.

[0242] In one embodiment, by using a wavelength of light where λ / d < 1, higher-order scattering orders can be detected, providing direct sensitivity to the parameter d. More specifically, by using light with wavelengths less than the width and height of the structure being measured, interference fringes of multiple cycles become available, providing sensitivity to height, width, and linear shape. In one embodiment, by using multiple incident and azimuth angles (for example, relative to the symmetry direction of the structure), three-dimensional information is obtained, providing three-dimensional shape sensitivity. The information obtained concerns dimensions that can have a critical impact on the performance of the device and must be controlled with very tight tolerances.

[0243] Figure 21, intended to help conceptualize the concepts related to this specification, shows a cross-sectional view of a periodic structure used in conventional scattering measurements with an incident beam having a single incident angle. Referring to Figure 21, a light beam 102 is irradiated onto the periodic structure 100 (also called a diffraction grating structure). The light beam 102 has an incident angle φi with respect to the horizontal plane 104 of the uppermost surface of the periodic structure 100. A scattered beam 106 is generated from the periodic structure 100. The scattered beam 106 may contain beams with different scattering angles, each providing different orders of information about the periodic structure 100. For example, as shown in Figure 21, three orders are shown: n=1, n=0, and n=-1, where the scattering angle for the n=-1 order has an angle of θ with respect to the horizontal plane 104 of the uppermost surface of the periodic structure 100. The arrangement in Figure 21 illustrates a conventional OCD or GISAS scattermeter approach.

[0244] Throughout this document, the use of the terms “periodic” or “lattice” structures refers to non-planar structures, and it should be understood that, depending on the context, they can all be considered three-dimensional structures. For example, referring again to Figure 21, the periodic structure 100 has features 108 that protrude in the z direction by a height h. Each feature 108 also has a width w along the x-axis and a length along the y-axis (i.e., in the plane of the paper). However, depending on the context, the term “three-dimensional” may also describe a periodic or lattice structure that has a length along the y-axis of the same order as its width w (reserved). In such contexts, the term “two-dimensional” may also describe a periodic or lattice structure that has a length along the y-axis that is substantially longer than its width w, for example, several orders of magnitude longer. In any case, periodic or diffraction grating structures have non-planar topography within the measurement area of, for example, a semiconductor wafer or substrate.

[0245] In contrast to Figure 21, Figure 22 is a cross-sectional view of a periodic structure used for scattering measurements using incident beams with multiple incident angles, according to one embodiment. Referring to Figure 22, a conical X-ray beam 202 is irradiated onto the periodic structure 100. The conical X-ray beam 202 has a central axis 203 with an incident angle φi with respect to the horizontal plane 104 of the uppermost surface of the periodic structure 100. Thus, the conical X-ray beam 202 includes a portion A with an incident angle φi. The conical X-ray beam 202 has a convergence angle φcone between the outermost portion B and the outermost portion C of the conical beam 202. Because the conical X-ray beam 202 has the convergence angle φcone, the portion of the conical beam 202 closer to the outer part of the cone is incident on the structure 100 at a different incident angle than the portion of the conical X-ray beam 202 that is in a straight line with the central axis 202. Therefore, the conical X-ray beam 202 simultaneously provides multiple incidence angles for incidence onto the periodic structure 100 with respect to the horizontal plane 104. A scattered beam 206 is generated from the periodic structure 100. The scattered beam 206 includes portions resulting from information of different orders of the periodic structure 100, examples of which are described in further detail below.

[0246] In addition to having an incident angle, the incident light beam can also have an azimuthal angle with respect to the periodic structure. Again for conceptual purposes, Figure 23 is a top view of a periodic structure used in conventional scattering measurements with an incident beam having a single azimuthal angle. Referring to Figure 23, the periodic structure 100 is shown from above the protrusion 108. Although not visible in Figure 21, the incident light beam 102 can also have an azimuthal angle θg with respect to the direction x perpendicular to the protrusion 108 of the periodic structure 100. In some cases, as depicted in Figure 23, θg is not zero. When θg is zero, the direction of the light beam 102 is along the x-direction in the top view. However, in all cases where a conventional OCD scattermeter or GISAS scattermeter is applied, the beam 102 has only one angle θg. Therefore, combining Figures 21 and 23, conventional scattering measurements are performed using a light beam having a single incident angle φi and a single azimuthal angle θg.

[0247] In contrast to Figure 23, Figures 24A and 24B show a top view of a periodic structure used for scattering measurements with an incident beam having multiple azimuthal angles, according to one embodiment. Referring to both Figures 24A and 24B, as described in Figure 22, a conical X-ray beam 202 with a central axis 203 is irradiated onto the periodic structure 100. Although not visible in Figure 22, the conical X-ray beam 202 also has a dimension along the y-direction. That is, the convergence angle φcone taken between the outermost part B and the outermost part C of the conical beam 202 also provides multiple incident angles along the y-direction, such as non-zero azimuthal angles of incidence.

[0248] Referring to Figure 24A, the central axis of the conical X-ray beam 202 has a zero angle θg along the x-axis when viewed from above. That is, portion A of the conical X-ray beam 202 has a zero azimuthal angle. On the other hand, even though the central axis 203 of the conical X-ray beam 202 is perpendicular to the periodic structure 100, portions B and C of the conical X-ray beam 202 have non-zero azimuthal angles.

[0249] Referring to Figure 24B, the central axis of the conical X-ray beam 202 has a non-zero angle θg along the x-axis when viewed from above. That is, portion A of the conical X-ray beam 202 has a non-zero azimuth angle. In addition, portions B and C of the conical X-ray beam 202 have non-zero azimuth angles that are different from the azimuth angle of portion A of beam 202.

[0250] In both cases shown in Figures 24A and 24B, since the conical beam 202 has a convergence angle φcone, the portion of the conical beam 202 closer to the outer part of the cone is incident on the periodic structure 100 at a different azimuth angle than the portion of the conical beam 202 aligned with the central axis 202. Therefore, the conical beam 202 simultaneously provides multiple azimuth angles with respect to the x-direction into which it is incident on the periodic structure 100.

[0251] Thus, according to one embodiment combining Figure 22 and either Figure 24A or Figure 24B, the method for measuring a sample by X-ray reflectivity scattering includes colliding an incident X-ray beam onto a sample having a periodic structure. The X-ray beam has a conical shape that simultaneously provides multiple incident angles φi and multiple azimuth angles θg as incidence onto the periodic structure. This incidence generates a scattered X-ray beam, and by collecting a portion (but not all) of it, information about the periodic structure can be obtained.

[0252] In one embodiment, the incident X-ray beam is a focused X-ray beam having a convergence angle φcone in the range of about 20 to 40 degrees. In one embodiment, the central axis of the focused X-ray beam has a fixed non-zero incident angle φi and a zero azimuthal angle θg with respect to the sample, as described in relation to Figure 24A. In another embodiment, the central axis of the focused X-ray beam has a fixed non-zero incident angle φi and a non-zero azimuthal angle θg with respect to the sample, as described in relation to Figure 24B. In either case, in a specific embodiment, the central axis of the focused X-ray beam has a fixed non-zero incident angle in the range of about 10 to 15 degrees from the horizontal. In yet another specific embodiment, the outermost part of the cone shape of the beam, the part closest to the periodic structure, for example, part C shown in Figure 22, has an angle of about 5 degrees with respect to the horizontal plane of the periodic structure.

[0253] In other embodiments, as will be described in more detail below, it may be preferable to use a narrower conical shape. For example, in one embodiment, the incident X-ray beam is a focused X-ray beam having a convergence angle in the range of approximately 2 to 10 degrees. In such an embodiment, the central axis of the focused X-ray beam has a fixed non-zero incident angle φi and a zero azimuthal angle θg with respect to the sample, as described in relation to Figure 24A. In another embodiment, the central axis of the focused X-ray beam has a non-zero fixed incident angle φi and a non-zero azimuthal angle θg with respect to the sample, as described in relation to Figure 24B.

[0254] In one embodiment, a low-energy X-ray beam is incident on a periodic structure. For example, in one embodiment, the low-energy X-ray beam has an energy of approximately 1 keV or less. By using such a low-energy source, it is possible to reduce the achievable spot size while increasing the incident angle. In one embodiment, the low-energy X-ray beam is a Kα beam generated from a source such as carbon (C), molybdenum (Mo), or rhodium (Rh), although this is not limited to the source.

[0255] In one embodiment, a low-energy X-ray beam is focused using a toroidal multilayer monochromator before it is incident on the periodic structure. In one embodiment, the monochromator provides an incident angle range of approximately + / - 30 degrees and an azimuth angle range of approximately + / - 10 degrees. In a specific embodiment, the toroidal multilayer monochromator provides an incident angle range of approximately + / - 20 degrees. It should be understood that the conical X-ray beam described herein does not have to be collimated, nor is it necessary to collimate it. For example, in one embodiment, the beam is not collimated between the focusing of the beam in the monochromator and the collision of the focused beam with the periodic sample. In one embodiment, the focused low-energy X-ray beam is impacted on the sample within an incident angle range smaller than the angle of a nominal first-order angle at zero degrees.

[0256] Referring again to Figure 22, in one embodiment, at least a portion of the scattered X-ray beam 206 is collected using a detector 250. In one embodiment, a two-dimensional detector is used, and the scattered signal intensity of portions of the scattered X-ray beam 206 scattered from multiple incident angles and multiple azimuthal angles is simultaneously sampled. The collected signals can then be subjected to scatterometry analysis, for example, by comparing the inverse transform of the scattering data with theory to determine the structural details of the periodic structure 100. In one such embodiment, the shape of the periodic structure of the sample is estimated by inverting the scattering solution with respect to the sampled scattered signal intensity, for example, by exactly solving Maxwell's equations relating to the periodic structure. In one embodiment, the X-ray beam incident on the sample has a wavelength shorter than the periodicity of the periodic structure 100. Therefore, the probing wavelength is equal to or less than the basic structural dimensions, providing a richer dataset from the scattered beam 206 compared to an OCD scattermeter.

[0257] As described above, in one embodiment, the incident conical X-ray beam used in XRS is a focused X-ray beam with a convergence angle φcone in the range of approximately 20 to 40 degrees. Such a relatively wide cone angle allows for the generation of a scattered beam that includes higher-order diffraction data in addition to zero-order reflection data. Therefore, in one embodiment, both zero-order and higher-order information can be obtained in parallel in a single collision operation.

[0258] In other scenarios, it may be desirable to separate zero-order reflection data from higher-order diffraction data. In one such embodiment, a relatively narrow cone angle can be used, for example, the incident X-ray beam is a focused X-ray beam with a convergence angle in the range of approximately 2 to 10 degrees. One or more measurements may be performed using a relatively narrow cone angle. For example, in one embodiment, as described in relation to Figure 24A, a first measurement is performed with the azimuth angle of the central axis of the focused beam set to zero. Then, a second measurement is performed with a non-zero azimuth angle of the central axis of the focused beam, as described in relation to Figure 24B. In a specific embodiment, the first measurement is performed sequentially to collect zero-order diffraction data rather than primary-order diffraction data for a sample with a periodic structure. In the second measurement, primary-order diffraction data is collected for the sample with a periodic structure, but zero-order diffraction data is not. In this way, zero-order data and higher-order data can be separated when the scattered beam is generated.

[0259] In relation to both parallel and sequential approaches, according to the embodiments described in this specification, X-ray reflectance scattering is used to separate different orders on an array detector by an approach at a non-zero azimuthal angle. Often, higher orders are more useful. Throughput can be improved by acquiring all orders cleanly in parallel. However, a sequential approach is also possible. Furthermore, a very focused beam is used to probe at various incident angles rather than a single incident angle. In one embodiment, the beam is not collimated because a collimated beam would require rotating the sample with continuously acquired data. By capturing higher orders, it is not necessary to use very small incident angles to obtain a strong reflected beam. In contrast, in one embodiment, even if the reflected beam of the specular (0th order) is relatively weak and, for example, the -1st order is very strong, incident angles of, for example, 10 to 15 degrees can be used.

[0260] In either of the above cases, whether collected in parallel or sequentially, the embodiments described in this specification can be used for data acquisition from zero-order (specular) reflections and data acquisition from diffraction (higher order). Conventional solutions have emphasized the use of either zero-order or diffraction (higher order), but it has not been possible to use both. The embodiments described in this specification can be further distinguished from the previously disclosed scattermeter approaches, some examples of which are described below.

[0261] Yun, U.S. Patent No. 7,920,676, describes a CD-GISAXS system and method in the first approach described above. The described approach analyzes the diffraction pattern of scattered X-rays generated from parallel beams and analyzes multiple orders of diffracted light. Because the diffraction order intervals are large, lower energies are used to provide a beam with higher focus. However, the diffraction order intervals are still quite narrow, and the unit of the convergence angle is microradians. Furthermore, diffraction is not collected for a large number of incidence angles.

[0262] In contrast, according to one or more embodiments described in this specification, a wide range of incidence angles are used in a single beam. In this approach, diffraction orders (other than 0th order) do not actually need to be captured for their usefulness. However, since + / -1st order may have different sensitivities to diffraction grating characteristics (particularly pitch), in one embodiment, at least one additional order is captured whenever possible. Even so, the majority of the information is contained in how the signal changes with the incidence angle. In contrast, U.S. Patent No. 7,920,676 essentially uses one incidence angle, and information is collected by observing multiple diffraction orders.

[0263] Furthermore, according to one or more embodiments described in this specification, the primary beam can be separated from the zero-order beam by shifting the primary beam towards the zero-order beam. In one embodiment, the periodic structure or grating structure is approached at a non-zero azimuthal angle. In this way, a highly focused beam can be used while achieving order separation. In an exemplary embodiment, by approaching the grating at an azimuthal angle of 45° (with respect to the central axis of the focused beam), the + / - primary-order diffracted beam is deflected towards the zero-order beam by at least 10°, and more so as the incident angle increases. In this case, a focused beam of up to approximately 10° can be used while avoiding overlap and data. It should be understood that the separation between orders can be increased or decreased depending on the pitch and X-ray energy specifications of the diffraction grating. Overall, in one embodiment, more useful information can be obtained by simultaneously collecting multiple incident and azimuthal angles compared to a single shot of a parallel beam.

[0264] Regarding the second approach described above, Mazor and other U.S. Patent No. 6,556,652 describe the measurement of critical dimensions using X-rays. The described approach is not actually based on the diffraction of the X-ray beam. Instead, a "shadow" is created in the parallel beam. This shadow is reflected from a pattern (e.g., a linear lattice structure). The contrast mechanism of the shadow is the difference in the critical angle for reflecting X-rays between the Si region at the bottom of the diffraction grating gap and the critical angle when the X-rays first pass through the ridge material (photoresist). In contrast, in the embodiments described in this specification, most of the information is obtained from signals at angles far beyond the critical angle.

[0265] As briefly described above and illustrated below, X-ray reflectivity scattering (XRS) can be considered a type of X-ray reflectometry (XRR) applied to two-dimensional and three-dimensional periodic or lattice structures. Conventional XRR measurements use a single X-ray source to probe a sample over a certain angular range. By changing the optical path length difference with angle, interference fringes can be identified, and film property information such as film thickness and density can be obtained. However, in XRR, due to the physical properties of X-ray interaction with material at higher source energies, the angular range is usually limited to minute incidences of about 3 degrees or less relative to the horizontal plane of the sample. As a result, the productivity / inline viability of XRR has been limited. In contrast, according to the embodiments described in this specification, the application of low-energy XRR / XRS enables the use of larger angles, due to changing optical film properties with energy that lead to larger angles of signal sensitivity.

[0266] An exemplary application of low-energy XRS is the measurement and analysis of fundamental semiconductor transistor building blocks. For example, the critical dimension (CD) of a semiconductor device refers to a characteristic that directly affects the device's performance and manufacturing yield. Therefore, the CD must be manufactured or controlled to tight specifications. Conventional examples of CD include gate length, gate width, trace width, trace spacing, and line width roughness (LWR). Semiconductor devices are highly sensitive to these dimensions, and even slight variations can have a significant impact on performance, device failure, and manufacturing yield. As the feature size of integrated circuits (ICs) continues to shrink, manufacturers face narrower process windows and tighter tolerances. This has significantly increased the demand for accuracy and sensitivity in CD measurement tools, as well as the need to perform non-destructive sampling early in the manufacturing cycle while minimizing the impact on the productivity of semiconductor device manufacturing plants and fabs.

[0267] The fabrication of non-planar semiconductor devices further complicates matters. For example, semiconductor devices fabricated on raised channels with non-planar topography, often called fins, require additional CDs, including fin dimensions, to be considered. Such fin field-effect transistors (fin-FETs) or multi-gate devices have high aspect ratio characteristics, making the need for three-dimensional (3D) profile information regarding the fins of the device structure, including sidewall angles and top and bottom dimensions, crucial. In other words, the ability to measure 3D profiles provides far more valuable information than conventional two-dimensional linewidth and spacing CD information.

[0268] Figure 25 shows a side view of an exemplary finFET device suitable for low-energy X-ray reflectance scattering measurements according to one embodiment. Referring to Figure 25, structure A shows a perspective cross-section of a semiconductor fin 502 on which a gate electrode stack 504 is positioned. The semiconductor fin 502 protrudes from a substrate 506 isolated by a shallow trench isolation (STI) region 508. The gate electrode stack 504 includes a gate dielectric layer 510 and a gate electrode 512. Structure B shows a cross-section of a semiconductor fin 520 protruding from the substrate 522 between STI regions 524. Side views of structure B, which provide important information through XRS measurements, include the fin corner rounding (CR), fin sidewall angle (SWA), fin height (H), fin notch, and STI thickness (T), all of which are depicted in structure B of Figure 25. Structure C shows a cross-section of a semiconductor fin 530 protruding from a substrate 532 between STI regions 534 and having a multilayer stack of films 536 on it. The layers 536 of the multilayer stack of films may include, but are not limited to, layers of materials such as titanium aluminum carbide (TiAlC), tantalum nitride (TaN), or titanium nitride (TiN). Comparing Structure B and Structure C, XRS measurements can be performed on bare fins, such as a bare silicon fin (Structure B), or on fins with different material layers placed on them.

[0269] Figure 26 shows a plot 600 of the zero-order reflectance versus scattering angle of a silicon (Si) fin having a periodic structure with a line / space ratio of 10 nm / 20 nm, and the corresponding structures (A) to (E), according to one embodiment. Referring to Figure 26, low-energy XRS measurements can be used to distinguish between nominal fin structures (structure A), structures with increased fin height (structure B), structures with reduced fin width (structure C), structures where the fin base CD is wider than the fin top CD (structure D), and structures where the fin top CD is narrower than the fin bottom CD (structure E). In this example, the Si fin is analyzed by zero-order cone diffraction at 45 degrees relative to the periodic structure. Compared with the optical data, the data fringing seen in plot 600 is a result of short wavelengths, and it can be seen that the region of the highest signal is reduced.

[0270] Figure 27 shows a plot 700 of the primary reflectance versus scattering angle of a silicon (Si) fin having a periodic structure with a line / space ratio of 10 nm / 20 nm, and the corresponding structures (A) to (E), according to one embodiment. Referring to Figure 27, low-energy XRS measurements can be used to distinguish between nominal fin structures (structure A), structures with increased fin height (structure B), structures with reduced fin width (structure C), structures where the fin base CD is wider than the fin top CD (structure D), and structures where the fin top CD is narrower than the fin bottom CD (structure E). In this example, the Si fin is analyzed by primary cone diffraction at 45 degrees relative to the periodic structure. Structures with varying pitches are also included in plot 700. As shown in plot 700, the primary data is very sensitive to the fin thickness (note that structure B is far from the signals from structures A and C to E). Also note that the primary data is very sensitive to changes in the pitch of the periodic structure, and the spectra when the pitch is changed are significantly distinguishable from the other spectra.

[0271] In another embodiment, an apparatus for performing X-ray reflectance scatterometry is described. Generally, in one embodiment, the apparatus includes a general-purpose X-ray source along with a two-dimensional focusing monochromator. The focusing monochromator can inject incident light into a periodic sample under two different incident angles: (i) an incident angle incident on the plane of the periodic structure and (ii) an incident angle incident azimuthal (and at a fixed incident angle) with respect to the symmetry of the structure. Detection of the scattered light is performed by a two-dimensional (2D) detector, which simultaneously samples the scattered signal intensity over a scattering angle range in two angular directions. In one embodiment, a constraint on the monochromator to ensure free of scattering order overlap in the detected signals is that the incident angle range is less than the nominal first-order angle of 0 degrees, i.e., θ = sin - l(1 - λ / d). As a result of using light with a characteristic wavelength shorter than the period of the diffraction grating, higher-order diffractions can be accessed, providing additional information about the diffraction grating structure. Furthermore, interference fringes of multiple thickness cycles can be used to determine the height, width, and shape of the lines. The final estimation of the shape and structure of the periodic structure is achieved through inversion of the scattering solutions compared to the 2D interference / scatter data.

[0272] As a more specific example, Figure 28 shows a periodic structure measurement system with XRS functionality according to one embodiment.

[0273] Referring to Figure 28, a system 800 for measuring a sample 802 by X-ray reflectance scattering includes an X-ray source 804 that generates an X-ray beam 806 with an energy of approximately 1 keV or less. A sample holder 808 is provided for positioning the sample 802, and the sample has a periodic structure. A monochromator 810 is positioned between the X-ray source 804 and the sample holder 802, and the X-ray beam 806 travels from the X-ray source 804 through the monochromator 810 to the sample holder 808. The monochromator 810 focuses the X-ray beam 806 and supplies an incident X-ray beam 812 to the sample holder 808. The incident X-ray beam 812 has multiple incident angles and multiple azimuthal angles simultaneously. The system 800 also includes a detector 814 that collects at least a portion of the scattered X-ray beam 816 from the sample 802.

[0274] Referring again to Figure 28, in one embodiment, the X-ray source 804, the sample holder 808, the monochromator 810, and the detector 814 are all housed within the chamber 818. In one embodiment, the system 800 further includes an electron gun 820. In this embodiment, the X-ray source 804 is the anode, and the electron gun is directed toward the anode. In certain embodiments, the anode is for generating low-energy X-rays and may include, but is not limited to, materials such as carbon (C), molybdenum (Mo), or rhodium (Rh). In one embodiment, the electron gun 820 is an electron gun of approximately 1 keV. Referring again to Figure 28, a magnetic electron suppression device 822 is included between the X-ray source 804 and the monochromator 810.

[0275] In one embodiment, the monochromator 810 is a toroidal multilayer monochromator, providing an incidence angle range of approximately + / - 30 degrees and an azimuth angle range of approximately + / - 10 degrees. In this embodiment, the toroidal multilayer monochromator provides an incidence angle range of approximately + / - 20 degrees. In one embodiment, as described above, no collimator is interposed between the monochromator 810 and the sample holder 808. The monochromator 810 can be positioned to provide a desired incidence beam for XRS measurement. For example, in the first embodiment, the monochromator 810 is positioned relative to the sample holder 808 to provide a focused X-ray beam with a central axis having a fixed non-zero incidence angle and a zero azimuth angle relative to the periodic structure of the sample 802. In the second embodiment, the monochromator 810 is positioned relative to the sample holder 808 to provide a focused X-ray beam with a central axis having a fixed non-zero incidence angle and a non-zero azimuth angle relative to the periodic structure of the sample 802. In one embodiment, the monochromator 810 consists of alternating metal (M) and carbon (C) layers deposited on a glass substrate, where M is a metal such as cobalt (Co) or chromium (Cr), but is not limited to M. In this particular embodiment, the multilayer monochromator is provided for reflecting carbon (C)-based Kα radiation and includes about 100 repeating layers of Co / C or Cr / C having a period of about 4 nanometers, i.e., slightly shorter than the wavelength of the reflected beam, which is about 5 nanometers. In one such embodiment, the Co or Cr layers are thinner than the C layers.

[0276] The sample holder 808 may be a movable sample holder. For example, in one embodiment, the sample holder 808 is rotatable to change the azimuth angle of the central axis of the X-ray beam 812 with respect to the periodic structure of the sample 802. In one embodiment, the sample holder 808 is rotatable to provide orthogonal motion by eucentric rotation, allowing for two or more sample rotations per measurement. In one embodiment, the sample holder 808 can be visually inspected by a navigation visual inspection device 824, as shown in Figure 28. In such an embodiment, a flip-in objective lens is included for a vision-based inspection system.

[0277] In one embodiment, the detector 814 is a two-dimensional detector. The two-dimensional detector can be configured to simultaneously sample the scattered signal intensity of a portion of the scattered X-ray beam 816 scattered from multiple incident angles and multiple azimuthal angles of the incident beam 812. In one embodiment, the system 800 further includes a processor or arithmetic system 899 coupled to the two-dimensional detector. In such an embodiment, the processor 899 estimates the shape of the periodic structure of the sample 802 by inversion of scattering solutions relative to the sampled scattered signal intensity. Instead of a two-dimensional detector, in another embodiment, a scanning slit may be implemented. In either case, the detector 814 can be configured to achieve data acquisition of approximately 1000 pixels across the dispersion range.

[0278] Embodiments may be provided as a computer program product or software including a machine-readable medium having instructions stored therein, which can be used to program a computer system (or other electronic device) to perform a process according to the embodiment. A machine-readable medium includes any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computer). For example, machine-readable (e.g., computer-readable) media include machine-readable (e.g., computer) storage media (e.g., read-only memory (ROM), random-access memory (RAM), magnetic disk storage media, optical storage media, flash memory devices, etc.), machine-readable (e.g., computer) transmission media (e.g., electrical signals, optical signals, acoustic signals, or other forms of transmitted signals (e.g., infrared signals, digital signals, etc.)), etc.

[0279] Figure 29 is a schematic representation of a machine in an exemplary form of a computer system 900 capable of executing a set of instructions for a machine to perform one or more of the methodologies described in this specification. In other embodiments, the machine may be connected to (e.g., networked) a machine in a local area network (LAN), intranet, extranet, or internet. The machine operates as a server or client machine in a client-server network environment, and as a peer machine in a peer-to-peer (or distributed) network environment. The machine may be a personal computer (PC), tablet PC, set-top box (STB), personal digital assistant (PDA), mobile phone, web appliance, server, network router, switch, bridge, or any machine capable of executing a set of instructions (sequential or otherwise) that specifies actions to be performed by such a machine. Furthermore, although only a single machine is illustrated, the term “machine” also includes any set of machines (e.g., computers) that individually or collectively execute a set (or more sets) of instructions for performing one or more of the methodologies described in this specification. For example, in one embodiment, a machine is configured to execute one or more sets of instructions for measuring a sample by X-ray reflectance scattering. In one example, the computer system 900 may be adapted for use with the computer system 899 of the XRS apparatus 800 described above.

[0280] The illustrated computer system 900 includes a processor 902, main memory 904 (e.g., read-only memory (ROM), flash memory, dynamic random access memory (DRAM), such as synchronous DRAM (SDRAM) or Rambus DRAM (RDRAM)), static memory 906 (e.g., flash memory, static random access memory (SRAM)), and secondary memory 918 (e.g., data storage) that communicate with each other via a bus 930.

[0281] The processor 902 represents one or more general-purpose processing units, such as a microprocessor or a central processing unit. More specifically, the processor 902 may be a composite instruction set computing (CISC) microprocessor, a reduced instruction set computing (RISC) microprocessor, a very long instruction word (VLIW) microprocessor, a processor implementing another instruction set, or a processor implementing a combination of instruction sets. The processor 902 may also be one or more special-purpose processing devices, such as an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), a digital signal processor (DSP), or a network processor. The processor 902 is configured to execute processing logic 926 for performing the operations described in this specification.

[0282] The computer system 900 may further include a network interface device 908. The computer system 900 may also include a video display device 910 (for example, a liquid crystal display (LCD) or cathode ray tube (CRT), an alphanumeric input device 912 (for example, a keyboard), a cursor control device 914 (for example, a mouse), and a signal generator 916 (for example, a speaker).

[0283] The secondary memory 918 may include a machine-accessible storage medium (more specifically, a computer-readable storage medium) 931 that stores one or more instruction sets (e.g., software 922) that embody one or more of the methodologies or functions described in this specification. The software 922 may also reside, all or at least partially, in the main memory 904 and / or processor 902 during its execution by the computer system 900, and the main memory 904 and processor 902 also constitute machine-readable storage media. The software 922 may also be transmitted or received via the network 920 through the network interface device 908.

[0284] Although the machine-accessible storage medium 931 is shown as a single medium in exemplary embodiments, the term “machine-readable storage medium” should be interpreted to include a single or multiple mediums (e.g., a centralized or distributed database, and / or associated caches and servers) that store one or more instruction sets. Furthermore, the term “machine-readable storage medium” includes any medium capable of storing or encoding instruction sets for machine execution, causing a machine to execute one or more of the methodologies of the embodiments. Thus, the term “machine-readable storage medium” includes, but is not limited to, solid memory, optical media, and magnetic media.

[0285] In one embodiment, a non-temporary, mechanically accessible storage medium stores instructions for performing a method of measuring a sample by X-ray reflectivity scattering. This method involves colliding an incident X-ray beam with a sample having a periodic structure to generate a scattered X-ray beam. The incident X-ray beam provides multiple incident angles and multiple azimuth angles simultaneously. This method also includes collecting at least a portion of the scattered X-ray beam.

[0286] In this way, we have described a method and system for measuring periodic structures using multi-angle X-ray reflectivity (XRS).

[0287] Any arrangement of components to achieve the same function is substantially “related” in such a way that the desired function is achieved. Therefore, in this specification, any two components combined to achieve a particular functionality can be considered “related” to each other, regardless of the architecture or intervening components, in such a way that the desired functionality is achieved. Similarly, any two components thus related can be considered “operably connected” or “operably coupled” to each other in such a way that the desired functionality is achieved.

[0288] Furthermore, those skilled in the art will recognize that the boundaries between the actions (operations) described above are merely illustrative. Multiple actions may be combined into a single action, a single action may be distributed into additional actions, and actions may be performed with at least partial overlap in time. In alternative embodiments, multiple instances of an action may be included, and the order of actions may be changed in various other embodiments.

[0289] Furthermore, in one embodiment, for example, the illustrated embodiment may be implemented as a circuit arranged on a single integrated circuit or within the same device. Alternatively, the illustrated embodiment may be implemented as any number of separate integrated circuits or separate devices interconnected in an appropriate manner.

[0290] Furthermore, for example, the embodiment or a part thereof can be implemented as a software or code representation of a physical circuit, or as a logical representation that can be converted to a physical circuit, such as any suitable type of hardware description language.

[0291] Furthermore, other modifications, variations, and substitutions are possible. Therefore, the specification and drawings are not limiting but rather illustrative.

[0292] In the claims, reference numerals placed in parentheses should not be interpreted as limiting the claims. The term “equipped with” does not preclude the existence of other elements or steps described in the claims. Furthermore, the terms “a” or “an” as used in this specification are defined as one or plural. Also, the use of introductory phrases such as “at least one” and “one or more” in the claims should not be interpreted as meaning that the introduction of another claim element by the indefinite article “a” or “an” limits a particular claim containing such introduced claim element to an invention containing only one such element, even if the same claim contains the introductory phrase “one or more” or “at least one” and an indefinite article such as “a” or “an”. The same applies to the use of definite articles. Unless otherwise stated, terms such as “first” and “second” are used to arbitrarily distinguish the elements described by such terms. Therefore, these terms are not necessarily intended to indicate a temporal or other priority of such elements. The mere fact that certain means are described in different claims does not indicate that a combination of these means cannot be used advantageously.

[0293] While this specification illustrates and describes certain features of the invention, many modifications, substitutions, alterations, and equivalents will arise for those skilled in the art. Therefore, it should be understood that the attached claims are intended to cover all modifications and alterations that fall within the true spirit of the invention.

[0294] The terms “including,” “comprising,” “having,” “consisting,” and “consisting” are essentially interchangeable. For example, any method may include at least the steps included in the drawings and / or specification, or may include only the steps included in the drawings and / or specification.

Claims

1. A method for performing model-based measurement and evaluation for semiconductor process control with respect to a perturbation target (1100) on a semiconductor wafer, A detection signal is obtained that indicates the X-ray signal received by the sensor from the perturbed object by irradiation of the perturbed object, which includes a perturbation (1103) on the order of wavelength of the X-ray signal. Based on the above detection signal, perform at least one model-based evaluation of the perturbed object. The execution of at least one of the above model-based evaluations, The perturbation of the above-mentioned perturbed object is represented by a plurality of non-perturbed objects (1101(1)...1101(N)), and the estimated field is calculated for each of the plurality of non-perturbed objects. This includes evaluating the X-ray signal based on the fields of the above-mentioned multiple non-perturbed objects, method.

2. At least one of the above model-based evaluations is the measurement of the roughness of the perturbed object. The method according to claim 1.

3. The perturbation of the above-mentioned perturbed object follows a perturbation distribution function, and the above-mentioned multiple non-perturbed objects are calculated based on the above-mentioned perturbation distribution function. The method according to claim 1.

4. The above perturbation distribution function is a stochastic function of the height parameter of the perturbation of the perturbed object. The method according to claim 3.

5. The calculation of the above multiple non-perturbed objects includes replacing the perturbed object region (121) having a rough interface (123) with multiple non-perturbed object sub-regions (174, 175) with different dielectric constants. The method according to any one of claims 1 to 4.

6. Multiple layers of unperturbed object sub-regions are arranged parallel to each other, thereby representing a rough interface with a refractive index gradient profile. The method according to claim 5.

7. The perturbed object has a plurality of rough interfaces, and the plurality of unperturbed objects have corresponding unperturbed interfaces that represent the plurality of rough interfaces. The method according to any one of claims 1 to 4.

8. The above X-ray signal is a non-diffusive X-ray signal, and the above evaluation includes calculating the intensity of the above non-diffusive X-ray signal. The method according to any one of claims 1 to 4.

9. The above X-ray signal is a diffuse X-ray signal, and the above evaluation includes determining the correlation length of the roughness of the perturbed object. The method according to any one of claims 1 to 4.

10. The perturbed object is a periodic structure on the semiconductor wafer, and the periodic structure is composed of fins, gates, or wiring. The method according to any one of claims 1 to 4.

11. A system comprising an X-ray source (21), a sensor (23), and a processor (Figure 29, 902) for performing model-based measurement and evaluation for semiconductor process control, The above processor, A detection signal indicating an X-ray signal received from a perturbed object (1100) on a semiconductor wafer is acquired from the sensor, and the perturbed object includes a perturbation (1103) on the order of the wavelength of the X-ray signal. Based on the above detection signal, perform at least one model-based evaluation related to the perturbed object. The above processor is The perturbation of the above-mentioned perturbed object is represented by a plurality of non-perturbed objects (1101(1)...1101(N)), and the estimated field is calculated for each of the plurality of non-perturbed objects. The X-ray signal is evaluated based on the fields of the above multiple non-perturbed objects. It is configured to perform at least one model-based evaluation by doing so. system.

12. The system according to claim 11, wherein at least one of the model-based evaluations is the measurement of the roughness of the perturbed object.

13. The above processor is configured to calculate the multiple non-perturbed objects by replacing the perturbed object region (121) having a rough interface (123) with a plurality of non-perturbed object sub-regions (174, 175) composed of multiple layers of stepped dielectric constants representing the rough interface. The system according to claim 11.

14. The perturbed object is a periodic nanostructure on the semiconductor wafer, and the evaluation determines the critical dimensions of the nanostructure selected from the group consisting of pitch, width, height, and sidewall angle. The system according to any one of claims 11 to 13.

15. Stores instructions configured to be executed by the processor, thereby causing the processor to perform any of the methods of claims 1 to 4. A non-temporary computer-readable medium.

Images