Systems and methods for regression filters and zero edge exclusion filters

Abstract

A computer device includes at least one processor in communication with at least one memory device. The at least one processor is programmed to: a) receive scan data of an object to be analyzed; b) generate a mask to apply to the scan data based on a shape of the object to be analyzed; c) apply the mask to the scan data; d) execute a multi-order Gaussian regression filter on the masked scan data to generate an output image of the object to be analyzed; e) analyze the output image of the object to be analyzed; and f) determine whether or not to approve the object based on the analysis.

Description

28744-6517 (231018.4) SYSTEMS AND METHODS FOR REGRESSION FILTERS AND ZERO EDGE EXCLUSION FILTERS CROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of and priority to U.S. Provisional Application No. 63 / 669,992, filed July 11, 2024, which application is hereby incorporated by reference in their entireties. FIELD

[0002] This disclosure relates generally to processing of flat surfaces and, more particularly, to systems and methods for analyzing small surface variations (e.g., the nanotopography or micro-roughness) of surfaces utilizing multi-order regression filters and zero edge exclusion filters. BACKGROUND

[0003] Semiconductor wafers are commonly used in the production of integrated circuit (IC) chips on which circuitry is printed. The circuitry is printed as identical integrated circuits (“die”) in miniaturized form onto surfaces of the wafers in a multi-stage fabrication process. Specifically, the process includes various stages of electron beam-lithographic or photolithographic processing steps (“lithography”) and chemical or physical processing steps (e.g., chemical mechanical polishing, etching, and passivation). At each stage, a new pattern layer is added to the surface of the wafer, or an existing layer is modified. Precise alignment of the layers (“overlay”) is critical for end performance of the chips.

[0004] Chip manufacturers require wafers that have extremely flat and parallel surfaces to mitigate or eliminate overlay error and ensure that a maximum number of chips can be fabricated from each wafer. Wafers are initially obtained from a single crystal ingot of suitable material (e.g., silicon). Wafers may be sliced from the ingot using, for example, a wire saw. The surfaces of the raw wafers are then subject28744-6517 (231018.4) to preliminary flattening and etching using additional front-end process tools, such as a grinding, lapping, or etching tool. The edges may also be grinded and / or rounded using a beveling tool. The surfaces are then polished to produce a smooth, highly reflective, mirrored wafer surface.

[0005] To enable maximizing the number of chips that can be produced from any given wafer, it is desirable to characterize the topology of the entire surface of the wafer up to a peripheral edge. Conventional techniques utilize edge exclusion filters that ignore a specified radial length extending inward from the peripheral edge, which could miss peripheral surface regions that have unacceptable topology for chip manufacture. Although there is a strong need for zero edge exclusion filters (ZEEF) for evaluation nano topography (NT) and micro roughness (MR) all the way to the edge of a sample, no convincing solution exists today. Further, currently known filters suffer from weak frequency separation, resulting in undesired form residuals (aka “Shape Bleed Through”) in the high pass filter result.

[0006] Accordingly, a system to enable surface analysis of wafers using zero edge exclusion filters is needed.

[0007] This Background section is intended to introduce the reader to various aspects of art that may be related to various aspects of the present disclosure, which are described and / or claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present disclosure. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions of prior art. BRIEF DESCRIPTION

[0008] In one aspect, a system includes a computing device that may include at least one processor in communication with at least one memory device. The at least one processor may be configured to: a) receive scan data of an object to be analyzed; b) generate a mask to apply to the scan data based on a shape of the object to be analyzed; c) apply the mask to the scan data; d) execute a multi-order Gaussian28744-6517 (231018.4) regression filter on the masked scan data to generate an output image of the object to be analyzed; e) analyze the output image of the object to be analyzed; and f) determine whether or not to approve the object based on the analysis. The system may have additional, less, or alternate functionalities, including those discussed elsewhere herein.

[0009] In another aspect, a computer-implemented method may be performed by a computer device including at least one processor in communication with at least one memory device. The method may include a) receiving scan data of an object to be analyzed; b) generating a mask to apply to the scan data based on a shape of the object to be analyzed; c) applying the mask to the scan data; d) executing a multi- order Gaussian regression filter on the masked scan data to generate an output image of the object to be analyzed; e) analyzing the output image of the object to be analyzed; and f) determining whether or not to approve the object based on the analysis. The method may have additional, less, or alternate functionalities, including those discussed elsewhere herein.

[0010] In a further aspect, a computer device includes at least one processor in communication with at least one memory device. The at least one processor may be configured to: a) receive scan data of an object to be analyzed; b) generate a mask to apply to the scan data based on a shape of the object to be analyzed; c) apply the mask to the scan data; d) execute a multi-order Gaussian regression filter on the masked scan data to generate an output image of the object to be analyzed; e) analyze the output image of the object to be analyzed; and f) determine whether or not to approve the object based on the analysis. The computer device may have additional, less, or alternate functionalities, including those discussed elsewhere herein.

[0011] In another aspect, at least one non-transitory computer- readable media having computer-executable instructions embodied thereon, when executed by a computing device including at least one processor in communication with at least one memory device, the computer-executable instructions may cause the at least one processor to: a) receive scan data of an object to be analyzed; b) generate a mask to apply to the scan data based on a shape of the object to be analyzed; c) apply the28744-6517 (231018.4) mask to the scan data; d) execute a multi-order Gaussian regression filter on the masked scan data to generate an output image of the object to be analyzed; e) analyze the output image of the object to be analyzed; and f) determine whether or not to approve the object based on the analysis. The non-transitory computer-readable media may have additional, less, or alternate functionalities, including those discussed elsewhere herein.

[0012] Advantages will become more apparent to those skilled in the art from the following description of the preferred embodiments which have been shown and described by way of illustration. As will be realized, the present embodiments may be capable of other and different embodiments, and their details are capable of modification in various respects. Accordingly, the drawings and description are to be regarded as illustrative in nature and not as restrictive. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The Figures described below depict various aspects of the systems and methods disclosed. Each Figure depicts an embodiment of a particular aspect of the disclosed systems and methods, and that each of the Figures is intended to accord with a possible embodiment. Further, wherever possible, the following description refers to the reference numerals included in the following Figures, in which features depicted in multiple Figures are designated with consistent reference numerals.

[0014] Figures 1A-1C illustrate filtering and ringing artefacts.

[0015] Figure 2 illustrates a graph of comparisons of different analyses of the circular data shown in Figure 1A.

[0016] Figure 3 illustrates a further graph of comparisons of different analyses of the circular data shown in Figure 1A.

[0017] Figure 4 illustrates graphs of length domain kernels for Gauss and Double-Gauss filtering using rough step approximation.28744-6517 (231018.4)

[0018] Figure 5A illustrates a graph of an exact double gauss kernel vs a step approximation of the double gauss kernel in accordance with at least one embodiment.

[0019] Figure 5B illustrates a graph of an exact gauss kernel a step approximation of a gauss kernel in accordance with at least one embodiment.

[0020] Figure 5C illustrates a graph of an exact double gauss kernel's transfer function vs a step approximation double gauss kernel's transfer function frequency response in accordance with at least one embodiment.

[0021] Figure 5D illustrates a graph of an exact gauss kernel's transfer function vs a step approximation gauss kernel's transfer function in accordance with at least one embodiment.

[0022] Figure 6 illustrates a graph in the logarithmic scale comparing multiple filters.

[0023] Figure 7 illustrates an example comparison of the results of the different orders of polynomial for a high pass filter, in accordance with each embodiment.

[0024] Figure 8A illustrates a wafer that has been analyzed using the Step Double Gauss filter as described herein.

[0025] Figure 8B illustrates a wafer that has been analyzed using the Gauss Regression Filter of order 2 as described herein.

[0026] Figure 8C illustrates a wafer that has been analyzed using the Gauss Regression Filter of order 3 as described herein.

[0027] Figure 8D illustrates a wafer that has been analyzed using the Gauss Regression Filter of order 5 as described herein.28744-6517 (231018.4)

[0028] Figure 8E illustrates a wafer that has been analyzed using the Gauss Regression Filter of order 7 as described herein.

[0029] Figure 8F illustrates a wafer that has been analyzed using the Gauss Regression Filter of order 9 as described herein.

[0030] Figures 9A-9E illustrate a set of graphs of normalized power kernels for GRFs of orders 1, 3, 5, 7, and 9, respectively.

[0031] Figures 10A and 10B illustrate views of the edge of wafers that have been analyzed with the order 5 GRF.

[0032] Figure 11A illustrates a view of the edge of the wafer that has been analyzed with the order 5 GRF.

[0033] Figure 11B illustrates a view of the edge of the wafer via the ERO signal.

[0034] Figure 11C illustrates a view of the edge of the wafer where the ERO signal was removed before being analyzed by the order 5 GRF.

[0035] Figure 12A illustrates a view of the edge of the wafer that has been analyzed with the order 5 GRF.

[0036] Figure 12B illustrates a view of the edge of the wafer that has been analyzed with a high-pass edge profile map.

[0037] Figure 12C illustrates a view of the edge of the wafer where the results of the high-pass edge profile map were subtracted from the high-pass filtered data that was filtered by the order 5 GRF.

[0038] Figure 13 illustrates a process for analyzing small surface variations (e.g., the nanotopography or micro-roughness) of surfaces utilizing multi- order regression filters and zero edge exclusion filters.28744-6517 (231018.4)

[0039] Figure 14 illustrates an example system for performing the process shown in Figure 13.

[0040] Figure 15 depicts an example configuration of user computer device.

[0041] Figure 16 depicts an example configuration of a server computer device.

[0042] Like reference symbols in the various drawings indicate like elements. DETAILED DESCRIPTION

[0043] The field of the disclosure relates to processing of flat surfaces such as semiconductor wafers and, more particularly, to systems and methods for analyzing small surface variations (e.g., the nanotopography or micro-roughness) of surfaces of semiconductor wafers utilizing zero edge exclusion filters.

[0044] Those having ordinary skill in the art would understand that although the present systems and methods are described in view of semiconductor wafers, the present systems and methods may also be applied to other surfaces in need of analysis, such as, but not limited to, mechanically machined surfaces. Furthermore, the present systems and methods could also be applied to higher dimensions than just two dimensions (2D), these include, but are not limited to, three dimensional (3D) and four dimensional (4D) embodiments.

[0045] Acceptable wafer geometry specifications can be defined by the shape and flatness of the wafer before lithography. Shape is the long wavelength component of the wafer geometry in an unchucked state, defined as the deviation of median surface of the wafer relative to a best-fit median surface reference plane. It can be characterized by global parameters such as warp, the sum of the maximum positive and negative deviations from the best-fit plane, and bow, the distance between the surface and the best-fit plane at a center of the wafer. Flatness is the variation of wafer28744-6517 (231018.4) thickness relative to the reference plane. It can be characterized by global parameters, such as the maximum variation of wafer thickness from an ideal flat back surface (GBIR), or local parameters, such as site flatness, front reference surface, least squares reference plane, range (SFQR).

[0046] Another consideration is the topology of the wafer surface. Poor topology can lead to non-uniform oxide layer removal in a later polishing (CMP) process. This can lead to substantial yield losses for the wafer users such as chip manufacturers. As the IC manufacturers move towards smaller process technology, the tolerances for topology are projected to become tighter.

[0047] In order to identify and address topology degradation concerns, device and semiconductor material manufacturers consider the nanotopography and micro-roughness of the wafer surfaces. For example, Semiconductor Equipment and Materials International (SEMI), a global trade association for the semiconductor industry (SEMI document 3089), defines nanotopography as the deviation of a wafer surface within a spatial wavelength of about 0.2 mm to about 20 mm. This spatial wavelength corresponds very closely to surface features on the nanometer scale for processed semiconductor wafers. Nanotopography measures elevational deviation of one surface of the wafer and does not consider thickness variations of the wafer, as with traditional flatness measurements. Wafer micro-roughness is surface roughness below 10 nm in P-V (peak-to-valley) value. The micro-roughness and nanotopography of the wafer surface can be generated using a high accuracy, optical inspection tool (e.g., a WaferSight™ 2 or 2+ bare wafer geometry metrology system manufactured by KLA- Tencor Corporation). These optical inspection tools use light reflected from a surface of the wafer to detect very small surface variations.

[0048] To enable maximizing the number of chips that can be produced from any given wafer, it is desirable to characterize the topology of the entire surface of the wafer up to a peripheral edge. Conventional techniques utilize edge exclusion filters that ignore a specified radial length extending inward from the peripheral edge, which could miss peripheral surface regions that have unacceptable28744-6517 (231018.4) topology for chip manufacture. Although there is a strong need for zero edge exclusion filters (ZEEF) for evaluation nano topography (NT) and micro roughness (MR) all the way to the edge of a sample, no convincing solution exists today. Further, currently known filters suffer from weak frequency separation, resulting in undesired form residuals (aka “Shape Bleed Through”) in the high pass filter result.

[0049] Reliable high-pass filtering is a necessary pre-condition for meaningful NT or MR measurements. The Wafer NT needs to be measured on front and back of a wafer. Many currently employed filters for high-pass filtering are Gauss and Double Gauss as described in “SEMI 3335D,” or gauss regression filters (GRF) or robust GRF (RGRF) of order 0 and order 2.

[0050] There are two major problems with the GRF and RGRF filters. First, they exhibit weak frequency separation. The order 0 RGRF / GRF and Gauss filters’ transfer function attenuates only with 2-2per octave. The order 2 RGRF / GRF and Double Gauss function attenuate with 2-4per octave. Second, most know filters have difficulty with filtering images that are not square and may leave behind artefacts. Third, known filters are limited, including GRF and RGRF are limited to second order polynomials. Additionally, the GRF and RGRF filters exhibit edge discontinuity. The wafer edge is a discontinuity that causes a power spectrum with sharply rising amplitudes towards low frequencies (about 6 per octave). The weak frequency separation of order 0 RGRF / GRF or Gauss filters, as well as order 2 RGRF / GRF and Double Gauss filters let a significant amount of edge discontinuity wavelengths pass, which results in an artefact known as “Edge Ringing”.

[0051] Figures 1A-1C illustrate filtering and ringing artefacts. Figure 1A illustrates a circular set of data, where the data is in the white circle. Figure 1B illustrates a power spectrum of the circular set of data shown in Figure 1B. Figure 1C illustrates a view of the circular data after being put through a high pass filter. Figure 1C shows ringing artefacts around the transition from the circular data to no data.

[0052] If the data is square, then one can apply any filter to it without significant filter artefacts. On data for a non-square, then the filters have a high28744-6517 (231018.4) possibility of leaving behind significant filter artefacts. High pass filters have the potential to leave filter ringing, due to the non-square shape of the data.

[0053] Figure 2 illustrates a graph 200 of comparisons of different analyses of the circular data shown in Figure 1A. Graph 200 shows filter transfer functions of different filters including a Gauss Transfer Function 210, a Double Gauss Transfer function 215, and a RGAUSS Order 9 Transfer Function 220, as well as fully transformed power spectrum 205 of the circular data. The transfer functions (filters) are configured to filter out the power spectrum data 205 of the disc shown in Figure 1 to the left of the transfer functions 210, 215, and 220, as shown in Figure 3.

[0054] Figure 3 illustrates a further graph 300 of comparisons of different analyses of the circular data shown in Figure 1A. Graph 300 shows the resulting power spectra of circular data after high-pass filtering by different filters including a Gauss filtered disc power spectrum 305, a Double Gauss filtered disc power spectrum 310, and a RGAUSS Order 9 filtered disc power spectrum 315. By comparing graph 200 and graph 300, the Gauss filtered 305 and Double Gauss filtered 310 include data that is to the left of their corresponding transfer functions 210 and 215. This data to the left is indicative of artefacts that have been introduced by the filtering. The Gauss transfer function has an attenuation of factor 4. The double Gauss function has an attention of factor 16. RGAUSS Order 9 has an attenuation of factor 1024. Further comparison can be seen in Table 1 described below. The RGAUSS Order 9315 shows that data that was to be filtered out has an effective amplitude of zero and is not show compared to the data that was desired after the filtering.

[0055] Figures 1A through 3 graphically illustrate some of the issues with filtering the data in a non-square shape. The same problem exists for the inside of a wafer. The power spectrum of a typical wafer shape has strong form wavelengths content, while the amplitudes of short wavelengths relevant for Nano Topography are very low. This results in artefacts that are known as “Shape Bleed Through.”28744-6517 (231018.4)

[0056] Both, “Edge Ringing” and “Shape Bleed Through,” are artefacts that cause inaccurate Nano-Topography results. In addition, “Edge Ringing” makes it impossible to perform Nano Topography measurements near the edge.

[0057] In an attempt to reduce “Edge Ringing,” the Gauss or Double Gauss cutoff wavelength is shortened as the filter approaches the edge (aka “Shrinking Filter”). However, there are several major problems with that.

[0058] First, while the “Edge Ringing” artefact is indeed avoided, the edge region is still not reliably usable for Nano Topography evaluation, because the filter cutoff wavelength is not the same in the center and at the edge. In the extreme case, when the filter cutoff wavelength shrinks all the way down to zero at the edge, the filter result becomes meaningless.

[0059] Second, if the filter cutoff wavelength does not shrink all the way down to zero, then the part of the edge region that is as wide as the edge cutoff wavelength must be excluded and is not available for Nano Topography evaluation. Alternatively, there are attempts to extrapolate the existing data out over the edge before filtering, however, the extrapolated data must be based on some sort of filtering. Either way, Nano Topography values in an edge region as wide as the shrinking filter’s center cutoff wavelength are unreliable.

[0060] Third, the two dimensions of a shrinking filter are not separable. This limits the implementation choices. The filter’s convolution operation can only work in the length domain and must be carried out for each pixel in x and y. Fourier based implementation is not possible. The result is an extremely slow algorithm. To overcome this and reduce computational resources needed, a very rough step approximation for the Gauss or Double-Gauss kernel is often used. The current industry standard for Gauss and Double-Gauss filtering in semiconductor flatness tools is a 4-step approximation (see Fig.4 below).

[0061] Figure 4 illustrates graphs of length domain kernels for Gauss 405 and Double-Gauss 410 filtering using rough step approximation. Such a step28744-6517 (231018.4) approximation introduces additional issues. The high pass transfer function of such a step kernel is not flat in the pass region (i.e., it partly suppresses frequencies of interest). In addition, the attenuation of the Step Double Gauss is not as strong as the real Double Gauss (1 / 16 per octave) around the cutoff. Below a window of strong suppression, the attenuation has a partial pass band around 1 / 8 of the cutoff frequency, causing undesirable form frequency bleed through, since form frequencies have significantly higher amplitudes.

[0062] Figure 5A illustrates a graph 500 of an exact double gauss kernel 505 vs a step approximation of a double gauss kernel 510 in accordance with at least one embodiment. Graph 500 shows a line for the double Gauss 505 and for the step double Gauss 510, where the double Gauss 505 is the ideal or goal.

[0063] Figure 5B illustrates a graph 520 of an exact gauss kernel 525 vs a step approximation of a gauss kernel 530 in accordance with at least one embodiment. Graph 520 shows a line for the Gauss 525 and for the step Gauss 530, where the Gauss 525 is the ideal or goal.

[0064] Figure 5C illustrates a graph 540 of an exact double gauss kernel's transfer function 545 vs a step approximation double gauss kernel's transfer function 550 in accordance with at least one embodiment. Graph 540 shows a line for the double Gauss response 545 and for the step double Gauss response 550, where the double Gauss response 545 is the ideal or goal. The double Gauss response 545 is theoretical.

[0065] Figure 5D illustrates a graph 560 of an exact gauss kernel's transfer function 545 vs a step approximation gauss kernel's transfer function 550 in accordance with at least one embodiment. Graph 560 shows a line for the Gauss response 565 and for the step Gauss response 570, where the Gauss response 565 is the ideal or goal. The double Gauss response 565 is theoretical.

[0066] Figure 6 illustrates a graph 600 in the logarithmic scale comparing multiple filters. Graph 600 shows the results of the step Gauss high pass28744-6517 (231018.4) 605, the step double Gauss high pass 610, the Gauss high pass 615, and the double Gauss high pass 620.

[0067] There are other filter proposals that describe non-linear gauss regression filters (GRF) up to order 2. The transfer function of an order 2 GRF has the same attenuation of 1 / 16 per octave as the double gauss filter (DG). These proposals describe a robust algorithm to make the filter suitable for step and scratch characterization on curved surfaces.

[0068] There are three additional important issues that so far have not been addressed. First, problems that arise from filtering non-square data areas (i.e., a wafer). In principle, a robust algorithm would be able to handle that, but at the expense of potentially unnecessary iterations and at the expense of not being able to run as a linear filter (without robust iterations) on non-square data areas.

[0069] Second, there is weak frequency separation. Although a GRF may have higher orders, so far only GRF up to order 2 have been described. Implementing higher than order 2 GRF requires a formula for the order dependency of cutoff frequency scaling factor (CFSF) and transfer function (TF). Previous proposals have only been solved for Order 0, 1 and 2 and are lacking for order 3 and above.

[0070] Third, reduced frequency separation occurs at the edges. As will be shown later, order 0, order 2, and all higher even order GRF, when running up to an edge, either due to robust weighing at a step or due to masking as proposed here, experience a change in their transfer function, resulting in factor 2 reduced attenuation power compared to the unrestricted filter in the inner part of the data. This phenomenon renders the currently known GRF not applicable as zero edge exclusion filters.

[0071] The herein presented systems and methods solve the above problems (edge ringing, shape bleed through, and weak frequency separation) by introducing a masked GRF of arbitrary polynomial order n with a cutoff wavelength. This includes a scaling factor s calculated as:28744-6517 (231018.4)

[0072] The systems and methods further include kernel truncation at and data padding by at least:

[0073] Additionally, the systems and methods include eroding the filter mask.

[0074] This system and method are designed to account for digitized data. If the data is digitized, then the kernel will need to be truncated at some point. Accordingly, the kernel is taken toAfterthe data is all zero. By using the truncation presented in EQ. 2, the filter works by ensuring that it doesn’t require too much in the way of computational resources and therefore can be practically useful, such as for analyzing wafers.

[0075] Systems and methods of the present disclosure can be used for analysis and inspection of any suitable semiconductor wafer product. Such systems and methods may suitably be used to characterize wafer thickness, shape, flatness metrics, and nanotopography of the wafer. In some embodiments, the present disclosure can be implemented using a WaferSight tool (e.g., a WS1 generation interferometry tool) available from KLA-Tencor, Milpitas, CA.

[0076] At least one improvements provided by the present disclosure includes setting a new standard for wafer analysis through the provision of true edge exclusion free metrics.

[0077] It is noted that embodiments of the present disclosure include use of two-dimensional data-maps. This is for example purposes. However, one having ordinary skill in the art would understand that the zero edge exclusion filters of the present disclosure are applicable to any number of dimensions.28744-6517 (231018.4)

[0078] Filtering areal data of non-rectangular (such as wafers) shape poses a problem to all linear filters. The invalid data points need to be filled with some values, or else a linear filter cannot be applied. Most commonly, invalid data points are filled with a constant or an extrapolation of the best fit plane or polynom. In any case, in Fourier-space this boundary represents a spectrum of high amplitude frequencies that overwhelm the filter’s attenuation. The result is the well-known phenomenon of “edge- ringing,” which occurs in traditional convolution filters as well as in the known order 0 and order 2 GRF.

[0079] As with the known order 0 and order 2 GRF, a masked arbitrary order GRF is also based on polynomial regression analysis in every point of a real map, convoluted with a Gauss weighing function. The difference to known GRF is that a masked GRF applies a mask map to discriminate between a-priori valid and invalid data points in the map and uses odd order polynomials of order 1 or higher. The inner transfer function was solved as analytical expression of polynomial order and wavelength as well as cutoff wavelength as analytical expression of arbitrary polynomial order.

[0080] Accordingly, a polynomial model of parameters pi,jcan be presented as:

[0081] When the model is fitted in each pixel of map z(x+x,y+y), where x,y here are relative to pixel coordinates x,y, this leads to:y) w(^xF + yF) Bx By EQ. 4with mask m(x,y) and Gaussian weight function28744-6517 (231018.4) with radial distance r from pixel and distance scaling factor s. The mask limits the data into a circle, which then allows it to be used with transforms. The mask is either 1 or 0 depending on if there is data in the circle or not.

[0082] The Fourier-transform of w(r) is: $(+) = 'M(hb)r EQ.6

[0083] Applying the minimization in EQ.4 leads to:x, 6 + y) w(^xF + yF# .+ ., EQ. 8andy) x`LeyaLfw(^xF + yF# .+ ., EQ. 9which leads to tensor equationwithandEQ.1228744-6517 (231018.4)

[0084] The transfer function of such a GRF can be found bysubstituting 7(5, 6) withFourier-transforming EQ. 10, and solvingfor 3^pD,D, +^.

[0085] Finding the transfer function can be greatly simplified byconsidering only one dimension, since the convolution kernel w(^5F + 6F) is separablein its dimensions

[0086] Two cases are considered: (a) inner transfer function with a mask value of 1 everywhere and (b) edge transfer function with the Heavyside Theta function as mask. For calculating the inner transfer function, EQ.15which is a convolutionis rewritten with the power-kerneland its Fourier-transformEQ.18 where & is the Euler-Gamma functionthe Kummer Confluent Hypergeometric function.

[0087] The matrix elements are constants. Their values are M=[ R,S .M[pw(i+j,5# .+ EQ. 1928744-6517 (231018.4)and their Fourier-transform isEQ.21

[0088] Taking the Fourier-transformation of EQ. 14 and 15 andsolving forleads to the inner transfer function.

[0089] This results in a universal inner transfer function for arbitrary polynomial order n.where # is the Regularized Gamma function.

[0090] The requirementleads to the scaling factor28744-6517 (231018.4) with polynomial order . and cutoff wavelength 8D.

[0091] Table 1 illustrates the various scale factors, transfer functions, weight functions, and attenuations at various polynomial orders.TABLE 1

[0092] The GRF behavior on edges cannot be fully characterized by a simple transfer function - convolution kernel pair. While a simple convolution kernel filter will always show edge artefacts, a masked GRF works different on edges and partially valid data. This is because the least square fit of the model polynomial enables the filter to follow the shape all the way to the edge, resulting in excellent edge behavior. However, a transfer function evaluation is useful to evaluate the qualitative difference between odd and even order polynomials, i.e., which one is better in suppressing wavelengths beyond the cut-off wavelength. To do transfer function evaluation, the following are performed: (a) analytically calculate the edge transfer function similar to the inner transfer function but with the Heaviside Theta function as mask and (b) experimentally verify the theoretical result by filtering an image containing a series of sinusoidal waves of different wavelengths.28744-6517 (231018.4)

[0093] For calculating the edge transfer function, the following is substituted pw(i+j,5# - )EQ.27where " 5 is the Heaviside Theta function, representing the masking. This edgepower kernel has the following Fourier-space representation:EQ. 28

[0094] The matrix elements on the edge are MeR,S = .[ M[pwe(i+j,5# .+EQ. 29with their Fourier-transform

[0095] Analog to EQ.16, the Fourier-transform of EQ. 28 is

[0096] Solving for @='(8) leads to the edge transfer function.

[0097] The solutions for the edge transfer functions don’t yield a universal solution for arbitrary polynomial orders as the regularized gamma function for the inner transfer function. And even for mathematical programs, the solutions become numerically unstable at orders higher than 5 due to the terms containing the28744-6517 (231018.4) imaginary error function erfi(). The edge transfer functions for orders 0, 1 and 2 look like this:EQ.35

[0098] The main discovery is that at the edge the attenuation power of odd order polynomials is the same as that of the unmasked transfer function, while for even order polynomials the attenuation power at the edge is factor 2 less than that of the unmasked transfer function. The conclusion is that odd order GRFs provide better edge performance than their next lower even order GRFs while having the exact same inner transfer function. Calculated edge transfer functions up to order 5. Also shown28744-6517 (231018.4) is the edge transfer function of a standard Double Gauss filter (EDG), which on the edge has the same attenuation power as a simple gauss filter. Accordingly, the regression filter behaves on the edge almost like the full filter in the center with just a very slight shift of the cut off behavior. Furthermore, the odd order polynomials have the same attenuation as the inside. There is a factor <1.5 in the cutoff wavelength on the edge.

[0099] Edge and inner transfer functions of order 0 GRF act the same as single Gauss. Order 2 GRF act as Double Gauss. While Double Gauss and order 2 GRF have the same inner attenuation power, on the edge the Double Gauss only has as little attenuation power as Order 1 GRF or Gauss.

[0100] Figure 7 illustrates an example comparison of the results of the different orders of polynomial for a high pass filter, in accordance with each embodiment. The large black line indicates the cutoff frequency, where all frequencies below the cutoff frequencies are removed.

[0101] Figure 8A illustrates a wafer 800 that has been analyzed using the Step Double Gauss filter as described herein. The wafer 800 shows several edge artefacts 805 around the edge of the wafer 800. With this set-up, the user / system can only get data up to 10 mm from the edge. Furthermore, an artefact 810 can be seen in the center of wafer 800. The cutoff wavelength for Figures 8A-8E is 20 mm.

[0102] Figure 8B illustrates a wafer 820 that has been analyzed using the Gauss Regression Filter of order 2 as described herein. This version has similar behavior for most of the wafer 820, but it has improved behavior on the edge. The darker edge artefacts 805 on the edge of wafer 800 appear to have higher amplitude than what is seen on the edge of wafer 820. However, the center artefact 810 can still be seen in the middle of the wafer 820.

[0103] Figure 8C illustrates a wafer 830 that has been analyzed using the Gauss Regression Filter of order 3 as described herein. In this version the viewable information has progressed towards the edge. This view of wafer 830 has an edge28744-6517 (231018.4) attenuation of 16, rather than 8 as shown by wafer 820 or 2 for wafer 800. Furthermore, the regular attenuation is the same (16) for wafer 800, 820, and 830. Accordingly, the center artefact 810 can be seen in all three wafers 800, 820, and 830.

[0104] Figure 8D illustrates a wafer 840 that has been analyzed using the Gauss Regression Filter of order 5 as described herein. Wafer 840 shows further improved visibility towards the edge. The only edge artefacts 805 appear to be from the holders of the wafer. And the center artefacts 810 are barely visible.

[0105] Figure 8E illustrates a wafer 850 that has been analyzed using the Gauss Regression Filter of order 7 as described herein. Figure 8F illustrates a wafer 860 that has been analyzed using the Gauss Regression Filter of order 9 as described herein. Both wafer 850 and 860 show improved edge imaging and the center artefacts appear to no longer exist. The periodic pattern seen on the wafers is a polishing pattern from the preparation of the corresponding wafers. In the wafer embodiment, the periodic pattern is the information that the nanotopology is being used to observe.

[0106] Implementing this filter requires a discrete Fourier-transform. Since a discrete Fourier-transform is always a periodic transform (it treats the data as periodically repeating), it will be necessary to truncate the power kernels and pad the original data by the length of the truncated power kernels. The normalized power- kernels of power j of an order n polynomial GRF are given by EQ.36. 04.

[0107] Figures 9A-9E illustrate a set of graphs of normalized power kernels for GRFs of orders 1, 3, 5, 7, and 9, respectively. The truncation point is be chosen such, that the area under the highest power kernel is fully captured. A good truncation value is where the highest power normalized power-kernel is smaller than 0.01 of the maximum of the last / highest order kernel. After the cut-off, the data is set to zero. Since this is digitized data, the truncation reduces the necessary processing.28744-6517 (231018.4)

[0108] The truncation point on the x-axis is calculated by solving: 6== 04. ^l np , ., .^ EQ. 37which isis the lower branch Lambert W function. The discrete power kernels willbe set to zero for all 5 > 5igjd^ and the raw data are extended by 5igjd^ and filledwith zeros. Additional padding may be added to arrive at a size that enables a highly efficient discrete Fourier transform.

[0109] The so generated discrete power kernels are then Fourier- transformed into discrete transfer functions. Generating these discrete transfer functions directly in Fourier-space would lead to incorrect results, because of the then missing kernel truncation.TABLE 2

[0110] Table 2 contains the different processing times for different filters described herein. For edge exclusion free filtering of typical wafers, it seems that an order 5 GRF sufficiently suppresses all long waves originating from wafer form28744-6517 (231018.4) and edge discontinuity. Higher orders do not bring significant benefit in those cases. Process time of a multi-threaded order 5 GRF is the same as the current wafer industry standard Step Double Gauss.

[0111] Figures 10A and 10B illustrate views of the edge of wafers that have been analyzed with the order 5 GRF. More specifically, Figure 10A illustrates the wafer with no mask erode. Figure 10B illustrates the wafer with a 0.8mm mask erode. The wafer bevel and edge roll-off region represent a sudden deviation from the otherwise flat surface. The edge roll-off and bevel are characterized by radially oriented wavelengths (2-10mm) in the pass region of a typical high-pass filter for Nano- Topography. This edge profile may be undesirable in the Nano-Topography evaluation and should be removed. If it is not removed, it may be desirable that the filter only runs up to the begin of the edge profile, but not in the sense of a hard edge exclusion. However, this leads to masking the low-pass filter such that the edge profile is excluded and the filter extrapolates the edge profile region based on the inner data. This can be accomplished by eroding the mask by 4 pixels at a resolution of 0.2mm / pixel which removes 0.8 mm of edge data that the filter will extrapolate instead of following. Here 0.8mm is about the size of the bevel.

[0112] Figure 11A illustrates a view of the edge of the wafer that has been analyzed with the order 5 GRF. Figure 11B illustrates a view of the edge of the wafer via the ERO signal. Figure 11C illustrates a view of the edge of the wafer where the ERO signal was removed before being analyzed by the order 5 GRF.

[0113] Another way to improve the edges are to remove the ERO signal before applying the GRF high-pass. The GRF is suitable for extracting the ERO signal. This can best be done by transforming the original data into polar coordinates. The polar map can then be filtered by a GRF with no padding and long cutoff wavelength in angular direction and short cutoff wavelength in radial direction. The GRF polynomial’s second parameter map in radial direction is the second derivative (ZDD) in radial direction times 2. This ZDD polar map is then filled with zeros up to the edge of the ERO region and then integrated twice to generate the ERO signal. The28744-6517 (231018.4) resulting map is transformed back to cartesian coordinates and subtracted from the original data. The resulting map is then high-pass filtered with the GRF (without mask erosion).

[0114] Figure 12A illustrates a view of the edge of the wafer that has been analyzed with the order 5 GRF. Figure 12B illustrates a view of the edge of the wafer that has been analyzed with a high-pass edge profile map. Figure 12C illustrates a view of the edge of the wafer where the results of the high-pass edge profile map were subtracted from the high-pass filtered data that was filtered by the order 5 GRF. Another way is to transform the high-pass filtered data to polar coordinates, low-pass filter with long cutoff wavelength in angular and short cutoff wavelength in radial direction to generate a high-pass edge profile map (not the same as ERO), transform the result back to cartesian coordinates and subtract from the high-pass filtered data.

[0115] Figure 13 illustrates a process 1300 for analyzing small surface variations (e.g., the nanotopography or micro-roughness) of surfaces utilizing multi- order regression filters and zero edge exclusion filters. In the example embodiment, process 1300 is performed by the surface analysis server 1410 (shown in Figure 13).

[0116] In the exemplary embodiment, the surface analysis server 1410 receives 1305 scan data of an object to be analyzed. The scan data are of a surface, potentially of a semiconductor wafer. While the above describes using the systems and processes described herein for analyzing silicon wafers, one having ordinary skill in the art would understand that these systems and methods may also be used for analyzing other surfaces. In at least one embodiment, the object to be analyzed is not square. In further embodiments, the object to be analyzed is a circular, semiconductor wafer. In additional embodiments, the scan data is of a three-dimensional or greater object. In other embodiments, the scan data is post-polishing nanotopography. In at least one embodiment, the scan data is one of four line scan data or eight line scan data of the object.

[0117] In the exemplary embodiment, the surface analysis server 1410 generates 1310 a mask to apply to the scan data based on a shape of the object to be28744-6517 (231018.4) analyzed. In some embodiments, the mask applies a 1 or a 0 to the scan data depending on whether or not the corresponding scan data is in or out of the shape, respectively. In some embodiments, the surface analysis server 1410 adjusts the mask to reduce an area covered by the shape of the object to be analyzed prior to applying the mask to the scan data. In these embodiments, the surface analysis server 1410 removes four pixels at a resolution of 0.2mm / pixel from the area covered by the shape of the object to be analyzed. In the exemplary embodiment, the surface analysis server 1410 applies 1315 the mask to the scan data.

[0118] In the exemplary embodiment, the surface analysis server 1410 executes 1320 a multi-order Gaussian regression filter on the masked scan data to generate an output image of the object to be analyzed. In some embodiments, the multi- order Gaussian regression filter is an odd numbered order. In further embodiments, the order is five.

[0119] In the exemplary embodiment, the surface analysis server 1410 analyzes 1325 the output image of the object to be analyzed. In the exemplary embodiment, the surface analysis server 1410 determines 1330 whether or not to approve the object based on the analysis. In other embodiments, the surface analysis server 1410 determines whether or not to adjust one or more devices based on the analysis.

[0120] In some further embodiments, the surface analysis server 1410 determines a cutoff frequency for the scan data. In these embodiments, the surface analysis server 1410 uses a high pass filter on the scan data to remove frequency data below the cutoff frequency.

[0121] Figure 14 illustrates an example system 1400 for performing the process 1300 (shown in Figure 13). In the example embodiment, the system 1400 is used for analyzing small surface variations (e.g., the nanotopography or micro- roughness) of surfaces utilizing multi-order regression filters and zero edge exclusion filters.28744-6517 (231018.4)

[0122] As described below in more detail, a surface analysis server 1410 is programmed for analyzing small surface variations (e.g., the nanotopography or micro-roughness) of surfaces utilizing multi-order regression filters and zero edge exclusion filters. The surface analysis server 1410 is programmed to a) receive 1305 scan data of an object to be analyzed; b) generate 1310 a mask to apply to the scan data based on a shape of the object to be analyzed; c) apply 1315 the mask to the scan data; d) execute 1320 a multi-order Gaussian regression filter on the masked scan data to generate an output image of the object to be analyzed; e) analyze 1325 the output image of the object to be analyzed; and f) determine 1330 whether or not to approve the object based on the analysis (as shown in Figure 13).

[0123] In the example embodiment, client devices 1405 are computers that include a web browser or a software application, which enables client devices 1405 to communicate with surface analysis server 1410 using the Internet, a local area network (LAN), or a wide area network (WAN). In some embodiments, the client devices 1405 are communicatively coupled to the Internet through many interfaces including, but not limited to, at least one of a network, such as the Internet, a LAN, a WAN, or an integrated services digital network (ISDN), a dial-up-connection, a digital subscriber line (DSL), a cellular phone connection, a satellite connection, and a cable modem. Client devices 1405 can be any device capable of accessing a network, such as the Internet, including, but not limited to, a desktop computer, a laptop computer, a personal digital assistant (PDA), a cellular phone, a smartphone, a tablet, a phablet, wearable electronics, smart watch, virtual headsets or glasses (e.g., AR (augmented reality), VR (virtual reality), or XR (extended reality) headsets or glasses), chat bots, voice bots, ChatGPT bots or ChatGPT-based bots, or other web-based connectable equipment or mobile devices.

[0124] In the example embodiment, surface analysis computer device 1410 (also known as surface analysis server 1410) is a computer that include a web browser or a software application, which enables the surface analysis server 1410 to communicate with client devices 1405 and cameras / sensors 1425 using the Internet, a local area network (LAN), or a wide area network (WAN). In some embodiments, the28744-6517 (231018.4) surface analysis server 1410 is communicatively coupled to the Internet through many interfaces including, but not limited to, at least one of a network, such as the Internet, a LAN, a WAN, or an integrated services digital network (ISDN), a dial-up-connection, a digital subscriber line (DSL), a cellular phone connection, a satellite connection, and a cable modem. The surface analysis server 1410 can be any device capable of accessing a network, such as the Internet, including, but not limited to, a desktop computer, a laptop computer, a personal digital assistant (PDA), a cellular phone, a smartphone, a tablet, a phablet, wearable electronics, smart watch, virtual headsets or glasses (e.g., AR (augmented reality), VR (virtual reality), or XR (extended reality) headsets or glasses), chat bots, voice bots, ChatGPT bots or ChatGPT-based bots, or other web-based connectable equipment or mobile devices.

[0125] A database server 1415 is communicatively coupled to a database 1420 that stores data. In one embodiment, the database 1420 is a database that includes a plurality of images from scans. In some embodiments, the database 1420 is stored remotely from the surface analysis server 1410. In some embodiments, the database 1420 is decentralized. In the example embodiment, a person can access the database 1420 via the client devices 1405 by logging onto surface analysis server 1410.

[0126] Camera / sensor 1425 may be any camera and / or sensor that the surface analysis server 1410 is in communication with that transmits images to the surface analysis server 1410. In the example embodiment, camera / sensors 1425 that are in communication with surface analysis server 1410 using the Internet, a local area network (LAN), or a wide area network (WAN). In some embodiments, the camera / sensor(s) 1425 are communicatively coupled to the Internet through many interfaces including, but not limited to, at least one of a network, such as the Internet, a LAN, a WAN, or an integrated services digital network (ISDN), a dial-up-connection, a digital subscriber line (DSL), a cellular phone connection, a satellite connection, and a cable modem.

[0127] Figure 15 depicts an example configuration 1500 of user computer device 1502. In the example embodiment, user computer device 1502 may28744-6517 (231018.4) be similar to, or the same as, client device 1405 (shown in Figure 14). User computer device 1502 may be operated by a user 1501.

[0128] User computer device 1502 may include a processor 1505 for executing instructions. In some embodiments, executable instructions may be stored in a memory area 1510. Processor 1505 may include one or more processing units (e.g., in a multi-core configuration). Memory area 1510 may be any device allowing information such as executable instructions and / or transaction data to be stored and retrieved. Memory area 1510 may include one or more computer readable media.

[0129] User computer device 1502 may also include at least one media output component 1515 for presenting information to user 1501. Media output component 1515 may be any component capable of conveying information to user 1501. In some embodiments, media output component 1515 may include an output adapter (not shown) such as a video adapter and / or an audio adapter. An output adapter may be operatively coupled to processor 1505 and operatively couplable to an output device such as a display device (e.g., a cathode ray tube (CRT), liquid crystal display (LCD), light emitting diode (LED) display, or “electronic ink” display) or an audio output device (e.g., a speaker or headphones).

[0130] In some embodiments, media output component 1515 may be configured to present a graphical user interface (e.g., a web browser and / or a client application) to user 1501. A graphical user interface may include, for example, an interface for viewing items of information provided by the surface analysis server 1410 (shown in Figure 14). In some embodiments, user computer device 1502 may include an input device 1520 for receiving input from user 1501. User 1501 may use input device 1520 to, without limitation, submit information either through speech or typing.

[0131] Input device 1520 may include, for example, a keyboard, a pointing device, a mouse, a stylus, a touch sensitive panel (e.g., a touch pad or a touch screen), a gyroscope, an accelerometer, a position detector, a biometric input device, and / or an audio input device. A single component such as a touch screen may function as both an output device of media output component 1515 and input device 1520.28744-6517 (231018.4)

[0132] User computer device 1502 may also include a communication interface 1525, communicatively coupled to a remote device such as surface analysis server 1410. Communication interface 1525 may include, for example, a wired or wireless network adapter and / or a wireless data transceiver for use with a mobile telecommunications network.

[0133] Stored in memory area 1510 are, for example, computer readable instructions for providing a user interface to user 1501 via media output component 1515 and, optionally, receiving and processing input from input device 1520. A user interface may include, among other possibilities, a web browser and / or a client application. Web browsers enable users, such as user 1501, to display and interact with media and other information typically embedded on a web page or a website from surface analysis server 1410. A client application may allow user 1501 to interact with, for example, surface analysis server 1410. For example, instructions may be stored by a cloud service, and the output of the execution of the instructions sent to the media output component 1515.

[0134] Figure 16 depicts an example configuration 1600 of a server computer device 1602. In the example embodiment, server computer device 1602 may be similar to, or the same as, surface analysis server 1410 and database server 1415 (both shown in Figure 14). Server computer device 1602 may also include a processor 1605 for executing instructions. Instructions may be stored in a memory area 1610. Processor 1605 may include one or more processing units (e.g., in a multi-core configuration).

[0135] Processor 1605 may be operatively coupled to a communication interface 1615 such that server computer device 1602 is capable of communicating with a remote device such as another server computer device 1602, surface analysis s server 1410, camera / sensors 1425, and client devices 1405 (shown in Figure 14) (for example, using wireless communication or data transmission over one or more radio links or digital communication channels). For example, communication28744-6517 (231018.4) interface 1615 may receive input from client devices 1405 via the Internet, as illustrated in Figure 14.

[0136] Processor 1605 may also be operatively coupled to a storage device 1625. Storage device 1625 may be any computer-operated hardware suitable for storing and / or retrieving data, such as, but not limited to, data associated with one or more models. In some embodiments, storage device 1625 may be integrated in server computer device 1602. For example, server computer device 1602 may include one or more hard disk drives as storage device 1625.

[0137] In other embodiments, storage device 1625 may be external to server computer device 1602 and may be accessed by a plurality of server computer devices 1602. For example, storage device 1625 may include a storage area network (SAN), a network attached storage (NAS) system, and / or multiple storage units such as hard disks and / or solid-state disks in a redundant array of inexpensive disks (RAID) configuration.

[0138] In some embodiments, processor 1605 may be operatively coupled to storage device 1625 via a storage interface 1620. Storage interface 1620 may be any component capable of providing processor 1605 with access to storage device 1625. Storage interface 1620 may include, for example, an Advanced Technology Attachment (ATA) adapter, a Serial ATA (SATA) adapter, a Small Computer System Interface (SCSI) adapter, a RAID controller, a SAN adapter, a network adapter, and / or any component providing processor 1605 with access to storage device 1625.

[0139] Processor 1605 may execute computer-executable instructions for implementing aspects of the disclosure. In some embodiments, the processor 1605 may be transformed into a special purpose microprocessor by executing computer- executable instructions or by otherwise being programmed. For example, the processor 1605 may be programmed with the instruction such as illustrated in Figure 13.28744-6517 (231018.4)

[0140] At least one of the technical problems addressed by this system may include: (i) improve analysis of wafers; (ii) decreased loss of material due to malfunction; (iii) earlier determination of wafer quality; (iv) increased accuracy in wafer analysis; and / or (v) increased accuracy in wafer analysis. ADDITIONAL CONSIDERATIONS

[0141] As will be appreciated based upon the foregoing specification, the above-described embodiments of the disclosure may be implemented using computer programming or engineering techniques including computer software, firmware, hardware or any combination or subset thereof. Any such resulting program, having computer-readable code means, may be embodied or provided within one or more computer-readable media, thereby making a computer program product, i.e., an article of manufacture, according to the discussed embodiments of the disclosure. The computer-readable media may be, for example, but is not limited to, a fixed (hard) drive, diskette, optical disk, magnetic tape, semiconductor memory such as read-only memory (ROM), and / or any transmitting / receiving medium such as the Internet or other communication network or link. The article of manufacture containing the computer code may be made and / or used by executing the code directly from one medium, by copying the code from one medium to another medium, or by transmitting the code over a network.

[0142] These computer programs (also known as programs, software, software applications, “apps,” or code) include machine instructions for a programmable processor and can be implemented in a high-level procedural and / or object-oriented programming language, and / or in assembly / machine language. As used herein, the terms “machine-readable medium” “computer-readable medium” refers to any computer program product, apparatus and / or device (e.g., magnetic discs, optical disks, memory, Programmable Logic Devices (PLDs)) used to provide machine instructions and / or data to a programmable processor, including a machine-readable medium that receives machine instructions as a machine-readable signal. The “machine-readable medium” and “computer-readable medium,” however, do not28744-6517 (231018.4) include transitory signals. The term “machine-readable signal” refers to any signal used to provide machine instructions and / or data to a programmable processor.

[0143] As used herein, the terms “processor” and “computer” and related terms, e.g., “processing device”, “computing device”, and “controller” are not limited to just those integrated circuits referred to in the art as a computer, but broadly refers to a microcontroller, a microcomputer, a programmable logic controller (PLC), a reduced instruction set circuit (RISC), an application specific integrated circuit (ASIC), logic circuits, and any other circuit or processor capable of executing the functions described herein. The above examples are example only and are thus not intended to limit in any way the definition and / or meaning of the term “processor.”

[0144] As used herein, the terms “software” and “firmware” are interchangeable, and include any computer program stored in memory for execution by a processor, including RAM memory, ROM memory, EPROM memory, EEPROM memory, and non-volatile RAM (NVRAM) memory. The above memory types are example only, and are thus not limiting as to the types of memory usable for storage of a computer program.

[0145] As used herein, the term “database” can refer to either a body of data, a relational database management system (RDBMS), or to both. As used herein, a database can include any collection of data including hierarchical databases, relational databases, flat file databases, object-relational databases, object-oriented databases, and any other structured collection of records or data that is stored in a computer system. The above examples are example only, and thus are not intended to limit in any way the definition and / or meaning of the term database. Examples of RDBMS’ include, but are not limited to including, Oracle® Database, MySQL, IBM® DB2, Microsoft® SQL Server, Sybase®, and PostgreSQL. However, any database can be used that enables the systems and methods described herein. (Oracle is a registered trademark of Oracle Corporation, Redwood Shores, California; IBM is a registered trademark of International Business Machines Corporation, Armonk, New York;28744-6517 (231018.4) Microsoft is a registered trademark of Microsoft Corporation, Redmond, Washington; and Sybase is a registered trademark of Sybase, Dublin, California.)

[0146] In another example, a computer program is provided, and the program is embodied on a computer-readable medium. In an example, the system is executed on a single computer system, without requiring a connection to a server computer. In a further example, the system is being run in a Windows® environment (Windows is a registered trademark of Microsoft Corporation, Redmond, Washington). In yet another example, the system is run on a mainframe environment and a UNIX® server environment (UNIX is a registered trademark of X / Open Company Limited located in Reading, Berkshire, United Kingdom). In a further example, the system is run on an iOS® environment (iOS is a registered trademark of Cisco Systems, Inc. located in San Jose, CA). In yet a further example, the system is run on a Mac OS® environment (Mac OS is a registered trademark of Apple Inc. located in Cupertino, CA). In still yet a further example, the system is run on Android® OS (Android is a registered trademark of Google, Inc. of Mountain View, CA). In another example, the system is run on Linux® OS (Linux is a registered trademark of Linus Torvalds of Boston, MA). The application is flexible and designed to run in various different environments without compromising any major functionality.

[0147] As used herein, an element or step recited in the singular and proceeded with the word “a” or “an” should be understood as not excluding plural elements or steps, unless such exclusion is explicitly recited. Furthermore, references to “example” or “one example” of the present disclosure are not intended to be interpreted as excluding the existence of additional examples that also incorporate the recited features. Further, to the extent that terms “includes,” “including,” “has,” “contains,” and variants thereof are used herein, such terms are intended to be inclusive in a manner similar to the term “comprises” as an open transition word without precluding any additional or other elements.

[0148] Furthermore, as used herein, the term “real-time” refers to at least one of the time of occurrence of the associated events, the time of measurement28744-6517 (231018.4) and collection of predetermined data, the time to process the data, and the time of a system response to the events and the environment. In the examples described herein, these activities and events occur substantially instantaneously.

[0149] In some embodiments, the system includes multiple components distributed among a plurality of computer devices. One or more components may be in the form of computer-executable instructions embodied in a computer-readable medium. The systems and processes are not limited to the specific embodiments described herein. In addition, components of each system and each process can be practiced independent and separate from other components and processes described herein. Each component and process can also be used in combination with other assembly packages and processes. The present embodiments may enhance the functionality and functioning of computers and / or computer systems.

[0150] The computer-implemented methods discussed herein can include additional, less, or alternate actions, including those discussed elsewhere herein. The methods can be implemented via one or more local or remote processors, transceivers, servers, and / or sensors (such as processors, transceivers, servers, and / or sensors mounted on vehicles or mobile devices, or associated with smart infrastructure or remote servers), and / or via computer-executable instructions stored on non-transitory computer-readable media or medium. Additionally, the computer systems discussed herein can include additional, less, or alternate functionality, including that discussed elsewhere herein. The computer systems discussed herein can include or be implemented via computer-executable instructions stored on non-transitory computer- readable media or medium.

[0151] As used herein, the term “non-transitory computer-readable media” is intended to be representative of any tangible computer-based device implemented in any method or technology for short-term and long-term storage of information, such as, computer-readable instructions, data structures, program modules and sub-modules, or other data in any device. Therefore, the methods described herein can be encoded as executable instructions embodied in a tangible, non-transitory, computer readable28744-6517 (231018.4) medium, including, without limitation, a storage device and / or a memory device. Such instructions, when executed by a processor, cause the processor to perform at least a portion of the methods described herein. Moreover, as used herein, the term “non- transitory computer-readable media” includes all tangible, computer-readable media, including, without limitation, non-transitory computer storage devices, including, without limitation, volatile and nonvolatile media, and removable and non-removable media such as a firmware, physical and virtual storage, CD-ROMs, DVDs, and any other digital source such as a network or the Internet, as well as yet to be developed digital means, with the sole exception being a transitory, propagating signal.

[0152] The patent claims at the end of this document are not intended to be construed under 35 U.S.C. § 112(f) unless traditional means-plus-function language is expressly recited, such as “means for” or “step for” language being expressly recited in the claim(s).

[0153] This written description uses examples to disclose the disclosure, including the best mode, and also to enable any person skilled in the art to practice the disclosure, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the disclosure is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal language of the claims.

Claims

28744-6517 (231018.4) WHAT IS CLAIMED IS:

1. A computer device comprising at least one processor in communication with at least one memory device, wherein the at least one processor programmed to: receive scan data of an object to be analyzed; generate a mask to apply to the scan data based on a shape of the object to be analyzed; apply the mask to the scan data; execute a multi-order Gaussian regression filter on the masked scan data to generate an output image of the object to be analyzed; analyze the output image of the object to be analyzed; and determine whether or not to approve the object based on the analysis.

2. The computer device of Claim 1, wherein the object to be analyzed is not square.

3. The computer device of Claim 1, wherein the object to be analyzed is a circular, semiconductor wafer.

4. The computer device of Claim 1, wherein the mask applies a 1 or a 0 to the scan data depending on whether or not the corresponding scan data is in or out of the shape, respectively.

5. The computer device of Claim 1, wherein the scan data is three- dimensional or greater.

6. The computer device of Claim 1, wherein the multi-order Gaussian regression filter is an odd numbered order.28744-6517 (231018.4) 7. The computer device of Claim 1, wherein the at least one processor is further programmed to determine a cutoff frequency for the scan data.

8. The computer device of Claim 7, wherein the at least one processor is further programmed to use a high pass filter on the scan data to remove frequency data below the cutoff frequency.

9. The computer device of Claim 1, wherein the at least one processor programmed to adjust the mask to reduce an area covered by the shape of the object to be analyzed prior to applying the mask to the scan data.

10. The computer device of Claim 9, wherein the at least one processor removes four pixels at a resolution of 0.2mm / pixel from the area covered by the shape of the object to be analyzed.

11. The computer device of Claim 1, wherein the scan data is post- polishing nanotopography.

12. The computer device of Claim 1, wherein the scan data is one of four line scan data or eight line scan data of the object.

13. The computer device of Claim 1, wherein the at least one processor is further programmed to determine whether or not to adjust one or more devices based on the analysis.

14. A computer-implemented method for analyzing an object, the computer-implemented method implemented by a computing device including at least one processor in communication with at least one memory device, the method comprising: receiving scan data of an object to be analyzed; generating a mask to apply to the scan data based on a shape of the object to be analyzed; applying the mask to the scan data;28744-6517 (231018.4) executing a multi-order Gaussian regression filter on the masked scan data to generate an output image of the object to be analyzed; analyzing the output image of the object to be analyzed; and determining whether or not to approve the object based on the analysis.

15. The computer-implemented method of Claim 14, wherein the object to be analyzed is not square.

16. The computer-implemented method of Claim 14, wherein the object to be analyzed is a circular, semiconductor wafer.

17. The computer-implemented method of Claim 14, wherein the mask applies a 1 or a 0 to the scan data depending on whether or not the corresponding scan data is in or out of the shape, respectively.

18. The computer-implemented method of Claim 14, wherein the multi-order Gaussian regression filter is an odd numbered order.

19. The computer-implemented method of Claim 14 further comprising: determining a cutoff frequency for the scan data; and using a high pass filter on the scan data to remove frequency data below the cutoff frequency.

20. The computer-implemented method of Claim 14 further comprising adjusting the mask to reduce an area covered by the shape of the object to be analyzed prior to applying the mask to the scan data.

Images