Dose mapping using substrate curvature to compensate for out-of-plane distortion

Abstract

A method may include generating a residual curvature map of a substrate, the residual curvature map based on measurements of a surface of the substrate. The method may include generating a dose map based on a residual curvature map, the dose map being used to process a substrate using a patterned energy source; and applying the dose map to process the substrate using the patterned energy source.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. Provisional Patent Application Serial No. 63 / 341,797, filed on May 13, 2022, entitled “DOSE MAPPING USING SUBSTRATE CURVATURE TO COMPENSATE FOR OUT-OF-PLANE DISTORTION,” and U.S. Provisional Patent Application Serial No. 63 / 425,060, filed on November 14, 2022, entitled “DOSE MAPPING USING SUBSTRATE CURVATURE TO COMPENSATE FOR OUT-OF-PLANE DISTORTION,” and the entire text of said patent applications is incorporated herein by reference. Technical Field

[0003] Embodiments of the present invention relate to stress control in substrates, and more particularly to stress compensation to reduce out-of-plane distortion in substrates. Background Art

[0004] Devices (such as integrated circuits, memory devices, and logic devices) may be fabricated on substrates (such as semiconductor wafers) by a combination of deposition processes, etching, ion implantation, annealing, and other processes. Often, the complete fabrication of a device and associated circuitry may require hundreds of operations, including dozens of photolithography operations. In particular, the photolithography operations may require that a given mask used to fabricate a structure in a given area or level be aligned to a pre-existing structure.

[0005] A common problem with manufacturing such devices and structures on substrates such as semiconductor wafers is the generation of in-plane distortion (IPD), which affects the overlay of layers relative to underlying reference layers. IPD is a complex quantity that is affected by the out-of-plane distortion (OPD) of the wafer and the alignment scheme employed in lithography. OPD is a fundamental wafer quantity, and the signature of residual OPD is critical to achievable overlay. For example, a commonly encountered type of OPD is global wafer curvature, which may be generated in many processing situations due to stress buildup in the wafer caused by processing operations.

[0006] In addition, device processing may produce complex OPD patterns on the wafer after any given processing stage, which often affects subsequent processing operations. In a specific example, the complex OPD pattern may generate overlay errors in subsequent photolithography mask operations.

[0007] In view of these and other considerations, embodiments of the present invention are provided. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figures 1A to 1C illustrates the principles of operation of embodiments of the present disclosure;

[0009] FIG. 2A to FIG. 2F depicts different representations of the OPD of a wafer at different processing stages according to an embodiment of the present disclosure;

[0010] Figure 2G is the resulting IPD assuming the HOWA3 alignment scheme on the scanner.

[0011] FIG. 3A to FIG. 5D Depicted is a sequence of operations for determining a dose map for processing a substrate in order to compensate for substrate OPD in accordance with an embodiment of the present disclosure;

[0012] FIG. 6A to FIG. 6B depicts different representations of ion implanters consistent with various embodiments of the present disclosure; and

[0013] Figure 7 An exemplary process flow is depicted;

[0014] Figure 8 Another exemplary process flow is depicted; and

[0015] Fig. 9 Additional exemplary process flows are depicted. DETAILED DESCRIPTION

[0016] Embodiments of the present invention will now be described more fully below with reference to the accompanying drawings, in which some embodiments are shown. The subject matter of the present disclosure can be embodied in many different forms and should not be construed as being limited to the embodiments set forth herein. On the contrary, since these embodiments are provided, the present disclosure will be thorough and complete, and will fully convey the scope of the subject matter to those skilled in the art. In the drawings, the same numbers always refer to the same elements.

[0017] Embodiments described herein relate to techniques and apparatus for improving control of out-of-plane distortion in a substrate and the associated control of the effects of OPD on substrate processing operations, such as device fabrication. Embodiments of the invention may employ novel techniques to determine a dose map applied by a patterned energy source to a compensation layer of a substrate in order to better correct for OPD and, therefore, reduce or minimize in-plane distortion (IPD) that affects device fabrication and other patterning processes. Non-limiting examples of patterned energy sources include ion beams or laser beams that may be scanned relative to a major plane of a substrate.

[0018] In various embodiments detailed herein, a substrate (also often referred to as a "wafer") may be measured to determine a substrate OPD map. This OPD map may then be used to extract a global OPD, the entity being defined as the best-fit parabola to the measured OPD. Calculations are also performed to extract a global substrate curvature component corresponding to the parabola, while a residual OPD is used to extract a local or residual substrate curvature.

[0019] Figures 1A to 1C The principles of operation of embodiments of the present disclosure are illustrated. Figure 1A , a three-dimensional diagram depicting the surface of a wafer is shown with reference to a Cartesian coordinate system shown. In particular, Figure 1A The diagram depicts the shape of a nominally round and flat wafer, where the XY plane may represent the nominal principal plane of the wafer, or equivalently, the ideal plane of a flat platen supporting the wafer. In one example, the units shown in the XY plane may be millimeters. The z-axis represents the normal to the principal plane of the substrate, and thus any location on the substrate that is not in the XY plane when z=0 may be considered to represent the OPD. Note that the z-axis is dimensionless and normalized to 1. During semiconductor wafer processing, stress buildup during fabrication of layers, devices, and the like may result in a global curvature (such as Figure 1B The OPD may be a parabolic shape as shown. Such a shape may be associated with biaxial tensile stress or compressive stress. In some non-limiting examples, the level of OPD may reach a maximum value in the range of hundreds of microns, such as 100 μm, 200 μm, 300 μm, 400 μm, etc.

[0020] According to the embodiments of the present disclosure, compensation can be made in a series of operations such as Figure 1A The OPD is represented by the shape of the wafer. Figure 1B In a first operation shown, a large portion of the OPD may be compensated using a uniform stress compensating layer applied to the back surface of the substrate, opposite to the front surface of the substrate in which the device is fabricated. Figure 1BThe graph of FIG. 1 shows the spatial distribution in the XY plane of the amount of strain or deformation (expressed along the Z axis) of the wafer that can be generated by the uniform stress compensation layer. Likewise, the relative deformation along the Z axis is normalized so that in the graph of FIG. 1 , the maximum deformation is at the center of the wafer. Figure 1B The operation of may be useful to compensate for the relatively large global OPD generated on the wafer, as determined by Figure 1B The shape of this OPD can be axisymmetric about the z-axis, and Figure 1B The operation can generally reduce stress in an axisymmetric manner. Figure 1B After application of the indicated operations, the global curvature of the wafer can be removed to a large extent.

[0021] Go to Figure 1C , there are diagrams showing examples of residual patterns of OPD that can be superimposed on Figure 1B Depending on the nature of the die layout and other patterned features on the wafer, even in a global OPD pattern (such as Figure 1B After removal of the residual OPD pattern, there may also be a complex "residual" OPD pattern that is not necessarily axisymmetric and may be more localized. Thus, embodiments of the present invention address this phenomenon by applying a so-called dose map to a patterned energy source (such as a scannable ion beam, electron beam, or laser beam). As described in detail below, the patterned energy source can be applied to the substrate in a non-uniform manner, such as in a preexisting compensation layer, to remove the residual OPD pattern.

[0022] FIG. 2A to FIG. 2F Depicted are different representations of the OPD of a wafer at different processing stages according to an embodiment of the present disclosure. In these examples, as in Figure 1A Like in Figure 2A , Figure 2C and Figure 2E The units of the x-axis and y-axis are illustrated in millimeters, for example, representing a 300 mm wafer. The units along the z-axis are in nm. Thus, these figures present a three-dimensional depiction of the wafer surface, where the z-axis coordinate of an ideally flat wafer would be constant throughout the xy plane, for example, 0.

[0023] exist Figure 2A In the example of , the wafer surface is represented by a three-dimensional array of points. The wafer surface can be characterized as a somewhat paraboloid shape characterized by a z-axis coordinate ranging from -150,000 nm to +150,000 nm, which corresponds to a maximum OPD of 300,000 nm or 300 μm. Figure 2B In a very general form Figure 2AA side cross-sectional view of a very small portion of a substrate (which in some embodiments may be silicon) of FIG. The front surface in this example is represented by the top surface in the figure, where additional device layers may or may not be present but are omitted for simplicity. Figure 2A The surface shown may represent the surface of a wafer prior to being processed to reduce OPD according to embodiments of the present disclosure.

[0024] Go to Figure 2C , showing the process for depositing a stress compensation layer (e.g. Figure 2D shown) and Figure 2B The wafer surface corresponding to the wafer of the wafer. According to different non-limiting embodiments, the stress compensation layer can be deposited by a known device (such as a physical vapor deposition (PVD) device, a chemical vapor deposition (CVD) device or other film deposition system). Examples of suitable materials for the stress compensation layer include silicon nitride, silicon oxide, silicon oxynitride, a layer containing any combination of Si-ONC, or other known materials. At this moment, the wafer surface can be characterized as an irregular shape, in which the absolute value of OPD is greatly reduced, so that the maximum value of OPD is only on the order of a few microns.

[0025] At this stage of processing, the stress compensating layer can be said to have removed global signatures of the stress state across the wafer that produce a generally regular parabolic shape for the wafer on a vertical scale of hundreds of microns. For example, deposition of a uniform stress compensating layer on the surface of the wafer can be expected to modify the average shape of the wafer based on the well-known Stoney equation that relates changes in substrate curvature to stress properties of layers in contact with the substrate. According to embodiments of the present disclosure, the layer thickness and stress state of the stress compensating layer can be determined based on, for example, Figure 2A The initial curvature level depicted in is selected to reduce the overall curvature of the wafer. As discussed further below, different possible models can be used to model the global curvature in order to provide a basis for determining the appropriate stress-compensating layer properties required to remove the global curvature. Figure 2C and Figure 2D In the example of FIG. 1 , a stress compensation layer having a suitable thickness, a suitable elastic modulus and a suitable stress state can be selected so as to remove Figure 2A Almost all the global curvature components of the maximum OPD of 300 mm are generated in Figure 2C In the example, what is left is a slightly irregular pattern of OPD that represents residual curvature that may be caused by artifacts present on the front surface of the wafer, such as die placement, certain device or circuit structures, etc. This irregular OPD pattern may cause unwanted IPD to appear at different areas of the substrate, leading to problems such as increased overlay misalignment of subsequent substrate patterning.

[0026] according to Figure 2E and Figure 2F implementation method, Figure 2C The residual curvature exhibited by the substrate can be removed, reduced or modified by performing exposure to a patterned energy source, as previously described. Figure 2F In the particular example shown, an implantation process has been performed to generate an implantation layer in the stress compensation layer, wherein the implantation process may involve a non-uniform direct write implantation process. In this context, a 'direct write' process, including a direct write implantation process, may refer to a process that employs relative movement of an ion beam without the use of a mask to produce a non-uniform ion dose pattern on the substrate surface. The non-uniform implantation process may reduce the OPD method to locally adjust the curvature of the wafer, such as Figure 2F In other embodiments, a direct write process involving exposure to electrons or photons (such as a laser beam) can be used to locally adjust the curvature of the wafer. As described in detail below, a dose map calculated based on measured values ​​of the initial surface of the wafer before the stress compensation layer is deposited can be used to perform a patterning process to locally adjust the curvature of the substrate. Note that the use of an appropriate dose map to modify the curvature of the substrate is not limited to the following embodiments. Figure 2C The OPD correction of the residual curvature can be converted into an IPD correction on the wafer, as in Figure 2G This figure shows a 2-dimensional plot in the xy plane, illustrating the magnitude and direction of the IPD correction as a function of the x,y coordinates in the wafer for a 300 mm wafer.

[0027] FIG. 3A to FIG. 5C Depicted is a sequence of operations that will be applied to determine a dose map for processing a substrate in order to compensate for substrate OPD in accordance with an embodiment of the present disclosure. In particular, FIG. 3A to FIG. 5C The illustrated developments illustrate approaches to eliminate residual curvature in a substrate surface.

[0028] exist FIG. 3A to FIG. 3C , details for determining the global curvature of a substrate in order to generate a global curvature map are shown. Figure 3A Describes the above FIG. 2A to FIG. 2E A three-dimensional representation of the wafer surface prior to extraction of the global curvature component is generally discussed. Figure 3B Illustrated Figure 3AA two-dimensional representation of a surface of a substrate, wherein the surface is generally parabolic in nature. In this example, the OPD ranges shown in the figure are exemplary only and may vary over a wide range, as will be appreciated by those skilled in the art. Although it is intended to use a blanket processing operation to deposit a blanket film on the back side of the substrate to remove the global curvature, this may not always be possible due to process variations. Therefore, a residual component of the global curvature may still remain on the wafer. This global curvature still has a parabolic OPD signature and appears on the curvature map to be a mostly uniform curvature across the wafer.

[0029] Figure 3C A global curvature graph representing the curvature value as a function of the x,y coordinates on the wafer surface is depicted. The unit k is in reciprocal km. According to various non-limiting embodiments of the present disclosure, the global curvature may be modeled based on a Gaussian curvature model or a mean curvature model. The modeling may be based on the use of two mutually orthogonal principal planes of curvature, such as Figure 3D As shown, these two mutually orthogonal principal planes of curvature extend perpendicular to the tangent plane of the surface. In the Gaussian model, the product of the maximum and minimum curvatures is taken, where k is given by

[0030] κ=κ1κ2 Equation (1)

[0031] In the mean model, the mean of the principal (maximum and minimum) curvatures is taken, where k is given by

[0032]

[0033] like Figure 3C As shown, the global curvature is mostly uniform across the wafer.

[0034] Figure 4A The parabolic term of the OPD is extracted and the Figure 3A A three-dimensional representation of the residual wafer surface corresponding to the same wafer showing the global surface. Figure 4B Illustrated Figure 4A Two-dimensional representation of the surface of , where the pattern of OPD is quite complex.

[0035] Figure 4C Depicts the expression for Figure 4A and Figure 4B A residual curvature map of a surface as a function of the curvature values ​​of the x,y coordinates on the wafer surface. According to embodiments of the present disclosure, the process for modeling global curvature as generally outlined above may be employed to model the global curvature based on Figure 4B The OPD diagram is generated Figure 4C Residual curvature plot.

[0036] like Figure 4CAs shown, the pattern of residual curvature shows a complex set of features. In general, the curvature value is relatively low over most of the wafer, while there is a donut-shaped region of negative curvature toward the center of the wafer. In some areas on the wafer, the curvature has positive values, such as around the periphery of the wafer, while along the donut-shaped region, the curvature has negative values.

[0037] Figure 4C The residual curvature map of can be regarded as the original residual curvature map, which is further processed to generate the final curvature map used to generate the dose map. Figure 3A to remove residual curvature features and thereby eliminate or reduce IPD caused by such features. Figure 5A An ion beam profile that can be used for actual wafer implantation is shown. This profile is used in the blur kernel operation to create the Figure 4C The residual curvature map of is then used to apply a blur kernel to attenuate the effects of high spatial frequencies on the implanter. The contour can then be used to generate Figure 5B The blurred residual curvature map is shown.

[0038] Figure 5B The blurred residual curvature map of presents positive and negative curvature regions of the same qualitative pattern, but the width of the region is wider and the curvature value within the region is slightly different from the unblurred counterpart. Given the finite size of the ion beam, this blurred curvature map may be more suitable for being achieved by a patterned energy source (such as a scanning ion beam).

[0039] Go to Figure 5C , showing that by Figure 5B The blurred residual curvature map is filtered to remove all positive curvature terms to generate a filtered residual curvature map, since the positive terms cannot be affected by the ion beam. This leaves two main, slightly linear regions with relatively higher negative curvature, and some regions with lower negative curvature protruding from the linear regions. This map can then be converted into a dose map, such as for a scannable ion beam, where the total ion dose applied on the two-dimensional surface (xy plane) of the wafer is based on Figure 5C Therefore, the pattern of ion dose of a suitable dose map may exhibit a feature having the same shape as the feature of the curvature map.

[0040] Figure 5D Provides a Figure 5C An exemplary ion dose map of a curvature map of Figure 5CThe curvature map of the wafer may be qualitatively similar to the curvature map of FIG. 1 . In this example, two parallel linear regions of the dose map corresponding to high curvature linear regions of the filtered curvature map will receive a much higher dose than the general 'background' regions. For example, the background regions over most of the surface of the wafer will receive a relative ion dose in the range of 15%, while the linear regions will receive a relative ion dose in the range of between approximately 50% and 85%.

[0041] Fig. 6A A schematic top view of an ion implantation system for controlling substrate OPD according to an embodiment of the present disclosure is depicted. The ion implantation system, referred to as an ion implanter 300, represents a processing chamber containing an ion source 304 and a series of beamline components and other components for generating an ion beam 308. The ion source 304 may include a chamber for receiving a gas stream and generating ions. The ion source 304 may also include a power source and an extraction electrode assembly (not shown) disposed near the chamber. The beamline components may include, for example, an analyzer magnet 320, a mass resolution slit (MRS) 324, a steering / focusing component 326, and an end station 330, which includes a substrate holder 331.

[0042] The ion implanter 300 further includes a beam scanner 336 positioned along a beam line 338 between the MRS 324 and the end station 330. The beam scanner 336 can be arranged to receive the ion beam 308 as a spot beam and scan the ion beam 308 along a fast scan direction (such as parallel to the X-axis in the Cartesian coordinate system shown). It is worth noting that the substrate 332 can be scanned along the Y-axis, so that a given ion treatment can be applied to a given area of ​​the substrate 332 while the ion beam 308 is scanned back and forth along the X-axis. The ion implanter 300 can have additional components, such as a collimator (not shown for clarity) as is known in the art, to direct the ions of the ion beam 308 along a series of mutually parallel trajectories to the substrate 332 after scanning, such as Fig. 6A In various embodiments, the ion beam can be scanned at a frequency of a few Hz, 10 Hz, 100 Hz, up to several kilohertz, or more. For example, the beam scanner 336 can use magnetic or electrostatic scanning elements to scan the ion beam 308, as is known in the art.

[0043] By rapidly scanning the ion beam 308 in a fast scan direction, such as scanning back and forth along the x-axis, the ion beam 308 configured as a spot beam can deliver a targeted ion dose to any given area of ​​the substrate in the xy plane. According to some non-limiting embodiments, suitable ions for the ion beam 308 may include any ion species capable of inducing stress changes at a suitable ion energy, including ions such as phosphorus, boron, argon, indium BF2, etc., wherein the ion energy is customized according to the exact ion species used. In order to achieve a dose map, the scanning speed of the ion beam along the x-axis can be adjusted at different locations of the substrate 332 according to the dose map so as to deliver different ion doses at different locations. In general, the ion beam 308 can scan back and forth on the substrate for any suitable number of scans, and is accompanied by scanning the substrate in a direction orthogonal to the beam scan direction until a targeted dose as specified by the dose map is received at the arrival area on the substrate 332.

[0044] For example, the ion implanter 300 may further include a controller 340 coupled to the beam scanner 336 to coordinate the operation of the beam scanner 336, and the substrate holder 331. Fig. 6A As further shown, the ion implanter 300 may include a user interface 342 that is also coupled to the controller 340. The user interface 342 may be embodied as a display and may include user selection devices, including a touch screen, a displayed menu, buttons, knobs, and other devices as known in the art. According to various embodiments, the user interface 342 may send instructions to the controller 340 to generate an appropriate implant pattern that may achieve an appropriate dose map for the substrate 332.

[0045] like Figure 6BAs further shown, the controller 340 may include a processor 352, such as a known type of microprocessor, a dedicated processor chip, a general purpose processor chip, or the like. The controller 340 may further include a memory or memory unit 354 coupled to the processor 352, wherein the memory unit 354 contains a dose map routine 356. The dose map routine 356 may be operable on the processor 352 to manage the scanning of the ion beam 308 and the substrate 332 so as to impart the calculated dose map into the substrate 332. The memory unit 354 may include an article of manufacture. In one embodiment, the memory unit 354 may include any non-transitory computer-readable medium or machine-readable medium, such as an optical, magnetic, or semiconductor storage device. The storage medium may store various types of computer-executable instructions to implement one or more logic flows described herein. Examples of computer-readable or machine-readable storage media may include any tangible media capable of storing electronic data, including volatile memory or non-volatile storage, removable or non-removable memory, erasable or non-erasable memory, writable or rewritable memory, and the like. Examples of computer executable instructions may include any suitable type of code, such as source code, compiled code, interpreted code, executable code, static code, dynamic code, object-oriented code, visual code, and the like. In this context, the embodiments are not limited.

[0046] Now go to Figure 7 , a process flow 700 according to some embodiments of the present disclosure is shown. At block 702, an initial substrate surface map is received. The substrate surface map may represent three-dimensional coordinates of a set of points on a substrate surface, and may represent a graph of OPD as a function of x,y coordinates, where the OPD is represented by the z coordinate of a given surface point relative to a reference x,y plane.

[0047] At block 704, a global curvature map is generated from the initial substrate surface map using the model. In some examples, the global curvature map may correspond to a surface modeled as a parabola using a mean model or a Gaussian model, as detailed above.

[0048] At block 706, a residual surface is extracted based on the initial substrate surface map and the global curvature map. Thus, the residual surface may include remnants or localized regions of OPD in different x,y portions of the substrate.

[0049] At block 708, a residual curvature map is generated based on the residual surface. The residual curvature map may plot the curvature as a function of the inverse length of the x,y position on the substrate in question.

[0050] At block 710, a blurred residual curvature map is generated from the residual curvature map using a blur kernel. The blurred residual curvature map may present regions of curvature of the same qualitative pattern as the residual curvature map, while the width of the region may be wider and the curvature values ​​may be different from the unblurred counterpart. This blurring may be used to account for size effects, such as the beam size of a scanning energy source used to achieve a dose map based on the residual curvature map.

[0051] At block 712, any positive curvature components from the blurred residual curvature map are subtracted to generate a filtered residual curvature map.

[0052] At block 714, a dose map is generated for processing the substrate based on the filtered residual curvature map.The dose map may exhibit a qualitatively similar pattern to the filtered residual curvature map, where the relative dose increases in x,y regions with relatively higher curvature.

[0053] Now go to Figure 8 , a process flow 800 according to some embodiments of the present disclosure is shown. At block 802, the process continues from block 704. In particular, a stress compensation layer deposition recipe is generated based on a global curvature map of a given substrate. The recipe may specify layer type, deposition conditions, and layer thickness, to name just a few parameters.

[0054] At block 804 , a backside layer is deposited on a given substrate based on a stress compensating layer deposition recipe.

[0055] Now go to Fig. 9 , a process flow 900 is shown according to some embodiments of the present disclosure. At block 902, flow continues from block 714 where a dose map as detailed in process flow 700 is received in a patterned energy tool such as an ion implanter.

[0056] At block 904 , flow continues from block 804 where a substrate having a backside layer based on a stress compensating layer deposition recipe is received in a patterned energy tool.

[0057] At block 906 , a dose map is applied to the backside layer using a patterned energy source of a patterned energy tool, such as a scanned ion beam.

[0058] The advantages provided by embodiments of the present invention are multifaceted. As a first advantage, the method allows subsequent devices to proceed with greater accuracy, such as subsequent photolithography steps that require low in-plane distortion. As a second advantage, the method more accurately reduces regions with greater in-plane distortion by targeting residual regions with greater substrate curvature for greater energy treatment.

[0059] The present disclosure is not limited in scope by the specific embodiments described herein. In fact, in addition to those embodiments and modifications described herein, various other embodiments and modifications of the present disclosure will be apparent to those skilled in the art from the foregoing description and accompanying drawings. Therefore, it is intended that such other embodiments and modifications fall within the scope of the present disclosure. In addition, the present disclosure has been described herein in the context of a specific implementation in a specific environment for a specific purpose, but it will be appreciated by those skilled in the art that usefulness is not limited thereto and the present disclosure can be beneficially implemented in any number of environments for any number of purposes. Therefore, the claims set forth below will be understood in view of the full breadth and spirit of the present disclosure as described herein.

Claims

1. A method, comprising: generating a residual curvature map of a substrate, the residual curvature map being based on measurements of a surface of the substrate; generating a dose map based on the residual curvature map, the dose map being used to process the substrate using a patterned energy source; and The dose map is applied to process the substrate using the patterned energy source.

2. The method of claim 1, wherein generating the residual curvature map comprises: modeling a global curvature map based on an initial substrate surface map of out-of-plane distortion of a surface of the substrate; extracting the global curvature map from the initial substrate surface map to generate an original residual curvature map; and A blur kernel operation is applied to the original residual curvature map. 3 . The method of claim 2 , said generating the residual curvature map further comprising applying a filter to filter out positive curvature from the residual curvature map.

4. The method of claim 2, wherein substrate curvature as represented by the global curvature map is removable by performing a blanket processing operation.

5. The method of claim 4, wherein the blanket processing operation comprises depositing a stress compensating layer on the back side of the substrate.

6. The method of claim 5, wherein the stress compensation layer comprises: A layer of silicon nitride, silicon oxide, silicon oxynitride, or any combination containing Si-ONC.

7. The method of claim 1, wherein applying the dose map comprises: exposing the stress compensating layer on the back side of the substrate to the patterned energy source, and The patterned energy source is scanned in a pattern over the stress compensating layer without using a mask to transfer the dose map into the substrate.

8. The method of claim 1, wherein the patterning energy source comprises an ion beam, an electron beam, or a laser beam.

9. A method comprising: receiving a substrate surface map of a substrate, the substrate surface map comprising a map of out-of-plane distortion of the substrate; modeling a global curvature map based on the substrate surface map; generating a residual curvature map after extracting the global curvature map from the substrate surface map; generating a dose map based on the residual curvature map, the dose map being used to process the substrate using a patterned energy source; and The dose map is applied to process the substrate using the patterned energy source.

10. The method of claim 9, wherein extracting the global curvature map from the substrate surface map generates an original residual curvature map, the method further comprising: creating a blur kernel using a beam profile of the patterned energy source; and The blur kernel is applied to the original residual curvature map to generate a blurred residual curvature map.

11. The method of claim 10, further comprising: A filter is applied to remove positive curvature from the blurred residual curvature map.

12. The method of claim 9, wherein substrate curvature as represented by the global curvature map is removable by performing a blanket processing operation.

13. The method of claim 12, wherein the blanket processing operation comprises depositing a stress compensating layer on the back side of the substrate.

14. The method of claim 13, wherein the stress compensation layer comprises: A layer of silicon nitride, silicon oxide, silicon oxynitride, or any combination containing Si-ONC.

15. The method of claim 9, wherein applying the dose map comprises: exposing the stress compensating layer on the back side of the substrate to the patterned energy source, and The patterned energy source is scanned in a pattern over the stress compensating layer without using a mask to transfer the dose map into the substrate.

16. The method of claim 9, wherein the patterning energy source comprises an ion beam, an electron beam, or a laser beam.

17. A method comprising: receiving a substrate surface map of a substrate, the substrate surface map comprising a map of out-of-plane distortion (OPD) of the substrate based on a set of measured OPDs; using a model to generate a global curvature map from the substrate surface map; extracting a residual surface based on the substrate surface map and the global curvature map; generating an original residual curvature map based on the residual surface; generating a dose map based on the original residual curvature map; and The dose map is applied to process the substrate using a patterned energy source.

18. The method of claim 17, wherein generating the dose map based on the original residual curvature map comprises: creating a blur kernel using a beam profile of the patterned energy source; applying the blur kernel to the original residual curvature map to generate a blurred residual curvature map; and A filter is applied to remove positive curvature from the blurred residual curvature map.

19. The method of claim 17, wherein the model comprises a Gaussian curvature model or a mean curvature model.

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