Evaluation of x-ray signals from perturbed objects

Abstract

A method, system, and non-transitory computer readable medium for evaluating an x-ray signal. The method may include calculating an estimation field for each of a plurality of non-perturbing objects, the plurality of non-perturbing objects representing perturbations of the perturbing object; perturbing an order having a wavelength of the non-diffusive x-ray signal; and evaluating the non-diffusive x-ray signal based on the field of the plurality of non-perturbing objects.

Description

[0001] This application is a divisional application of the Chinese patent application with application number 202180094965.X.

[0002] Cross-references

[0003] This application claims priority to U.S. Provisional Patent No. 63 / 205,631, filed on December 31, 2021, and U.S. Provisional Patent No. 63 / 205,630, filed on December 31, 2021 - both of which are incorporated herein by reference. Background Art

[0004] In the x-ray range, the roughness is comparable to the wavelength.

[0005] Figure 1 A typical wire 11 is shown whose edges 12 and 13 are rough and which have a critical dimension (the distance between the edges 12 and 13) 15 - in this case the length of the wire.

[0006] Figure 2 An x-ray system is shown having an x-ray source 21 and optics which focus an x-ray beam 31 onto a small spot 33 on a sample 100, typically via a mirror symbolically represented in the figure as a lens 22. The x-rays 32 reflected from the sample are detected by a CCD camera 23 located in the far field region. Figure 2 Also shown are the illumination angle 41 and the collection angle 32 .

[0007] The illumination cone can be different from the collection cone, which is usually larger than the primer to allow detection of "scattered" X-rays. These are rays diffracted from the sample that do not enter the mirror direction.

[0008] In this scheme, several scattering directions are collected simultaneously by shining on different pixels of the CCD camera, thus reducing the need to scan the source / sample or both for the sample / detector orientation.

[0009] However, this means that scattered rays arising from one direction of incidence may interfere at the detector with those arising from another direction of incidence.

[0010] When the roughness size is comparable to the wavelength, the effect of the roughness on the detected signal is significant and should be considered - especially when using model-based approaches to interpret the detected signal. Summary of the invention

[0011] A system, method, and non-transitory computer-readable medium storing instructions for evaluating an x-ray signal from a disturbed object may be provided.

[0012] A method for evaluating a non-diffuse x-ray signal received from a perturbed object due to illumination by the perturbed object may be provided, the method may include: calculating an estimated field for each of a plurality of non-diffuse objects, the plurality of non-diffuse objects representing a perturbation of the perturbated object; the perturbations having an order of a wavelength of the non-diffuse x-ray signal; and evaluating the non-diffuse x-ray signal based on the fields of the plurality of non-diffuse objects.

[0013] A method, system, and non-transitory computer readable medium for evaluating an x-ray signal may be provided. The method may include estimating a field generated by a disturbance of a disturbance object, the disturbance having an order of a wavelength of the x-ray signal, wherein the estimation includes calculating a general function of the field contributed by a single disturbance in response to the disturbance of the disturbance object, the general function being applicable to the disturbance object of arbitrary shape; and evaluating the x-ray signal based on one or more statistical properties of the field and the disturbance. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to understand the invention and to see how it can be put into practice, a preferred embodiment will now be described, by way of non-limiting example only, with reference to the accompanying drawings:

[0015] Figure 1 A prior art line is shown;

[0016] Figure 2 shows the schematic operation of a prior art x-ray system;

[0017] Figure 3 Examples of reflectance versus angle spectra of disturbed objects and disturbed objects are shown;

[0018] Figure 4 Examples of structural elements are shown;

[0019] Figure 5 An example of a continuous perturbation on a surface is shown;

[0020] Figure 6 Examples of possible interfaces carrying roughness are shown;

[0021] Figure 7 Example showing non-diffuse reflectance at a wavelength of 4.47nm;

[0022] Figure 8 Shows examples of a perturbed object and multiple non-perturbed objects;

[0023] Fig. 9 Examples showing the simulated effect of roughness on periodic structures;

[0024] Fig.10 An example of a method is shown;

[0025] Fig.11 An example of a method is shown;

[0026] Fig.12 An example of signal versus grazing angle is shown;

[0027] Fig.13 An example of a method is shown;

[0028] Fig.14 Examples of perturbed and non-perturbed objects are shown;

[0029] Fig.15 Examples of perturbed and non-perturbed objects are shown;

[0030] Fig.16 An example of signal versus grazing angle is shown;

[0031] Fig.17 An example of a non-perturbed object is shown;

[0032] Fig.18 An example of a non-perturbed object is shown;

[0033] Fig.19 An example of a non-perturbed object is shown;

[0034] Fig. 20A An example of signal versus grazing angle is shown;

[0035] Fig. 20B An example of a method is shown;

[0036] Fig.21 A cross-sectional view of a periodic structure showing conventional scattering measurements using an incident beam with a single angle of incidence;

[0037] Fig. 22 A cross-sectional view of a periodic structure for scattering measurement using incident light beams having multiple incident angles according to an embodiment of the present invention is shown;

[0038] Fig.23 shows a top view of a periodic structure for conventional scattering measurements using an incident beam with a single azimuth angle;

[0039] Fig.24A A top view of a periodic structure for scatterometry using incident beams with multiple azimuth angles according to an embodiment of the present invention is shown, wherein the central axis has a zero azimuth angle;

[0040] Fig. 24B A top view of a periodic structure for scatterometry using incident light beams with multiple azimuth angles according to an embodiment of the present invention is shown, wherein the central axis has a non-zero azimuth angle;

[0041] Fig.25Aspects of an exemplary fin-FET device suitable for low energy X-ray reflectoscatter measurements according to embodiments of the present invention are shown;

[0042] Fig.26 A graph of 0-order reflectivity versus scattering angle silicon (Si) fins having a periodic structure with a 10 nm / 20 nm line / space ratio and corresponding structures according to an embodiment of the present invention;

[0043] Fig. 27 A graph of first order reflectivity versus scattering angle silicon (Si) fins having a periodic structure with a 10 nm / 20 nm line / space ratio and a corresponding structure according to an embodiment of the present invention;

[0044] Fig.28 is a diagram showing a periodic structure measurement system with X-ray reflectometry (XRS) capability according to an embodiment of the present invention; and

[0045] Fig.29 A block diagram of an exemplary computer system according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0046] In the following detailed description, many specific details are set forth in order to provide a thorough understanding of the present invention. However, it should be understood by those skilled in the art that the present invention can be implemented without these specific details. In other cases, well-known methods, processes and components are not described in detail to avoid obscuring the present invention.

[0047] The subject matter which is regarded as the invention is particularly pointed out and distinctly claimed in the concluding portion of the specification. However, the organization and method of operation of the invention, together with objects, features, and advantages thereof, may best be understood by reference to the following detailed description when read in connection with the accompanying drawings.

[0048] It should be understood that for simplicity and clarity of illustration, the elements shown in the figures are not necessarily drawn to scale. For example, for clarity, the size of some elements may be enlarged relative to other elements. In addition, reference numerals may be repeated in the drawings to indicate corresponding or similar elements where deemed appropriate.

[0049] Any reference in this specification to any of a system, a method, and a non-transitory computer-readable medium shall apply mutatis mutandis to any of the system, the method, and the non-transitory computer-readable medium. For example - any reference to a system shall apply mutatis mutandis to a method executable by the system and a non-transitory computer-readable medium that may store instructions executable by the system.

[0050] Because at least one embodiment of the invention shown can be implemented to a large extent using electronic components and circuits known to those skilled in the art, in order to understand and appreciate the basic concepts of the invention and in order not to obscure or distract from the teachings of the invention, the details will not be explained to a greater extent than is deemed necessary as described above.

[0051] Any numbers or values ​​shown below should be considered as non-limiting examples.

[0052] The phrase "A based on B" may mean that A is based only on B or that A is based on B and one or more other elements and / or parameters and / or information. The calculation of A is affected by B and / or the value of A is a function of the value of B.

[0053] The term "evaluate" may refer to measure, estimate, simulate, calculate, approximate, verify, generate a model, and the like.

[0054] Evaluating the x-ray signal may include performing an evaluation of the x-ray signal that should be detected as a result of the irradiation of the object.

[0055] The term "obtaining" may include generating, receiving, etc. For example - receiving a detection signal may include generating a detection signal, illuminating a perturbation object and generating a detection signal, receiving or retrieving a detection signal without generating a detection signal, etc.

[0056] The x-ray signal may be a diffuse x-ray signal and a non-diffuse x-ray signal. An evaluation based on a non-diffuse x-ray signal (rather than based on a diffuse signal) may be referred to as a non-diffuse evaluation. An evaluation based on a diffuse x-ray signal (rather than based on a non-diffuse signal) may be referred to as a diffuse evaluation.

[0057] A solid stack is a structure comprising a stack of layers parallel to each other.

[0058] To simplify the description, most examples refer to rough surfaces and various non-perturbed surfaces that should be horizontal (in the absence of roughness). It should be noted that the horizontal orientation is only an example of an orientation, and the rough surfaces and non-perturbed surfaces can be oriented in any orientation. References to top, upward, top, bottom, bottommost, and downward should apply to any orientation.

[0059] The proposed solutions are considered to be the first solutions applicable to perturbed objects of arbitrary shape - and are not limited to solid stacks. For example, these solutions can be applied to perturbed periodic structures and / or perturbed pseudo-periodic (periodic up to phase) structures or perturbed non-periodic structures.

[0060] Any reference to structure shall apply mutatis mutandis to structural elements, samples, periodic structures, basic units of periodic structures and objects. The various objects, structural elements, samples or structures shown in the various figures may form a grating, or may be arranged in a periodic manner. For example - structural element 61 may be a basic unit of a periodic structure.

[0061] A system, method, and non-transitory computer readable medium storing instructions for evaluating the emission of x-ray signals from a perturbed object of arbitrary shape may be provided.

[0062] The terms disturbance and roughness are used interchangeably. A disturbed object is an object that is affected by the roughness.

[0063] The disturbed surface or rough surface exhibits a roughness on the order of the x-ray wavelength (e.g., between 10% and 1000%). The wavelength of the x-rays can be in the range of 0.01 to 10 nanometers. Thus, the disturbed surface can have nanometer dimensions - for example, between 0.01 nanometers and 80 nanometers, less than 0.01 nanometers or greater than 80 nanometers. A single x-ray beam can form a spot that can simultaneously illuminate multiple elementary units of the periodic structure.

[0064] The detector for detecting x-ray radiation may be a two-dimensional detector and its pixels may be classified into diffuse pixels for sensing diffuse radiation and non-diffuse pixels for sensing non-diffuse radiation. The classification may be for each object and / or for each illumination and / or detection scheme.

[0065] Figure 3 Included are graphs showing examples of simulations describing how the reflectivity (ratio of reflected intensity to incident intensity) of x-rays 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.

[0066] Figure 3 The reflectivity is shown as a function of elevation angle - theta, assuming that both the source and detector produce / capture light through very narrow illumination / collection cones. Since this is a solid stack, the reflected signal is primarily in the specular direction, so the reflection angle is equal to the illumination angle, so a single angle theta is needed to parameterize the plot. Not shown in the figure are the reflectivities for non-specular directions, although these are also present when roughness is present.

[0067] There is also a need to characterize periodic (non-solid) structures that include roughness, and algorithms are needed to evaluate the response of periodic samples with roughness at their interfaces to x-ray irradiation.

[0068] Derivation of the scattered electric field of isolated small perturbations.

[0069] The reflectivity and internal fields of roughness-free (i.e., undisturbed) periodic samples are first evaluated by rigorous well-known solutions to the electromagnetic scattering problem. These are evaluated for two different directions and polarizations of illumination - an arbitrary incident ray, and the reverse direction of an arbitrary outgoing direction.

[0070] In the case of illumination / collection with a finite cone (or other finite shape), superposition is employed to accumulate the contribution from each single direction separately.

[0071] For a given irradiation direction k inc and the input polarization state p inc , at a specific point inside the structural element (r t The internal electric field vector at t) is expressed as follows:

[0072] (0)

[0073] Note again that this field is evaluated for an unperturbed structural element. We show as follows that in order to fully determine the effect of roughness, and under the assumption of “small” perturbations, two different internal electric fields are required:

[0074] a. When the illumination (with unit amplitude and zero phase measured at reference point O) comes from the actual illumination direction k inc and the input polarization state p inc The point generated when (r t , t) at the -infield format is as follows:

[0075] (1)

[0076] b. When the illumination (with unit amplitude and zero phase measured at reference point O) comes from the collection direction k sc and the output polarization state p sc The point generated when the reverse direction is (r t , t) at - infield:

[0077] (2)

[0078] To illustrate how these two fields can be used to determine the diffraction signal from a perturbed profile (not necessarily probabilistic), we first illustrate how to do it for a profile that has been perturbed by a small isolated volume.

[0079] Figure 4 A structural element is shown, which is mainly non-perturbative and made of a first material, which interfaces with an environment (representing, for example, air) having a surrounding material different from the first material. We assume that the object includes a repetition of the structural element, for example a periodic repetition along the horizontal direction, in Figure 4Only a single cycle is depicted.

[0080] The structural element 61 has a smooth outer surface and may be referred to as a nominal surface 62 (in Figure 4 , this is illustrated as the top surface), the nominal surface 62 has a leftmost horizontal portion, followed by a positively sloping portion, followed by another (higher) horizontal portion, followed by a negatively sloping portion, which is followed by a rightmost horizontal portion.

[0081] Figure 4 It shows that the coordinate (r t , 0) is located on the negative slope portion of the reference point 65 - it has a field and The fields at the reference point are as described above. The first coordinate r t represents the position on the outer surface (e.g., a two-dimensional coordinate), and the second coordinate t is at point r t The second coordinate is the distance from the surface at coordinate r t The distance along the normal of surface 65.

[0082] The structural element is slightly perturbed by adding a new element 63 of small volume (relative to the volume of the structural element 61 ).

[0083] The geometry of the new element 63 is determined by specifying its “center of mass” 64 on the nearest boundary surface (at coordinate r t ) and is represented by the distance of its center from the surface (represented by the 1D coordinate t). The new element 63 has a 1D coordinate t. 2 r t (Parallel to Figure 4 The inclined surface orientation in FIG. 4 represents a very small (differential) base area, as well as a small (differential) height dt (measured perpendicular to the surface).

[0084] Instead of evaluating radiation that will be emitted from the structural element and impinge on a point on the detector, the evaluation will take into account "reverse" radiation that will virtually impinge (denoted 33) on the structural element from a point on the detector and will be virtually emitted "backwards" (scattered - denoted 33) from the structural element towards the illumination source.

[0085] exist Figure 4 In FIG. 3 , radiation impinging on the structural element is indicated by 31 , and radiation emitted (eg scattered) from the structural element is indicated by 32 .

[0086] Using these notations, when the unit amplitude zero phase field component (as measured at the same reference point O) is derived from a field with polarization state p inc Direction k inc When the sample is illuminated, the Fourier components of the complex-valued scattered field (amplitude and phase), i.e., the scattered field with polarization state psc Direction k sc , is given by the following expression (under the “small” perturbation approximation): (3)

[0088]

[0089] In this expression:

[0090] E unperturbed is the field that occurs when the disturbance is absent.

[0091] i is the unit imaginary complex number.

[0092] k0 is obtained through the relationship The wave number associated with the wavelength λ.

[0093] ε0 is the dielectric constant of vacuum.

[0094] ε old is the dielectric constant of the material at the volume into which the perturbation is introduced.

[0095] ε New is the dielectric constant of the material at the volume into which the perturbation is introduced.

[0096] We will later use a shorthand notation for the difference between the two dielectric constants.

[0097] (4) Δε=ε New -ε Old

[0098] Note that this difference usually depends on (r t , t).

[0099] If the perturbation is "small enough", equation (3) (also called the "Born first-order approximation") is valid. More precisely, the conditions for its validity are given by:

[0100] (5) {Volume of disturbance}<<1

[0101] Using superposition to generalize to the case of continuous perturbations

[0102] When considering the case of a continuous disturbance on a surface, e.g. Figure 5 Example shown.

[0103] The structural element 61 is disturbed, which is represented by the nominal surface 62 (undisturbed) and the deviation from the undisturbed surface (disturbance).

[0104] For example, the deviation may include a disturbance 66 and another disturbance 66', the disturbance 66' including a plurality of new elements represented by the center of gravity 64 and the reference point 65, such as Figure 4 New components in .

[0105] It can be divided into a collection of many non-overlapping "cubes" that include the continuous geometry of the perturbation so that it is completely covered. Under the first Born approximation, in this case, the separate scattered fields produced by each of these collections of cubes can be superimposed {summed} to give the resulting overall field.

[0106] This sum is mathematically given by the coordinates (r t , t), where the 2D coordinate r t is integrated over the entire nominal surface 62 (e.g., if the object is a periodic structure, the 2D coordinate r of the entire object t can be integrated over the entire periodic structure), although the coordinate t (measured perpendicular to the nominal surface) is the integrated normal from its value at the surface (t=0) to the distance from the surface spanned by the perturbation (e.g. with reference to the reference point 65, the height h (r t )67 is equal to the distance from point 69 (an outer point extending from reference point 65 along the perturbation perpendicular to nominal surface 62)).

[0107] Since the height above (positive value) / below (negative value) the nominal surface 62 depends on the nominal position r t , so the height h itself is r t function, so h=h(r t ). Therefore, the total field scattered by the perturbation distribution is given by equation (6):

[0108]

[0109] where “Sur” is the surface of the perturbed object. Note that in this expression, h(r t ) can acquire positive or negative values ​​to represent perturbations above or below the nominal interface boundary. The value of Δε will acquire the appropriate sign change to faithfully represent the difference in dielectric constant above / below the boundary.

[0110] Equation (6) calculates the field for a particular illumination angle and a single collection angle combination. Equation (6) can be calculated for different combinations of collection angles and illumination angles. For example, assuming the x-ray radiation has a certain numerical aperture - then the field at a certain collection angle can be the sum of the electric fields contributed by different illumination angles within the numerical aperture of the x-ray radiation.

[0111] Different combinations of illumination angles and collection angles are considered to apply mutatis mutandis to all calculations in the specification (eg, intensity calculations).

[0112] Evaluate electric field strength and apply randomness and ergodicity

[0113] The intensity associated with the scattered electric field derived above can now be evaluated by multiplying the field by its complex conjugate.

[0114] (7)I(inc→sc)=E(inc→sc)*E*(inc→sc)

[0115] Among them, we will function the independent variable The long notation of is changed to a shorter notation (inc→sc). Therefore, for a given deterministic perturbation distribution, there is an associated strength.

[0116] Assuming that the area on the sample being illuminated is very large (eg micrometer scale), one can assume that the spot "covers" many different possible contours (nanometer scale) (each contour belonging to another part of the sample, say another pitch).

[0117] We can consider this variation in profile as a random effect representing the probabilistic nature of the rough profile, and further assume that the large size of the dots justifies the assumption that all possible random profiles resulting from the given statistics are present in the illuminated area of ​​the specimen, and that the actual intensity measured is therefore expected to be the average of the intensities over “all possible random profiles”. This assumption, which introduces randomness into the analysis, is henceforth called the ergodic assumption.

[0118] We will express this average using the following mathematical notation:

[0119] (8)

[0120] And using this notation, the strength under the ergodic assumption is given by:

[0121] (9)

[0122] Separation of intensity into "diffuse" and "non-diffuse" terms, and their properties.

[0123] Therefore, the intensity appears as the average of the products of the electric fields. By adding and subtracting the product of the average values ​​of the fields, we can reformulate the expression for intensity as the sum of two terms, as shown in equation (10):

[0124]

[0125] (10)

[0126] The reflected signal in the presence of roughness can therefore be decomposed into two additional terms:

[0127] a. "Non-diffuse" intensity - this carries only the roughness-related mean field squared contribution to the diffraction orders.

[0128] b. "Diffuse" intensity - this describes the effect of roughness related field-field covariance.

[0129] It follows that while the "diffuse" term depends only on the statistics of the roughness at each point along the boundary, and is independent of the statistics at any other point, the "non-diffuse" term also depends on the correlation of the roughness between any two points along the boundary.

[0130] Since the "non-diffuse" term is a sum of functions, each of which depends individually on the perturbation at a single point along the boundary, the correlation between any two perturbations along the surface is not taken into account in this term, and this term can therefore be calculated as if any two such perturbations were perfectly correlated. This correlation greatly simplifies the evaluation of this term, as it allows the effect of roughness to be evaluated without lifting the assumption of periodicity, and thus only affecting the intensity of the diffraction orders, but otherwise without additional signals into directions that are not part of the diffraction orders. This feature is further explained below.

[0131] In contrast, the "diffuse" term is proportional to the field-field covariance, and therefore does include correlation, and requires more statistics of the random distribution in order to evaluate this term.

[0132] The difference between these two terms also affects the angular dependence of the scattered intensity of each term for a given incident direction:

[0133] a. The "non-diffuse" term has no contribution to scattering directions that are not part of the sample's usual (undisturbed) diffraction order directions.

[0134] b. The "diffuse" term generally contributes to scattering in arbitrary directions.

[0135] Represents intensity based on the statistical properties of a random distribution.

[0136] Evaluation of non-diffuse terms

[0137] The expression for the non-diffuse term requires evaluating the average value of the electric field over all possible random distributions away from the boundary:

[0138] (11)

[0139] This average can be based on the and Since each of these fields can be expanded in a Fourier series when viewed as a function of t, their dot product (essentially the perturbation term that goes into equation (6)) can also be recast in this form according to the convolution theorem, where the amplitude of each frequency and the frequency itself are derived from the solution of the unperturbed problem. Thus: (12)

[0141]

[0142] in:

[0143] For a given incident (inc) and scattered (sc) direction, A n (r t ,inc,sc) corresponds to the point r along the boundary t The magnitude of the Fourier component of . Its value can be retrieved by solving the unperturbation problem.

[0144] For a given incident (inc) and scattered (sc) directions, k n (r t ,inc,sc) corresponds to the point r along the boundary t The frequency of the Fourier component of . Its value can also be retrieved by solving the unperturbation problem.

[0145] For periodic structures, 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.

[0146] The expression in equation (12) still needs to be in t (from 0 to h), in r t The integration is then performed over all possible values ​​of h and the average needs to be taken. Assuming the probability density function of h is known and given by f(h), the average electric field can be estimated via equation (13): (13)

[0148]

[0149] Typically, the integral over h can be evaluated numerically, but there are cases where it can be evaluated analytically. For example, if f(h) is a Gaussian distribution function with mean 0 and standard deviation σ, then the integral over t and h in Equation 10 can be evaluated analytically and given by A n (r t ,inc,sc) and k n (r t ,inc,sc), both of which are known from the solution of the undisturbed problem.

[0150] Evaluation of Diffuse Term

[0151] This term requires more complex evaluation. It is proportional to the covariance of the field and thus involves the correlation of the perturbations between any two points along the boundary. It is therefore also necessary to know the function g(h, h′; r t , r′ t )-the perturbation along the boundary at point rt between h and h+dh and at point r t r′t The joint probability function between h' and h'+dh'. This is also a characteristic of a rough boundary. Using this function, the mean of the field-field product (which is part of the definition of the field-field covariance) can then be evaluated using equation (14): (14)

[0153]

[0154] Figure 6 An example of two possible interfaces carrying roughness is shown in . A first part 71 of the object has a first roughened surface 73 and a second part 72 of the object has a second disturbed surface 74 .

[0155] Due to 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) is solved by adding the contribution intensity from each boundary separately (assuming that the roughness between two points belonging to two different boundaries is uncorrelated).

[0156] Figure 7 Included are curves 81-86, which show examples of non-diffuse reflectance at a wavelength of 4.47 nm from roughness bearing roughness samples consisting of oxide layers with varying thicknesses deposited on a silicon substrate. The figure shows both measurements and simulations, and highlights the need to introduce roughness to properly simulate the observed roughness effects.

[0157] Figure 8 An example simulated effect of roughness on a periodic structure is shown (see curves 91 representing the roughness of the top surface with a standard deviation of 20 angstroms, a smooth top surface and 94), the structure 95 being made of oxide lines etched on a silicon substrate. The uppermost interface of the line has roughness and the effect of the non-diffuse part of the signal on all diffraction orders is shown compared to the case without roughness.

[0158] Fig. 9 An example of method 200 is shown.

[0159] The method 200 may be used to evaluate x-ray signals received from a perturbed object due to illumination of the perturbed object.

[0160] This model can be used for various purposes, for example by determining the roughness of the disturbed object.

[0161] For example, reference models of the disturbed object with different roughness values ​​may be generated. Once the disturbed object being evaluated is evaluated, the x-ray signal received from the object being evaluated may be compared with the reference model to find one or more similar reference models. The roughness of the disturbed object being evaluated may be determined based on the roughness of the one or more similar reference models.

[0162] Method 200 may begin at step 210 of estimating a field produced by a disturbance of a perturbed object. The disturbance is of the order of the wavelength of the x-ray signal.

[0163] Step 210 may include calculating (step 220) a general function of the field contributed by a single disturbance in response to the disturbance of the object.

[0164] The general function is applicable to perturbed objects of different shapes, such as perturbed objects of arbitrary shapes. It is not only applicable to perturbed objects including multiple layers parallel to each other.

[0165] Step 220 may include at least some of steps 221 , 222 , 223 , and 224 .

[0166] Step 221 may include calculating the general function by integrating a first integrable function that is independent of the shape of the perturbed object.

[0167] Step 221 may include integrating a first integrable function based on (a) the difference in dielectric constant coefficient (Δε) between the perturbed object and its surroundings at the location of one of the individual perturbations, (b) the field contributing to the illumination of one of the individual perturbations at the illumination angle (see equation (1)), and (c) the field contributing to the collection of illumination from the individual perturbations at a particular collection angle (see equation (2)).

[0168] See equation (6) - the first integrable function can be

[0169] The field contributing to the collection of illumination from a single perturbation at a particular collection angle is calculated by calculating the field contributing to the illumination of one of the single perturbations from the illumination angle relative to the collection angle. See e.g.

[0170] Step 222 may include calculating the general function by (a) first integrating the first integrable function over a range of heights to provide a second integrable function, the range of heights representing the height of one of the individual disturbances relative to an unperturbed version of the perturbed object. See equation (6) - o and h(r t ) is the first integral between .

[0171] 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 perturbations onto an unperturbed version of the surface of the perturbed object. This area may be represented in equation (6) as d 2 r t .

[0172] Step 224 may include: performing a second integration of the third integrable function over one or more surfaces of the perturbed object to provide a fourth function; and adding to the fourth function an estimate of the field generated by illuminating the non-perturbed version of the perturbed object. For equation (6), see the nominal interface surface The double integral on .

[0173] Step 220 may be followed by step 240 of performing an evaluation based on one or more statistical characteristics of the field and the disturbance.

[0174] Step 240 may include at least one of steps 241 , 242 , 243 , 244 , 245 , 246 , and 247 .

[0175] Step 241 may include evaluating the roughness of the disturbed object.

[0176] Step 242 may include evaluating an x-ray signal generated from a disturbed object having a given roughness.

[0177] Step 243 may include determining one or more other characteristics of the disturbed object (other than roughness).

[0178] Step 244 may include validating the roughness estimate.

[0179] Step 245 may include evaluating the strength of the x-ray signal based on statistics of the field and the amount of disturbance of the disturbed object.

[0180] Step 246 may include calculating a diffuse intensity and calculating a non-diffuse intensity.

[0181] Step 247 calculates the non-diffuse intensity by averaging the fields obtained over possible perturbed versions of the perturbed object. See, e.g.

[0182] Step 247 may include calculating multiple integrals over various functions, wherein the calculation of the multiple integrals includes calculating an initial integral between (a) the field contributing to the illumination of one of the single perturbations at the illumination angle and (b) the field contributing to the collection of illumination from the single perturbation at a particular collection angle.

[0183] Step 247 may include computing the dot product by computing a Fourier series representing the dot product.

[0184] The x-ray signal may be a diffuse x-ray signal, and step 240 may include calculating an intensity of the diffuse x-ray signal.

[0185] The x-ray signal may be a non-diffuse x-ray signal, and step 240 may include calculating an intensity of the non-diffuse x-ray signal.

[0186] 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.

[0187] Step 240 may include confirming or determining the intensity of the diffuse x-ray signal based on the intensity of the non-diffuse x-ray signal.

[0188] Step 240 may include determining a characteristic of the disturbed object based on the intensity of the non-diffuse x-ray signal and the intensity of the diffuse x-ray signal.

[0189] The method 200 may be performed based on real illumination of a real perturbation object.

[0190] Additionally or alternatively, the method 200 may be performed based on a simulated irradiation of the perturbation object.

[0191] The method 200 may be performed multiple times on perturbed objects (simulated or real) having different roughnesses to provide an estimate of the x-ray signal obtained when irradiating the perturbed objects having different roughnesses.

[0192] These estimates can be used to determine the roughness of newly evaluated disturbance objects.

[0193] Fig.10 An example of a method 300 for evaluating a non-diffuse x-ray signal received from a perturbed object due to illumination of the perturbed object is shown.

[0194] The method 300 may include a step 310 of calculating a plurality of non-perturbed objects representing a perturbation of a perturbed object. The perturbation of the perturbated object is of the order of the wavelength of the non-diffuse x-ray signal.

[0195] Step 310 may be followed by step 320 of computing an estimated field for each of a plurality of non-perturbed objects representing a perturbation of the perturbed object.

[0196] Step 320 may be followed by step 330 of evaluating a non-diffuse x-ray signal based on a field of a plurality of non-perturbed objects.

[0197] Each of the perturbation object and the plurality of non-perturbation object interfaces may have a uniform dielectric constant.

[0198] The disturbance of the disturbed object may follow a disturbance distribution function. Step 310 may include calculating the plurality of non-disturbed objects based on the disturbance distribution function.

[0199] The disturbance distribution function may be a probability function of a height parameter of a disturbance of the disturbed object.

[0200] The height parameter of a given protrusion in relation to the interface of the perturbed object is the distance between the protrusion and the interface of the perturbed object, wherein the given protrusion belongs to the perturbation.

[0201] The perturbed object may have a single rough interface. The plurality of non-perturbed objects may have corresponding non-perturbed interfaces, each of the plurality of non-perturbed objects having a corresponding non-perturbed interface.

[0202] The perturbation distribution function of the perturbed height parameter of a single rough interface may be substantially equal to the perturbation distribution function of the height parameter of a corresponding given unperturbed interface.

[0203] The 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. The multiple non-perturbed objects may have different non-perturbed surfaces representing combinations of perturbation distribution functions of the multiple rough interfaces. Different combinations of positions of non-perturbed interfaces representing different rough interfaces should be evaluated.

[0204] Fig. 9 An example of a plurality (N) of non-perturbing objects 1101(1)-1101(N) having non-perturbing surfaces 1101(1)-1103(N), one for each non-perturbing object, is shown, which represents a perturbing object 1100 having a perturbing surface 1103. The plurality of non-perturbing objects is shown to include a non-perturbing object 1101(M) having a non-perturbing surface 1101(M).

[0205] exist Fig. 9 In FIG. 1 , points along the disturbed surface 1103 are distributed by a height distribution (eg, having a y-axis coordinate). The heights of the non-perturbed surfaces 1101 ( 3 )- 1103 (N) may follow the height distribution of the disturbed surface.

[0206] The height of the non-perturbed surface 1103 ( 1 ) represents the highest point of the perturbed surface 1101 .

[0207] The height of the non-perturbed surface 1103 (N) represents the lowest point of the perturbed surface 1101 .

[0208] The height (M) of the non-perturbed surface 1103 represents the midpoint of the perturbed surface 1101 .

[0209] exist Fig. 9 There is a single example of the highest point, a single example of the lowest point, and two examples of intermediate heights. This can be represented by the number of non-perturbed objects assigned to each height, the weights associated with the calculations related to each height, etc.

[0210] Fig. 9 Also shown are points 1104 and 1104(1)-1104(N) where the field is calculated. The field can be calculated at any reference point.

[0211] Fig.11 An example of a method 300 for evaluating a non-diffuse x-ray signal received from a perturbed object due to illumination of the perturbed object is shown.

[0212] Method 300 may begin with step 310 of calculating an unperturbed object representing a perturbed object, wherein the unperturbed object includes one or more variable permittivity regions representing uniform permittivity regions of one or more perturbed objects.

[0213] Step 310 may be followed by step 320 of calculating an estimated field of the non-perturbed object.

[0214] Step 320 may be followed by step 330 of evaluating the non-diffuse x-ray signal based on the estimated field of the non-perturbed object.

[0215] The perturbation of the perturbation object may follow a perturbation distribution function, wherein a variable dielectric constant of the one or more regions is calculated based on the perturbation distribution function.

[0216] In the region of variable dielectric constant, the dielectric constant may vary in any manner: continuous, discontinuous, stepped, graded, etc. To simplify the description, some of the following examples show sub-regions within the region of variable dielectric constant that form a step change in dielectric constant.

[0217] Step 310 may include replacing the perturbed object region with a plurality of non-perturbed object sub-regions having different dielectric constants from each other. The plurality of non-perturbed object sub-regions may be multi-layered or may have any other shape.

[0218] The plurality of non-disturbance object sub-regions may include (a) an upper disturbance sub-region located above a nominal surface of the disturbance object region, and (b) a lower disturbance sub-region located below the nominal surface of the disturbance object region.

[0219] The perturbed object has a perturbed object region with a nominal surface. The nominal surface of the perturbed region is a non-perturbed version of the perturbed region.

[0220] The upper perturbation sub-region and the lower perturbation sub-region may have a thickness equal to the coefficient multiplied by the standard deviation of the perturbation distribution function of the perturbation of the perturbation object.

[0221] The dielectric constant of the upper perturbation sub-region may be different from the dielectric constant of the lower perturbation sub-region, and the dielectric constant of the upper perturbation sub-region and the dielectric constant of the lower perturbation sub-region are the weighted sum of (a) the dielectric constant (ε1) of the disturbance object region and (b) the dielectric constant (ε2) of another region connected to the disturbance object region.

[0222] The following figures show examples of computing the field for a non-perturbed object instead of computing the field for a perturbed object.

[0223] Fig.12 An example of signal versus grazing angle is shown. Curve 111 shows this relationship for a grating (object) without roughness, curve 112 shows this relationship for a perturbed object, and point 113 shows the relationship based on an evaluation of N=100 non-perturbed objects representing a perturbed object.

[0224] Fig.13 An example of method 400 is shown.

[0225] The method 410 may begin with step 410 of calculating a non-perturbed object representing a perturbed object, wherein the non-perturbed object includes one or more variable permittivity regions representing one or more perturbed object regions having a uniform permittivity.

[0226] Step 410 may be followed by step 420 of calculating an estimated field of the non-perturbed object.

[0227] Step 420 may be followed by step 430 of evaluating the non-diffuse x-ray signal based on the estimated field of the non-perturbed object.

[0228] Fig.14 A perturbed object 120 and a non-perturbed object 126 are shown with a non-perturbed region 127 of variable dielectric constant.

[0229] The disturbed object 120 comprises a disturbed region 121 (with uniform permittivity ε1) with a rough surface 123. The reflected field is averaged over many of these profiles and is characterized by a common disturbance distribution function (taken as Gaussian in the example of the figure), which is equivalent to the field obtained from a non-perturbed object 126 with a non-perturbed region 127 with a variable permittivity, such as a graded disturbed object with a plane orthogonal to the rough surface 123 of the disturbed object 120. The graded permittivity is a weighted sum of the variations along the normal according to the cumulative distribution function, which is in Fig.14 In the case of , it can be the error function and the complementary error function.

[0230] The disturbance object 120 includes a disturbance region 121 (with a uniform dielectric constant ε1) having a rough surface 123, and also includes other regions 122. The disturbance object is connected to a surrounding environment 124 (air or another object) having another dielectric constant (ε2).

[0231] The non-perturbed object 126 has a non-perturbed region 127 of variable dielectric constant and another region 122. The dielectric constant value of each point of the non-perturbed region 127 of variable dielectric constant is represented by the gray scale at the point.

[0232]

[0233] A method is provided which may require cutting the contour of an object along its axial (up-down) direction to form each layer having a uniform dielectric constant.

[0234] Fig.15 An example of a perturbed object 170 is shown having a top region with a dielectric constant ε1 and having a rough interface 171. The height distribution of the rough surface has a standard deviation σ.

[0235] The disturbed object 170 is represented by the non-disturbed object 173, and the rough interface is represented by a plurality of (R) upper layers 174(1)-174(R) and a plurality of (R) lower layers 175(1)-175(R). The dielectric constant of the upper layer is determined by the cumulative distribution function and the distance of the layer from the plane representing the rough interface.

[0236] The total height of all upper floors is denoted as h up .

[0237] The total height of all lower layers is denoted as h down .

[0238] The effective dielectric constant of all layers is denoted as ε and is a function of the variable t, which represents the position relative to the nominal top surface (smooth).

[0239]

[0240] h up =h down =4σ

[0241] By varying the number of layers chosen, graded refractive index profiles can be approximated with increasing accuracy.

[0242] Fig.16 An example of the relationship between the signal of the zero-order field and the grazing angle is shown.

[0243] a. Non-perturbed plant - curve 181.

[0244] b. Object with R=1—curve 182 .

[0245] c. Object with R=2—curve 183 .

[0246] d. Subject with R=5—curve 184 .

[0247] e. Object with R=10—curve 185 .

[0248] f. Object with roughness—curve 186 .

[0249] Fig.16 It is shown that the more layers used, the more accurate the approximation of the graded refractive index. Fig.16The right graph of focuses on a specific angle of incidence and shows how the exact result (curve 181) can be better approximated by increasing the number of layers (curve 182). For reference, curve 181 represents the non-perturbed object.

[0250] The computation time associated with field assessment is proportional to the number of layers, and it may be desirable to reduce the number of layers to speed up computation time.

[0251] To do this in the case of rough interfaces, without sacrificing accuracy, it may be necessary to optimize the thickness and dielectric constant of the layers by requiring them to best match the effect of the perturbation with the normal distance to the interface, up to some given order of the field.

[0252] To achieve a second-order best match in this area, it was found that one could use above-interface and below-interface monolayers with a specific thickness (proportional to the roughness) and a specific dielectric constant (which is some fixed weighted sum of the dielectric constants of the materials above and below the roughness-free interface).

[0253] Each of the two layers may include two parts on the right and left sides of the center of the object. S, e.g. Fig.17 .

[0254] Fig.17 An example of a non-disturbance object 130 including a bottom region 133 (having an inverted T-shape), a lower layer 131, an upper layer 132, and other regions 122 is shown. The lower layer 131 and the upper layer 132 represent a single disturbance region (in Fig.14 The interface between the lower layer and the upper layer 132 is located at plane 125 which represents the nominal surface of the disturbance zone.

[0255] The height of the upper layer 132 is denoted as h eff1 , the height of the bottom layer 132 is represented by h eff2 , the dielectric constant of the upper layer is denoted as ε eff1 , the dielectric constant of the bottom layer is denoted as ε eff2 .

[0256]

[0257] To optimally match fields up to order 4, two upper and two lower layers are required, as Fig.18 shown.

[0258] Fig.18 An example of a non-perturbed object 140 including a bottom region 145 (having an inverted T-shape), a lowest layer 142, a lower layer 144, a top layer 141, an upper layer 143, and other regions 122 is shown. The lowest layer 142, the lower layer 144, the top layer 141, and the upper layer 143 represent a single perturbed region (in Fig.14 121 in FIG.

[0259] The height of the top layer 141 is denoted as h eff1 , the height of the lowest layer 142 is denoted as h eff2 , the height of the upper layer 143 is represented by h eff3 , and the height of the lower layer 144 is denoted as h eff4 .

[0260] The dielectric constant of the top layer 141 is denoted as ε eff1 , the dielectric constant of the lowest layer 142 is represented by ε eff2 , the dielectric constant of the upper layer 143 is expressed as ε eff3 , and the dielectric constant of the lower layer 144 is expressed as ε eff4 .

[0261]

[0262] h eff1 =h eff2 =(2.15-0.773)σ

[0263] h eff3 =h eff4 =0.773σ

[0264]

[0265] To best match the field up to the sixth order, three upper and three lower layers are required, e.g. Fig.19 shown.

[0266] Fig.19 An example of a non-perturbed object 150 is shown, which includes a bottom region 159 (having an inverted T-shape), a lowest layer 152, a lower middle layer 154, a lower layer 156, a top layer 151, an upper middle layer 153, an upper layer 155, and other regions 122. The lowest layer 152, the lower middle layer 154, the lower layer 156, the top layer 151, the upper middle layer 153, and the upper layer 155 represent a single perturbed region (in Fig.14 121 in FIG.

[0267] The height of the top layer 151 is denoted as h eff1 , the height of the lowest layer 152 is denoted as h eff2 , the height of the upper intermediate layer 153 is represented by h eff3 , the height of the lower intermediate layer 154 is denoted as h eff4 , the height of the upper layer 155 is denoted as h eff5 , the height of the lower layer 156 is denoted as h eff6 .

[0268] The dielectric constant of the top layer 151 is denoted as ε eff1 , the dielectric constant of the lowest layer 152 is denoted as εeff2 , the dielectric constant of the upper intermediate layer 153 is expressed as ε eff3 , the dielectric constant of the lower intermediate layer 154 is expressed as ε eff4 , the dielectric constant of the upper layer 155 is expressed as ε effs , the dielectric constant of the lower layer 156 is expressed as ε eff6 .

[0269]

[0270] h eff1 =h eff2 =(2.7735-1.4321-0.456)σ

[0271] h eff3 =h eff4 =(1.4321-0.456)σ

[0272] h eff5 =h eff6 =0.456σ

[0273] Fig. 20A An example of signal versus grazing angle for a non-perturbed object (curve 161) is shown when using a graded dielectric constant method (representing a perturbed region with a layer having thickness between 0 and 4σ), see curve 162, where the object is the path - curve 163, and for the optimal layer, see curve 164.

[0274] Fig. 20B An example of method 601 is shown.

[0275] Method 601 may include steps 610 , 620 , and 630 .

[0276] Step 610 may include obtaining a detection signal indicative of an x-ray signal received by a sensor from a perturbation object due to illumination by the perturbation object.

[0277] Acquiring may include generating a detection by a sensor, simulating a detection signal, or receiving a detection signal from a storage unit or any other source.

[0278] Step 610 may be followed by step 620 of performing at least one model-based assessment related to the disturbance object based on the detection signal.

[0279] Step 620 may include a step 622 of comparing the detection signal to a reference detection signal associated with a reference model of a reference disturbance object associated with one or more reference parameters.

[0280] Any of the steps of methods 200 , 300 , and 400 may be used to calculate the reference model.

[0281] Step 622 may be followed by step 624, selecting one or more selected reference models of the reference disturbance object, and determining parameters of the disturbance object based on parameters of the one or more selected reference models of the reference disturbance object. Any selection parameters may be best match, distance-based selection, etc.

[0282] Step 624 may be followed by step 626 of setting one or more parameters of the disturbance object to one or more parameters of the selected reference disturbance object modeled by the selected reference model. This may include applying interpolation, interpolation, weighted sums of any other functions using statistical functions when there is more than one selected reference model.

[0283] One or more parameters of the disturbed object may be related to the roughness, related to the size of the disturbed object, and the like.

[0284] The reference model may be calculated in any manner—eg, by applying any of the steps of methods 200 , 300 , and 400 .

[0285] Step 620 may include at least one of the following:

[0286] a. Measure the roughness of the disturbed object.

[0287] b. Measuring the roughness of the disturbed object, and (b) performing additional evaluations related to the disturbed object.

[0288] c. Perform additional evaluation based on the roughness of the disturbed object.

[0289] d. Measure dimensions related to the disturbed object.

[0290] e. Determine the standard deviation of the roughness of the disturbed object and the correlation length of the roughness based on the diffuse signal.

[0291] f Non-diffuse based model for determining the disturbance signal based on correlation.

[0292] g. After obtaining a model of the disturbed object - modifying the model. The model is determined based on one or more statistical properties of the field and the disturbance.

[0293] h. After obtaining a model of the perturbed object - modifying the model. The model is based on additional information about the perturbation model. The additional information is not based on the detection signal indicative of the x-ray signal.

[0294] i. Evaluate the diffuse-based roughness of the perturbed object.

[0295] j. Modify the non-diffuse based model of the perturbed object.

[0296] U.S. Patent 9588066, which is incorporated herein by reference, describes a system for measuring periodic structures. The periodic structure includes a repetition of a basic unit. Examples of basic units are shown in the previous figures and text, and are also shown in the following text and figures.

[0297] The system described in US patent 9588066 may be modified to apply any of the methods described above. Additionally or alternatively, measurements taken by the system shown in US patent 9588066 may be used as input to the methods described above.

[0298] Embodiments relate to methods and systems for measuring periodic structures using multi-angle X-ray reflectometry (XRS).

[0299] In one embodiment, a method for measuring a sample by X-ray reflection scattering includes impinging an incident X-ray beam on a sample having a periodic structure to generate a scattered X-ray beam, the incident X-ray beam simultaneously providing multiple incident angles and multiple azimuth angles. The method also includes collecting at least a portion of the scattered X-ray beam.

[0300] In another embodiment, a system for measuring a sample by X-ray reflection scattering includes an X-ray source for generating an X-ray beam having an energy of about 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 located between the X-ray source and the sample holder. The monochromator is used to focus the X-ray beam to provide an incident X-ray beam to the sample holder. The incident X-ray beam has multiple incident angles and multiple azimuth angles at the same time. The system also includes a detector for collecting at least a portion of the scattered X-ray beam from the sample.

[0301] Methods and systems for measuring periodic structures using multi-angle X-ray reflectometry (XRS) are described. In the following description, many specific details, such as X-ray beam parameters and energies, are set forth in order to provide a thorough understanding of embodiments of the present invention. It will be apparent to those skilled in the art that embodiments of the present invention may be practiced without these specific details. In other cases, well-known features such as entire semiconductor device stacks are not described in detail in order to avoid unnecessarily obscuring embodiments of the present invention. In addition, it should be understood that the various embodiments shown in the figures are illustrative representations and are not necessarily drawn to scale.

[0302] One or more embodiments described herein relate to the use of an X-ray source configured in a manner to perform X-ray reflection scattering measurements using multiple incident beam angles simultaneously incident on a periodic (grating) structure. Embodiments can detect scattered light in two angular directions, and use the reflected X-ray intensity to infer the shape and spacing of the periodic structure. Embodiments can provide precision and stability measurements of the shape and size of complex two-dimensional (2D) and three-dimensional (3D) periodic structures in a semiconductor manufacturing environment. Such measurements can include the shape profile of the periodic structure, as well as the dimensions of the periodic structure, such as width, height, and sidewall angle.

[0303] To provide context, prior art shape metrology solutions utilize optical techniques with spectral sources of single wavelength or nominal wavelength greater than 150 nanometers. Spectroscopic solutions are typically fixed wavelength, and single wavelength sources where the angle of incidence can vary. Such solutions are in the wavelength / energy regime where 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 limit.

[0304] According to one embodiment, by using a wavelength of light with λ / d<1, higher order scattering levels are available for detection and provide direct sensitivity to parameter d. More specifically, by using a wavelength of light that is smaller than the width and height of the structure being measured, multiple periods of interference fringes are available and provide sensitivity to height, width, and line shape. In one embodiment, by using multiple angles of incidence as well as azimuths (e.g., directions symmetric relative to the structure), three-dimensional information is obtained, providing three-dimensional shape sensitivity. The information obtained involves dimensions that can seriously affect the performance of the device and need to be controlled to very tight tolerances.

[0305] To help conceptualize the concepts covered in this article, Fig.21 A cross-sectional view of a periodic structure showing conventional scattering measurements using an incident beam with a single angle of incidence. Fig.21 , a periodic structure 100 (also referred to as a grating structure) is acted upon by a light beam 102. The light beam 102 has an incident angle relative to a horizontal plane 104 of the uppermost surface of the periodic structure 100. A scattered light beam 106 is generated from the periodic structure 100. The scattered light beam 106 may include light beams with different scattering angles, each light beam providing information of a different order of the periodic structure 100. For example, Fig.21 As shown, three orders are shown, n=1, n=0, n=−1, wherein the scattering angle of the n=−1 order has an angle θ relative to the horizontal plane 104 of the uppermost surface of the periodic structure 100 . Fig.21 The arrangement is an example of conventional OCD or GISAS scatterometry.

[0306] It should be understood that the term "periodic" or "grating" structure used throughout this document refers to non-planar structures, and in some contexts, may be considered as three-dimensional structures. For example, referring again to Fig.21 , the periodic structure 100 has features 108 protruding in the z-direction with a height h. Each feature 108 also has a width w along the x-axis and a length along the y-axis (i.e., into the page). However, in some contexts, the term "three-dimensional" is reserved for describing periodic or grating structures having a length along the y-axis of the same order as the width w. In such contexts, the term "two-dimensional" is reserved for describing periodic or grating structures having a length along the y-axis that is substantially longer than the width w, e.g., several orders of magnitude longer. In any case, a periodic or grating structure is a structure having a non-planar topography within a measurement area, such as a semiconductor wafer or substrate.

[0307] and Fig.21 on the contrary, Fig. 22 A cross-sectional view of a periodic structure illustrating scatterometry using incident light beams having multiple incident angles according to one embodiment. Fig. 22 , the periodic structure 100 is subjected to the action of a cone-shaped X-ray beam 202. The cone-shaped X-ray beam 202 has a central axis 203 having an incident angle relative to a horizontal plane 104 of the uppermost surface of the periodic structure 100. Thus, the cone-shaped X-ray beam 202 includes a beam having an incident angle A. The conical X-ray beam 202 has a convergence angle It is taken between the outermost portion B and the outermost portion C of the cone beam 202. Since the cone X-ray beam 202 has a convergence angle The portion of the cone beam 202 near the outside of the cone thus has a different angle of incidence on the structure 100 than the portion of the cone beam 202 aligned with the central axis 202. Thus, the cone beam 202 simultaneously provides a plurality of angles of incidence taken relative to the horizontal plane 104 for striking the periodic structure 100. A scattered beam 206 is generated from the periodic structure 100. The scattered beam 206 may include portions of different information levels attributable to the periodic structure 100, examples of which are described in more detail below.

[0308] In addition to having an angle of incidence, the incident beam can also have an azimuthal angle relative to the periodic structure. Again for conceptual purposes, Fig.23 A top-down view of a periodic structure is shown for conventional scattering measurements using an incident beam with a single azimuth angle. Fig.23 , the periodic structure 100 is shown from above the protrusion 108. Fig.21, the incident light beam 102 may also have an azimuthal angle θg relative to a direction x that is perpendicular to the protrusions 108 of the periodic structure 100. In some cases, θg is non-zero, such as Fig.23 In the case where θg is zero, the direction of the beam 102 is in the x direction relative to the top-down view. However, in all cases where conventional OCD or GISAS scatterometry is applied, the beam 102 has only one angle θg. Therefore, Fig.21 and Fig.23 Putting it all together, traditionally, using a single angle of incidence and a single beam at an azimuth angle θg to perform scatterometry.

[0309] and Fig.23 On the contrary, according to the embodiment, Fig.24A and Fig. 24B A top view of a periodic structure is shown for scattering measurements using incident beams with multiple azimuth angles. Fig.24A and Fig. 24B , the periodic structure 100 carries a conical X-ray beam 202 having a central axis 203, such as in combination with Fig. 22 Although from Fig. 22 , the cone-shaped X-ray beam 202 also has a dimension in the y direction. That is, the convergence angle between the outermost portion B and the outermost portion C of the cone-shaped beam 202 is Multiple angles of incidence along the y-direction are also provided, for example, non-zero azimuthal angles of incidence are provided.

[0310] Reference only Fig.24A , the central axis of the cone X-ray beam 202 has a zero angle θg along the x-direction relative to the top-down view. Thus, portion A of the cone X-ray beam 202 has a zero azimuth angle. Nevertheless, portions B and C of the cone X-ray beam 202 have non-zero azimuth angles, even though the central axis 203 of the cone X-ray beam 202 is orthogonal to the periodic structure 100.

[0311] Reference only Fig. 24B , the central axis of the cone X-ray beam 202 has a non-zero angle θg along the x-direction relative to a top-down view. Thus, portion A of the cone X-ray beam 202 has a non-zero azimuth angle. Additionally, portions B and C of the cone X-ray beam 202 have non-zero azimuth angles that are different from the azimuth angle of portion A of the beam 202.

[0312] exist Fig.24A and Fig. 24B In both cases shown, since the cone beam 202 has a convergence angle The portion of cone beam 202 near the outside of the cone has a different azimuth angle incident on periodic structure 100 than the portion of cone beam 202 aligned with central axis 202. Thus, cone beam 202 provides multiple azimuth angles to impinge on periodic structure 100 simultaneously with respect to the x-direction.

[0313] Therefore, Fig. 22 and Fig.24A or Fig. 24B In one embodiment, a method for measuring a sample by X-ray reflection scattering includes causing an incident X-ray beam to be incident on a sample having a periodic structure. The X-ray beam has a cone shape to provide multiple incident angles simultaneously when incident on the periodic structure. and multiple azimuthal angles θg. The impact produces a scattered X-ray beam, a portion (if not all) of which can be collected in order to gather information about the periodic structure.

[0314] In one embodiment, the incident X-ray beam is a converging angle A converging X-ray beam in the range of about 20-40 degrees. In one such embodiment, the central axis of the converging X-ray beam has a fixed non-zero angle of incidence relative to the sample. and zero azimuth angle θg, such as combined Fig.24A In another such embodiment, the central axis of the converging X-ray beam has a fixed non-zero angle of incidence relative to the sample. and non-zero azimuth angle θg, such as combined Fig. 24B In either case, in a particular embodiment, the central axis of the converging X-ray beam has a fixed non-zero angle of incidence approximately in the range of 10-15 degrees from the horizontal. In another specific embodiment, the outermost portion of the cone of the beam and the portion closest to the periodic structure, such as Fig. 22 Portion C is shown having an angle of about 5 degrees relative to the horizontal plane of the periodic structure.

[0315] In other embodiments, examples of which are described in more detail below, it is preferred to use a narrower cone. For example, in one embodiment, the incident X-ray beam is a converging X-ray beam having a convergence angle in the range of about 2-10 degrees. In one such embodiment, the central axis of the converging X-ray beam has a fixed non-zero angle of incidence relative to the sample. and zero azimuth angle θg, such as combined Fig.24A In another such embodiment, the central axis of the converging X-ray beam has a fixed non-zero angle of incidence relative to the sample. and non-zero azimuth angle θg, such as combined Fig. 24B as described.

[0316] In one embodiment, a low energy X-ray beam is irradiated on the periodic structure. For example, in one such embodiment, the low energy X-ray beam has an energy of about 1 keV or less. Using such a low energy source can allow for a larger angle of incidence, but with a smaller achievable spot size. In one embodiment, the low energy X-ray beam is a Kα beam generated from a source such as, but not limited to, carbon (C), molybdenum (Mo), or rhodium (Rh).

[0317] In one embodiment, a low energy X-ray beam is focused using an annular multilayer monochromator before striking the periodic structure. In one such embodiment, the monochromator provides an incident angle range of approximately + / -30 degrees and an azimuth angle range of approximately + / -10 degrees. In a particular such embodiment, the annular multilayer monochromator provides an incident angle range of approximately + / -20 degrees. It should be understood that the conical X-ray beam described herein may not or need not be collimated. For example, in one embodiment, between focusing the beam on the above-mentioned monochromator and irradiating the focused beam on the periodicity, the beam is not collimated. In one embodiment, the focused low energy X-ray beam is incident on the sample with an incident angle range of angles less than the nominal first order angle at zero degrees.

[0318] Reference again Fig. 22 In one embodiment, at least a portion of the scattered X-ray beam 206 is collected using a detector 250. In one such embodiment, a two-dimensional detector is used to simultaneously sample the scattered signal intensity of the portion of the scattered X-ray beam 206 scattered from multiple incident angles and multiple azimuth angles. The collected signals can then be subjected to a scatterometry analysis, for example, where an inversion of the scattering data is compared to theory to determine 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 relative to the sampled scattering signal intensity, such as by rigorously solving Maxwell's equations on the periodic structure. In one embodiment, the X-ray beam impinging on the sample has a wavelength that is smaller than the periodicity of the periodic structure 100. Therefore, the detection wavelength is comparable to or smaller than the fundamental structure size, providing a richer data set from the scattered beam 206 compared to OCD scatterometry.

[0319] As described above, in an embodiment, the incident cone X-ray beam for XRS is a converging angle A converging X-ray beam in the range of approximately 20-40 degrees. This relatively wide cone angle can produce a scattered beam that includes higher order diffraction data in addition to zero order reflection data. Thus, in one embodiment, zero order and higher order information is obtained in parallel with a single impact operation.

[0320] In other cases, it may be desirable to separate zero-order reflection data from higher order diffraction data. In one such embodiment, a relatively narrow cone angle may be used, for example, the incident X-ray beam is a converging X-ray beam having a convergence angle in the range of about 2-10 degrees. More than one measurement may be made using a relatively narrow cone angle. For example, in one embodiment, a first measurement is made with the central axis of the converging beam having an azimuth of zero, such as in combination with Fig.24A A second measurement is then performed in the case where the central axis of the converging beam has a non-zero azimuth angle, such as in combination with Fig. 24B In a specific embodiment, a first measurement is performed in a sequential manner to collect 0th order rather than 1st order diffraction data of a sample having a periodic structure. A second measurement is performed to collect 1st order rather than 0th order diffraction data of a sample having a periodic structure. In this way, when generating a scattered beam, zeroth order data can be separated from higher order data.

[0321] Again with respect to parallel and sequential methods, according to an embodiment described herein, X-ray reflection scattering measurement is used to separate different orders on an array detector by approaching at a non-zero azimuth angle. In many cases, higher orders are more useful. In one case, throughput can be improved by obtaining all orders cleanly in parallel. However, sequential methods can also be used. In addition, a very focused beam is used to detect at multiple incident angles rather than at a single incident angle. In one embodiment, the beam is not collimated because for a collimated beam, the sample will need to be rotated, where the data is acquired serially. By capturing higher orders, it is not necessary to use a very small incident angle to obtain a strong reflected beam. On the contrary, in one embodiment, even if the mirror (0th order) reflected beam is relatively weak but, for example, the -1st order is very strong, an incident angle of, for example, 10 to 15 degrees can be used.

[0322] In any of the above described cases, whether collected in parallel or sequentially, the embodiments described herein can be used to acquire data from both the zeroth order (specular) reflection and from the diffraction (higher) orders. Conventional solutions emphasize the use of either the zeroth order or the diffraction (higher) orders, but not both. The embodiments described herein can be further distinguished from previously disclosed scatterometry methods, two examples of which are described below.

[0323] In the first approach described previously, U.S. Pat. No. 7,920,676 to Yun et al. describes a CD-GISAXS system and method. The method described includes analyzing the diffraction pattern of scattered X-rays generated from a collimated beam and analyzing multiple orders of diffracted light. Lower energies are used to provide a beam of higher convergence because the diffraction orders are spaced farther apart. However, the orders are still fairly closely spaced, and the convergence angles described are microradians. In addition, diffraction is not collected for multiple angles of incidence.

[0324] In contrast, in accordance with one or more embodiments described herein, a wide range of incident angles is used in a single beam. In the present approach, it is not actually necessary to capture useful diffraction orders (other than the zeroth order). However, the + / - 1 orders can have different sensitivities to grating characteristics (particularly the spacing), so in one embodiment, at least one additional order is captured when possible. Even so, a great deal of information is included in the form of a signal that varies with incident angle. In contrast, in U.S. Pat. No. 7,920,676, essentially one incident angle is used, and information is collected by observing multiple diffraction orders.

[0325] In addition, according to one or more embodiments described herein, the first-order beam can be separated from the zero-order beam by moving the first-order beam to one side of the zero-order beam. In one such embodiment, the periodic or grating structure is approached at a non-zero azimuth angle. In this way, a highly convergent beam can be used while still achieving orderly separation. In an exemplary embodiment, by approaching the grating at a 45° azimuth angle (for the central axis of the converging beam), the + / -1-order diffracted beam is deflected to one side of the zero-order beam by at least 10 degrees, and even more as the incident angle increases. In this case, a converging beam of up to about 10 degrees can be used while avoiding overlap or data. It should be understood that the intervals between each level can be made larger or smaller depending on the details of the grating spacing and the X-ray energy. In summary, in one embodiment, by collecting multiple incident angles and azimuth angles simultaneously, more useful information is obtained compared to a single irradiation of a collimated beam.

[0326] In a second approach described previously, U.S. Patent No. 6,556,652 to Mazor et al. describes the use of X-rays to measure critical dimensions. The method described is not actually based on diffraction of an X-ray beam at all. Instead, a "shadow" is created in a collimated beam. The shadow is reflected from a pattern (e.g., a linear grating structure). The contrast mechanism of the shadow is the difference between the critical angle at which the x-ray is reflected from the Si region at the bottom of the grating gap and the critical angle when first passing through the ridge material (photoresist). In contrast, according to the embodiments described here, most of the information comes from the signal at angles well above the critical angle.

[0327] As briefly mentioned above and exemplified below, X-ray reflectometry (XRS) can be viewed as a type of X-ray reflectometry (XRR) applied to two-dimensional and three-dimensional periodic or grating structures. Conventional XRR measurements involve the use of a single source X-ray that probes a sample over a range of angles. The angularly varying optical path length differences provide interference fringes that can be discerned to gather film property information such as film thickness and film density. However, in XRR, the physics of X-ray interactions with matter at higher source energies limits the angular range to grazing incidence, typically less than about 3 degrees relative to the sample horizontal plane. As a result, XRR has limited production / on-line feasibility. In contrast, according to the embodiments described herein, the application of low energy XRR / XRS enables the use of larger angles due to the use of energies that result in larger signal sensitivity angles to change the optical film properties.

[0328] In an exemplary application of low energy XRS, basic semiconductor transistor building blocks can be measured and analyzed. For example, the critical dimension (CD) of a semiconductor device refers to a feature that has a direct impact on the performance of the device or its manufacturing yield. Therefore, the CD must be manufactured or controlled to strict specifications. Examples of more conventional CDs include gate length, gate width, interconnect line width, line spacing, and line width roughness (LWR). Semiconductor devices are very sensitive to such dimensions, and small changes potentially lead to significant effects on performance, device failure, or manufacturing yield. As the integrated circuit (IC) feature size of semiconductor devices continues to shrink, manufacturers face ever-shrinking process windows and tighter tolerances. This significantly increases the accuracy and sensitivity requirements for CD metrology tools, as well as the need for non-destructive measurement sampling early in the manufacturing cycle, with minimal impact on the productivity of semiconductor device manufacturing plants or processing plants.

[0329] Non-planar semiconductor device manufacturing presents even further complications. For example, semiconductor devices fabricated on raised channels with non-planar topography, commonly referred to as fins, also include fin dimensions as an additional CD that must be considered. Such fin field effect transistors (fin-FETs) or multi-gate devices have high aspect ratio features, and the need for three-dimensional (3D) profile information on the fins of the device structure, including sidewall angles, and top and bottom dimensions, has become critical. Therefore, the ability to measure 3D profiles provides more valuable information than traditional two-dimensional line width and spacing CD information.

[0330] Fig.25 According to an embodiment, aspects of an exemplary fin-FET device suitable for low energy X-ray reflectoscattering measurements are shown. Fig.25, Structure A shows an angled cross-sectional view of a semiconductor fin 502 with a gate electrode stack 504 disposed thereon. The semiconductor fin 502 protrudes from a substrate 506 isolated by shallow trench isolation (STI) regions 508. The gate electrode stack 504 includes a gate dielectric layer 510 and a gate electrode 512. Structure B shows a cross-sectional view of a semiconductor fin 520 protruding from a substrate 522 between STI regions 524. Aspects of Structure B that can provide important information through XRS measurements include fin corner rounding (CR), fin sidewall angle (SWA), fin height (H), fin notch, and STI thickness (T), all of which are measured in Fig.25 534 and has a multilayer film stack 536 thereon. The multilayer film stack 536 may include material layers such as, but not limited to, titanium aluminum carbide (TiAlC), tantalum nitride (TaN), or titanium nitride (TiN). Comparing Structures B and C, XRS measurements can be performed on a bare fin (Structure B), such as a bare silicon fin, or on a fin with different material layers disposed thereon.

[0331] Fig.26 A graph 600 of 0-order reflectivity versus scattering angle for a silicon (Si) fin having a periodic structure with a 10 nm / 20 nm line / space ratio and corresponding structures (A)-(E) according to one embodiment is included. Fig.26 , low energy XRS measurements can be used to distinguish between a nominal fin structure (Structure A), a structure with increased fin height (Structure B), a structure with reduced fin width (Structure C), a structure with a wider CD at the bottom of the fin than the CD at the top of the fin (Structure D), and a structure with a narrower CD at the bottom of the fin than the CD at the top of the fin (Structure E). In this exemplary case, the Si fins were analyzed with a 0th order conical diffraction at 45 degrees to the periodic structure. It should be appreciated that the reduced area of ​​highest signal compared to the optical data is achieved by the fringes in the data seen in curve 600 as a result of the short wavelength.

[0332] Fig. 27 A graph 700 of first order reflectivity versus scattering angle for a silicon (Si) fin including a periodic structure having a 10 nm / 20 nm line / space ratio and corresponding structures (A)-(E) according to one embodiment. Fig. 27, low energy XRS measurements can be used to distinguish between a nominal fin structure (Structure A), a structure with increased fin height (Structure B), a structure with reduced fin width (Structure C), a structure with a wider CD at the bottom of the fin than the CD at the top of the fin (Structure D), and a structure with a narrower CD at the bottom of the fin than the CD at the top of the fin (Structure E). In this exemplary case, the Si fin is analyzed using a first order conical diffraction at 45 degrees to the periodic structure. In addition, structures with varying spacing are included in curve 700. As shown in curve 700, the first order data is very sensitive to fin thickness (note that structure B is clearly separated from the signal due to structures A and CE). Moreover, the first order data is very sensitive to spacing variations in the periodic structure, note that the spectrum of varying spacing can also be clearly distinguished from the other spectra.

[0333] On the other hand, a device for performing X-ray reflection scattering measurements is described. Generally, in one embodiment, such a device includes a conventional X-ray source and a focusing monochromator that extends in two dimensions. The focusing monochromator allows the incident light to hit the periodic sample at two varying angles of incidence, (i) incident on the plane of the periodic structure, and (ii) in azimuth relative to the symmetry of the structure (and at a fixed angle of incidence). Detection of scattered light is achieved by a two-dimensional (2D) detector that simultaneously samples the scattered signal intensity over a scattering angle range in two angular directions. In one embodiment, the constraint of the monochromator that ensures that the detected signal has no scattering order overlap requires that the incident angle range is less than the angle of the nominal first-order angle of 0 degrees, i.e., θ=sin-1(1-λ / d). Since light with a characteristic wavelength smaller than the grating period is used, higher-order diffraction orders are obtained and additional information about the grating structure is provided. In addition, interference fringes of multiple thickness periods can be used to determine the height, width, and shape of the line. The final estimate of the shape and structure of the periodic structure is achieved by inversion of the scattering solution compared to the 2D interference / scattering data.

[0334] As a more specific example, Fig.28 is a diagram illustrating a periodic structure measurement system with XRS capabilities according to an embodiment.

[0335] refer to Fig.28, a system 800 for measuring a sample 802 by X-ray reflection scattering includes an X-ray source 804 for generating an X-ray beam 806 having an energy of about 1 keV or less. A sample holder 808 is provided for positioning the sample 802, the sample having a periodic structure. A monochromator 810 is located between the X-ray source 804 and the sample holder 802, wherein the X-ray beam 806 travels from the X-ray source 804 to the monochromator 810, and then to the sample holder 808. The monochromator 810 is used to focus the X-ray beam 806 and provide an incident X-ray beam 812 to the sample holder 808. The incident X-ray beam 812 has multiple incident angles and multiple azimuth angles at the same time. The system 800 also includes a detector 814, a detector 814 for at least a portion of the scattered X-ray beam 816 of 802.

[0336] Reference again Fig.28 In one embodiment, the X-ray source 804, sample holder 808, monochromator 810, and detector 814 are all housed in cavity 818. In one embodiment, system 800 also includes an electron gun 820. In one such embodiment, the X-ray source 804 is an anode and the electron gun is aimed at the anode. In a specific embodiment, the anode is used to produce low energy X-rays and includes materials such as, but not limited to, carbon (C), molybdenum (Mo), or rhodium (Rh). In one embodiment, the electron gun 820 is an electron gun of approximately 1 keV. Again referring to Fig.28 , the magnetic electron suppression device 822 is included between the X-ray source 804 and the monochromator 810.

[0337] In one embodiment, the monochromator 810 is an annular multilayer monochromator that provides an incident angle range of approximately + / -30 degrees and an azimuth angle range of approximately + / -10 degrees. In one such embodiment, the annular multilayer monochromator provides an incident angle range of approximately + / -20 degrees. In one embodiment, as described above, there is no collimator inserted between the monochromator 810 and the sample holder 808. The monochromator 810 can be positioned to provide a desired incident beam for XRS measurement. For example, in a first embodiment, the monochromator 810 is positioned relative to the sample holder 808 to provide a converging X-ray beam having a central axis with a fixed non-zero incident angle and a zero azimuth relative to the periodic structure of the sample 802. In a second embodiment, the monochromator 810 is positioned relative to the sample holder 808 to provide a converging X-ray beam having a central axis with a fixed non-zero incident angle and a non-zero azimuth relative to the periodic structure of the sample 802. In one embodiment, the monochromator 810 is composed of alternating layers of metal (M) and carbon (C) disposed on a glass substrate, where M is a metal, such as but not limited to cobalt (Co) or chromium (Cr). In a particular such embodiment, a multilayer monochromator is provided for reflecting carbon (C) based Kα radiation and includes about 100 repeating layers of Co / C or Cr / C with a period of about 4 nanometers, i.e., a period slightly less than the wavelength of the reflected light beam, which may be about 5 nanometers. In one such embodiment, the Co or Cr layers are thinner than the C layers.

[0338] The sample holder 808 can be a movable sample holder. For example, in one embodiment, the sample holder 808 can be rotated to change the azimuth of the central axis of the X-ray beam 812 relative to the periodic structure of the sample 802. In one embodiment, the sample holder 808 can be rotated to provide orthogonal operation with isocentric rotation, so that two or more samples can be rotated per measurement. In one embodiment, the navigation visual inspection device 824 allows visual inspection of the sample holder 808, such as Fig.28 In one such embodiment, a flip-up objective for a vision-based inspection system is included.

[0339] 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 the portion of the scattered X-ray beam 816 scattered from multiple incident angles and multiple azimuth angles of the incident beam 812. In one embodiment, the system 800 also includes a processor or computing system 899 coupled to the two-dimensional detector. In one such embodiment, the processor 899 is used to estimate the shape of the periodic structure of the sample 802 by inverting the scattering solution relative to the sampled scattering signal intensity. In another embodiment, a scanning slit can be implemented to replace the two-dimensional detector. In either case, the detector 814 can be configured to achieve data collection of approximately 1000 pixels over the dispersion range.

[0340] Embodiments may be provided as computer program products or software, which may include machine-readable media having instructions stored thereon, which instructions may be used to program a computer system (or other electronic device) to perform a process according to an embodiment. Machine-readable media include any mechanism for storing or transmitting information in a machine (e.g., computer) readable form. For example, machine-readable (e.g., computer-readable) media include machine (e.g., computer) readable storage media (e.g., read-only memory ("ROM"), random access memory ("RAM"), disk storage media, optical storage media, flash memory devices, etc.), machine (e.g., computer) readable transmission media (electrical, optical, acoustic or other forms of propagation signals (e.g., infrared signals, digital signals, etc.)), etc.

[0341] Fig.29A graphical representation of a machine is shown in the exemplary form of a computer system 900, in which a set of instructions for causing the machine to perform any one or more methods discussed herein can be executed. In alternative embodiments, the machine may be connected (e.g., networked) to other machines in a local area network (LAN), an intranet, an extranet, or the Internet. The machine may operate in the capacity of a server or client in a client-server network environment, or as a peer machine in a peer-to-peer (or distributed) network environment. The machine may be a personal computer (PC), a tablet PC, a set-top box (STB), a personal digital assistant (PDA), a cellular phone, a web device, a server, a network router, a switch or a bridge, or any machine capable of executing a set of instructions (sequential or otherwise) specifying the actions to be taken by the machine. In addition, although only a single machine is shown, the term "machine" should also be understood to include any set of machines (e.g., computers) that execute a set (or multiple sets) of instructions individually or jointly to perform any one or more methods discussed herein. For example, in one embodiment, the machine is configured to execute a set or multiple sets of instructions for measuring a sample by X-ray reflection scattering measurement. In one example, computer system 900 may be adapted to use computer system 899 of XRS device 800 described above.

[0342] The exemplary computer system 900 includes a processor 902, a 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)), a static memory 906 (e.g., flash memory, static random access memory (SRAM), etc.), and an auxiliary memory 918 (e.g., a data storage device) that communicate with each other via a bus 930.

[0343] The processor 902 represents one or more general-purpose processing devices, such as a microprocessor, a central processing unit, etc. More specifically, the processor 902 may be a complex instruction set computing (CISC) microprocessor, a reduced instruction set computing (RISC) microprocessor, a very long instruction word (VLIW) microprocessor, a processor implementing other instruction sets, 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), a network processor, etc. The processor 902 is configured to execute processing logic 926 for performing the operations discussed herein.

[0344] The computer system 900 may also include a network interface device 908. The computer system 900 may also include a video display unit 910 (e.g., a liquid crystal display (LCD) or a cathode ray tube (CRT)), an alphanumeric input device 912 (e.g., a keyboard), a cursor control device 914 (e.g., a mouse), and a signal generating device 916 (e.g., a speaker).

[0345] The secondary memory 918 may include a machine-accessible storage medium (or more specifically a computer-readable storage medium) 931 on which is stored one or more sets of instructions (e.g., software 922) that embody any one or more of the methods or functions described herein. The software 922 may also reside completely or at least partially within the main memory 904 and / or within the processor 902 during execution of the software 922 by the computer system 900, the main memory 904 and the processor 902 also constituting machine-readable storage media. The software 922 may also be sent or received over the network 920 via the network interface device 908.

[0346] Although the machine-accessible storage medium 931 is shown as a single medium in the exemplary embodiment, the term "machine-readable storage medium" should be understood to include a single medium or multiple media (e.g., a centralized or distributed database, and / or associated caches and servers) that store one or more sets of instructions. The term "machine-readable storage medium" should also be understood to include any medium that can store or encode a set of instructions for execution by a machine and cause the machine to perform any one or more methods of the embodiments. Therefore, the term "machine-readable storage medium" should be considered to include, but is not limited to, solid-state memories and optical and magnetic media.

[0347] According to an embodiment, a non-transitory machine-accessible storage medium has stored thereon instructions for executing a method for measuring a sample by X-ray reflection scattering measurement. The method includes impinging an incident X-ray beam on a sample having a periodic structure to produce a scattered X-ray beam. The incident X-ray beam simultaneously provides multiple incident angles and multiple azimuth angles. The method also includes collecting at least a portion of the scattered X-ray beam.

[0348] Thus, methods and systems for measuring periodic structures using multi-angle X-ray reflectometry (XRS) have been described.

[0349] Any arrangement of components that achieve the same functionality is effectively "associated" so as to achieve the desired functionality. Thus, any two components combined herein to achieve a particular functionality may be considered to be "associated" with each other such that the desired functionality is achieved, regardless of architectures or intermediate components. Likewise, any two components so associated may also be considered to be "operably connected" or "operably coupled" to each other to achieve the desired functionality.

[0350] Furthermore, those skilled in the art will recognize that the boundaries between the above operations are merely illustrative. Multiple operations may be combined into a single operation; a single operation may be distributed among additional operations, and operations may be performed at least partially overlapping in time. Furthermore, alternative implementations may include multiple examples of operations, and the order of operations may be changed in various other implementations.

[0351] For another example, in one embodiment, the illustrated examples may be implemented as circuits located on a single integrated circuit or within the same device. Alternatively, these examples may be implemented as any number of separate integrated circuits or separate devices interconnected with each other in an appropriate manner.

[0352] As another example, the examples or portions thereof may be implemented as soft or code representations of physical circuitry or logical representations convertible into physical circuitry, such as in any appropriate type of hardware description language.

[0353] However, other modifications, changes, and substitutions are possible. Accordingly, the specification and drawings are to be regarded as illustrative rather than restrictive.

[0354] In the claims, any reference numerals placed between brackets shall not be construed as limiting the claims. The word "comprising" does not exclude the presence of other elements or steps than those listed in the claim. In addition, the term "a" as used herein is defined as one or more than one. In addition, the use of introductory phrases such as "at least one" and "one or more" in the claims should not be interpreted as implying that the introduction of another claim element by the indefinite article "one" or "an" will limit any particular claim including such introduced claim element to an invention including only one such element, even when the same claim includes the introductory phrases "one or more" or "at least one" and an indefinite article such as "one" or "an". The same applies to the use of determining articles. Unless otherwise specified, terms such as "first" and "second" are used to arbitrarily distinguish the elements described by these terms. Therefore, these terms are not necessarily intended to indicate the time or other priority of these elements. The fact that certain measures are recited in mutually different claims does not mean that the combination of these measures cannot be used advantageously.

[0355] Although certain features of the present invention have been illustrated and described herein, many modifications, substitutions, changes and equivalents will now occur to those skilled in the art. It is therefore to be understood that the appended claims are intended to cover all such modifications and changes that fall within the true spirit of the invention.

[0356] The terms "comprise", "include", "have", "consist of" and "consist essentially of" can be used interchangeably. For example, any method can include at least the steps included in the drawings and / or the specification, or only the steps included in the drawings and / or the specification.

Claims

1. A method for evaluating a non-diffuse x-ray signal received from a disturbed object due to illumination of the disturbed object, the disturbed object being an object having a roughness that affects the x-ray signal, the roughness being comparable to the x-ray wavelength, the method comprising: calculating an estimated field for each of a plurality of non-perturbed objects, the plurality of non-perturbed objects representing a perturbation of the perturbed object; The perturbation is of the order of the wavelength of the non-diffuse x-ray signal; as well as The non-diffuse x-ray signal is evaluated based on the field of the plurality of non-perturbed objects.

2. The method according to claim 1, wherein: Each of the disturbance object and the plurality of non-disturb objects has a uniform dielectric constant.

3. The method according to claim 1, wherein: The disturbance of the disturbance object follows a disturbance distribution function, wherein the plurality of non-disturb objects are calculated based on the disturbance distribution function.

4. The method according to claim 3, wherein: The disturbance distribution function is a probability function of a height parameter of the disturbance of the disturbance object.

5. The method according to claim 4, wherein: The height parameter of a given protrusion associated with the interface of the disturbance object, to which the given protrusion belongs, is the distance between the protrusion and the interface of the disturbance object.

6. The method according to claim 4, wherein: The perturbed object has a single rough interface, wherein the plurality of non-perturbed objects have corresponding non-perturbed interfaces, each of the plurality of non-perturbed objects has a corresponding non-perturbed interface, wherein a perturbation distribution function of a height parameter of the perturbation of the single rough interface is equal to a perturbation distribution function of a height parameter of a corresponding given non-perturbed interface.

7. The method according to claim 4, wherein: The perturbed object has a plurality of rough interfaces, and the plurality of non-perturbed objects have corresponding non-perturbed interfaces, each of the plurality of non-perturbed objects having a plurality of corresponding non-perturbed interfaces.

8. A non-transitory computer readable medium for evaluating a non-diffuse x-ray signal received from a perturbed object due to illumination of the perturbed object, the perturbed object being an object having a roughness that affects the x-ray signal, the roughness being comparable to the x-ray wavelength, the non-transitory computer readable medium storing instructions for: calculating an estimated field for each of a plurality of non-perturbed objects, the plurality of non-perturbed objects representing a perturbation of the perturbed object; the perturbation having an order of the wavelength of the non-diffuse x-ray signal; and The non-diffuse x-ray signal is evaluated based on the field of the plurality of non-perturbed objects.

9. A system for evaluating a non-diffuse x-ray signal received from a disturbed object due to illumination of the disturbed object, the disturbed object being an object having a roughness that affects the x-ray signal, the roughness being comparable to the x-ray wavelength, the system comprising a processor configured to: calculating an estimated field for each of a plurality of non-perturbed objects, the plurality of non-perturbed objects representing a perturbation of the perturbed object; the perturbation having an order of the wavelength of the non-diffuse x-ray signal; and The non-diffuse x-ray signal is evaluated based on the field of the plurality of non-perturbed objects.

10. A method for evaluating a non-diffuse x-ray signal received from a disturbed object due to illumination of the disturbed object, the disturbed object being an object having a roughness that affects the x-ray signal, the roughness being comparable to the x-ray wavelength, the method comprising: computing an unperturbed object representative of the perturbed object, wherein the unperturbed object comprises one or more regions of variable permittivity representing one or more perturbed object regions of uniform permittivity; computing an estimated field of the unperturbed object; and evaluating the non-diffuse x-ray signal based on the estimated field of the unperturbed object.

11. The method according to claim 10, wherein: The disturbance of the disturbance object follows a disturbance distribution function, wherein a variable dielectric constant of one or more regions is calculated based on the disturbance distribution function.

12. The method according to claim 10, wherein: One or more regions of variable dielectric constant have a stepped dielectric constant.

13. The method according to claim 10, wherein: The one or more regions of variable dielectric constant have a step-graded dielectric constant.

14. The method according to claim 10, wherein: The calculation of the non-perturbed object includes replacing the perturbed object region by a plurality of non-perturbed object sub-regions having different dielectric constants from each other.

15. The method according to claim 14, wherein: The plurality of non-perturbed object sub-regions are a plurality of layers.

16. The method according to claim 14, wherein: The plurality of non-disturbance object sub-regions include (a) an upper disturbance sub-region located above a nominal surface of the disturbance object region, and (b) a lower disturbance sub-region located below a nominal surface of the disturbance object region.

17. The method according to claim 16, wherein: The upper perturbation sub-region and the lower perturbation sub-region have a thickness equal to a coefficient multiplied by a standard deviation of a perturbation distribution function of a perturbation of the perturbation object.

18. The method according to claim 17, wherein: The dielectric constant of the upper perturbation sub-region is different from the dielectric constant of the lower perturbation sub-region, and wherein the dielectric constant of the upper perturbation sub-region and the dielectric constant of the lower perturbation sub-region are (a) the dielectric constant (ε up ) and (b) the dielectric constant (ε) of another region connected to the disturbance object region down ) is the weighted sum of .

19. A non-transitory computer readable medium for evaluating a non-diffuse x-ray signal received from a perturbed object due to illumination by the perturbed object, the perturbed object being an object having a roughness that affects the x-ray signal, the roughness being comparable to the x-ray wavelength, the non-transitory computer readable medium storing instructions for: calculating a non-perturbed object representative of the perturbed object, wherein The non-perturbed object includes one or more regions of variable permittivity representing one or more perturbed object regions of uniform permittivity; calculating an estimated field of the non-perturbed object; and evaluating the non-diffuse x-ray signal based on the estimated field of the non-perturbed object.

20. A system for evaluating a non-diffuse x-ray signal received from a perturbed object due to illumination by the perturbed object, the perturbed object being an object having a roughness that affects the x-ray signal, the roughness being comparable to the x-ray wavelength, the system comprising a processor configured to: compute a non-perturbed object representative of the perturbed object, wherein: The non-perturbed object includes one or more regions of variable permittivity representing one or more perturbed object regions of uniform permittivity; calculating an estimated field of the non-perturbed object; and evaluating the non-diffuse x-ray signal based on the estimated field of the non-perturbed object.

21. A method for evaluating an x-ray signal received from a perturbed object due to irradiation of the perturbed object, the perturbed object being an object having a roughness that affects the x-ray signal, the roughness being comparable to the x-ray wavelength, the method comprising: estimating a field produced by a perturbation by the perturbation object, the perturbation being of the order of the wavelength of the x-ray signal, wherein the estimating comprises computing a general function of the field contributed by a single perturbation in response to the perturbation by the perturbation object, the general function being applicable to perturbation objects of arbitrary shape; and The x-ray signal is evaluated based on one or more statistical characteristics of the field and the disturbance.

22. The method according to claim 21, wherein: The calculation of the general function is applicable to disturbance objects of arbitrary shapes.

23. The method according to claim 21, wherein: The calculation of the general function includes integrating a first integrable function that is independent of the shape of the perturbed object.

24. The method according to claim 21, wherein: Calculation of the general function includes integrating a first integrable function based on (a) the difference between the dielectric constant coefficients of the disturbed object and the surrounding environment of the disturbed object at the location of one of the single disturbances; (b) the field contributing to the illumination of one of the single disturbances at the illumination angle; and (c) the field contributing to the collection of the illumination from the single disturbance at a specific collection angle.

25. The method according to claim 24, wherein: The field contributing to the collection of illumination from the single perturbation at a particular collection angle is calculated by calculating the field contributing to the illumination of one of the single perturbations from an illumination angle relative to the collection angle.

26. The method according to claim 21, wherein: The computation of the general function includes first integrating a first integrable function over a range of altitudes representing an altitude of one of the single perturbations relative to a non-perturbed version of the perturbed object to provide a second integrable function.

27. The method according to claim 26, wherein: The calculation of the general function includes calculating a third integrable function based on the second integrable function and an area of ​​a normal projection of one of the single perturbations onto a non-perturbed version of a surface of the perturbed object.

28. The method according to claim 27, wherein: Computing the general function includes performing a second integration of the third integrable function over one or more surfaces of the perturbed object to provide a fourth function; and adding to the fourth function an estimate of the field resulting from illuminating a non-perturbed version of the perturbed object.

29. The method according to claim 21, wherein: The received evaluation includes evaluating the intensity based on statistics of the field and the disturbance of the disturbance object.

30. The method of claim 29, wherein: The evaluation of the intensity includes calculating the diffuse intensity and calculating the non-diffuse intensity.

31. The method according to claim 30, wherein: The calculation of the non-diffuse intensity comprises averaging the field obtained over possible perturbed versions of the perturbed object.

32. The method according to claim 31, wherein: Averaging includes calculating multiple integrals over various functions, wherein the calculation of the multiple integrals includes calculating an initial integral between (a) a field contributing to the illumination of one of the single perturbations at an illumination angle and (b) a field contributing to the collection of illumination from the single perturbation at a particular collection angle.

33. The method of claim 32, computing the dot product by computing a Fourier series representing the dot product.

34. A non-transitory computer readable medium for evaluating an x-ray signal received from a perturbed object due to irradiation of the perturbed object, the perturbed object being an object having a roughness that affects the x-ray signal, the roughness being comparable to the x-ray wavelength, the non-transitory computer readable medium storing instructions for: estimating a field produced by a perturbation of the perturbation object, the perturbation being of the order of the wavelength of the x-ray signal, wherein The estimating comprises calculating a general function of a field contributed by a single disturbance in response to a disturbance through the disturbance object, the general function being applicable to disturbance objects of arbitrary shapes; as well as The x-ray signal is evaluated based on one or more statistical characteristics of the field and the disturbance.

35. The non-transitory computer readable medium of claim 34, wherein: The calculation of the general function is applicable to disturbance objects of arbitrary shapes.

36. A method for performing a model-based assessment associated with a perturbed object, the perturbed object being an object having a roughness that affects an x-ray signal, the roughness being comparable to the x-ray wavelength, the method comprising: obtaining a detection signal indicative of an x-ray signal received by a sensor from a disturbance object due to illumination by the disturbance object; The perturbation object includes a perturbation having an order of the wavelength of the x-ray signal; performing at least one model-based assessment related to the disturbance object based on the detection signal; wherein the performing of the at least one model-based assessment comprises comparing the detection signal with a reference detection signal, the reference detection signal being associated with a reference model of a reference disturbance object associated with one or more reference parameters; selecting one or more reference models of the reference disturbance object, and determining parameters of the disturbance object based on parameters of the one or more reference models of the reference disturbance object; and One or more parameters of the disturbance plant are set to one or more parameters of the reference disturbance plant modeled by the reference model, if more than one reference model exists, using a statistical function applying an interpolation and a weighted sum of any other functions.

37. The method of claim 36, wherein: The at least one model-based assessment related to the disturbing object is a measure of the roughness of the disturbing object.

38. The method of claim 36, wherein: The at least one model-based assessment associated with the disturbed object includes (a) a measure of the roughness of the disturbed object, and (b) an additional model-based assessment associated with the disturbed object.

39. The method of claim 38, wherein: The additional model-based evaluation is based on the roughness of the disturbed object.

40. The method of claim 39, wherein: The additional model-based estimate is a measure of a dimension associated with the perturbed object.

41. The method of claim 36, wherein: The detection signal is a diffuse detection signal, and wherein the performing of the at least one model-based evaluation comprises determining a roughness and a correlation of the disturbance object.

42. The method according to claim 41, wherein: The performing of the at least one model-based evaluation includes determining a non-diffuse-based model of the disturbance signal based on the correlation.

43. The method of claim 36, comprising obtaining a model of the disturbed object, the model determined based on a field generated by the disturbance and one or more statistical characteristics of the disturbance.

44. The method of claim 43, wherein: The performing of the at least one model-based assessment includes revising a disturbance model based on additional information about the model, wherein the additional information is not based on the detection signal indicative of an x-ray signal.

45. The method of claim 36, wherein: The detection signal is a diffuse detection signal; wherein the performing of the at least one model-based evaluation comprises evaluating a diffuse-based roughness of the perturbed object.

46. ​​The method of claim 45, comprising wherein: The performing of the at least one model-based evaluation includes revising a non-diffuse-based model of the perturbation object.

Images