Surface topography detection method, detection device, readable medium, program product

Abstract

The present disclosure provides a surface topography detection method, comprising: applying a predetermined magnetic field to a Hall sensor, acquiring a first voltage across the second conductor and a second voltage across the third conductor when a current is provided to the first conductor, and acquiring a third voltage across the first conductor and a fourth voltage across the second conductor when a current is provided to the third conductor; determining a cell angle of a cell where the Hall sensor is located according to the corresponding first voltage, second voltage, third voltage and fourth voltage; determining cell positions of a plurality of cells according to the cell angles of the plurality of cells; and determining a surface topography of a surface to be detected according to the cell positions of the plurality of cells. The present disclosure also provides a detection device, a computer readable medium and a computer program product.

Description

Technical Field

[0001] This disclosure relates to the field of surface morphology detection technology, and in particular to a surface morphology detection method, detection equipment, computer-readable medium, and computer program product. Background Technology

[0002] Existing surface topography detection technologies cannot determine the three-dimensional (3D) morphology of a surface, which leads to the loss of surface topography information. Summary of the Invention

[0003] This disclosure provides a surface morphology detection method, detection equipment, computer-readable medium, and computer program product.

[0004] In a first aspect, embodiments of this disclosure provide a surface morphology detection method, wherein the surface to be detected is provided with a plurality of Hall sensors arranged in an array; each Hall sensor includes a first conductor extending along a first direction, a second conductor extending along a second direction, and a third conductor extending along a third direction, wherein the first conductor, the second conductor, and the third conductor overlap at an overlap portion, and any two of the first direction, the second direction, and the third direction intersect; the method includes:

[0005] A predetermined magnetic field is applied to the Hall sensor, and when current is supplied to the first conductor, a first voltage across the second conductor and a second voltage across the third conductor are obtained respectively; when current is supplied to the third conductor, a third voltage across the first conductor and a fourth voltage across the second conductor are obtained respectively.

[0006] The angle of the surface element where the Hall sensor is located is determined based on the corresponding first voltage, second voltage, third voltage, and fourth voltage.

[0007] The positions of the multiple face elements are determined based on their face angles.

[0008] The surface morphology of the surface to be detected is determined based on the positions of the multiple surface elements.

[0009] Secondly, embodiments of this disclosure provide a detection device, which includes:

[0010] A control module is used for electrical connection to the substrate to be tested, and for detecting the surface morphology of the surface to be tested according to any surface morphology detection method of the present disclosure; one surface of the substrate to be tested is the surface to be tested.

[0011] A support module is provided for supporting the substrate to be tested.

[0012] A magnetic field module is used to apply a predetermined magnetic field to the Hall sensor.

[0013] Thirdly, embodiments of this disclosure provide a computer-readable medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements any of the surface morphology detection methods of this disclosure.

[0014] Fourthly, embodiments of this disclosure provide a computer program product, which includes a computer program, and the computer program, when executed by a processor, is any of the surface morphology detection methods of embodiments of this disclosure.

[0015] In this embodiment of the disclosure, each Hall sensor includes three conductors. By detecting the potential difference (voltage) between the two ends of the other two conductors when current is passed through each conductor, the angle of the Hall sensor itself relative to the predetermined magnetic field can be calculated, which is the angle of the surface element where the Hall sensor is located. Since multiple Hall sensors are distributed in an array on the surface to be detected, by analyzing the angles of multiple surface elements, the 3D surface element positions of multiple surface elements can be determined, which means the 3D morphology of the surface to be detected can be determined, thus achieving smoother and more detailed surface morphology detection. Attached Figure Description

[0016] In the accompanying drawings of the embodiments disclosed herein:

[0017] Figure 1 This is a top view of the array of Hall sensors on the surface to be detected in a surface morphology detection method provided in this embodiment of the present disclosure.

[0018] Figure 2 This is a perspective three-dimensional structural diagram of a Hall sensor provided in an embodiment of this disclosure.

[0019] Figure 3 This is a schematic flowchart of a surface morphology detection method provided in an embodiment of the present disclosure.

[0020] Figure 4 This is a schematic diagram of the first stage of detection process of a Hall sensor in a surface morphology detection method provided in this embodiment of the present disclosure.

[0021] Figure 5 This is a schematic diagram of the second-stage detection process of a Hall sensor in a surface morphology detection method provided in this embodiment of the present disclosure.

[0022] Figure 6 This diagram illustrates the role of the Hall effect in another surface morphology detection method provided in this embodiment of the present disclosure.

[0023] Figure 7 This is a flowchart illustrating some steps of another surface morphology detection method provided in this embodiment of the present disclosure.

[0024] Figure 8This is a schematic diagram illustrating the calculation process of surface element positions in another surface morphology detection method provided in this embodiment of the present disclosure.

[0025] Figure 9 This is a schematic diagram illustrating the positional relationship between a reference surface element and adjacent surface elements in another surface topography detection method provided in this embodiment of the present disclosure.

[0026] Figure 10 This is a schematic diagram illustrating the positional relationship between a reference surface element and adjacent surface elements in another surface topography detection method provided in this embodiment of the present disclosure.

[0027] Figure 11 This is a schematic diagram of a surface element image acquired in another surface morphology detection method provided in this embodiment of the present disclosure.

[0028] Figure 12 This is a schematic diagram illustrating the process of analyzing displacement based on a surface element image in another surface morphology detection method provided in this embodiment of the present disclosure.

[0029] Figure 13 This is a schematic diagram illustrating the positional relationship between a reference surface element and adjacent surface elements in another surface topography detection method provided in this embodiment of the present disclosure.

[0030] Figure 14 This is a schematic diagram illustrating the process of constructing the surface morphology of the surface to be detected based on feature points in another surface morphology detection method provided in this embodiment of the present disclosure.

[0031] Figure 15 This is a schematic diagram illustrating the process of constructing the surface morphology of the surface to be detected based on vertices in another surface morphology detection method provided in this embodiment of the present disclosure.

[0032] Figure 16 This is a schematic diagram illustrating the coplanar relationship between multiple feature points and a common vertex in another surface topography detection method provided in this embodiment of the present disclosure.

[0033] Figure 17 This is a schematic diagram illustrating the coplanar relationship between multiple vertices and a feature point in another surface topography detection method provided in this embodiment of the present disclosure.

[0034] Figure 18 This is a block diagram of a detection device provided in an embodiment of the present disclosure.

[0035] Figure 19 This is a block diagram of another detection device provided in an embodiment of the present disclosure.

[0036] Figure 20 This is a block diagram illustrating the composition of a computer-readable medium provided in an embodiment of the present disclosure.

[0037] In this embodiment of the disclosure, the meanings of some reference numerals are as follows:

[0038] X, First direction; Y, Second direction; Z, Third direction; 1, Hall sensor; 11, First conductor; 12, Second conductor; 13, Third conductor; 19, Overlapping part; 2, Surface element; 51, Magnetic field module; 52, Probe; 53, Base; 54, Sample stage; 55, Balance block; 56, Worktable; 9, Substrate to be tested; CCD, Image acquisition unit. Detailed Implementation

[0039] To enable those skilled in the art to better understand the technical solutions of this disclosure, the surface morphology detection method, detection equipment, computer-readable medium, and computer program product provided in the embodiments of this disclosure will be described in detail below with reference to the accompanying drawings.

[0040] The present disclosure will be described more fully below with reference to the accompanying drawings; however, the embodiments shown may be embodied in different forms, and the present disclosure should not be construed as limited to the embodiments set forth below. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will enable those skilled in the art to fully understand the scope of the disclosure.

[0041] The accompanying drawings of the embodiments disclosed herein are provided to further illustrate the embodiments of this disclosure and form part of the specification. They are used together with the detailed embodiments to explain this disclosure and do not constitute a limitation thereof. The above and other features and advantages will become more apparent to those skilled in the art from the description of the detailed embodiments with reference to the accompanying drawings.

[0042] This disclosure may be described with reference to plan and / or cross-sectional views using the ideal schematic diagrams of this disclosure. Therefore, the example illustrations may be modified according to manufacturing techniques and / or tolerances.

[0043] Where there is no conflict, the various embodiments of this disclosure and the features thereof in the embodiments may be combined with each other.

[0044] The terminology used in this disclosure is for the purpose of describing particular embodiments only and is not intended to limit the disclosure. The term "and / or" as used in this disclosure includes any and all combinations of one or more of the associated enumerated entries. The singular forms "a" and "the" as used in this disclosure are also intended to include the plural forms, unless the context clearly indicates otherwise. The terms "comprising," "made of," etc., as used in this disclosure specify the presence of the stated feature, integral, step, operation, element, and / or component, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components, and / or groups thereof.

[0045] Unless otherwise specified, all terms used in this disclosure (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art. It will also be understood that terms such as those defined in commonly used dictionaries should be interpreted as having a meaning consistent with their meaning in the context of the relevant art and this disclosure, and will not be interpreted as having an idealized or overly formal meaning, unless expressly so defined in this disclosure.

[0046] This disclosure is not limited to the embodiments shown in the accompanying drawings, but includes modifications to the configuration based on the manufacturing process. Therefore, the areas illustrated in the drawings are schematic, and the shapes of the areas shown illustrate specific shapes of the areas of an element, but are not intended to be limiting.

[0047] The surface flatness of substrates such as packaging (e.g., electronic packaging) substrates and wafers is crucial for the accurate formation of subsequent structures and the guarantee of product performance. Therefore, it is necessary to inspect the surface morphology of the substrate to determine whether there is warping or other deformation.

[0048] In related technologies, warpage detection of packaging substrates and wafers mainly adopts Shadow Moiré technology. That is, a grid is set on the surface to be detected, and the deformation of the surface to be detected will cause the grid to deform and produce moiré patterns. Therefore, by acquiring images of moiré patterns by an image acquisition unit (such as a camera) and analyzing them, the height information of different positions on the surface to be detected can be determined.

[0049] However, moiré images are two-dimensional (2D), while the actual surface topography is obviously three-dimensional (3D). Therefore, although the ShadowMoiré technique can obtain height information at various locations, it will inevitably cause some information (such as the curvature and orientation of local surfaces) to be filtered out and lost.

[0050] Firstly, referring to Figures 1 to 17 This disclosure provides a surface morphology detection method.

[0051] The surface to be detected is provided with a plurality of Hall sensors 1 arranged in an array; each Hall sensor 1 includes a first conductor 11 extending along a first direction X, a second conductor 12 extending along a second direction Y, and a third conductor 13 extending along a third direction Z; the first conductor 11, the second conductor 12, and the third conductor 13 overlap at an overlap portion 19; any two of the first direction X, the second direction Y, and the third direction Z intersect.

[0052] This embodiment is used to detect the surface morphology of the surface to be tested.

[0053] Reference Figure 1The surface to be tested is pre-set with multiple Hall sensors 1 arranged in an array, and the angle of each Hall sensor 1 can represent the angle of a local area (surface element 2) of the surface to be tested.

[0054] Reference Figure 2 Each Hall sensor 1 includes a first conductor 11, a second conductor 12, and a third conductor 13. Any two of the extension directions of the three conductors (first direction X, second direction Y, and third direction Z) intersect (i.e., are not parallel). Moreover, the three conductors have a common "overlapping portion 19 (indicated by the part outlined by the bold short dashed line in each figure)," that is, the overlapping portion 19 belongs to the first conductor 11, the second conductor 12, and the third conductor 13 simultaneously.

[0055] The conductors of Hall sensor 1 are made of conductive materials, such as aluminum (Al) and copper (Cu).

[0056] Furthermore, the array of Hall sensors 1 can be "integrated" into the substrate to be detected, where the surface to be detected is located.

[0057] For example, the array of Hall sensors 1 can be formed directly on the surface to be detected during the preparation of wafers, packaging substrates, and other substrates.

[0058] It should be understood that the substrate to be tested may also contain circuits for applying signals to the Hall sensor 1 and detecting those signals, which will not be described in detail here.

[0059] In some embodiments, refer to Figure 2 The overlapping portion 19 is located in the middle of the first conductor 11; the overlapping portion 19 is located in the middle of the second conductor 12; the overlapping portion 19 is located in the middle of the third conductor 13.

[0060] Reference Figure 2 As one embodiment of this disclosure, for each conductor (first conductor 11, second conductor 12, third conductor 13), the overlapping portion 19 may be located relatively in the middle of itself, so as to facilitate the application of current and detection voltage through both ends of the conductor.

[0061] In some embodiments, refer to Figure 2 Any two of the first direction X, the second direction Y, and the third direction Z are perpendicular to each other.

[0062] Reference Figure 2 As one embodiment of this disclosure, the first direction X, the second direction Y, and the third direction Z can be orthogonal to each other, so that the first conductor 11, the second conductor 12, and the third conductor 13 constitute a "double cross structure".

[0063] In some embodiments, refer to Figure 2 The first conductor 11 is a cube, the second conductor 12 is a cube, the third conductor 13 is a cube, and the overlapping portion 19 is a cube; along the first direction X, the dimensions of the overlapping portion 19, the second conductor 12, and the third conductor 13 are equal; along the second direction Y, the dimensions of the overlapping portion 19, the first conductor 11, and the third conductor 13 are equal; along the third direction Z, the dimensions of the overlapping portion 19, the first conductor 11, and the second conductor 12 are equal.

[0064] Reference Figure 2 As one embodiment of this disclosure, when the first direction X, the second direction Y, and the third direction Z are orthogonal to each other, the first conductor 11, the second conductor 12, and the third conductor 13 can all be in the form of a cube, and thus the overlapping part 19 is also a cube.

[0065] Furthermore, refer to Figure 2 , Figure 6 The overlapping portion 19, the second conductor 12, and the third conductor 13 have equal dimensions in the first direction X, all being L; the overlapping portion 19, the first conductor 11, and the third conductor 13 have equal dimensions in the second direction Y, all being W; the overlapping portion 19, the first conductor 11, and the second conductor 12 have equal dimensions in the third direction Z, all being D.

[0066] Reference Figure 3 The surface morphology detection method of this disclosure includes:

[0067] S101. Apply a predetermined magnetic field B to the Hall sensor 1. When current is supplied to the first conductor 11, obtain the first voltage V1 across the second conductor 12 and the second voltage V2 across the third conductor 13 respectively. When current is supplied to the third conductor 13, obtain the third voltage V3 across the first conductor 11 and the fourth voltage V4 across the second conductor 12 respectively.

[0068] S102. Determine the angle of the surface element 2 where the Hall sensor 1 is located based on the corresponding first voltage V1, second voltage V2, third voltage V3, and fourth voltage V4.

[0069] S103. Determine the positions of multiple face elements 2 based on their face element angles.

[0070] S104. Determine the surface morphology of the surface to be detected based on the positions of the multiple surface elements 2.

[0071] In the surface morphology detection method of this embodiment, multiple Hall sensors 1 are first detected. Specifically, when detecting each Hall sensor 1, the detection is performed in two stages under the condition that a predetermined magnetic field B (i.e., a magnetic field with known direction and intensity) is applied:

[0072] Reference Figure 4 In the first stage of detection, a current I is supplied to the first conductor 11 of the Hall sensor 1 (that is, the current flows in from one end of the first conductor 11 and flows out from the other end), and the first voltage V1 (or the potential difference between the two ends) across the second conductor 12 and the second voltage V2 across the third conductor 13 are detected respectively.

[0073] Reference Figure 5 In the second stage of detection, a current I is supplied to the third conductor 13 of the Hall sensor 1, and the third voltage V3 across the first conductor 11 and the fourth voltage V4 across the second conductor 12 are detected respectively.

[0074] It should be understood that in the embodiments of this disclosure, when different Hall sensors 1 are detected as described above, their predetermined magnetic field B (direction and magnitude) and current I (direction and magnitude) may be the same or different.

[0075] One approach is to apply a localized predetermined magnetic field B to the Hall sensor 1 being detected via a movable magnetic field module (such as a magnetic field module mounted on the probe), or to apply a predetermined magnetic field B to all Hall sensors 1 simultaneously via a fixed magnetic field module.

[0076] It should be understood that there are various ways to detect multiple Hall sensors 1, and specifically which Hall sensors 1 to detect.

[0077] For example, one Hall sensor 1 can be selected and detected "only" at a time by address selection, while multiple Hall sensors 1 can be detected "sequentially" by selecting different addresses.

[0078] Alternatively, multiple Hall sensors 1 can be detected "simultaneously".

[0079] For example, the number of detections T can be preset, and one Hall sensor 1 can be selected for detection each time. If the number of Hall sensors 1 detected is less than T after detection, another Hall sensor 1 can be selected to continue detection until the number of Hall sensors 1 detected reaches T.

[0080] Alternatively, all Hall sensors 1 in the array can be detected, or only a selected portion of the Hall sensors 1 can be detected.

[0081] According to the Hall effect, when a current in a conductor is subjected to a magnetic field (or a component of the magnetic field) perpendicular to its direction, an electromotive force will be generated in a direction perpendicular to both the direction of the current and the direction of the magnetic field.

[0082] Therefore, based on the first voltage V1, the second voltage V2, the third voltage V3, and the fourth voltage V4, the relative angle between the Hall sensor 1 and the predetermined magnetic field B can be calculated, which is the direction of the predetermined magnetic field B in the local coordinate system of the Hall sensor 1 (such as the coordinate system defined by the first direction X, the second direction Y, and the third direction Z).

[0083] For example, refer to Figure 6 For each Hall sensor 1, in its local coordinate system, the angle between the predetermined magnetic field B and the directions of the two currents (the first direction X and the third direction Z) is divided into... And θ, and can be divided into two directional components B1 and B2, so that in the first stage of detection, the obtained V1 and V2 satisfy the following formulas (1) and (2) respectively:

[0084]

[0085] V2=I·B1·W=I·B·W·cosθ (2);

[0086] Similarly, in the second-stage detection, the obtained V3 and V4 satisfy the following formulas (3) and (4), respectively:

[0087]

[0088] Dividing formula (4) by (3) gives the angle. As shown in formula (5):

[0089]

[0090] Dividing formulas (1) and (2) yields formula (6):

[0091]

[0092] Furthermore, substituting formula (5) into formula (6), we can obtain the angle θ as expressed in formula (7):

[0093]

[0094] Using formulas (5) and (7), the expression for the vector of the predetermined magnetic field B in the local coordinate system of Hall sensor 1 can be further calculated.

[0095] Since the direction of the predetermined magnetic field B is known, the angle of each Hall sensor 1 relative to the predetermined magnetic field B can be used to represent the angle of the Hall sensor 1 itself in the global coordinate system (such as the coordinate system based on the substrate to be detected). Moreover, for a sufficiently small surface element 2, it can be considered that the Hall sensor 1 will rotate with the surface element 2 it is located in. Therefore, the angle of the Hall sensor 1 is the surface element angle of the surface element 2 it is located in, or the angle of a local area of ​​the surface to be detected.

[0096] Furthermore, since each surface element 2 is obviously "continuous", the surface element position of multiple surface elements 2 in three-dimensional space (3D) can be calculated by the surface element angles of multiple surface elements 2 (multiple Hall sensors 1).

[0097] Based on the positions of multiple face elements 2, the overall surface morphology of the surface to be detected can be determined, and it is a 3D surface morphology.

[0098] In this embodiment of the present disclosure, each Hall sensor 1 includes three conductors. By detecting the potential difference (voltage) between the two ends of the other two conductors when current is passed through each conductor, the angle of the Hall sensor 1 relative to the predetermined magnetic field B can be calculated, which is the angle of the surface element 2 where the Hall sensor 1 is located. Since multiple Hall sensors 1 are distributed in an array on the surface to be detected, by analyzing multiple surface element angles, the 3D surface element position of multiple surface elements 2 can be determined, which means the 3D morphology of the surface to be detected can be determined, thus achieving smoother and more detailed surface morphology detection.

[0099] In some embodiments, determining the surface angle of the surface element 2 where the Hall sensor 1 is located based on the corresponding first voltage V1, second voltage V2, third voltage V3, and fourth voltage V4 (S102) includes:

[0100] S102A1. Determine the local magnetic field detected by Hall sensor 1 based on the corresponding first voltage V1, second voltage V2, third voltage V3, and fourth voltage V4.

[0101] S102A2, Construct a system of nonlinear equations.

[0102] The nonlinear equations represent that the local magnetic field, after being rotated by the rotation matrix, is equal to the predetermined magnetic field B.

[0103] S102A3, Solve the nonlinear equations to obtain the rotation matrix.

[0104] S102A4. Determine the angle of the surface element 2 where Hall sensor 1 is located based on the rotation matrix.

[0105] As one embodiment of this disclosure, for each surface element 2, the expression of a predetermined magnetic field B in the local coordinate system of its Hall sensor 1 (such as a local magnetic field in vector form) can be detected. This local magnetic field and the predetermined magnetic field B expressed in the global coordinate system are actually the same magnetic field with the same direction. Thus, a "nonlinear equation set" can be established based on these two magnetic field expressions. This nonlinear equation set shows that in the global coordinate system, the predetermined magnetic field can be obtained by rotating the local magnetic field through a rotation matrix.

[0106] Therefore, by solving the nonlinear equations, the rotation matrix R can be obtained, which represents the relative angular relationship between the local coordinate system and the global coordinate system of Hall sensor 1, that is, the surface angle of surface element 2.

[0107] For example, the vector representation of the predetermined magnetic field B in the local and global coordinate systems is A. local and A global , as in formula (8);

[0108]

[0109] Where r is the modulus of the predetermined magnetic field B, or the strength of the predetermined magnetic field B.

[0110] Assume the basis loss n of a surface element 2 (or Hall sensor 1) x n y n z In the global coordinate system, this is expressed as formula (9):

[0111]

[0112] Then, based on the constraints of the basis loss (orthogonality, normalization), we can obtain formulas (10) and (11):

[0113] n x ·n y =0, n x ·n z =0, n y ·n z =0 (10);

[0114] ||n x ||=||n y ||=||n z || = 1 (11).

[0115] Accordingly, a rotation matrix R can be constructed, as shown in formula (12):

[0116] R = [n x n y n z (12);

[0117] As before, A local After rotation by rotation matrix R, we can obtain A. global That is, there is R·A local =A global That is, there is formula (13):

[0118]

[0119] Thus, the nonlinear equation system (14) can be obtained:

[0120]

[0121] It can be seen that the nonlinear equation system (14) has 9 unknowns (x1, x2, x3, y1, y2, y3, z1, z2, z3) and 9 equations, so it is a positive definite equation system and must have a numerical solution.

[0122] Since numerical algorithms are prone to divergence, geometric decomposition can be used to further simplify the above nonlinear equations.

[0123] First, parameters α, β, and γ can be set as shown in formula (15):

[0124]

[0125] γ=rcosθ (15).

[0126] Among them, due to r, θ, All are known (θ, (As obtained through the above two stages of detection), α, β, and γ are also known. Thus, x1, x2, x3, y1, y2, and y3 in the nonlinear equation system can be simplified to equation system (16), while z1, z2, and z3 can be simplified to equation system (17).

[0127]

[0128] Therefore, based on the two sets of equations (16) and (17), all the unknowns in the nonlinear set of equations (14) can be obtained through analytical solutions or numerical solutions.

[0129] For example, to find an analytical solution, one can first solve the system of equations (17) and then substitute it into the system of equations (16); while to find a numerical solution, one can iteratively solve the system of equations (17) and then obtain all the numerical solutions based on the system of equations (16).

[0130] As can be seen, the nine unknowns x1, x2, x3, y1, y2, y3, z1, z2, z3 of the nonlinear equation system (14) can be obtained in the above way, which is equivalent to determining the rotation matrix R, that is, the angle of the face element 2.

[0131] It should be understood that in some cases, a system of nonlinear equations may not be able to find a unique solution, and this situation represents A local A global Directly parallel (therefore, the angle of the surface element is determined at this time), and the rotation matrix R at this time is the identity matrix G. Therefore, the overall expression of the rotation matrix R can be expressed as formula (18).

[0132]

[0133] Furthermore, if we assume that the first direction X and the second direction Y of the Hall sensor are perpendicular to each other and parallel to the surface element 2 it is located on, and the third direction Z is perpendicular to surface element 2 (and also perpendicular to the first direction X and the second direction Y), and the surface angle is represented by the normal vector of surface element 2 (the vector perpendicular to the surface of surface element 2), then n z It is the normal vector that can represent the angle of the surface element, so we can obtain n. z With n′ in global coordinates z The relationship satisfies the following formulas (19) and (20):

[0134] R·n z =n′ z (19)

[0135]

[0136] In some embodiments, determining the surface angle of the surface element 2 where the Hall sensor 1 is located based on the corresponding first voltage V1, second voltage V2, third voltage V3, and fourth voltage V4 (S102) includes:

[0137] S102B1. Determine the local magnetic field detected by Hall sensor 1 based on the corresponding first voltage V1, second voltage V2, third voltage V3, and fourth voltage V4.

[0138] S102B2, Determine the local normalized vector after normalizing the local magnetic field, and the predetermined normalized vector after normalizing the predetermined magnetic field B.

[0139] S102B3. Determine the vector rotation axis and vector rotation angle of the local normalized vector relative to the predetermined normalized vector.

[0140] S102B4. Determine the angle of the surface element 2 where Hall sensor 1 is located based on the vector rotation axis and the vector rotation angle.

[0141] As another embodiment of this disclosure, the vector representation of the predetermined magnetic field B in the local coordinate system and the global coordinate system can be normalized first, and then the rotation axis (vector rotation axis) and rotation angle (vector rotation axis) between the two normalized vectors (local normalized vector and predetermined normalized vector) can be determined, and then the surface element angle can be determined based on them.

[0142] For example, the vector representations Alocal and Aglobal of the predetermined magnetic field B in the local and global coordinate systems are normalized respectively to obtain the locally normalized vector. and the pre-defined normalized vector As in formula (21):

[0143]

[0144] Next, we continue to calculate the vector rotation axis K and rotation angle ψ between the two normalized vectors, as shown in formulas (22) and (23):

[0145]

[0146] According to Rodrigues's rotation formula, the rotation matrix R can be obtained through matrix operations as shown in formula (24):

[0147] R = G + sinψ·K + (G - cosψ)·K 2 (twenty four);

[0148] Where G is the identity matrix, as shown in formula (25):

[0149]

[0150] Similarly, when A local A global When directly parallel, the unique solution of R cannot be found according to this method. That is, it can be considered that when there is no unique solution, the rotation matrix R is the identity matrix G. Therefore, the overall expression of the rotation matrix R can be expressed as formula (26).

[0151]

[0152] In some embodiments, refer to Figure 7 Based on the angles of multiple face elements 2, the positions of the face elements 2 are determined (S103), including:

[0153] S1031. Select a reference surface element from multiple surface elements 2.

[0154] S1032. Select surface element 2, which shares a common edge with the reference surface element, as the adjacent surface element.

[0155] S1033. Determine the position of adjacent face elements based on the face element position and angle of the reference face element and the face element angle of adjacent face elements.

[0156] S1034. In response to the failure to meet the preset termination condition, the process returns to the step of selecting a face 2 that shares a common adjacent edge with the reference face as the adjacent face (step S1032).

[0157] Reference Figure 7 , Figure 8 As one embodiment of this disclosure, one can first select one from multiple face elements 2 (of course, face elements 2 whose face angles have been calculated in the above manner) as the "benchmark" for judging the face element positions of all face elements 2 of the surface to be detected. That is, the face element positions of other face elements 2 are relative to the face element positions of the benchmark face element.

[0158] For example, the reference elements above can be selected "randomly", and their positions can be represented by coordinates in the global coordinate system, such as setting their coordinates to (0,0,0).

[0159] It should be understood that the above selection method for reference elements is not limited to "random". For example, a specific element 2 (such as element 2 located in a specific corner of the surface to be detected) can also be used as the reference element.

[0160] Then, select a surface element 2 that is adjacent to the reference surface element as the "adjacent surface element".

[0161] Since the adjacent face element and the reference face element share a common adjacent edge, their relative positions are subject to certain restrictions. Therefore, based on the face element angle of the reference face element and the face element angle of the adjacent face element, their relative positional relationship can be determined. Then, based on the face element position of the reference face element, the face element position of the adjacent face element can be determined.

[0162] After determining the positions of adjacent face elements, you can refer to Figure 8 The adjacent surface element is re-identified as the reference surface element, and referenced... Figure 7 Then, select a new neighboring cell 2 (which cannot be a cell 2 that has been used as a reference cell before) as the neighboring cell, and recalculate the cell position of the new neighboring cell until the preset termination condition is met.

[0163] Therefore, based on the above method, the positions of multiple face elements 2 in the surface to be detected can be determined.

[0164] It should be understood that there are various ways to select adjacent face elements, such as random selection or selection according to a predetermined "route".

[0165] It should be understood that the above termination conditions can take many forms, such as calculating the positions of a predetermined number of face elements 2, or calculating the positions of all pre-defined face elements 2.

[0166] In some embodiments, surface element 2 is rectangular, the surface element position is characterized by the position of a feature point located at its geometric center, and the surface element angle is characterized by a normal vector perpendicular to it; determining the surface element position of adjacent surface elements based on the surface element position and angle of the reference surface element and the surface element angle of adjacent surface elements (S1033) includes:

[0167] S1033A1. Determine the neighboring edge vector of the common neighboring edge based on the normal vector of the reference surface element and the normal vector of the adjacent surface element.

[0168] S1033A2. Based on the adjacent edge vector, the normal vector of the reference surface element, and the normal vector of the adjacent surface element, determine the first vector whose end point is located at the midpoint of the common adjacent edge, and the second vector whose starting point is located at the midpoint of the common adjacent edge.

[0169] The first vector is perpendicular to the adjacent edge vector and the normal vector of the reference surface element, and the second vector is perpendicular to the adjacent edge vector and the normal vector of the adjacent surface element; the lengths of the first vector and the second vector are both equal to half the dimension of the reference surface element along the direction of the first vector.

[0170] S1033A3, Determine the displacement vector from the beginning of the first vector to the end of the second vector.

[0171] S1033A4. Determine the position of the feature point of the adjacent surface element from the feature point of the reference surface element through the displacement vector.

[0172] As one embodiment of this disclosure, reference is made to... Figure 9 Surface element 2 can be a rectangle, and the position of the surface element is characterized by the position of the feature point of the geometric center of the surface element 2, while the angle of the surface element is represented by the normal vector perpendicular to the surface element 2 itself.

[0173] As one embodiment of this disclosure, it can be "approximately determined" that surface element 2 will only rotate without shape distortion. That is, surface element 2 is always a rectangle with unchanged shape and size. Therefore, adjacent surface elements will only rotate around the reference surface element by a certain angle with their common adjacent side as the axis.

[0174] Therefore, referring to Figure 9 Based on the normal vectors of the two face elements 2, the neighboring edge vectors of the common neighbor can be calculated; based on the normal vectors of the two face elements 2 and the above neighboring edge vectors, the first vector pointing from the feature point of the reference face element to the midpoint of the common neighbor and the second vector pointing from the midpoint of the common neighbor to the feature point of the adjacent face element can also be calculated.

[0175] Furthermore, the displacement vector from the beginning of the first vector to the end of the second vector can also be calculated. This displacement vector is the same as the vector from the feature point of the reference surface element to the feature point of the adjacent surface element. Therefore, by adding the displacement vector to the position of the feature point of the reference surface element, the position of the feature point of the adjacent surface element can be calculated, which is the surface element position of the adjacent surface element.

[0176] For example, refer to Figure 9 The reference plane element and its adjacent plane elements are both rectangles, and their common adjacent side is PQ. Their adjacent side vector (represented by a unit vector) is: The length of the edge perpendicular to PQ of the reference surface element and its adjacent surface elements (that is, the dimension in the direction of the first vector) is 'a'. The normal vector (surface element angle) of the reference surface element is... The geometric center (feature point, facet position) is C1(x,y,z), both of which are known; while the normal vectors (facet angles) of adjacent facets are... It is known that its geometric center (feature point, surface element position) is C2(x',y',z'). The position of C2 is the position of the surface element of the adjacent surface element, which needs to be calculated.

[0177] Among them, reference Figure 9 Assuming that adjacent face elements only rotate around their common adjacent edge PQ without shape distortion, it can be known that and They are perpendicular to each other, from which we can obtain The expression is as shown in formula (27):

[0178]

[0179] Furthermore, calculate separately and The cross product, and and The cross product is shown in formulas (28) and (29):

[0180]

[0181] Among them, the cross product and Since the modulus of all vectors is 1, the first vector (represented as a unit vector) pointing from C1 to the midpoint M of the common adjacent side can be obtained according to formulas (30) and (31). And the second vector (represented as a unit vector) pointing from the midpoint M of the common adjacent edge to C2.

[0182]

[0183] Correspondingly, from C1 to C2 (from The beginning of the direction points to displacement vector of the end) As shown in formula (32):

[0184]

[0185] Substituting formulas (30) and (31) into formula (32), we obtain formula (33):

[0186]

[0187] As before, it can be assumed that C1 passed through C2 can then be achieved, hence formula (34):

[0188]

[0189] Furthermore, substituting formula (33) into formula (34), we can obtain formula (35) for calculating the position C2(x′,y′,z′) of adjacent face elements:

[0190]

[0191] In some embodiments, any two of the first direction X, the second direction Y, and the third direction Z are perpendicular to each other, and the first direction X and the second direction Y are both parallel to surface element 2; surface element 2 is a convex quadrilateral, the surface element position is characterized by the position of the feature point located at its geometric center, and the surface element angle is characterized by the normal vector perpendicular to it; determining the surface element position of adjacent surface elements based on the surface element position and surface element angle of the reference surface element and the surface element angle of adjacent surface elements (S1033) includes:

[0192] S1033B1: Acquire pixel images including the reference pixel and adjacent pixels.

[0193] S1033B2. Based on the surface image, determine the first displacement of the feature points of adjacent surface elements relative to the feature points of the reference surface element in the first direction X, and the second displacement in the second direction Y.

[0194] S1033B3. Based on the first displacement, the second displacement, the normal vector of the reference surface element, and the normal vector of the adjacent surface element, determine the third displacement of the feature point of the adjacent surface element relative to the feature point of the reference surface element in the third direction Z.

[0195] S1033B4. Determine the positions of the feature points of adjacent surface elements based on the positions of the feature points of the reference surface element, the first displacement, the second displacement, and the third displacement.

[0196] As another embodiment of this disclosure, the first direction X, the second direction Y, and the third direction Z can be set to be pairwise orthogonal, wherein the first direction X and the second direction Y are both parallel to surface element 2; and for the convex quadrilateral surface element 2, it can be considered that adjacent surface elements and reference surface elements, in addition to rotating relative to each other around their common adjacent side, may also undergo distortion in their own plane (as shown in the reference). Figure 11 (The rectangle is distorted into a parallelogram).

[0197] Therefore, an image acquisition unit (such as a CCD) can be used to acquire an image of the surface to be detected, resulting in a surface image including a reference surface element and adjacent surface elements. By analyzing the relative positions of the patterns of Hall sensor 1, the first displacement of the feature points of the adjacent surface elements relative to the feature points of the reference surface element in the first direction X and the second displacement in the second direction Y can be determined.

[0198] Based on the first displacement, the second displacement, the normal vector of the reference surface element, and the normal vector of the adjacent surface element, the third displacement of the feature point of the adjacent surface element relative to the feature point of the reference surface element in the third direction Z can be further calculated.

[0199] In this context, the position of the feature point of the reference surface element after the first, second, and third displacements can be considered as the position of the feature point of the adjacent surface element, thus the surface element position of the adjacent surface element can be calculated.

[0200] For example, refer to Figure 10 The reference plane element and its adjacent plane elements were originally rectangles, with their common adjacent side being PQ. The normal vector (plane element angle) of the reference plane element is... The geometric center (feature point, facet position) is C1(x,y,z), both of which are known; while the normal vectors (facet angles) of adjacent facets are... It is known that its geometric center (feature point, surface element position) is C2(x',y',z'), and C2 is the surface element position of the adjacent surface element, which needs to be calculated.

[0201] Reference Figure 10 , Figure 11 It should be understood that at this time, among the two face elements 2, the line passing through feature points C1 and C2 and perpendicular to the normal vector line ( Figure 10 , Figure 11 The intersection of the dashed line (in the diagram) and the common adjacent edge PQ may no longer be the midpoint of the common adjacent edge, but instead be divided into two points M1 and M2.

[0202] Furthermore, referring to Figure 11 The system acquires a surface image including a reference surface element and adjacent surface elements. Based on this surface image, it can analyze the first displacement ΔX of C2 relative to C1 in the first direction X and the second displacement ΔY of C2 relative to C1 in the second direction Y.

[0203] For example, you can refer to Figure 12 The displacement of the same part of the Hall sensor 1 of two surface elements 2 in the surface image (such as the geometric center of the Hall sensor 1; if the Hall sensor 1 is located at the geometric center of the surface element 2, it is also the position of the feature point of the surface element 2) in the corresponding direction is taken as the first displacement amount ΔX and the second displacement amount ΔY.

[0204] Among them, reference Figure 13 It can be assumed that the distortion of surface element 2 does not change its surface element angle (normal vector), therefore, the above adjacent edge vectors can be considered as... Still with They are perpendicular to each other, and the displacement vectors are perpendicular to each other. and Since they are all coplanar, we have formula (36):

[0205]

[0206] Furthermore, the third displacement ΔZ of C2 relative to C1 in the third direction Z can be calculated as shown in formula (37):

[0207]

[0208] As before, since ΔX, ΔY, and ΔZ are the displacements of C2 relative to C1 in the first direction X, the second direction Y, and the third direction Z, respectively, the formula (38) for calculating the position C2(x',y',z') of adjacent surface elements can be obtained:

[0209]

[0210] In some embodiments, the position of a surface element is characterized by the position of its internal feature points; determining the surface topography of the surface to be detected based on the positions of the surface elements 2 (S104) includes:

[0211] S104A1. Construct the surface morphology of the surface to be detected based on the positions of the feature points of multiple surface elements 2.

[0212] The surface morphology of the surface to be inspected can be characterized by the positions of a series of points. Therefore, as one embodiment of this disclosure, refer to... Figure 14 When the position of the feature point is used as the position of the surface element, after calculating the position of each feature point, the surface morphology of the surface to be detected can be directly constructed based on the position of these feature points. In other words, the surface to be detected is considered to be the surface that passes through the above feature points.

[0213] For example, when constructing a surface morphology in the above manner, to determine the warpage height H of the surface to be inspected, the maximum value z can be selected from the Z-axis (the axis perpendicular to the undeformed surface to be inspected) coordinates of all feature points.max and minimum value z min And calculate according to formula (39):

[0214] H = z max -z min (39)

[0215] In some embodiments, the position of a surface element is characterized by the position of its internal feature points; determining the surface topography of the surface to be detected based on the positions of the surface elements 2 (S104) includes:

[0216] S104B1. Determine the position of the vertex of surface element 2 based on the position of the feature points and the angle of the surface element.

[0217] S104B2. Construct the surface morphology of the surface to be detected based on the positions of the vertices of multiple surface elements 2.

[0218] As another embodiment of this disclosure, refer to Figure 15 After determining the positions of the feature points of multiple face elements 2, the positions of each vertex of face element 2 can be calculated based on the positions of these feature points and the face element angles. Then, the surface morphology of the face to be detected can be constructed based on the positions of these vertices, which means that the face to be detected is considered to be a face that passes through the above vertices.

[0219] In some embodiments, determining the position of the vertex of surface element 2 based on the position of the feature points of surface element 2 and the surface element angle (S104B1) includes:

[0220] S104B11. Based on the position of the feature points of surface element 2 and the surface element angle, construct an overdetermined system of equations.

[0221] Among them, the overdetermined equation system represents the coplanar constraint between the feature points and vertices of surface element 2.

[0222] S104B12. Determine the position of the vertex based on the overdetermined system of equations.

[0223] As one embodiment of this disclosure, the feature points and vertices of surface element 2 are obviously "coplanar". Therefore, an overdetermined set of equations can be determined based on the coplanar constraint relationship between multiple feature points and multiple vertices. Furthermore, the position of the vertex can be determined based on the above overdetermined set of equations.

[0224] It should be understood that an overdetermined system of equations refers to a system of equations in which the number of valid equations is greater than the number of unknowns. Therefore, an overdetermined system of equations does not have an exact analytical solution, but can only yield a relatively optimized numerical solution, that is, the position of the relatively optimized vertex.

[0225] In some embodiments, the overdetermined equations represent that feature points of multiple face elements 2 sharing a common vertex are coplanar with the common vertex; determining the position of the vertex according to the overdetermined equations (S104B12) includes:

[0226] S104B121. Solve the overdetermined system of equations using the least squares method to determine the local vertex positions of the common vertex.

[0227] S104B122. Following the direction that reduces the global error term, iteratively optimize the local vertex positions to determine the vertex positions.

[0228] The global error term includes a coplanarity error term and a smoothing error term. The coplanarity error term represents the coplanarity error between the common vertex and the feature points of each of its constituent face elements 2. The smoothing error term represents the error between the position of the common vertex and the positions of multiple vertices adjacent to the common vertex.

[0229] As one embodiment of this disclosure, the coplanar constraint represented by the above "overdetermined equation set" can be a set of feature points of multiple face elements 2 that share a common vertex, each of which is coplanar with the common vertex.

[0230] Therefore, an overdetermined system of equations can be constructed using the above coplanar constraints, and the local vertex positions (initialized local numerical solutions) can be obtained using the least squares method. Then, through specific global error terms, the local vertex positions can be iteratively optimized globally using methods such as the Jacobian matrix until a suitable time is reached (such as reaching a preset convergence accuracy), at which point the final vertex positions can be obtained.

[0231] Since the actual surface shape of an object tends to follow the "principle of minimum energy", and the solution of overdetermined equations by the least squares method is more in line with the above principle, the position of the vertex obtained by the least squares method is more accurate.

[0232] For example, refer to Figure 16 Suppose that four adjacent face elements 2 share a common vertex V. i,j Then, due to the common vertex V i,j It belongs to all four face elements 2, therefore it is related to the feature point P of the four face elements 2. i+i,l P i+1,j+1 P i,j P i,j+1 Since they are all coplanar, we can arrive at the overdetermined system of equations as shown in equation (40):

[0233] (V i,j -P k,l )·N k,l =0, k∈[i,i+1], l∈[j,j+1] (40);

[0234] Where, N k,lFor feature point P k,l The normal vector (angle of the face element) of the face element 2.

[0235] The least squares solution to the above overdetermined system of equations can be shown in equation (41):

[0236]

[0237] Where Neighbors represents adjacent, and the summation term is the residual of the planar constraint (coplanar error term), denoted as E. plane w i,j λ and λ are the optimization parameters of the least squares method, where the term containing λ is a regularization term introduced to prevent matrix singularity.

[0238] Therefore, the numerical solution for the initial local vertex positions can be obtained using the least squares method, i.e., the initialized local V. k,l .

[0239] Furthermore, the normal equation corresponding to the least squares solution can be obtained for parameter optimization. The normal equation is shown in formula (42):

[0240]

[0241] in, Indicates N i,j The generalized inverse.

[0242] Multiplying both sides of the equation by the inverse matrix of the first term of the left side of formula (42), we can transform it into formula (43):

[0243] P k,l =(A+λG) -1 b (43);

[0244] Where G is the identity matrix, and A and b are defined as follows (44):

[0245]

[0246] Furthermore, in addition to the above coplanarity error term E plane In the global error term used for global iterative optimization, a smoothing error term E, which characterizes the Laplace smoothness of the vertices, can also be introduced. smooth and optional area error term E area As shown in formulas (45) and (46) respectively:

[0247]

[0248] Thus initialized local V k,lWe can substitute these values ​​into the following formula (47), which is an extension of formula (41) based on formulas (45) and (46), to perform global optimization and obtain the final vertex position:

[0249]

[0250] Where λ and u are E area and E smooth The optimized parameters, and (E) plane +λ·E area +μ·E smooth ) represents the global error term, and where, due to E area Error items are not as good as E plane and E smooth It is universal, therefore it is optional.

[0251] Alternatively, as another embodiment of this disclosure, a constraint method in which a feature point is coplanar with multiple vertices can also be adopted.

[0252] For example, refer to Figure 17 For a face element 2(F) i,j Feature point P i,j Its four vertices V of surface element 2 i+1,j V i+1,j+1 V i,j V i,j+1 They are all coplanar, and therefore, based on these constraints, we can obtain formula (48):

[0253] (V k,l -P i,j )·N i,j =0 (48);

[0254] Furthermore, the initial local V at this point i,j It can be expressed as a vector form of formula (49):

[0255]

[0256] Where α and β are optimization parameters.

[0257] Meanwhile, the above coplanar error term E plane This can be expressed as formula (50):

[0258]

[0259] The smoothing error term E smooth and optional area error term E area You can refer to formulas (45) and (46) above.

[0260] Therefore, it can also be based on E planeE smooth E area For the initialized local V i,j Perform iterative global optimization until the final vertex position is obtained.

[0261] Secondly, referring to Figure 18 , Figure 19 This disclosure provides a detection device, which includes:

[0262] A control module is used for electrical connection to the substrate 9 to be tested, and for detecting the surface morphology of the surface to be tested according to any surface morphology detection method of the present disclosure; wherein, one surface of the substrate 9 to be tested is the substrate surface to be tested.

[0263] Support module, which is used to support the substrate 9 to be tested.

[0264] Magnetic field module 51, which is used to apply a predetermined magnetic field to the Hall sensor.

[0265] This disclosure provides a testing device for performing the above-mentioned surface morphology detection on a substrate 9 to be tested with the above-mentioned Hall sensor array, thereby obtaining the surface morphology of the surface to be tested of the substrate 9.

[0266] The support module is used to support the substrate 9 to be tested, that is, to stably set the substrate 9 to be tested at a predetermined position in the testing equipment; the magnetic field module 51 is used to apply the predetermined magnetic field to the Hall sensor; and the control module is used to apply a signal to the substrate 9 to be tested in order to complete the surface morphology detection.

[0267] In some embodiments, the magnetic field module 51 is a fixedly installed magnet.

[0268] As one embodiment of this disclosure, reference is made to... Figure 19 The magnetic field module 51 can be a fixed magnet (such as an electromagnet) that directly applies a predetermined magnetic field to all Hall sensors.

[0269] In some embodiments, the detection device of this disclosure further includes a probe module; the probe module includes a probe 52 and a driving mechanism; the probe 52 is provided with an image acquisition unit CCD and / or a magnetic field module 51; the driving mechanism is used to drive the probe 52 to move relative to the surface to be detected of the substrate 9 on the support module.

[0270] As one embodiment of this disclosure, the detection device may further include a probe module, which includes a movable probe 52 and a drive mechanism for driving the probe 52 to move.

[0271] The probe 52 may be equipped with an image acquisition unit (CCD) so that when the probe moves to the required position, the above-mentioned surface image can be acquired.

[0272] Among them, reference Figure 18 In another embodiment of this disclosure, the magnetic field module 51 can also be disposed on the probe 52, so that when the probe 52 moves to the desired position, a magnetic field can be applied to the corresponding Hall sensor for detection.

[0273] The support module may include a base 53, a sample stage 54, a sample transfer mechanism, and a counterweight 55. The base 53 provides mechanical support for all other components of the testing equipment. The substrate 9 to be tested can be adsorbed onto the sample stage 54. The sample transfer mechanism is used to input or remove the substrate 9 to be tested. The counterweight 55 distributes the weight and reduces the pressure on the moving bearings (especially under multi-axis coupling) and guide rails.

[0274] The specific form of the driving mechanism of probe 52 can be varied.

[0275] For example, you can refer to Figure 18 The sample stage 54 is also the work stage 56, specifically the XY work stage (which can move along the X and Y directions), while the probe is set on another work stage 56, specifically the Z&θ work stage (which can move along the Z axis and rotate). Thus, the two work stages work together to drive the probe to achieve movement in four degrees of freedom: X, Y, Z, and θ.

[0276] Alternatively, it can be a reference. Figure 19 The sample stage 54 is fixed, while the probe is located on the worktable 56, specifically the XYZ&θ worktable.

[0277] The control module may include a control unit, a detection unit, a motor unit, an input / output unit, etc.

[0278] The control unit controls the operation of the entire testing equipment, the detection unit inputs current to the Hall sensor and detects its voltage, the motor unit provides power to each workbench 56 (therefore it is also part of the drive mechanism), and the input / output unit connects the control unit to the outside world.

[0279] Thirdly, referring to Figure 20 This disclosure provides a computer-readable medium having a computer program stored thereon, which, when executed by a processor, implements any of the surface morphology detection methods of this disclosure.

[0280] Fourthly, embodiments of this disclosure provide a computer program product, which includes a computer program, and the computer program, when executed by a processor, is any of the surface morphology detection methods of embodiments of this disclosure.

[0281] Among them, the processor is a device with data processing capabilities, including but not limited to the central processing unit (CPU); the memory is a device with data storage capabilities, including but not limited to random access memory (RAM, more specifically SDRAM, DDR, etc.), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), and flash memory (FLASH); the I / O interface (read-write interface) is connected between the processor and the memory, enabling information exchange between the memory and the processor, including but not limited to the data bus (Bus).

[0282] Those skilled in the art will understand that all or some of the steps, systems, and devices disclosed above, as functional modules / units, can be implemented as software, firmware, hardware, or suitable combinations thereof.

[0283] In hardware implementations, the division between functional modules / units mentioned in the above description does not necessarily correspond to the division of physical components; for example, a physical component may have multiple functions, or a function or step may be executed by several physical components working together.

[0284] Some or all of the physical components may be implemented as software executed by a processor, such as a central processing unit (CPU), digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit (ASIC). Such software may be distributed on a computer-readable medium, which may include computer storage media (or non-transitory media) and communication media (or transient media). As is known to those skilled in the art, the term computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technique for storing information (such as computer-readable instructions, data structures, program modules, or other data). Computer storage media include, but are not limited to, random access memory (RAM, more specifically SDRAM, DDR, etc.), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory (FLASH) or other disk storage; read-only optical disc (CD-ROM), digital versatile disc (DVD) or other optical disc storage; magnetic cartridges, magnetic tapes, disk storage or other magnetic storage; and any other media that can be used to store desired information and can be accessed by a computer. Furthermore, as is known to those skilled in the art, communication media typically contain computer-readable instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

[0285] This disclosure has disclosed exemplary embodiments, and although specific terminology has been used, it is for general illustrative purposes only and should not be construed as limiting. In some instances, it will be apparent to those skilled in the art that features, characteristics, and / or elements described in conjunction with particular embodiments may be used alone, or in combination with features, characteristics, and / or elements described in conjunction with other embodiments, unless otherwise expressly indicated. Therefore, those skilled in the art will understand that various changes in form and detail may be made without departing from the scope of this disclosure as set forth by the appended claims.

Claims

1. A surface morphology detection method, wherein the surface to be detected is provided with a plurality of Hall sensors arranged in an array; each Hall sensor includes a first conductor extending along a first direction, a second conductor extending along a second direction, and a third conductor extending along a third direction, wherein the first conductor, the second conductor, and the third conductor overlap at an overlapping portion, and any two of the first direction, the second direction, and the third direction intersect each other; The method includes: A predetermined magnetic field is applied to the Hall sensor, and when current is supplied to the first conductor, a first voltage across the second conductor and a second voltage across the third conductor are obtained respectively; when current is supplied to the third conductor, a third voltage across the first conductor and a fourth voltage across the second conductor are obtained respectively. The angle of the surface element where the Hall sensor is located is determined based on the corresponding first voltage, second voltage, third voltage, and fourth voltage. The positions of the multiple face elements are determined based on their face angles. The surface morphology of the surface to be detected is determined based on the positions of the multiple surface elements. Determining the position of multiple face elements based on their face element angles includes: Select a reference surface element from the plurality of surface elements; Select the face elements that share a common adjacent edge with the reference face element as adjacent face elements; The position of the adjacent surface element is determined based on the surface element position and angle of the reference surface element and the surface element angle of the adjacent surface element. In response to the failure to meet the preset termination condition, the process returns to the step of selecting a face with a common adjacent edge to the reference face as the adjacent face, using the adjacent face as the reference face.

2. The method according to claim 1, wherein, The step of determining the angle of the surface element where the Hall sensor is located based on the corresponding first voltage, second voltage, third voltage, and fourth voltage includes: The local magnetic field detected by the Hall sensor is determined based on the corresponding first voltage, second voltage, third voltage, and fourth voltage. Construct a system of nonlinear equations; the system of nonlinear equations represents that the local magnetic field, after being rotated by a rotation matrix, is equal to the predetermined magnetic field; Solving the nonlinear equations yields the rotation matrix; The angle of the surface element where the Hall sensor is located is determined based on the rotation matrix.

3. The method according to claim 1, wherein, The step of determining the angle of the surface element where the Hall sensor is located based on the corresponding first voltage, second voltage, third voltage, and fourth voltage includes: The local magnetic field detected by the Hall sensor is determined based on the corresponding first voltage, second voltage, third voltage, and fourth voltage. Determine the local normalized vector after normalizing the local magnetic field, and the predetermined normalized vector after normalizing the predetermined magnetic field; Determine the vector rotation axis and vector rotation angle of the local normalized vector relative to the predetermined normalized vector; The angle of the surface element where the Hall sensor is located is determined based on the vector rotation axis and the vector rotation angle.

4. The method according to claim 1, wherein, The face element is rectangular, the position of the face element is characterized by the position of the feature point located at its geometric center, and the angle of the face element is characterized by the normal vector perpendicular to it. The step of determining the position of the adjacent surface element based on the surface element position and angle of the reference surface element and the surface element angle of the adjacent surface element includes: Based on the normal vector of the reference surface element and the normal vector of the adjacent surface element, determine the adjacent edge vector of the common adjacent edge; Based on the adjacent edge vector, the normal vector of the reference surface element, and the normal vector of the adjacent surface element, a first vector ending at the midpoint of the common adjacent edge and a second vector starting at the midpoint of the common adjacent edge are determined; the first vector is perpendicular to the adjacent edge vector and the normal vector of the reference surface element, and the second vector is perpendicular to the adjacent edge vector and the normal vector of the adjacent surface element; the lengths of the first vector and the second vector are both equal to half the dimension of the reference surface element along the direction of the first vector; Determine the displacement vector from the beginning of the first vector to the end of the second vector; The position of the feature point of the adjacent surface element is determined by the displacement vector starting from the feature point of the reference surface element.

5. The method according to claim 1, wherein, Any two of the first direction, the second direction, and the third direction are perpendicular to each other, and the first direction and the second direction are both parallel to the surface element; the surface element is a convex quadrilateral, the position of the surface element is characterized by the position of the feature point located at its geometric center, and the angle of the surface element is characterized by the normal vector perpendicular to it; The step of determining the position of the adjacent surface element based on the surface element position and angle of the reference surface element and the surface element angle of the adjacent surface element includes: Acquire a surface image including the reference surface element and the adjacent surface elements; Based on the surface image, determine the first displacement of the feature points of the adjacent surface relative to the feature points of the reference surface in the first direction, and the second displacement in the second direction; Based on the first displacement, the second displacement, the normal vector of the reference surface element, and the normal vector of the adjacent surface element, determine the third displacement of the feature point of the adjacent surface element relative to the feature point of the reference surface element in the third direction. The positions of the feature points of the adjacent surface elements are determined based on the positions of the feature points of the reference surface element, the first displacement, the second displacement, and the third displacement.

6. The method according to claim 1, wherein, The position of a surface element is characterized by the position of its internal feature points; determining the surface morphology of the surface to be detected based on the positions of the surface elements of the plurality of surface elements includes: The surface morphology of the surface to be detected is constructed based on the positions of the feature points of the multiple surface elements.

7. The method according to claim 1, wherein, The position of a surface element is characterized by the position of its internal feature points; determining the surface morphology of the surface to be detected based on the positions of the surface elements of the plurality of surface elements includes: The position of the vertex of the face element is determined based on the position of the feature points of the face element and the face element angle; The surface morphology of the surface to be detected is constructed based on the positions of the vertices of the multiple surface elements.

8. The method according to claim 7, wherein, The step of constructing the surface topography of the surface to be detected based on the positions of the vertices of the multiple surface elements includes: Based on the position of the feature points and the angle of the face element, an overdetermined system of equations is constructed; the overdetermined system of equations represents the coplanar constraint between the feature points and vertices of the face element. The position of the vertex is determined based on the overdetermined system of equations.

9. The method according to claim 8, wherein, The overdetermined system of equations represents that the feature points of multiple face elements with a common vertex are coplanar with the common vertex. Determining the position of the vertex based on the overdetermined system of equations includes: The local vertex positions of the common vertex are determined by solving the overdetermined system of equations using the least squares method. The positions of the local vertices are iteratively optimized in the direction that reduces the global error term to determine the position of the vertex. The global error term includes a coplanar error term and a smoothing error term. The coplanar error term represents the coplanar error between the common vertex and the feature points of its respective face elements. The smoothing error term represents the error between the position of the common vertex and the positions of multiple vertices adjacent to the common vertex.

10. A testing device, comprising: A control module is used for electrical connection to the substrate to be tested, and for detecting the surface morphology of the surface to be tested according to any one of claims 1 to 9; one surface of the substrate to be tested is the surface to be tested. A support module is provided for supporting the substrate to be tested. A magnetic field module is used to apply a predetermined magnetic field to the Hall sensor.

11. The testing equipment according to claim 10, wherein, The magnetic field module is a fixed magnet.

12. The testing equipment according to claim 10, wherein, It also includes a probe module; the probe module includes a probe and a drive mechanism; The probe is equipped with an image acquisition unit and / or the magnetic field module; The driving mechanism is used to drive the probe to move relative to the surface to be tested of the substrate on the support module.

13. A computer-readable medium having a computer program stored thereon, which, when executed by a processor, implements the surface morphology detection method according to any one of claims 1 to 9.

14. A computer program product comprising a computer program that, when executed by a processor, implements the surface topography detection method according to any one of claims 1 to 9.

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