Influence function based mitigation of substrate deformation due to film deposition and ion implantation

Abstract

The disclosed system and technique are directed to correcting out-of-plane (OPD) deformation of a substrate by depositing a stress compensation layer (SCL) on the substrate and obtaining a profile of the OPD of the substrate using optical inspection data. The technique further includes obtaining a dataset including a representation of an influence function of the substrate, the influence function characterizing a deformation response of the substrate caused by a point-like mechanical influence. The technique further includes performing a regression calculation to determine a distribution of stress relaxation exposure of the SCL that relieves the OPD of the substrate based on at least the profile of the OPD of the substrate and the influence function. The technique further includes performing a stress relaxation exposure of the SCL using the determined distribution of stress relaxation exposure.

Description

[Technical Field]

[0001] FIELD OF THE DISCLOSURE This disclosure relates to semiconductor manufacturing, including wafer manufacturing. [Background technology]

[0002] Modern semiconductor devices, such as processing circuits, memory devices, photodetectors, solar cells, and light-emitting semiconductor devices, are often fabricated on silicon wafers (or other suitable substrates). The wafers may undergo numerous processing steps, such as physical vapor deposition, chemical vapor deposition, etching, photomasking, polishing, and / or various other processes. In a continuing effort to reduce the cost of semiconductor devices, multilayer stacks of dies, insulating films, patterned and / or doped semiconductor films, and / or other features are often deposited on a single wafer, resulting in high-aspect-ratio devices used, for example, in 3D flash memory devices and other applications. The deposition, patterning, etching, polishing, etc. of the multilayer stacks often imparts significant stress to the underlying wafer. Such stresses result in both out-of-plane and in-plane distortion of features supported by the wafer. These distortions can lead to misalignment of the deposited features, significantly reducing the quality of the fabricated devices. [Brief explanation of the drawings]

[0003] The present disclosure will become more fully understood from the following detailed description and accompanying drawings of various embodiments of the disclosure.

[0004] [Figure 1] 1A-E illustrate a schematic process for stress compensating a backside deposited film using additional ion implantation, according to at least one embodiment. [Figure 2] FIG. 2 shows an example of a Zernike polynomial decomposition, in arbitrary units, of the actual deformation of one of the wafers (top left) into a parabolic curvature deformation (top right), a saddle-shaped deformation (bottom left), and a residual deformation (bottom right), according to at least one embodiment. [Figure 3]FIG. 3 illustrates stress and strain relief in one exemplary wafer using the process disclosed in connection with FIGS. 1A-E, according to at least one embodiment. [Figure 4] FIG. 4 illustrates one exemplary profile of a Gaussian ion beam that may be used to relieve stress and deformation in a wafer, according to at least one embodiment. [Figure 5] FIG. 5 illustrates an exemplary silicon wafer having a silicon nitride film deposited thereon having a saddle-shaped deformation, according to at least one embodiment. [Figure 6] FIG. 6 is a flow diagram illustrating an exemplary process for influence function based mitigation of wafer deformation, according to at least one embodiment. [Figure 7A] FIG. 7A illustrates ion implantation using a spot beam centered at a series of radial points, according to at least one embodiment. [Figure 7B-C] 7B-7C illustrate ion implantation using a spot beam centered at a series of radial points, according to at least one embodiment. [Figure 8] FIG. 8 shows simulation results of deformations caused by an ion implantation beam directed at different locations on a wafer / membrane structure, according to at least one embodiment. [Figure 9] 9A is a schematic diagram of an ion implantation system capable of performing ion implantation into a stress compensation layer, according to at least one embodiment, and FIG. 9B illustrates the delivery of ions to a wafer at an arbitrary angle of incidence by the ion implantation system of FIG. 9A, according to at least one embodiment. [Figure 10] FIG. 10 illustrates a block diagram of an exemplary computer system capable of supporting the processes of the present disclosure, according to at least one embodiment. Summary of the Invention

[0005] In one embodiment, a method for correcting out-of-plane deformation of a substrate is disclosed, comprising depositing a stress compensation layer (SCL) on the substrate. The method further comprises obtaining a profile of the out-of-plane deformation of the substrate using optical inspection data. The method further comprises obtaining, by a processing device, a dataset including a representation of an influence function of the substrate, the influence function characterizing a deformation response of the substrate caused by a point-like mechanical influence. The method further comprises performing a regression calculation to determine a distribution of stress relaxation exposure of the SCL that relieves the OPD of the substrate based on at least the profile of OPD of the substrate and the influence function. The method further comprises performing the stress relaxation exposure of the SCL using the determined distribution of stress relaxation exposure.

[0006] In another implementation, a system for depositing an SCL on a substrate is disclosed, including a memory and a processing device communicatively coupled to the memory. The processing device is further configured to acquire a profile of an OPD of the substrate using the optical inspection data. The processing device is further configured to acquire a dataset including a representation of an influence function of the substrate, the influence function characterizing a deformation response of the substrate caused by a point-like mechanical influence. The processing device is further configured to perform a regression calculation to determine a distribution of stress-relaxation exposure of the SCL that relaxes the OPD of the substrate based on at least the profile of OPD of the substrate and the influence function. The processing device is further configured to perform the stress-relaxation exposure of the SCL using the determined distribution of stress-relaxation exposure.

[0007] In another embodiment, a system is disclosed that includes a memory and a processing device communicatively coupled to the memory. The processing device is configured to deposit a SCL on a substrate and acquire an OPD profile of the substrate using optical inspection data. The processing device is configured to acquire a dataset including a representation of an influence function of the substrate, the influence function characterizing a deformation response of the substrate caused by a point-like mechanical influence. The processing device is configured to perform a regression calculation to determine a distribution of stress relaxation exposure of the SCL that relieves the OPD of the substrate based on at least the OPD profile of the substrate and the influence function. The processing device is further configured to perform the stress relaxation exposure of the SCL using the determined distribution of stress relaxation exposure.

[0008] In yet another embodiment, a non-transitory computer-readable memory is disclosed that stores instructions that, when executed by a processing device, cause the processing device to perform steps including depositing an SCL on a substrate. The steps further include obtaining a profile of an OPD of the substrate using optical inspection data. The steps further include obtaining a dataset including a representation of an influence function of the substrate, the influence function characterizing a deformation response of the substrate caused by the point-like mechanical influence. The steps further include performing a regression calculation to determine a distribution of stress-relaxing irradiance of the SCL that relaxes the OPD of the substrate based on at least the profile of OPD of the substrate and the influence function. The steps further include performing stress-relaxing irradiance of the SCL using the determined distribution of stress-relaxing irradiance. DETAILED DESCRIPTION OF THE INVENTION

[0009] Existing technologies include many methods for addressing wafer deformation. For example, a deformed (warped) wafer with various films and features deposited on one side (referred to herein as the front, top, or main side) can be coated on the other side (referred to herein as the back or bottom side) with a film that imposes compressive or tensile stress on the wafer. Such backside-deposited deformation-compensating films, also referred to herein as stress-compensating layers, typically impart a uniform (or global) stress across the wafer and are unable to compensate for local stress adjustment and / or anisotropic stress. Additional compensation can be achieved by implanting ions into the stress-compensating layer, e.g., using an ion beam bombarding the stress-compensating layer, to adjust the stress of the stress-compensating layer, thereby further mitigating the deformation of the underlying wafer.

[0010] As used herein, "wafer" refers to any substrate or any material surface formed on a substrate on which film processing is performed during a manufacturing process. For example, wafer surfaces on which processing can be performed include materials such as silicon, silicon oxide, silicon nitride, strained silicon, silicon-on-insulator, carbon-doped silicon oxide, amorphous silicon, doped silicon, germanium, gallium arsenide, glass, sapphire, and any other materials such as metals, metal nitrides, metal alloys, and other conductive materials, depending on the application. Wafers include, but are not limited to, semiconductor wafers. In some cases, wafers can include plastic substrates. Wafers may be exposed to pre-treatment processes to polish, etch, reduce, oxidize, hydroxylate, anneal, UV cure, electron beam (e-beam) cure, and / or bake the substrate surface. In addition to film processing directly on the surface of the wafer itself, any of the disclosed film processing steps may also be performed on underlying layers formed on the wafer, as disclosed in more detail below. The term "wafer surface" is intended to include such underlying layers as the context indicates. Thus, for example, if a film / layer or partial film / layer is being deposited on a wafer surface, the exposed surface of the newly deposited film / layer becomes the wafer surface. In some embodiments, the wafer has a thickness in the range of 0.25 mm to 1.5 mm, or in the range of 0.5 mm to 1.25 mm, or in the range of 0.75 mm to 1.0 mm, or greater. In some embodiments, the wafer has a diameter of about 10 cm, 20 cm, 30 cm, or greater.

[0011] Deposition of the stress compensation layer by ion implantation provides uniform and isotropic stress It can be very efficient to correct TIFF2026506870000002.tif4170. On the other hand, Location on TIFF2026506870000003.tif5170 TIFF2026506870000004.tif4170, Anisotropic stress Relieving stresses that vary in one direction, e.g., TIFF2026506870000006.tif5170 compressed along the orthogonal direction This can cause tensile stress along the wafer, resulting in the formation of a saddle-shaped wafer, such as that shown in FIG. 5. Such saddle-shaped features can arise, for example, in stacks of materials with directional patterning, such as the patterning of word lines in flash memory devices. Correcting such anisotropic saddle-shaped deformation in wafers remains a challenging task.

[0012] Aspects and embodiments of the present disclosure address these and other challenges of current semiconductor manufacturing technologies by providing systems and techniques that can mitigate non-uniform and / or anisotropic stress and deformation (e.g., out-of-plane deformation) in wafers. In some embodiments, the deformation of the wafer can be measured (e.g., using optical metrology techniques), and parameters of the stress compensation layer (e.g., layer material, thickness, etc.) can be determined so that the sign of the stress is the same across the wafer. For example, if the deformation of the wafer is concave, the parameters of the stress compensation layer can be selected to overcompensate the wafer to a convex shape. An ion implantation map (local dose distribution of ion implantation) can then be generated. TIFF2026506870000008.tif5170 can be calculated to reduce the local stress within the wafer to the extent that the convex shape becomes flat (or nearly flat). TIFF2026506870000009.tif5170 is a wafer point Point on wafer caused by point force applied to TIFF2026506870000010.tif5170 Influence functions characterizing the response (e.g., deformation) of the wafer in TIFF2026506870000011.tif5170 TIFF2026506870000012.tif6170. In some embodiments, the influence function, also known as the Green's function, TIFF2026506870000013.tif6170 can be determined from computational simulations or analytical calculations. In some embodiments, the influence function can be determined from one or more experiments, which can include performing ion implantation into films deposited on reference wafers.

[0013] In one embodiment, the vertical profile of the deformation of the wafer TIFF2026506870000014.tif5170 can be measured using optical metrology techniques. For example, the profile The interference of the wafer can be obtained using optical interferometry measurements. The wafer profile can then be calculated through several parameters that qualitatively and quantitatively characterize the geometry of the wafer deformation. TIFF2026506870000016.tif5170. In some embodiments, a set of Zernike (or a similar set) polynomials can be used to represent the wafer profile, TIFF2026506870000017.tif11170 where, TIFF2026506870000018.tif3170 is the radial coordinate in the (mean) plane of the wafer, TIFF2026506870000019.tif5170 is a polar coordinate. Continuous coefficients TIFF2026506870000020.tif5170 is the corresponding Zernike polynomial The first three coefficients represent the weights of the specific geometric features (elementary deformations) of the wafer described by TIFF2026506870000021.tif5170. TIFF2026506870000022.tif5170 Coefficients associated with the polynomial TIFF2026506870000023.tif5170), TIFF2026506870000024.tif4170 No deformation corresponding to rotation around axis TIFF2026506870000025.tif3170 slope ( TIFF2026506870000026.tif5170 Coefficients associated with the polynomial TIFF2026506870000027.tif5170), and can be eliminated by realigning the coordinate axes. TIFF2026506870000028.tif3170 No deformation corresponding to rotation around axis TIFF2026506870000029.tif3170 slope ( TIFF2026506870000030.tif5170 Coefficients associated with the polynomial TIFF2026506870000031.tif5170), so it is less important. TIFF2026506870000032.tif5170 is Associated with TIFF2026506870000033.tif5170, characterizes isotropic parabolic deformations ("curvature"). TIFF2026506870000034.tif5170 and the 6th The coefficients of TIFF2026506870000035.tif5170 are TIFF2026506870000036.tif5170 Polynomial and TIFF2026506870000037.tif5170Associated with polynomials, characterizing saddle deformations. TIFF2026506870000038.tif5170 Coefficients are diagonal TIFF2026506870000039.tif4170 along the top ( TIFF2026506870000040.tif5170) or below ( TIFF2026506870000041.tif5170) curved and diagonal TIFF2026506870000042.tif4170 along the bottom ( TIFF2026506870000043.tif5170) or above ( It features a saddle-shaped curved shape (TIFF2026506870000044.tif5170). TIFF2026506870000045.tif5170 coefficients are TIFF2026506870000046.tif3170 Up along the axis ( TIFF2026506870000047.tif5170) or below ( TIFF2026506870000048.tif5170) curved, TIFF2026506870000049.tif4170 Down along the axis ( TIFF2026506870000050.tif5170) or above ( TIFF2026506870000051.tif5170) characterizes the curved saddle shape. Higher coefficient TIFF2026506870000052.tif5170, TIFF2026506870000053.tif5170 etc. show deformation of the wafer along the radial direction, azimuthal direction, or both. TIFF2026506870000054.tif5170, which characterizes the progressively faster fluctuations and collectively represents the residual deformation ( TIFF2026506870000055.tif6170. FIG. 2 illustrates one actual deformation of a wafer, according to at least one embodiment. Parabolic curve transformation of TIFF2026506870000056.tif5170 (upper left) in any unit. TIFF2026506870000057.tif5170 (top right), saddle deformation TIFF2026506870000058.tif5170 (bottom left), and residual deformation TIFF2026506870000059.tif5170 (bottom right) shows an example of Zernike polynomial decomposition 200.

[0014] In some embodiments, the thickness of the stress compensation film TIFF2026506870000060.tif4170 selection of parabolic curvature coefficient 1A-E schematically illustrate a backside deposited film stress compensation process using additional ion implantation, according to at least one embodiment. FIG. 1A depicts a wafer 102 having deformations, including a parabolic curvature deformation (negative coefficient TIFF2026506870000062.tif5170) and other deformations, such as saddle-shaped deformations and residual deformations (neither of which are shown in FIGS. 1A-1E for brevity and clarity). Wafer 102 has a front side 104 and a back side 106. Front side 104 may have any number of features (e.g., deposition and / or etch patterns), dies, photomasks, and / or any other structures deposited or etched thereon. In some embodiments, back side 106 may be free of deposited / etched features / structures. In some embodiments, back side 106 may also have one or more deposited / etched features / structures. FIG. 1B illustrates a schematic deposition of a stress compensation layer on the back side of wafer 102. In some embodiments, stress compensation layer 108 may include one or more films of different materials. The individual films may have thicknesses ranging from 10 nm to 200 nm, or from 20 nm to 180 nm, or from 30 nm to 160 nm, or from 40 nm to 140 nm, or greater. The total thickness of the stress compensation layer may be up to several microns or greater. In some embodiments, the stress compensation layer 108 is deposited at a temperature ranging from 100° C. to 500° C. or higher.

[0015] The material (type) of the stress compensation layer 108 is determined by the coefficient You can select based on the sign of TIFF2026506870000063.tif5170. For example, in the case of negative curvature ( TIFF2026506870000064.tif5170), the stress compensation layer 108 can be selected to have compressive stress after deposition, while the bottom surface of the wafer has tensile stress (as illustrated in Figures 1A-E). In the case of a silicon wafer, such a film can be a silicon nitride (Si3N4) film. Conversely, in the case of a positive curvature ( TIFF2026506870000065.tif5170), the stress compensation layer 108 may be selected to have a tensile stress (not shown in FIGS. 1A-E). The stress compensation layer 108 may be deposited using any suitable deposition technique, including physical vapor deposition (e.g., sputtering), chemical vapor deposition (e.g., plasma-assisted deposition), epitaxy, and / or exfoliation. Deposition may be performed at room temperature or at a temperature different from room temperature (e.g., elevated temperature). In some embodiments, the thickness of the stress compensation layer 108 may be 0.15 μm or less. The thickness-dependent parabolic curvature correction can be chosen to overcorrect the deformation to some extent, as shown, for example, in Figure 1C, where negative parabolic curvature becomes positive parabolic curvature. TIFF2026506870000067.tif5170 shows the deformation of the wafer. From TIFF2026506870000068.tif5170 Changes to TIFF2026506870000069.tif5170: TIFF2026506870000070.tif5170

[0016] The overcompensation is selected in conjunction with the implant species, energy, and dose to ensure maximum compensation from the stress compensation. The overcompensation allows the combined structure of the wafer 102 and the stress compensation layer 108 to further control the stress (and thus the deformation of the wafer). TIFF2026506870000071.tif5170). As shown in FIG. 1D, an ion beam implanter 110 can generate an ion beam 112 that bombards the stress-compensating layer 108 and deposits ions therein. The ion beam 112 can carry silicon ions, phosphorus ions, argon ions, neon ions, xenon ions, and / or krypton ions, among others. In some embodiments, the energy and type of ions in the ion beam 112 can be selected to confine the implanted ions to the volume of the stress-compensating layer 108 without allowing the ions to reach the wafer 102. Ions present in the stress-compensating layer 108 create substitutional defects therein. Additionally, the ions leave a trail of vacancy defects along their propagation paths within the stress-compensating layer 108. The substitutional defects and / or vacancies can modify (e.g., reduce) the stress in the stress-compensating layer 108 and reduce the degree of stress overcompensation caused by film deposition. This planarizes the combination of wafer 102 and stress compensation layer 108.

[0017] Specifically, although the stress-relief beam used to modify the stress in the stress-compensating layer 108 is referred to throughout this disclosure as an ion beam (e.g., ion beam 112), the stress-relief beam (irradiation) can include other material particles (e.g., electrons), electromagnetic waves (e.g., UV light, visible light, infrared light, etc.), and / or suitable combinations thereof. The stress-relief beam impinges on the stress-compensating layer 108 and alters the bond network of the stress-compensating layer 108. For example, a low-energy stress-relief beam can interact with surface atoms of the stress-compensating layer 108, e.g., remove some of the surface atoms, effectively etching the surface region of the stress-compensating layer 108. The effectiveness of such etching can be controlled by the selection of ion species / radicals / ambient gas. In another example, a high-energy stress-relief beam can deposit ions within the stress-compensating layer 108. The ions and / or photons can break bonds in the bond network (or crystal lattice) of the stress-compensating layer 108, forming vacancies therein, which can further cause annealing through localized heating, UV curing, and / or other effects.

[0018] In some embodiments, a small area of ​​the wafer TIFF2026506870000072.tif5170 Number of ions deposited per TIFF2026506870000073.tif5170 shows the saddle deformation, residual deformation, and parabolic curvature deformation overcompensated by the deposition of the stress compensation layer 108. Corrected deformations that may include parts of TIFF2026506870000074.tif5170 The desired local density of ions can be determined using simulations (performed as described in more detail below) based on the local values ​​of TIFF2026506870000075.tif5170. TIFF2026506870000076.tif5170 shows the scanning speed of the ion beam 112. In some embodiments, the ion beam 112 has a profile that can be approximated by a Gaussian function, e.g., an ion flux TIFF2026506870000078.tif5170. TIFF2026506870000079.tif3170 and TIFF2026506870000080.tif4170 is in Cartesian coordinates, TIFF2026506870000081.tif5170 is the maximum ion flux at the center of the beam, TIFF2026506870000082.tif3170 and TIFF2026506870000083.tif4170 is, TIFF2026506870000084.tif3170Axis and TIFF2026506870000085.tif4170 is the characteristic spread of the beam along the axis. Correspondingly, the distance from the center of the beam path is The point located at TIFF2026506870000086.tif4170 receives an ion dose containing the following number of ions: TIFF2026506870000087.tif13170 Correspondingly, the scanning speed By lowering the ion beam size, various areas of the stress compensation layer 108 can receive more ions, and vice versa. In addition, the ion beam 112 may be configured such that various points on the stress compensation layer 108 receive different factors that can be averaged to the target dose. TIFF2026506870000089.tif5170 to receive multiple ion doses with different offsets TIFF2026506870000090.tif4170, each of which may be scanned from the center of the ion beam 112 to a region Different distances to TIFF2026506870000091.tif5170 In TIFF2026506870000092.tif4170, the ion beam implantation device 110 After n passes in TIFF2026506870000093.tif4170, the total ion dose received by this area is: As shown in FIG. 1E, implanted layer 114 formed as part of stress compensation layer 108 provides significant deformation relief for wafer 102, particularly the saddle-shaped and residual portions thereof.

[0019] 3 illustrates stress and strain relaxation 300 in one exemplary wafer using the process disclosed in connection with FIGS. 1A-E, according to at least one embodiment. As shown in FIG. 3, the maximum negative strain A 30 cm silicon wafer 102 having a tensile stress compensation layer 108 is first prepared using a silicon nitride tensile stress compensation layer 108. The stress in the stress compensation layer 108 is then reduced by forming an implanted layer 114 using an ion beam, and the final maximum deformation is TIFF2026506870000097.tif5170 Figure 4 shows one example profile 400 of a Gaussian ion beam 112 that may be used to relieve stress and deformation in a wafer, according to at least one embodiment.

[0020] The techniques for mitigating strain and deformation shown in Figures 1-3 are based on the stress tensor components TIFF2026506870000098.tif4170 and The present invention can also be applied to wafers with complex deformations, such as wafers with different signs, causing the wafer to have a saddle-shaped deformation. Figure 5 shows an example wafer 500 (e.g., a silicon wafer with a silicon nitride film deposited thereon) with a saddle-shaped deformation, according to at least one embodiment. As can be seen in Figure 502 of TIFF2026506870000100.tif3170, the stress components TIFF2026506870000101.tif4170 may be lower on the wafer (top layer) than on the film deposited on the backside of the wafer (bottom layer). As shown in Figure 504 of TIFF2026506870000102.tif4170, the stress components TIFF2026506870000103.tif4170 may be higher in the wafer than in the film. In some embodiments, the stress state in the wafer can be represented by a position-dependent stress tensor, which can be approximated by the following equation: This structure of the stress tensor is usually a good approximation because the wafer is typically in pure bending and is independent of the shear stresses represented by the off-diagonal terms of the stress tensor. Correction for the saddle shape requires special treatment in the dose map calculation and optimization to ensure that no additional residual terms are introduced into the wafer as a result.

[0021] FIG. 6 is a flow diagram illustrating an example process 600 for mitigation based on an influence function of wafer deformation, according to at least one embodiment. Process 600 can be performed using a semiconductor manufacturing system including one or more processing chambers, such as one or more deposition chambers, one or more plasma chambers, one or more etching chambers, one or more polishing chambers, one or more film removal chambers, one or more beam irradiation chambers, and / or one or more optical inspection chambers. The processing chambers can be connected to one or more transfer chambers, which can include one or more robots for handling wafers, e.g., transferring wafers into and out of the processing chambers. The transfer chambers can further be connected to a load lock chamber (front-end interface), which can be coupled to one or more Front Opening Unified Pod (FOUP) carriers that hold bare wafers, processed wafers, and / or partially processed wafers, etc. Operations performed by the semiconductor manufacturing system, including any, some, or all of the steps of process 600, can be performed in response to instructions issued by a suitable computing device having a memory for storing processing logic and instructions.

[0022] In block 610, the process 600 determines the shape of the wafer, for example, the displacement of the surface (e.g., top or bottom) of the wafer. TIFF2026506870000105.tif5170 can be converted to any suitable in-plane coordinate system, e.g., polar coordinate system TIFF2026506870000106.tif5170, Cartesian coordinates TIFF2026506870000107.tif5170, or some other set of coordinates as a function of the wafer deformation. TIFF2026506870000108.tif5170 can be represented through a decomposition of the shape determined by an appropriate set of basis functions, for example Zernike polynomials, or other polynomial sets. TIFF2026506870000109.tif5170 is the effective deformation pressure exerted on the upper surface of a wafer as a result of local stresses caused by wafer patterning / etching, deposition of one or more films on the upper surface of the wafer, and / or any other technological operations performed on the wafer. The relationship between the wafer deformation and the effective deformation pressure can be described by the classical plate equation: TIFF2026506870000111.tif5170 where, TIFF2026506870000112.tif3170 is the wafer thickness, TIFF2026506870000113.tif5170 is the bending stiffness of the wafer; TIFF2026506870000114.tif4170 and TIFF2026506870000115.tif3170 are Young's modulus and Poisson's ratio, respectively. TIFF2026506870000116.tif5170 is the planar Laplacian operator. Wafer deformation TIFF2026506870000117.tif5170 involves a plane stress, which at the bottom surface of the wafer is: TIFF2026506870000118.tif10170The plane stress is negative (compressive) in some areas of the wafer ( TIFF2026506870000119.tif5170), while other areas of the wafer are positive (tensile) ( TIFF2026506870000120.tif5170) is possible.

[0023] In block 620, the determined transformation TIFF2026506870000121.tif5170 can be used to identify the properties (e.g., material and thickness) of the target stress-compensating film to be deposited on the wafer. In some embodiments, the film compensates for the stress in the new wafer / film structure. 3, the bottom side of the Si wafer 102 has compressive stress, e.g. The stress compensation layer 108 is applied to the wafer 102 so that the sign of the wafer stress on the bottom side of the wafer 102 is reversed to make it tensile across the entire area of ​​the wafer ( TIFF2026506870000124.tif5170) can be selected. More specifically, the stress compensation film (layer) can be used to effectively reduce local pressure. TIFF2026506870000125.tif5170 is added and the deformation of the wafer is changed ( TIFF2026506870000126.tif5170), where: The material and thickness of the stress compensation layer 108 are determined to ensure that: TIFF2026506870000128.tif5170 can be chosen to be large enough (in absolute value) This is advantageous because, although ion implantation can reduce the amount of stress in a film, it can be more difficult to reverse the sign of tension in a film using ions.

[0024] 6, the process 600 may include depositing a film (stress compensation layer) of a selected material and thickness on the wafer. In some embodiments, the process 600 may include depositing a film of a selected material and thickness on the wafer (stress compensation layer). ... TIFF2026506870000130.tif5170 (e.g., using an optical interferometer). In some embodiments, instead of performing a remeasurement, the modified wafer deformation may be TIFF2026506870000131.tif5170 as value In some embodiments, the estimation can be based on TIFF2026506870000132.tif5170. TIFF2026506870000133.tif5170 can have uniform values ​​across the area of ​​the wafer (e.g., caused by a deposited film of uniform thickness): TIFF2026506870000134.tif5170, where: TIFF2026506870000135.tif4170 is the membrane thickness, TIFF2026506870000136.tif4170 are empirically determined coefficients that depend on the specific material type. Different materials have coefficients with different magnitudes and signs. It can be characterized by TIFF2026506870000137.tif4170.

[0025] Measured (and / or estimated) deformation of the wafer Using TIFF2026506870000138.tif5170, stress Relax TIFF2026506870000139.tif5170 and reduce the deformation to zero (or nearly zero) ( TIFF2026506870000140.tif5170) Ion implantation dose map TIFF2026506870000141.tif5170 can be determined. Non-uniform ion implantation reduces the uniform pressure exerted by the membrane to an amount determined by the local ion dose. Reduced to TIFF2026506870000142.tif5170: TIFF2026506870000143.tif5170 where, TIFF2026506870000144.tif4170 is a constant that depends on the type of ion, the energy of the ion, the angle of ion implantation, and / or other parameters of the ion implantation process. Under ideal conditions, the correction of ion implantation TIFF2026506870000145.tif5170 can be selected so that the total pressure disappears ( TIFF2026506870000146.tif5170). Effective deformation pressure TIFF2026506870000147.tif5170 is difficult to estimate, so correction of ion implantation TIFF2026506870000148.tif5170 determines the deformation stresses caused by various features patterned on the wafer and by the deposited films. Deformation caused by TIFF2026506870000149.tif5170 Based on TIFF2026506870000150.tif5170, it can be done more efficiently. Ion implantation correction to compensate TIFF2026506870000151.tif5170 TIFF2026506870000152.tif5170 follows the formula: TIFF2026506870000153.tif5170

[0026] Block 635 may include calculating the influence function (Green's function) for the classical plate equation: TIFF2026506870000154.tif6170 where, TIFF2026506870000155.tif5170 is the Dirac delta function. According to its definition, the influence function is TIFF2026506870000156.tif4170, caused by a unit force applied to the point Characterize the deformation of the wafer (e.g., the undeformed wafer) at TIFF2026506870000157.tif4170. Once the influence function is determined, apply the ion implant correction The deformation caused by TIFF2026506870000158.tif5170 can be determined by integration over the area of ​​the wafer: As will be described below in conjunction with TIFF2026506870000159.tif9170 block 650, the solution to this equation can determine the local density of ions for ion implantation.

[0027] In some embodiments, the integral over the area of ​​the wafer is It can be calculated as a discrete sum over patches of TIFF2026506870000160.tif5170. For example, for a wafer with a diameter of 30 cm, the discrete patches are TIFF2026506870000161.tif5170, and / or 12 mm, etc. In various embodiments, the influence function is expressed in Cartesian coordinates TIFF2026506870000162.tif5170= TIFF2026506870000163.tif6170, and the integral is similarly performed in Cartesian coordinates. In some embodiments, the influence function (and the deformation) may be expressed in any other coordinate system, e.g., polar coordinates. TIFF2026506870000164.tif5170 and the integral scale is adjusted accordingly ( TIFF2026506870000165.tif6170).

[0028] Influence Function TIFF2026506870000166.tif5170 can be determined using various techniques. In one embodiment, as indicated by block 615, the influence function TIFF2026506870000167.tif5170 can be determined using experimental data. For example, the reference intensity (flux) TIFF2026506870000168.tif5170 spot ion beam at different points on a film of known thickness on a reference wafer, e.g., an undeformed wafer. TIFF2026506870000169.tif5170, reference time TIFF2026506870000170.tif4170 (hence per unit area of ​​membrane) TIFF2026506870000171.tif5170 ions) and the resulting deformation caused by the beam. In some embodiments, the spot beam can measure changes in: TIFF2026506870000173.tif3170 Range along axis TIFF2026506870000174.tif3170 and TIFF2026506870000175.tif4170 Range along axis Gaussian beam with TIFF2026506870000176.tif4170 TIFF2026506870000177.tif6170 (in some embodiments, the beam profile is symmetric ( TIFF2026506870000178.tif4170). Different points on the radius of the wafer, e.g., in a given radial direction (e.g., in this example TIFF2026506870000179.tif3170 (spacing along the axis) A set of points that can be separated by spacing TIFF2026506870000180.tif4170 TIFF2026506870000181.tif5170 etc. can be detected. TIFF2026506870000182.tif4170 is of the same order of magnitude as the size of the discretization patch, e.g., TIFF2026506870000183.tif5170 and / or TIFF2026506870000184.tif5170. In some embodiments, the interval TIFF2026506870000185.tif4170 can be position dependent, e.g., larger intervals TIFF2026506870000186.tif4170 (lower resolution) is used to probe the wafer deformation caused by the spot beam 112 centered near the center of the wafer / membrane (near the center of the wafer / membrane) and smaller spacing TIFF2026506870000187.tif4170 (higher resolution) can be used to probe wafer deformation caused by a spot beam 112 centered near the edge of the wafer / film.

[0029] 7A-7C illustrate ion implantation using spot beams centered at a series of points 702, 704, 706 along a radial direction 710, according to at least one embodiment. The spot beams may have a Gaussian shape 712 or any other suitable shape. Centered on TIFF2026506870000188.tif5170, duration The amount of deformation caused by the spot beam 112 applied to the membrane during TIFF2026506870000189.tif4170 can be expressed via an influence function as follows: TIFF2026506870000190.tif9170Using the discrete form of this equation (replacing integrals with sums), we can calculate the influence function TIFF2026506870000191.tif5170 can be determined. More specifically, the measured deformation TIFF2026506870000192.tif5170 - illustrated schematically via heatmap 714 - represents the experimental input, the shape of the ion implantation beam TIFF2026506870000193.tif5170 can be known fixed inputs (e.g., determined by the ion implanter settings), and the influence function TIFF2026506870000194.tif5170 can be obtained using an inverse matrix multiplication technique. In some embodiments, the points 702, 704, 706, etc. at which the spot beam 112 is focused can be located along the same radial line, and the axial symmetry of the wafer 102 can be used to determine the influence function for other points. More specifically, the influence function can then be assumed to be the same (axially symmetric) at other locations of the point of origin. Expressed in polar coordinates, this axial symmetry results in the influence function TIFF2026506870000195.tif5170 is the "point of origin" TIFF2026506870000196.tif6170 and "Arrival Point" Relative angle between TIFF2026506870000197.tif5170 Depends on TIFF2026506870000198.tif5170, TIFF2026506870000199.tif5170 and TIFF2026506870000200.tif5170. In some embodiments, real wafers (and / or wafer / membrane structures) may be slightly asymmetric, so that deformations caused by applying spot beams 112 along different directions may be minimized. TIFF2026506870000201.tif5170 are measured and then averaged (after appropriate rotation and proper superposition), and the average value is used as the influence function TIFF2026506870000202.tif6170. In another embodiment, the influence function TIFF2026506870000203.tif6170, the point of occurrence Measurements can be taken of a specific portion of TIFF2026506870000204.tif5170 (e.g., a quadrant of the wafer 102) and then expanded to the entire area of ​​the wafer 102.

[0030] In some embodiments, the linearity of the wafer deformation is performed on a single wafer (wafer / membrane structure). This can be advantageously used for multiple measurements of TIFF2026506870000205.tif5170. More specifically, a wafer with uniformly deformed deposited films is measured at a series of points. TIFF2026506870000206.tif5170, TIFF2026506870000207.tif5170, TIFF2026506870000208.tif5170, etc., are irradiated with ion beam 112, and successive deformation increments are obtained after each ion beam irradiation. TIFF2026506870000209.tif5170, TIFF2026506870000210.tif5170, TIFF2026506870000211.tif5170 etc. can be measured, and each increment TIFF2026506870000212.tif6170 represents the deformation independent of other doses previously received. This can be repeated until the film is implanted with a large ion dose. At such a high dose (where a significant percentage of the atomic bonds in the film are broken by the ions), the deformation of the wafer becomes saturated, and further doses applied to the same part of the film do not produce any further significant changes in the deformation of the wafer. Once the film is saturated with ions, the film can be removed (chemically or physically), a new film can be deposited on the same wafer, and a further series of ion implantation experiments can be performed.

[0031] 6, in some embodiments, instead of (or in addition to) performing one or more spot beam simulations 615, process 600 may include performing spot beam simulation 625. More specifically, a finite element analysis (FEA) method is used to analyze the pressure exerted by the ion-modified membrane. Transformation by TIFF2026506870000213.tif5170 TIFF2026506870000214.tif5170 can be simulated. For example, deformation The simulated deformation can be determined by solving the classical wave equation with appropriate boundary conditions (e.g., support boundary conditions, free boundary conditions, etc.). TIFF2026506870000216.tif5170, for example, as described above in conjunction with deformations measured in one or more spot beam experiments 615, It can be used for calculation 635 of TIFF2026506870000217.tif6170.

[0032] In some embodiments, process 600 may include obtaining an analytical solution for the spot beam, as indicated in block 627. For example, the operation of block 627 may include obtaining an influence function TIFF2026506870000218.tif6170 and the appropriate set of functions, e.g., TIFF2026506870000219.tif5170 and TIFF2026506870000220.tif5170 may include calculating the influence function as a series over a set of radial polynomials, such as Bessel polynomials, Raguel polynomials, and / or Zernike polynomials. In some embodiments, the operation of block 627 The method may include obtaining an approximate analytical representation of TIFF2026506870000221.tif6170.

[0033] The influence function obtained in block 635 TIFF2026506870000222.tif6170, the computing device performs a regression calculation 650 to obtain film-dependent (e.g., material-dependent and / or thickness-dependent) coefficients. Ion implantation map with TIFF2026506870000223.tif4170 TIFF2026506870000224.tif5170 can be determined. The regression calculation 650 determines the inverse influence function TIFF2026506870000225.tif6170, followed by calculating the convolution of the inverse influence function with the deformation of the wafer / membrane structure: TIFF2026506870000226.tif9170

[0034] In some embodiments, the convolution is a matrix multiplication: TIFF2026506870000227.tif11170, each element area Mesh points associated with TIFF2026506870000228.tif5170 Radius-vector for TIFF2026506870000229.tif6170 In some embodiments, a two-dimensional transformation can be implemented using a discretized representation of TIFF2026506870000230.tif6170. TIFF2026506870000231.tif5170 (and similarly, ion implantation maps TIFF2026506870000232.tif6170) can be represented as a column-oriented (or row-oriented) vector whose dimension (number of components) is equal to the number of points in the mesh. Because wafers are generally circular in shape, the number of points associated with different horizontal and vertical lines on the wafer are not necessarily the same. Similarly, the influence function TIFF2026506870000233.tif6170 and inverse influence function TIFF2026506870000234.tif6170 can be a matrix with the same representation. The inverse influence function can be calculated as the inverse matrix of the influence function: TIFF2026506870000235.tif11170 where, TIFF2026506870000236.tif5170 is the Kronecker delta symbol.

[0035] In some embodiments, the regression calculations are applied directly to at least some points of the wafer / membrane structure. Negative ion density in TIFF2026506870000237.tif6170 TIFF2026506870000238.tif6170 can be obtained. A negative ion density means that the stress in the film must be increased, rather than decreased, for the corresponding point. However, while ions can reduce stress in the film (e.g., by breaking the crystalline bonds of the film material), increasing stress can be more difficult under some conditions. This situation can be addressed using several different techniques. In one embodiment, for example, a larger thickness can be achieved by adding more material to the film already deposited on the wafer and recalculating the ion implantation map 660 (e.g., by repeating blocks 630-650). TIFF2026506870000239.tif3170 film (which will cause larger distortions in the wafer) can be deposited on the wafer. In another embodiment, the film thickness may be left unmodified. Instead, target wafer deformation TIFF2026506870000240.tif6170 can be modified. For example, instead of trying to achieve a perfectly flat wafer with the following formula: TIFF2026506870000241.tif11170 Ion implantation dose TIFF2026506870000242.tif5170 is a well-chosen cost function TIFF2026506870000243.tif4170 may be selected to be minimized. In some embodiments, the cost function may be a least mean square cost function, for example: TIFF2026506870000244.tif11170

[0036] In some embodiments, one or more constraints may be included in the cost function. For example, some of the constraints may include one or more of the following: a condition that the density of implanted ions is a positive function ( TIFF2026506870000245.tif5170), the condition that the density of implanted ions at any position in the film is limited by some maximum value ( TIFF2026506870000246.tif5170), the maximum density of implanted ions is a certain number Minimum density for TIFF2026506870000247.tif3170 TIFF2026506870000248.tif4170 ( TIFF2026506870000249.tif4170), the condition that the range of variation in the density of implanted ions is limited to a specific range ( TIFF2026506870000250.tif5170), constraints on maximum membrane density, maximum absolute deformation Constraints on maximum residual stress, TIFF2026506870000251.tif6170 Constraints on TIFF2026506870000252.tif6170, and / or any other constraints that may be set by the process supervisor.

[0037] In block 670, the calculated ion implantation map 660 can be applied to a stress compensation film, for example, as disclosed in conjunction with FIGS. 9A-B.

[0038] 8 illustrates simulation results of deformations caused by an ion implantation beam directed at different locations on a wafer / membrane structure, according to at least one embodiment. In example 802, the ion implantation beam is directed at the center of the wafer / membrane structure, resulting in deformation 804. Note that lighter (darker) areas of the wafer / membrane structure indicate greater (lesser) deformations. In example 806, the ion implantation beam 112 is directed at the center of the wafer / membrane structure, resulting in deformation 808. In example 810, the ion implantation beam 112 is directed at the edge of the wafer / membrane structure, resulting in deformation 812.

[0039] FIG. 9A schematically illustrates an ion implantation system 900 capable of performing ion implantation into a stress-compensating layer, according to at least one embodiment. The ion implantation system 900 may be part of a semiconductor manufacturing system including one or more processing chambers for processing wafers. The ion implantation system 900 may be or include the ion beam implanter 110 of FIG. 1. Specifically, although the stress-relief beam used to modify the stress in the stress-compensating layer 108 is referred to in some embodiments as an ion beam (e.g., ion beam 112), the stress-relief beam may include other material particles (e.g., electrons), electromagnetic waves (e.g., UV light, visible light, infrared light, etc.), and / or suitable combinations thereof. The ion implantation system 900 may include an ion source 902 for generating an ion beam 904. The ion source 902 may include a chamber (e.g., a plasma chamber) for generating ions. The ion source 902 may be powered by a power supply 906 and may include an extraction electrode assembly (not shown). The ion implantation system 900 may include a mass spectrometer 908 and a collimating and focusing column 910. The collimating and focusing column 910 may direct the ion beam 112 toward the wafer 102. The wafer 102 may be supported by a support stage 912. In some embodiments, the support stage 912 and wafer 102 may remain stationary while the ion beam 112 scans the wafer 102, but components of the ion implantation system 900 may be repositioned relative to the wafer 102. In some embodiments, the ion implantation system 900 may be stationary, but the support stage 912 may reposition the wafer 102. The scanning by the ion beam 112 may occur along multiple directions according to any suitable predetermined pattern, for example, TIFF2026506870000253.tif3170 Along the axis and TIFF2026506870000254.tif4170 Along the axis, for example, TIFF2026506870000255.tif3170 axis, back and forth, in a spiral pattern, etc. In various embodiments, the ion beam 112 can be scanned at a frequency of a few Hz, tens of Hz, hundreds of Hz, thousands of Hz, or greater.

[0040] Operation of the ion implantation system 900 can be controlled by a controller 914, which can include any suitable computing device having a processor, such as a central processing unit (CPU), field programmable gate array (FPGA), and / or application specific integrated circuit (ASIC), microcontroller, or other processing device, and memory devices, such as random access memory (RAM), read-only memory (ROM), and / or flash memory, or any combination thereof. The controller 914 can control the operation of the power supply 906, the support stage 912, and / or various other components and modules of the ion implantation system 900. The controller 914 can include an ion beam simulation module 916 that can perform simulations to determine target intensities of the ion beam 112 used to mitigate various wafer deformations. In some embodiments, the support stage 912 can be tilted, for example, in one or two spatial directions relative to the wafer 102 to vary the angle of incidence of the ion beam 112 with respect to the wafer 102. In some embodiments, instead of tilting the wafer 102 , the controller 914 can tilt the ion implantation system 900 relative to the wafer 102 .

[0041] FIG. 10 shows a block diagram of an exemplary computer system 1000 capable of supporting operations of the present disclosure, according to at least one embodiment. In various examples, exemplary computer system 1000 can be controller 914 of FIG. 9 or can include controller 1114. Computer system 1000 can be connected to other computer systems in a local area network (LAN), an intranet, an extranet, and / or the Internet. Computer system 1000 can operate in a server capacity in a client-server network environment. Computer system 1000 can be a personal computer (PC), a set-top box (STB), a server, a network router, switch, or bridge, or any device capable of executing a set of instructions (sequential or otherwise) that specify operations to be performed by the device. Furthermore, while only a single exemplary computer system is shown, the term "computer" should also be understood to include any collection of computers that, individually or collectively, execute an instruction set (or sets of instructions) to perform any method or methods described herein.

[0042] The exemplary computer system 1000 may include a processing device 1002 (also referred to as a processor or CPU), a main memory 1004 (e.g., read-only memory (ROM), flash memory, dynamic random access memory (DRAM) such as synchronous DRAM (SDRAM), etc.), a static memory 1006 (e.g., flash memory, static random access memory (SRAM), etc.), and a secondary memory (e.g., a data storage device 1018), which may communicate with each other via a bus 1030.

[0043] The processing device 1002 represents one or more general-purpose processing devices, such as a microprocessor or central processing unit. The processing device 1002 may include processing logic 1026. The processing device 1002 may be a complex instruction set computing (CISC) microprocessor, a reduced instruction set computing (RISC) microprocessor, a very long instruction word (VLIW) microprocessor, a processor implementing other instruction sets, or a processor implementing a combination of instruction sets. The processing device 1002 may also be one or more special-purpose processing devices, such as an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a digital signal processor (DSP), or a network processor. According to one or more aspects of the present disclosure, the processing device 1002 may be configured to execute instructions implementing the example process 600 for mitigating wafer deformation based on an influence function.

[0044] The exemplary computer system 1000 may further include a network interface device 1008 that may be communicatively coupled to a network 1020. The exemplary computer system 1000 may further include a video display 1010 (e.g., a liquid crystal display (LCD), touch screen, or cathode ray tube (CRT)), an alphanumeric input device 1012 (e.g., a keyboard), a cursor control device 1014 (e.g., a mouse), and an audio signal generating device 1016 (e.g., a speaker).

[0045] The data storage device 1018 may include a computer-readable storage medium (or more specifically, a non-transitory computer-readable storage medium) 1024 having stored thereon one or more sets of executable instructions 1022. According to one or more aspects of the present disclosure, the executable instructions 1022 may include executable instructions that implement the example process 600 for mitigating wafer deformation based on an influence function.

[0046] The executable instructions 1022 may also reside, completely or at least partially, within the main memory 1004 and / or within the processing device 1002 during execution by the exemplary computer system 1000, with the main memory 1004 and the processing device 1002 also constituting computer-readable storage media. The executable instructions 1022 may also be transmitted or received over a network via the network interface device 1008.

[0047] Although computer-readable storage medium 1024 is shown in Figure 10 as a single medium, the term "computer-readable storage medium" should be interpreted to include a single medium or multiple media (e.g., a centralized or distributed database, and / or associated caches and servers) that store one or more sets of operating instructions. The term "computer-readable storage medium" should also be interpreted to include any medium that can store or encode a set of machine-executed instructions that cause the machine to perform any one or more of the methodologies described herein. Accordingly, the term "computer-readable storage medium" should be interpreted to include, but is not limited to, solid-state memory and optical and magnetic media.

[0048] Some portions of the foregoing detailed descriptions are presented in terms of algorithms and symbolic representations of operations on data bits within a computer memory. These algorithmic descriptions and representations are the means used by those skilled in the data processing arts to most effectively convey the substance of their invention to others skilled in the art. An algorithm is here, and generally, conceived to be a self-consistent sequence of steps leading to a desired result. These steps are steps requiring physical manipulations of physical quantities. Usually, though not necessarily, these quantities take the form of electrical or magnetic signals capable of being stored, transferred, combined, compared, and otherwise manipulated. It has proven convenient at times, principally for reasons of common usage, to refer to these signals as bits, values, elements, symbols, characters, terms, numbers, or the like.

[0049] It should be noted, however, that all of these and similar terms should be associated with the appropriate physical quantities and are merely convenient labels applied to these quantities. As will become apparent from the following description, unless otherwise specified, throughout this description, descriptions utilizing terms such as "identifying," "determining," "storing," "adjusting," "causing," "returning," "comparing," "creating," "stopping," "loading," "copying," "throwing," "replacing," or "performing" should be understood to refer to the operations and processes of a computer system or similar electronic computing device. Such a computer system or similar electronic computing device manipulates and converts data represented as physical (electronic) quantities in the computer system's registers and memory into other data represented as physical (electrical) quantities in the computer system's memory or registers or such other information storage, transmission, or display device.

[0050]

[0010] Embodiments of the present disclosure also relate to apparatus for performing the methods described herein. This apparatus may be specially constructed for the required purposes, or it may be a general-purpose computer system selectively programmed by a computer program stored in the computer system. Such a computer program may be stored on a computer-readable storage medium, such as any type of disk including, but not limited to, optical disks, CD-ROMs, and magneto-optical disks, read-only memory (ROM), random-access memory (RAM), EPROM, EEPROM, magnetic disk storage media, optical storage media, flash memory devices, other types of machine-accessible storage media, or any type of medium suitable for storing electronic instructions, each coupled to a computer system bus.

[0051] The methods and displays presented herein are not inherently related to any particular computer or other apparatus. Various general-purpose systems may be used with programs in accordance with the teachings herein, or it may prove convenient to construct more specialized apparatus to perform the required method steps. The required structure for a variety of such systems will be apparent as set forth in the description below. Additionally, the scope of the present disclosure is not limited to any particular programming language. It will be understood that a variety of programming languages ​​can be used to implement the teachings of the present disclosure.

[0052] It should be understood that the above description is intended to be illustrative, not limiting. Many other exemplary embodiments will be apparent to those skilled in the art upon reading and understanding the above description. While particular examples have been described in the present disclosure, it will be recognized that the systems and methods of the present disclosure are not limited to the examples described herein, but can be practiced with modification within the scope of the claims. Accordingly, the specification and drawings are to be regarded in an illustrative, rather than limiting sense. The scope of the present disclosure should, therefore, be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled.

Claims

1. 1. A method for correcting out-of-plane deformation (OPD) of a substrate, comprising: depositing a stress compensation layer (SCL) on the substrate; obtaining a profile of the OPD of the substrate using optical inspection data; and - obtaining, by a processing device, a dataset comprising a representation of an influence function of the substrate, the influence function characterizing a deformation response of the substrate caused by a point-like mechanical influence; performing a regression calculation to determine a distribution of stress relaxation dose of the SCL that relaxes the OPD of the substrate based on at least the profile of the OPD of the substrate and the influence function; performing stress relaxation irradiation of the SCL using the determined distribution of stress relaxation irradiation; A method comprising:

2. The method of claim 1 , wherein the influence function is determined based on one or more simulations characterizing the OPD of a reference substrate caused by known mechanical influences.

3. The method of claim 2 , wherein the one or more simulations use finite element analysis.

4. 2. The method of claim 1, wherein the influence function is determined using one or more experiments, each of the one or more experiments comprising a measurement of a reference substrate OPD caused by a reference stress relaxation beam directed at a reference SCL deposited on the reference substrate.

5. The method of claim 1 , wherein the regression calculation is subject to one or more constraints.

6. The method of claim 1 , wherein the distribution of the stress-relieving exposure of the SCL is determined to minimize the mean square OPD of substrate deformation after the stress-relieving exposure of the SCL.

7. The method of claim 1 , wherein the substrate includes a front side and a back side, the front side including one or more fabricated features, and the SCL is deposited on the back side of the substrate.

8. depositing the SCL onto the substrate; using optical inspection data to determine a profile of the OPD of the substrate; performing a polynomial decomposition of the identified profile to determine a plurality of polynomial coefficients, each of the plurality of polynomial coefficients characterizing a respective one of a plurality of elementary deformation shapes of the substrate; identifying one or more characteristics of a stress compensation layer (SCL) of the substrate based on at least a subset of the plurality of polynomial coefficients, wherein the one or more characteristics of the SCL include: the material of the SCL, or The thickness of the SCL identifying one or more characteristics of a stress compensation layer (SCL) of the substrate, including at least one of: The method of claim 1 , comprising:

9. determining a setting for the stress relaxation irradiation of the SCL, the setting comprising: The type of particles in the stress relaxation beam used in the stress relaxation irradiation of the SCL; the energy of the particles of the relaxation beam, or the angle of incidence of the particles of the stress relaxation beam on the SCL; The method of claim 1 , comprising one or more of:

10. Memory and a processing device communicatively coupled to the memory; a processing device for processing a signal from the processing device; depositing a stress compensation layer (SCL) on a substrate; obtaining an out-of-plane deformation (OPD) profile of the substrate using optical inspection data; - obtaining, by a processing device, a dataset comprising a representation of an influence function of the substrate, the influence function characterizing a deformation response of the substrate caused by a point-like mechanical influence; performing a regression calculation based on at least the profile of the OPD of the substrate and the influence function to determine a distribution of stress relaxation dose of the SCL that relaxes the OPD of the substrate; performing stress relaxation irradiation of the SCL using the determined distribution of stress relaxation irradiation; A system that performs the following:

11. The system of claim 10 , wherein the influence function is determined based on one or more simulations characterizing the OPD of a reference substrate caused by known mechanical influences.

12. The system of claim 11 , wherein the one or more simulations use finite element analysis.

13. 11. The system of claim 10, wherein the influence function is determined using one or more experiments, each of the one or more experiments including a measurement of a reference substrate OPD caused by a reference stress relaxation beam directed at a reference SCL deposited on the reference substrate.

14. The system of claim 10 , wherein the regression calculation is subject to one or more constraints.

15. The system of claim 10 , wherein the distribution of the stress-relieving exposure of the SCL is determined to minimize a mean square OPD of substrate deformation after the stress-relieving exposure of the SCL.

16. 11. The system of claim 10, wherein the substrate includes a front side and a back side, the front side including one or more fabricated features, and the SCL is deposited on the back side of the substrate.

17. To deposit the SCL onto the substrate, the processing device using optical inspection data to determine a profile of the OPD of the substrate; performing a polynomial decomposition of the identified profile to determine a plurality of polynomial coefficients, each of the plurality of polynomial coefficients characterizing a respective one of a plurality of elementary deformation shapes of the substrate; identifying one or more characteristics of a stress compensation layer (SCL) of the substrate based on at least a subset of the plurality of polynomial coefficients, wherein the one or more characteristics of the SCL include: the material of the SCL, or The thickness of the SCL identifying one or more characteristics of a stress compensation layer (SCL) of the substrate, including at least one of: The system of claim 10,

18. the processing device further comprising: The setting of the stress relaxation irradiation of the SCL is determined, and the setting The type of particles in the stress relaxation beam used in the stress relaxation irradiation of the SCL; the energy of the particles of the relaxation beam, or the angle of incidence of the particles of the stress relaxation beam on the SCL; The system of claim 10, comprising one or more of:

19. one or more processing chambers for processing substrates; Computing device and 1. A semiconductor manufacturing system comprising: depositing a stress compensation layer (SCL) on a substrate; obtaining an out-of-plane deformation (OPD) profile of the substrate using optical inspection data; - obtaining a dataset comprising a representation of an influence function of the substrate, the influence function characterizing a deformation response of the substrate caused by a point-like mechanical influence; performing a regression calculation to determine a distribution of stress relaxation dose of the SCL that relaxes the OPD of the substrate based on at least the profile of the OPD of the substrate and the influence function; performing stress relaxation irradiation of the SCL using the determined distribution of stress relaxation irradiation; A semiconductor manufacturing system that performs the above.

20. The influence function is one or more simulations characterizing the OPD of a reference substrate caused by known mechanical effects; or one or more experiments, each including a measurement of a reference substrate OPD caused by a reference relaxation beam directed at a reference SCL deposited on said reference substrate.

20. The semiconductor manufacturing system of claim 19, wherein the determination is based on at least one of:

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