Method and system for determining charged particle beam exposure with respect to local pattern density

Abstract

To provide a method for reducing a charged particle beam writing time by reducing the dose required to expose a shot or feature.SOLUTION: A method for exposing a pattern at a region on a surface using a charged particle beam system includes inputting a set of original exposure information for the region and inputting a target post-proximity effect corrected (PEC) maximum dose. The local pattern density is determined for the region of the pattern on the basis of the set of original exposure information. The maximum pre-PEC dose is determined for the region. The set of original exposure information is modified with the maximum pre-PEC dose.SELECTED DRAWING: Figure 17

Description

Technical Field

[0001] Related Applications This application claims the benefit of U.S. Non-Provisional Patent Application No. 16 / 422,269, filed May 24, 2019, entitled "METHOD AND SYSTEM FOR DETERMINING A CHARGED PARTICLE BEAM EXPOSURE FOR A LOCAL PATTERN DENSITY", which is hereby incorporated by reference in its entirety for all purposes.

Background Art

[0002] The present disclosure relates to lithography, and more particularly to the design and manufacture of a reticle, wafer, or any other surface that may be a surface using charged particle beam lithography.

[0003] Three general types of charged particle beam lithography are non-shaped (Gaussian) beam lithography, shaped charged particle beam lithography, and multi-beam lithography. In all types of charged particle beam lithography, the charged particle beam emits energy onto a surface coated with a resist to expose the resist.

[0004] Shaped charged particle beam lithography can be variable shaped beam (VSB) or character projection (CP), where precise electron beam shots are shaped and steered to expose a resist-coated surface such as the surface of a wafer or the surface of a reticle. In VSB, these shapes are simple shapes, typically limited to rectangles of a specific minimum and maximum size, with sides parallel to the axes of the planes of the Cartesian coordinate system (i.e., in the "Manhattan" direction), and right triangles at 45 degrees of a specific minimum and maximum size (i.e., a triangle with three interior angles of 45 degrees, 45 degrees, and 90 degrees). At a given position, the administration of electrons in these simple shapes is emitted onto the resist. The total write time of this type of system increases with the number of shots. In CP, it can be complex shapes such as straight lines, linear at any angle, circular, nearly circular, annular, nearly annular, elliptical, nearly elliptical, partially circular, partially nearly circular, partially annular, partially nearly annular, partially nearly elliptical, or any curved shape, and there can be various apertures or characters that can be a connected set of complex shapes or a group of disconnected sets of connected sets of complex shapes, and there is a stencil in the system. By irradiating the electron beam onto the characters of the stencil, a more complex pattern can be efficiently generated on the reticle. Theoretically, such a system can be faster than a VSB system because it can emit more complex shapes with each time-consuming shot. Thus, the emission of an E-shaped pattern in a VSB system takes 4 shots, while the same E-shaped pattern can be emitted in 1 shot in a CP system.

[0005] Shaped charged particle beam lithography can use a single shaped beam or multiple shaped beams that simultaneously expose a surface, and the multiple shaped beams produce a faster write speed than a single shaped beam. When multiple charged particle beams simultaneously expose a surface, charged particle beam lithography is frequently called multi-beam lithography. Multi-beam lithography can be multiple beams of shaped or unshaped charged particle beam lithography.

[0006] In lithography, a lithographic mask or reticle is a circular pattern that is integrated onto a substrate. The reticle includes a geometric pattern that corresponds to the components of a circuit. The patterns used to manufacture the reticle may be generated utilizing computer-aided design (CAD) software or programs. In designing the pattern, the CAD program may follow a set of predefined design rules to create the reticle. These rules are set by process, design, and end-use limitations. An example of an end-use limitation is defining the geometry of a transistor so that it cannot operate satisfactorily at the required supply voltage. In particular, design rules may define the spacing tolerance between circuit devices or interconnect lines. Design rules are used, for example, to ensure that the devices or lines of a circuit do not interact with each other in undesired ways. For example, design rules are used to ensure that lines cannot get too close to each other and cause a short circuit. Design rule limitations reflect, among other things, the minimum dimensions that can be reliably fabricated. When referring to these small dimensions, the concept of critical dimensions is usually brought into play. These are defined, for example, as the critical width or area of a feature, or the critical space between two features, or the critical spatial area, and these dimensions require precise control.

[0007] In the fabrication or manufacture of semiconductor devices such as integrated circuits, optical lithography can be used to fabricate semiconductor devices. Optical lithography is a printing process that uses a lithography mask or photomask or reticle to transfer a pattern onto a substrate such as a semiconductor or silicon wafer to create an integrated circuit (IC). Other substrates may also include flat panel displays, holographic masks, or even other reticles. Conventional optical lithography typically uses radiation with a wavelength of 193 nm or greater. Extreme ultraviolet (EUV) or X-ray lithography is also considered a type of optical lithography but uses wavelengths much shorter than 193 nm of conventional optical lithography. One or more reticles may contain circuit patterns corresponding to individual layers of an integrated circuit, and this pattern can be imaged onto specific regions of a substrate coated with a layer of radiation-sensitive material known as photoresist or resist. Conventional optical lithography writers typically reduce the photomask pattern by a factor of one-fourth during the optical lithography process. Therefore, the pattern formed on the reticle or mask must be four times the size of the intended pattern on the substrate or wafer.

[0008] In the fabrication or manufacture of semiconductor devices such as integrated circuits, non-optical methods can be used to transfer a pattern on a lithography mask onto a substrate such as a silicon wafer. Nanoimprint lithography (NIL) is an example of a non-optical lithography process. In NIL, the pattern of the lithography mask is transferred onto the substrate by contact between the lithography mask and the substrate. The lithography mask for NIL is typically fabricated during the fabrication of the surface using charged particle beam lithography.

[0009] In the fabrication or manufacture of semiconductor devices such as integrated circuits, it is also possible to manufacture semiconductor devices using maskless direct writing. Maskless direct writing is a printing process that uses charged particle beam lithography to transfer a pattern onto a substrate such as a semiconductor or silicon wafer to create an integrated circuit. Other substrates may include flat panel displays, imprint masks for nanoimprinting, and even reticles. The desired pattern of the layer is written directly onto the surface, which in this case is also the substrate. Once the patterned layer is transferred, that layer can go through various other processes such as etching, ion implantation (doping), metallization, oxidation, and polishing. These processes are used to finish the individual layers of the substrate. If multiple layers are required, the entire process or variations thereof are repeated for each new layer. Some layers can be written using optical lithography, while other layers can be written using maskless direct writing for the same substrate manufacture. Also, some patterns of a given layer can be written using optical lithography and other patterns can be written using maskless direct writing. Ultimately, a combination of multiple devices or integrated circuits are present on the substrate. Next, these integrated circuits are separated from each other by dicing or sawing and then fixed into individual packages. In a more general case, the surface pattern can be used to define artifacts such as display pixels, holograms, or magnetic recording heads.

[0010] One goal in the fabrication of integrated circuits by optical lithography is to reproduce the original circuit design onto a substrate by using a reticle, which may also be called a mask or photomask, and the reticle is a surface that can be exposed using charged particle beam lithography. Fabricators of integrated circuits are always trying to use the space on a semiconductor wafer as efficiently as possible. Engineers keep reducing the size of circuits to enable the integrated circuits to contain more circuit elements and use less power. As the size of the critical dimensions of the integrated circuits decreases and their circuit density increases, the critical dimensions of the circuit pattern or physical design approach the limit of the resolution of the optical exposure tools used in conventional optical lithography. As the critical dimensions of the circuit pattern become smaller and approach the value of the resolution of the exposure tool, it becomes difficult to accurately transfer the physical design to the actual circuit pattern developed in the resist layer. To facilitate the use of optical lithography to transfer patterns having features smaller than the light wavelength used in the optical lithography process, a process known as optical proximity correction (OPC) has been developed. OPC modifies the physical design to compensate for distortions caused by effects such as optical diffraction and optical interaction with neighboring features of the feature. Resolution enhancement techniques performed using a reticle include OPC and inverse lithography technology (ILT).

[0011] OPC can add lithography features of sub-resolution to the mask pattern to mask the pattern and reduce the difference between the original physical design pattern, i.e., the design, and the final transferred circuit pattern on the substrate. The lithography features of sub-resolution interact with each other and with the original pattern of the physical design and compensate for the proximity effect to improve the pattern of the final transferred circuit. One feature added to improve the pattern transfer is called a serif. A serif is a small feature that enhances the accuracy or resilience against manufacturing variations in the printing of a specific feature. An example of a serif is a small feature placed at the corner of a pattern to sharpen the corner of the final transferred image. The pattern intended to be printed on the substrate is called the main feature. The serif is part of the main feature. It is customary to describe the pattern decorated with OPC written on the reticle in terms of the main feature, i.e., the feature reflecting the design before OPC decoration, and the OPC features that may include serifs, jogs, sub-resolution assist features (SRAFs), and negative features. The OPC features are exposed to various design rules, such as rules based on the size of the smallest feature that can be transferred to the wafer using optical lithography. Other design rules may arise from the mask manufacturing process or, when using a character projection charged particle beam writing system to form the pattern on the reticle, from the stencil manufacturing process.

[0012] SRAF features are used to improve pattern transfer. The accuracy or precision required in the surface manufacturing process of SRAFs is often lower than that of the main features. There are similar decorations introduced by OPC as negative features. Inside large features, narrow spaces may be introduced to enhance the lithography performance. Since these narrow spaces are more difficult to write reliably than similarly narrow lines, these negative features often become the most difficult part to write reliably on the surface. SUMMARY OF THE INVENTION

Means for Solving the Problem

[0013] A method of exposing a pattern in a region on a surface using a charged particle beam system includes inputting a set of original exposure information for the region and inputting a maximum dose after target proximity effect correction (PEC). The maximum dose after target PEC is based on the maximum write time. The local pattern density is determined for the region of the pattern based on the set of original exposure information. The maximum dose before PEC is determined for the local pattern density based on the maximum dose after target PEC. The set of original exposure information is changed with the maximum dose before PEC, and a set of changed exposure information is created.

Brief Description of the Drawings

[0014]

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DETAILED DESCRIPTION OF THE INVENTION

[0015] The present disclosure describes a method for shortening the write time of a charged particle beam by reducing the dose required to expose a shot or shape. The method includes dynamically calculating a maximum pre-proximity effect correction (pre-PEC) dose based on the density of the pattern to be written. The method also includes calculating the maximum pre-PEC dose in a region by casting an artificial background dose in a relatively low-density exposure region.

[0016] The cost of charged particle beam lithography is directly related to the time required to expose patterns on a surface such as a reticle or a wafer. Conventionally, the exposure time has been related to the exposure dose required to write a pattern. In the case of the most complex integrated circuit designs, forming a set of patterns for a layer on either a set of reticles or a substrate is a process that requires cost and time. Therefore, it would be advantageous to reduce the exposure required to form these patterns, such as by reducing the time required to write them on the reticle and other surfaces.

[0017] Referring now to the drawings, like numerals refer to like items, and FIG. 1 shows an embodiment of a lithography system, such as an electron beam writer system 100, that uses a variable shape beam (VSB) to fabricate a surface 112. The electron beam writer system 100 includes an electron beam source 114 that projects an electron beam 116 toward an aperture plate 118. The plate 118 has an aperture 120 formed therein that permits the electron beam 116 to pass therethrough. When the electron beam 116 passes through the aperture 120, it is directed, i.e., deflected, by a lens system (not shown) as an electron beam 122 toward another rectangular aperture plate, i.e., a stencil mask 124. The stencil 124 forms a number of apertures, i.e., openings 126, that define various simple shapes such as rectangles and triangles. Each opening 126 formed in the stencil 124 can be used to form a pattern on a surface 112 of a substrate 134, such as a silicon wafer, a reticle, or another substrate. An electron beam 130 exits from one of the openings 126 and passes through an electromagnetic or electrostatic reduction lens 138, which reduces the size of the pattern emerging from the opening 126. In commonly available charged particle beam writer systems, the reduction factor is between 10 and 60. The reduced electron beam 140 exits the reduction lens 138 and is directed as a pattern 128 onto the surface 112 by a series of deflectors 142. The surface 112 is coated with a resist (not shown) that reacts to the electron beam 140. The electron beam 122 can be directed to overlap a variable portion of the opening 126 and affect the size and shape of the pattern 128. A blanking plate (not shown) can be used to deflect the beam 116 or the shaped beam 122 to prevent the electron beam from reaching the surface 112 during the period after each shot, at which time the lens and deflectors 142 that direct the beam 122 can be readjusted for the next shot. The stencil 124 can function as a deflector by deflecting the beam 116 to strike a non-aperture portion of the stencil 124.Typically, the blanking plate is arranged to deflect the electron beam 116 and prevent it from irradiating the aperture 120. Conventionally, the blanking period can be of a fixed length or it can vary depending on, for example, how much the deflector 142 has to be readjusted with respect to the position of the next shot. Note that the VSB system can be considered a special (simple) case of character projection where the character is exactly a simple character, usually a rectangle or a 45-degree right triangle. Partially expose the character. It is also possible to cause. This can be done, for example, by blocking a part of the particle beam. In the present disclosure, partial projection is used to mean both character projection and VSB projection.

[0018] In the electron beam lithography system 100, the substrate 134 is attached to a movable platform, i.e., a stage 132. The stage 132 enables the repositioning of the substrate 134 so that patterns larger than the maximum deflection ability or field size of the charged particle beam 140 can be written onto the surface 112 in a series of subfields, where each subfield is within the ability of the deflector 142 to deflect the beam 140. In one embodiment, the substrate 134 can be a reticle. In this embodiment, after being exposed with the pattern, the reticle goes through various manufacturing processes to become a lithography mask or a photomask. Next, the mask can be used in an optical lithography machine to project an image of the reticle pattern 128, generally of reduced size, onto a silicon wafer to manufacture an integrated circuit. More generally, the mask is used in another device or machine to transfer the pattern 128 to a substrate (not shown).

[0019] The dose of a shot of a charged particle beam writer such as an electron beam writer system is a function of the intensity of the beam source 114 and the exposure time per shot, regardless of whether it is a VSB, CP, or multi-beam machine. In this example of VSB, usually, the intensity of the beam remains fixed, and the exposure time is varied to obtain a variable shot dose. The exposure time may be varied to compensate for backscattering in processes such as mid-range effect correction (MEC), loading effect correction (LEC), fogging effect correction (FEC), and other long-range effects, as well as proximity effect correction (PEC). In the present disclosure, the term PEC is used to describe MEC, LEC, FEC, and backscattering correction. In an electron beam writer system, usually, an overall dose called the base dose can be set. This affects all the shots in the exposure pass. Some electron beam writer systems do not allow dose compensation calculations to be performed within the electron beam writer system itself and do not allow the dose of each shot to be individually assigned as part of the input shot list, so there is an unassigned shot dose in the input shots. In such an electron beam writer system, there is a base dose for all the shots before PEC. In other electron beam writer systems, the dose can be assigned for each shot. In an electron beam writer system that allows the assignment of dose per shot, the number of available dose levels may be as many as 64 to 4096 or more, or there may be a relatively small number of available dose levels such as 3 to 8 levels. Some embodiments of the present disclosure are directed to use in a charged particle beam writing system that allows the assignment of dose levels.

[0020] A charged particle beam system can expose a surface with a plurality of individually controllable beams, i.e., beamlets. FIG. 2 shows a schematic diagram of an electro-optical system in which there are three charged particle beamlets 210. Associated with each beamlet 210 is a beam controller 220. Each beam controller 220 can, for example, enable the associated beamlet 210 to impinge on the surface 230 and can also prevent the beamlet 210 from impinging on the surface 230. In some embodiments, the beam controller 220 can also control the beam blur, magnification, size, and / or shape of the beamlet 210. In the present disclosure, a charged particle beam system having a plurality of individually controllable beamlets is referred to as a multi-beam system. In some embodiments, charged particles from a single source can be subdivided to form a plurality of beamlets 210. In other embodiments, a plurality of sources can be used to create a plurality of beamlets 210. In some embodiments, the beamlets 210 can be shaped by one or more apertures, although in other embodiments there may be no apertures for shaping the beamlets. Each beam controller 220 can be enabled to control the exposure period of the associated beamlet individually. Generally, the beamlets are reduced in size by one or more lenses (not shown) before hitting the surface 230, and the surface 230 is typically coated with a resist. In some embodiments, each beamlet can have a separate electro-optical lens, although in other embodiments, a plurality of beamlets, optionally including all the beamlets, can share an electro-optical lens.

[0021] Figures 3A - 3D show various types of shots. Figure 3A shows an example of a rectangular shot 310. A VSB charged particle beam system can form rectangular shots, for example, with various x and y dimensions. Figure 3B shows an example of a CP shot 320, which is circular in this example. The CP shot can represent any shape, such as an octagon, or a more complex shape like the letter E. For the purposes of this disclosure, a shot is the exposure of a surface area over a period of time. This area can be composed of a plurality of discontinuous small areas. A shot can be composed of a plurality of other shots, which may or may not overlap and may or may not be exposed simultaneously. A shot may or may not have a specified dose. A shot can use a shaped beam, an unshaped beam, or a combination of a shaped beam and an unshaped beam.

[0022] Figure 3C shows an example of a shot 350 that is an array of circular patterns 352. Shot 350 can be formed in various ways, including a plurality of shots of a single circular CP character, one or more shots of a CP character that is an array of circular apertures, and one or more multi - beam shots that use circular apertures. Figure 3D shows an example of a shot 360 that is a sparse array of rectangular patterns 362 and 364. Shot 360 can be formed in various ways, including a plurality of VSB shots, CP shots, and one or more multi - beam shots that use rectangular apertures. In some embodiments of the multi - beam, shot 360 can include a plurality of interleaved groups of other multi - beam shots. For example, pattern 362 can be fired simultaneously, and then pattern 364 can be fired simultaneously at a different time from pattern 362.

[0023] Figure 4 shows an embodiment of a charged particle beam exposure system 400. The charged particle beam system 400 is a multi-beam system in which a plurality of individually controllable shaped beams can simultaneously expose a surface. The multi-beam system 400 has an electron beam source 402 that generates an electron beam 404. The electron beam 404 is directed by a condenser 406 that may include electrostatic and / or magnetic elements toward an aperture plate 408. The aperture plate 408 is irradiated by the electron beam 404 and has a plurality of apertures 410 through which the electron beam 404 passes to form a plurality of shaped beamlets 436. Thus, the multi-beam charged particle beam system 400 includes a charged particle beam source 402 and an aperture plate 408, and the aperture plate 408 includes a plurality of apertures 410 irradiated by the charged particle beam source 402. In some embodiments, the multi-beam charged particle beam system includes a single aperture plate 408. In some embodiments, the aperture plate 408 may have hundreds or thousands of apertures 410. Figure 4 shows an embodiment with a single electron beam source 402, and in other embodiments, the apertures 410 may be irradiated by electrons from a plurality of electron beam sources. As shown in Figure 4, the apertures 410 can be circular or can have different shapes such as the rectangular aperture 120 shown in Figure 1. Next, a set of beamlets 436 illuminates a blanking controller plate 432. The blanking controller plate 432 has a plurality of blanking controllers 434, each of which is aligned with a beamlet 436. Each blanking controller 434 can individually control the associated beamlet 436 to allow the beamlet 436 to strike the surface 424 or to prevent the beamlet 436 from striking the surface 424. The length of time the beam hits the surface is controlled by the total energy or "dose" applied by that beamlet. Typically, a multi-beam writer scans the entire area to be exposed. Thus, the write time is constant regardless of the number or complexity of the shapes.

[0024] The substrate 426 is disposed on a movable platform or stage 428 that can be repositioned using the actuator 430. By moving the stage 428, the beam 440 can expose an area larger than the dimensions of the largest pattern formed by the beamlet group 440 using a plurality of exposures or shots. In some embodiments, the stage 428 remains stationary during the exposure and is then repositioned for the next exposure. In other embodiments, the stage 428 moves continuously at a variable speed. In yet other embodiments, the stage 428 moves continuously but at a constant speed, thereby increasing the accuracy of the stage positioning. In these embodiments where the stage 428 moves continuously, a set of deflectors (not shown) can be used to move the beam to match the direction and speed of the stage 428 so that the beamlet group 440 can continue to remain stationary with respect to the surface 424 during the exposure. In still other embodiments of the multi-beam system, the individual beamlets of the beamlet group can be deflected across the surface 424 independently of the other beamlets of the beamlet group.

[0025] Other types of multi-beam systems can create a plurality of non-shaped beamlets 436, such as by using a plurality of charged particle beam sources to create an array of Gaussian beamlets. Although the present disclosure has been described with respect to charged particle beam lithography, the methods described can also be applied to laser lithography, particularly multi-beam laser lithography.

[0026] The dose is controlled in any high-precision eBeam writer by controlling the exposure time, rather than dynamically changing the beam current density. In fact, it is understood that the exposure time can be controlled much more accurately than the current density. Therefore, high-dose exposure is achieved by increasing the time the beam is on, compared to low-dose exposure. It is conceivable that the eBeam writer has a variable current density. This disclosed embodiment is applicable when dose control is at least partially achieved by controlling the exposure time. The exposure time of each beamlet 436 of the beamlet group can be individually controlled using the blanking controller 434. Thus, the multi-beam writing time is determined by the maximum dose that needs to be applied. In a writer where the stage stops in each beamlet group, such as a stripe, the highest-dose beamlet affects the exposure time of the entire stripe. In a writer with a stage moving at a constant speed, the speed can be constant throughout the design, and the setting can be a subset of the reticle, the entire reticle or wafer, or any other surface. Alternatively, it may be partially constant for a certain period. Therefore, the highest-dose beamlet of the stripe can determine the speed of the stage and thus the writing time for the entire design or surface. Even with a stage having a variable speed, since the stage is weighted to provide stability, the change in speed cannot be made significantly faster, consuming a lot of energy for acceleration or deceleration and causing vibration and blur.

[0027] At advanced process nodes, the features that need to be written accurately onto the mask are less than 3 times in size compared to the combined blur radius of forward scatter and resist blur of typical resists used to print the mask at a speed sufficient to be commercially viable. For typical state-of-the-art masks, sub-resolution assist features (SRAFs) with widths less than 60 nm are written onto the mask, and the range of combined blur exceeds 20 nm. For masks used in EUV lithography, generally SRAFs with widths of about 30 nm are typically expected to be required on the mask. In the steps of optical proximity correction (OPC) or inverse lithography technology (ILT) that generate the mask shape, if smaller shapes (such as SRAFs) can be printed accurately onto the wafer, the wafer performance can be further improved. However, it is also important that the mask shapes generated by OPC / ILT can actually be reliably generated on the mask across the variations in the mask process. Mask design rules are established, such as the width of the minimum allowable feature on the mask and the spacing between minimum allowable features, which represent a trade-off. OPC / ILT needs to ensure that the output conforms to the mask design rules. The mask manufacturer needs to produce masks that accurately conform to the mask design rules across the manufacturing variations according to specific agreed specifications. When the shape is narrow, it becomes even more difficult to write onto the mask. The smallest square shape is the most difficult to write. However, since the smallest square shape has a small impact on wafer performance, usually in the processing of state-of-the-art masks, the need to accurately write narrow SRAFs is important.

[0028] In the presence of other larger shapes, writing such small shapes onto the mask with the same mask is typically achieved by dose modulation. Since the overall mask writing time is one of the major factors in the cost of the mask, a resist with sufficient sensitivity to achieve the desired accuracy for the larger "main" features is selected to represent the trade-off between accuracy and speed / cost. However, it is also necessary to accurately write SRAFs and other small shapes, and it is a common technique to enhance, i.e., increase, or partially enhance the dose of the SRAF to improve the printing of the SRAF.

[0029] In the industry, the amount by which the normal dose is enhanced can typically vary from 1.2 times the normal dose to 3 times the normal dose, but the dose can be any multiple of the normal dose. More enhancement leads to a longer writing time but may lead to more accurate printing of smaller shapes. FIGS. 5A - 5B show the difference between a sufficiently large shape 502 and its dose profile (i.e., dose curve) 512, and a smaller SRAF shape 506 and its dose profile 522. Both shots are at the normal dose measured along lines 504 and 508 through the contours of the shots of shapes 502 and 506 respectively, and have the same resist threshold as indicated by line 514. Shapes 502 and 506 are divided to show a rectangular shape much longer than wide, and each shape is irradiated onto the resist at half the normal dose threshold using the normal dose. Doses below the resist threshold are not printed.

[0030] In a VSB machine, the outline of a shot is the shape of the projection of the eBeam directed towards the writer. In a multi-beam machine, the outline of a shot has the desired shape directed towards the writer, leading to rasterization to pixels and various doses of eBeam projection depending on the pixels used for shape drawing. To simplify the understanding, in this disclosure, the dose profile is depicted and described as if the machine were a VSB, but the embodiments can also be applied to multi-beams. In a multi-beam machine, rasterization to pixels makes the dose profile even more complex and depends on the position of the shape relative to the pixel grid. These additional complexities of multi-beam writing are not relevant for understanding the concepts of this disclosure.

[0031] For a sufficiently large shape, the dose profile 512 reaches a plateau at the normal dose. This plateau is at the same dose even if the width of the shape 502 is larger. For a smaller shape as shown by the shape 506, there is not enough energy to reach the peak of the dose profile at the normal dose. The shape of the dose profile 522 has no plateau. Furthermore, the dose profile 522 does not exceed the resist threshold 514 at the same position as the width of the shape 506. Due to the lack of sufficient energy, the shape exposed to the resist becomes narrower than the desired width.

[0032] The dose margins at the left ends of the shapes 502 and 506 are indicated by the edge slopes 516 and 528 respectively. The slope 528 is shallower than the slope 516. The narrower the shape 506, The dose profile becomes lower and the slope 528 becomes gentler. When the shape 502 has a width sufficient for the dose profile 512 to intersect the plateau, the wide shape does not change the slope 516. The gentler the slope, the worse the dose margin, that is, the critical dimension (CD), which is the width of the shape, is more likely to undergo more variations when a specific dose variation is applied. The term dose margin here represents the tolerance for any type of manufacturing variation, including dose-related variations of a pattern defined by a series of charged particle beam shots. A better dose margin indicates higher tolerance. It is generally understood by those skilled in the art that the resilience to dose variations is an excellent surrogate for many causes of manufacturing variations. One conventional method for improving the elasticity against manufacturing variations indicated by the dose margin is to use a higher base dose than normal for smaller shapes, as shown by the dose profile 532 in FIG. 5C. In this example where the dose is selected such that the CD, indicated by the distance between the points of the dose profile 532 that exceed the resist threshold 514, becomes the desired width of the target shape 506, a base dose exceeding 1.0 is used. In the industry, many combinations of dose adjustment and shape adjustment are used. FIG. 5C is an example where only dose adjustment is deployed. In this example, when the dose is calculated for the shape 506, the dose margin exceeding the threshold 514 can be measured by calculating the slope 538 of the dose profile 532. Note that the slope of the edge 538 is better (i.e., has a steeper slope) than the slope of the edge 528, but may still be worse than the slope of the edge 516.

[0033] Due to the contrast, the dose margin is also important for the printability of small features. The contrast is the difference in the amount of energy applied to the resist inside and outside the immediate vicinity of the exposed area. The immediate vicinity of semiconductor mask processing can be from a few nanometers to dozens of nanometers. Since the dose profile is a continuous function of the length scale of interest, the dose margin and contrast are highly correlated with each other. If the contrast is insufficient, the shape cannot be resolved. Reducing the minimum size of the shape that can be reliably resolved with a given resist is important for the economics of mask manufacturing.

[0034] There is another factor that affects the amount of dose that an eBeam writer has to directly cast in order to print a shape on the surface. This is called proximity effect correction (PEC), and corrects for the backscattering of electrons emitted by the "shot(s)" of eBeam around the area of interest. FIGS. 6A - 6B show the resulting dose corresponding to the shots of FIGS. 5A - 5B after PEC has been applied. In FIG. 6A, the backscattering of electrons within the distance range up to a typically 10μm order shot cast by shape 502 and its surrounding shots is shown by the dashed line of backscattering 618. When the exposure is dense in the peripheral area, the backscattering 618 becomes higher order. When the surrounding areas are sparsely arranged, the backscattering 618 is lower and likely closer to zero. Since PEC repeatedly optimizes the applied dose for a sufficiently large shape 502 as is generally practiced, the dose applied to the shape 502 of the shot will have the width of shape 502 printed accurately despite the additional dose brought about by backscattering. The corrected dose profile 612 of the exposure (excluding backscattering) has less dose than the dose profile 512. The edge slope 616 is shallower than the edge slope 516. When the amount of backscattering received from adjacent areas is large, the dose margin deteriorates. FIG. 6B shows the same PEC applied to a smaller shape such as an SRAF. Since PEC is usually applied in the same way to all shapes of all sizes, after PEC is applied, the size of the resulting post - PEC dose profile 622 becomes even smaller compared to the dose profile 522 (excluding the baseline dose from backscattering shown by the horizontal dashed line of backscattering 618). Thus, the edge slope 628 becomes even shallower than the edge slope 528, substantially shallower than the edge slope 616, deteriorating the dose margin, and these shapes are subject to manufacturing variations Much more susceptible to the influence of. Figure 6C shows the dose profile after PEC of the shot described in Figure 5C, in which the dose was increased to meet the desired critical dimension (CD). The slope 638 of the edge is less steep (worse) than the slope 538 of the pre-PEC edge before PEC is applied, but better than the slope 628 of the edge after PEC at the normal dose.

[0035] Backscattering is caused by charged particles such as electrons that "bounce back" after colliding with the resist and the material under the resist. The effective radius of backscattering can be, for example, 10 microns, which is much larger than the size of the shot. Therefore, all backscattering from nearby shots within that effective radius of the shot adds dose at the location of the shot. Without correction, backscattering can add more dose to the shot than the intended dose of the shot, making the pattern wider, even larger in regions with high exposure density, and potentially being recorded.

[0036] As is known in the art, FIGS. 7A-7G show the iterative sequence applied by PEC to correct the dose used to emit each shape in order to correct the backscattering effect. FIG. 7A shows an example of the outline of a rectangular shot 702. The break indicates that the shot 702 can be arbitrarily long in the vertical direction. The width of the shot 702, the distance between "g" and "h", is assumed to be between 100 nm and 300 nm in this example for the sake of explanation, assuming a commonly used mask manufacturing process, which is significantly smaller than the assumed backscattering range of about 10 μm. The shot size of a multi-beam machine is typically 5-20 nm. In the case of a multi-beam machine, a set of shots is combined to emit a shape such as the shot 702. Backscattering is applied to a single shot in the same way as to a set of shots, and the PEC correction is applied in the same way. FIG. 7B shows an example of a dose graph 710, showing the dose along a line 704 through the outline 702 of the shot at the dose of a normal shot with little backscattering. Other long-distance effects are also assumed not to contribute to the background exposure in FIG. 7B, leading to a background exposure level of nearly zero. The total dose supplied to the resist is shown on the y-axis and is 1.0 times the normal dose. Since the background exposure is nearly zero, the total dose and the shot dose are nearly the same. The dose graph 710 also shows the resist threshold 714 at half the normal dose. The change in CD of the shape represented by the dose graph 710 in the x direction is inversely proportional to the slope of the dose curve (i.e., the dose profile) 712 at the x coordinates "g" and "h" where it intersects the resist threshold 714. The slope 716 of the edge of the dose curve 712 at the threshold 714 is shown as the hypotenuse of a right triangle.

[0037] The exposure condition of nearly zero background in FIG. 7B does not reflect the actual design. In the actual design, usually, there are many other shots within the backscattering distance range of shot 702. FIG. 7C shows an example of a dose graph 720 of a shot at a normal dose with backscattering 728 caused by 50% exposure density. In dose graph 720, dose curve 722 shows the dose of the cross-section of shot 702 in addition to the background exposure (backscattering 728). The slope 726 of the edge of dose curve 722 at threshold 714 is shown as the hypotenuse of a right triangle. The CD variation of curve 722 is larger (worse) than the CD variation of curve 712, as shown by the gentler edge slope 726 where curve 722 intersects the resist threshold 714 beyond points "g" and "h". The reason for the gentler edge slope 726 is that the lower part of the dose curve with a worse dose margin due to the background exposure caused by backscattering 728 intersects the resist threshold. The intersection of dose curve 722 at resist threshold 714 is wider than points "g" and "h", indicating that the printed CD is larger than the desired size. Since backscattering 728 "pre-exposes" the resist, when dose curve 722 is emitted at a normal dose in the presence of backscattering 728, the CD is printed larger than desired.

[0038] Figure 7D shows the new dose curve 732 after PEC. The intermediate dose graph 725 still shows 50% backscatter 728, but the dose curve 732 has decreased and is calculated so that the intersection of the dose curve 732 and the resist threshold 714 at the current backscatter is accurately measured at "g" and "h". This is the result of the first iteration of PEC to correct for the overexposure caused by the presence of backscatter. In this iteration, since there is no way to know what the new backscatter will be after PEC is performed on all surrounding shots, the amount of backscatter is assumed to be the same as backscatter 728. The PEC calculation reduces the dose applied to shot 702 so that the resist threshold 714 intersects the dose profile 732 at "g" and "h". The slope 736 of the edge of the dose curve 732 at the threshold 714 is shown as the hypotenuse of a right triangle. Note that the slope 736 is shallower than the slope 716 because the dose margin deteriorates due to PEC.

[0039] The dose graph 730 in Figure 7E shows the reason why PEC requires multiple iterations. The PEC calculation performed as shown in Figure 7D hits "g" and "h" accurately only if the backscatter 738 is the same as the backscatter 728. However, since PEC is performed on all shots, PEC is applied to all shots around this shot and the dose of each shot decreases, so the backscatter 738 decreases (because the dose of this shot decreased from curve 722 to curve 732). The new backscatter is shown in Figure 7E as backscatter 738. The backscatter 738 is lower than the backscatter 728. As can be seen, the reduction in backscatter results in a size of the aligned pattern that is smaller than the desired size of the original shot 702.

[0040] In the second iteration of PEC, this is corrected by recalculating PEC with this new (reduced) amount of backscatter (backscatter 738). Now that the backscatter is lower, to print a shape like shot 702 with the correct CD, it is necessary to increase the dose corresponding to the target "g" and "h" to enhance the dose profile 732.

[0041] As shown in the dose graph 740 of FIG. 7F, enhancing the dose of the PEC in all shapes of the design results in a dose profile 742 higher than the dose curve 732. Subsequently, after all other neighboring shapes are adjusted, a backscatter 748 higher than the backscatter 738 occurs. In the third iteration of the PEC, this is corrected by using this new (increased) amount of backscatter to recalculate the PEC once again. These iterations continue alternately until they converge to a predetermined tolerance of the amount of backscatter as shown by the dose level 758 of the dose graph 750 in FIG. 7G, and a dose profile 752 that correctly generates the original shot 702 of the desired size at the threshold 714. Next, the converged dose is used to fire the individual shapes of the mask, and as a result of the PEC, a set of backscatter-corrected doses for all shapes is generated.

[0042] Figures 8A - 8B show an example of how the PEC affects isolated shapes. In FIG. 8A, shapes 810 and 815 are isolated patterns within an area not otherwise occupied by other exposures. The initial dose can be calculated as 1.0 times the normal dose for both shapes. FIG. 8B shows that the dose calculated after the PEC is still approximately 1.0 of the normal dose and is not substantially affected as a result of having no ambient backscatter other than that caused by shapes 810 and 815.

[0043] Figures 8C - 8D show an example of how the PEC affects shapes in an area with a 50% exposure density, i.e., an area where 50% of the area is covered by patterns. In FIG. 8C, shapes 820, 822, 824, 826, and 828 are shown as a repeated line and space pattern, and the administered shapes and the spaces between them are of equal width in all directions, and the line and space pattern is repeated with an effective radius of 10 μm. For each shape, the initial dose can be calculated as 1.0 times the normal dose. FIG. 8D shows, as an example, that during the PEC, for all shapes of the repeating pattern, the dose decreases to 0.67 of the normal dose due to ambient backscatter from adjacent shapes. For each shape, the initial dose can be calculated as 1.0 times the normal dose. FIG. 8D shows, as an example, that during the PEC, for all shapes of the repeating pattern, the dose decreases to 0.67 of the normal dose due to ambient backscatter from adjacent shapes.

[0044] Figures 8E - 8F show examples of how PEC affects the shape of high - density regions. In Figure 8E, shapes 830, 832, and 834 are shown, where shape 832 is the target shape. Shapes 830 and 834 are wide exposure regions with widths exceeding the effective radius of 10 μm, and the pattern is extended up and down by the effective radius of 10 μm. For each shape, the initial dose can be calculated as 1.0 times the normal dose. Figure 8F shows that the dose decreases, for example, to 0.5 of the normal dose of shape 832 due to ambient backscattering from adjacent shapes in the PEC. The PEC mathematically reduces the dose of each exposure by an appropriate amount to make the CD equal to the CD in the case of no backscattering for sufficiently large shapes. Thus, the PEC effectively eliminates the influence of backscattering. Backscattering is always a positive value. Therefore, the PEC always reduces the dose to compensate.

[0045] Since the PEC functions by "flattening" the Gaussian distribution, the dose required to expose the shape in a region with large backscattering is significantly reduced. The difference in the required dose between a region with large backscattering (where the shape is surrounded by a high dose density) and a region with no backscattering (where the shape is surrounded by a low dose density) can be more than twice. The changed dose D of a pixel or a normal - dose shot in the first iteration of the PEC calculation pec is obtained by the following formula.

[0046]

Equation

[0047] T at the resist threshold of 0.5 of the normal dose emp is the ratio of forward scattering at the resist threshold, and eta (η) is a normalization constant. T emp is 0.5, eta (η) is 0.5, and the exposure density is 100%, D pecIt is calculated to be 0.5. Although the SRAF is assigned to be emitted at twice the normal dose (2.0 times), if it is in a high-density area with significant backscattering, the pixel or shot will become approximately 1.0 times the normal dose, i.e., 0.5×(2.0)=1.0, after the first iteration of the PEC calculation.

[0048] This is because the area is highly exposed to the energy from backscattering. Therefore, only a small part of the energy from this pixel or shot is required to cast enough energy to reach the threshold for exposing the resist.

[0049] The area with almost zero backscattering has the most eBeam dose per shot. Therefore, in a multi-beam writer with a fixed writing time, the overall writing time of the machine is usually paced by writing isolated patterns at the highest dose, such as in the case of narrow shapes like SRAF. General test masks have a mixture of patterns in high-density areas and low-density areas. Typical production masks have much less variation. Some masks have all high-density patterns (e.g., an average exposure density of 70%). Other masks have all sparse patterns (e.g., an average exposure density of 25%). However, many production masks combine some test patterns in them and cannot guarantee low variation. In any case, the multi-beam writing speed is determined by pixels with a combination of high doses in an environment with little backscattering, especially in the case of a writer with a fixed writing time. Although to a lesser extent, it is still important that the writing speed of variable writing time writers such as VSB writers and, in some cases, multi-beam writers is paced by shots with a combination of highly enhanced doses in an environment with little backscattering.

[0050] Artificial background dose In some embodiments, an artificial background dose is introduced in regions of otherwise low backscatter to reduce the pixel or shot dose, and thus reduce the overall write time. As a result, the pixel or shot has a lower dose after PEC, the maximum value of the dose of the pixels or shots of the mask or section of the mask is reduced, and the stage movement speed is increased, thereby significantly reducing the overall write time.

[0051] Figures 9A - B show how the introduction of an artificial background dose according to some embodiments can mimic a 50% density similar to Figures 8C and 8D. Figure 9A shows isolated shapes 910 and 915 similar to Figure 8A, but with an artificial background dose added in the form of shape 913. The initial dose is set to 1.0 times the normal dose of the previous shapes 910 and 915, and the artificial background dose is 0.30 of the normal dose of shape 913 in this example. It is important to note that the dose applied to this new shape 913 is below the printing threshold. Figure 9B shows a similar dose reduction at 0.67 of the normal dose after PEC, similar to Figure 8D, reducing the overall dose required to print the previously separated shapes 910 and 915. In some embodiments, shape 913 also reduces to 0.20 of the normal dose. In this simplified example, shape 913 is assumed to extend beyond the backscatter radius away from shapes 910 and 915. In most cases, shape 913 is significantly reduced in size to add an artificial background dose only to the region immediately surrounding shapes 910 and 915. Other such artificial background doses for other shapes surrounding shapes 910, 913, and 915 result in actual backscatter for these shapes. In this embodiment, all such energy contributions are calculated using PEC when the actual dose after PEC for shapes 910 and 915 is calculated. In some embodiments, the dose of shape 913 is not changed by all iterations of PEC. In some embodiments, the dose of shape 913 is changed by all iterations of PEC.

[0052] The artificial background dose can be added to regions where the backscatter is low enough and the dose margin after PEC is sufficiently better than "sufficiently good" according to several parameters set by convention. Figures 10A-10F show some examples of the artificial background dose, and the added artificial background dose is in the form of an additional pattern (pattern of aggregated filled lines) that is emitted in combination with the desired pattern. The artificial background dose is an exposure below the threshold. That is, it is a dose lower than the resist threshold required for printing. Figure 10A shows a method of casting an artificial background dose shape 1001 over a region containing a desired pattern shape 1000 printed on the surface to completely cover the pattern of that region. Figure 10B shows the shape 1002 of the artificial background dose in the region, but the desired pattern shape 1000 already exists and does not cover the pattern. Figure 10C shows the shape 1003 of the artificial background dose in a region that surrounds the desired pattern shape 1000 with a certain margin, for example, up to 3 sigma away from the edge of the pattern. In the case of a pattern as large as the pattern shape 1010 in Figure 10D, the artificial background dose shapes 1011 and 1012 are applied only beyond a predetermined distance from the edge of the pattern shape 1010 printed on the surface. Creating a margin around features such as edges, ends of lines, SRAFs, etc., the artificial background dose applied in this way may be superior to simply increasing the background exposure everywhere. Alternatively, the artificial background dose can be added anywhere in the region, for example, as shown in Figures 10E and 10F respectively, and the artificial background dose shapes 1004 and 100 5 partially cover the shape 1000 of the desired pattern, respectively.

[0053] Dynamic maximum dose The artificial background dose can be safely increased up to a specific dose level below the resist threshold. The writing time of the machine varies depending on the maximum dose after PEC. One way to ensure the specified writing time is to limit the maximum dose after PEC and truncate any dose exceeding it. However, truncating the dose may cause printing errors. In this embodiment, a method that may be called the dynamic maximum dose (DMD) is described, where the maximum dose after the target PEC is selected and used to determine the maximum dose before PEC. The calculation is performed dynamically based on the pattern density, and the resulting dose after PEC does not exceed the selected (target) maximum dose after PEC, eliminating the need to truncate the dose. In some embodiments, the maximum dose after the target PEC is input. FIG. 11 shows an example of calculating the maximum dose before PEC to meet the maximum dose after the target PEC using a line-space pattern at a density of 50% (i.e., value 0.5) as an exemplary scenario. In this embodiment, a maximum dose before PEC of 1.5, 1110, results in a maximum dose after PEC of 1.07, 1120, according to the conventional PEC method. This calculation of the maximum dose after PEC from the maximum dose before PEC, 1110, is indicated by the downward arrow in FIG. 11. A dose before PEC of 1.5 would typically print features larger than their desired size, but such a dose may be desirable for small features as a way to perform linearity correction. According to some embodiments, the user may determine that the dose after PEC of 1.07 is sufficient for all pattern densities to be written and may select the dose 1120 (dose value 1.07) as the target maximum dose after PEC. As a result, for other pattern densities (e.g., 10%, 20%, etc.), the maximum dose before PEC is then calculated based on the selected maximum dose after PEC (i.e., the dose before PEC that becomes the target maximum dose after PEC), as shown by the upward arrow in FIG. 11.Calculating the dose before PEC based on the maximum dose after the target PEC and adjusted to the pattern density as written in this embodiment has not been contemplated in the art, but the calculation between the dose before and after PEC can be performed using conventional PEC methods.

[0054] Returning to FIGS. 8A - 8F, particularly FIGS. 8B, 8D, and 8F, these figures show that as the pattern density increases, the dose corrected by PEC decreases to compensate for the additional exposure due to increased backscattering. Further, the increase in backscattering and the resulting PEC dose decrease also decrease the dose margin as shown in FIGS. 7A - 7G. Thus, at normal doses, the dose margin decreases as the pattern density increases. In some embodiments, providing a sufficient dose margin includes increasing the dose such that the maximum dose after PEC is within a pre - set limit (such as 0.7 to 1.3 times the normal dose) and performing a linearity correction to ensure the correct shape size.

[0055] FIGS. 12 - 13 show how enhancement of the dose margin by the maximum dose after PEC can be achieved using the shape data of the pixel dose array. As is known to those skilled in the art, in advanced mask processes in semiconductor device manufacturing, for example, when a shape with a mask dimension smaller than about 100 nm is exposed with a normal 1.0 dose shot, the edge has a worse dose margin than a larger shot. FIG. 12 shows a pixel array 1200 where the pixel dose reflects the linearity correction performed to improve the dose margin for the end of a thin line having a width of 60 nm. In this example, the pixel size is 10 nm in both the X and Y directions. The calculated edge 1210 is determined from this data and represents the pattern at the end of the line. Truncating the dose above 1.0 results in a smaller shape shown at 1220, and the dose margin has deteriorated. is.

[0056] In contrast, FIG. 13 shows how exposure information can be modified to shorten the write time and maintain the pattern size while achieving an acceptable dose margin, according to some embodiments. In this example, for an embodiment that uses a maximum post-PEC dose of 0.9 as the target, FIG. 13 shows the post-PEC dose resulting from the modified exposure information. The dose margin in FIG. 12 is better than the dose margin in FIG. 13, but the dose margin in FIG. 12 may be much larger than necessary compared to a given threshold dose margin. In FIG. 13, the dose margin is also better than the threshold dose margin, but the write time is shorter than in FIG. 12 because the dose is lower. FIG. 13 shows the resulting pixel array 1300, which achieves the size indicated by 1310 with a pixel dose lower than the maximum dose and a sufficient dose margin.

[0057] As disclosed in U.S. Patent No. 9,372,391, "Method and System for Forming Patterns Using Charged Particle Beam Lithography with Variable Pattern Dosage," optimization techniques can be used to determine the lowest dose achievable in the interior portion of a pattern. It is by the assignee of the present application and is incorporated herein by reference. In some embodiments, these optimization techniques include calculating the resist response for a set of shots, such as using particle beam simulation, where the set of shots is determined to form a desired pattern according to certain parameters, such as within a given tolerance. It should be noted that when creating shots for a charged particle beam writer that supports only unassigned dose shots, the gaps in the interior region of the pattern can be used to reduce the dose in the region. In particular, by simulating the "corner cases" of manufacturing tolerances, the writing time can be shortened and the edge slope can be improved, and a lower dose or gap design can be determined in advance to safely emit the target shape. Similarly, overlapping shots can be used to increase the dose in the region. The use of overlapping shots is disclosed in U.S. Patent No. 7,754,401, "Method for Manufacturing a Surface and Integrated Circuit Using Variable Shaped Beam Lithography," which is owned by the assignee of the present application and is incorporated herein by reference.

[0058] FIG. 14 shows a graph of dose margin versus pattern density for the maximum dose after PEC of 1, 0.9, 0.8, and 0.75. The acceptable dose margin of 0.5 in this embodiment is represented by the dotted line 1450. The graph shows that for pattern densities of less than about 0.3 (i.e., 30%), the maximum dose after PEC at 1.0 (curve 1410) and 0.9 (curve 1420) for a particular pattern density exceeds the acceptable dose margin with respect to the normal dose of 1.0 (line 1400) before PEC, and reaches the acceptable dose margin (i.e., below line 1450) even at higher pattern densities. That is, at the normal dose indicated by the dashed line 1400, the dose margin deteriorates as the pattern density increases. To address this problem of controlling the dose margin, in some embodiments, when selecting the target maximum dose after PEC, the target dose margin is considered along with the pattern density. For example, the range of the maximum dose after PEC shown in FIG. 14 indicates that for all pattern densities, the dose margin remains sufficient and less than 0.5 as shown along the dotted line 1450, and the maximum dose after PEC ranges from 0.9 along line 1420 to 1.0 along line 1410. When the maximum dose after PEC is 0.9, the write time is reduced by 10% compared to when the maximum dose after PEC is 1.0. At lower maximum doses after PEC of 0.8 along line 1430 and 0.75 along line 1440, the dose margin deteriorates for pattern densities of less than 30%. Therefore, the user can select 0.9 as the target maximum dose after PEC to limit the write time while satisfying the target dose margin. Dynamic maximum dose with artificial background dose

[0059] ​FIG. 15 is a graph of dose margin versus pattern density when an artificial background dose is added. By adding an artificial background dose to a region 1510 where the pattern density is below a specific threshold such as 30%, an acceptable dose margin can be achieved as shown in FIG. 15. That is, the dose margin is constant in region 1510 of FIG. 15, which is an improvement over the varying dose margin versus pattern density in the same region of FIG. 14. In some embodiments, an artificial background dose is added to increase the local pattern density to a desired threshold, e.g., 30%, allowing a maximum dose reduction of up to 25% with a sufficient dose margin. Further, the maximum dose before PEC is calculated to enhance critical dimension uniformity (CDU) and line edge roughness (LER) among other measures of resilience to manufacturing variations. The improvement of CDU and LER includes enhancing the dose margin and improving the uniformity of the dose margin across the mask features. The enhancement of the dose margin (edge slope) is disclosed in U.S. Patent No. 8,473,875, "Method and System for Forming High Accuracy Patterns Using Charged Particle Beam Lithography," owned by the assignee of the present application and incorporated herein by reference.

[0060] In some embodiments, a predetermined artificial background dose, such as in the range of 20% to 30%, is defined and applied everywhere. A minimum target backscatter amount, or a predetermined threshold, such as 30%, is defined. In some embodiments, if the PEC does not have sufficient natural backscatter to reduce the dose, the ambient dose is increased by adding an artificial background dose to meet the minimum backscatter amount. In some embodiments, the additional backscatter caused by the artificial background dose may or may not take into account the amount of the artificial background dose added by pre-calculating the additional backscatter caused by the artificial background dose. The embodiments described herein are examples, and other variants of adding an artificial background dose are possible. In some embodiments, the minimum backscatter amount has an embedded margin to account for the additional backscatter resulting from the artificial background dose. Since the amount of backscatter behaves mathematically linearly, the amount of backscatter added by the artificial background dose can be calculated independently of the dose of the shot in any given region. In some embodiments, the total mask area is subdivided into partitions of some one or more sizes, the artificial background dose is determined for each partition, and each partition has one artificial background dose within the partition, but different partitions potentially have different artificial background doses. Typically, the PEC is calculated on a coarse grid such as a 50 nm grid or a 300 nm grid. For each grid or partition, a PEC adjustment is calculated. In some implementations, the PEC adjustment at any location within a partition is interpolated based on the calculated PEC adjustments of adjacent partitions. In some embodiments, the calculation of the artificial background dose is performed on the same grid as the grid used for the PEC. In such an embodiment, the received backscatter amount at each PEC grid is compared with the specified minimum target backscatter amount, and an artificial background dose is determined to provide a region covered by the PEC grid.In some embodiments, the artificial background dose at any location within an individual partition is interpolated across the partition, such as by interpolation based on the artificial background dose of adjacent partitions. The next PEC step reduces the dose for that shot / pixel and reduces the write time for that shot / pixel. Doing this for all shots / pixels on a mask or section of a mask reduces the dose and thus reduces the write time for that section of the mask. In the next PEC step, the artificial backg. The addition of the round dose and any additional backscatter introduced by the artificial background dose are taken into account. PEC adjusts the shot dose of all shots to the mask such that all CDs are adjusted to hit the target in exactly the same way that PEC has always functioned for natural backscatter. The dose margin of the adjusted shots is worse than before adding the artificial background dose. However, depending on the parameters adjusted by the user to minimize backscatter, the dose margin can remain within the acceptable dose margin determined for a particular mask process.

[0061] In a conventional VSB machine, when casting any kind of dose (even if the dose is very small), a blanking time is required to separate individual shots from multiple shots. Since the blanking time is usually approximately the same as the exposure time at normal dose, at normal dose, the shot time may be considered to require a reasonable first approximation in units of 2 hours. In this estimate, a 10% dose shot requires 1.1 hours. Write time is of utmost importance for optimizing both the cost and yield of the mask, and it is already known that complex advanced masks take an excessive amount of time to write, so it is not commercially viable to add artificial background dose to all locations where there are no other shots. Nevertheless, in a VSB mask writer, the mask stage, which is usually of variable speed, is heavy, so the mask stage can only change its speed gradually. Therefore, reducing the peak dose density can encourage shortening the write time of the VSB machine.

[0062] Particularly in the case of a VSB machine, some embodiments of the present disclosure include intentionally leaking some eBeam energy during the blanking time to generate an artificial background dose. It is not necessary to precisely control the exact location where the leaked eBeam is cast. Since backscattering is a large-scale effect within a radius of 10 μm, nm-level control of the position is not important. The amount leaked and the time of leakage during the blanking time can be accurately calculated. Such calculations can be used to calculate the path along which the eBeam is moving and avoid casting the leakage near any pattern edges that require precise control (i.e., within the combined forward blur).

[0063] Surface writing of state-of-the-art technology nodes typically involves multiple passes of charged particle beam writing. This is a process called multi-pass exposure, by which a specific shape is written and overwritten on a reticle. Typically, 2 to 4 passes are used to write the reticle, averaging out the accuracy errors of the charged particle beam writer to enable the creation of a more accurate photomask. Also, typically, the list of shots including the dose is the same for all passes. In one variation of multi-pass exposure, the list of shots may vary between exposure passes, but the combination of shots in any exposure pass covers the same area. Multi-pass writing can reduce the overheating of the resist that coats the surface. Multi-pass writing also averages out the random errors of the charged particle beam writer. Multi-pass writing using different shot lists for different exposure passes can also reduce the impact of specific system errors in the writing process. In some embodiments, in VSB and multi-pass writing, only one or some of the writing passes cast an artificial background dose. In other words, in some embodiments, the original set of exposure information includes information for multiple exposure passes, and the artificial background dose is added only in the exposure passes. Since accuracy is not important for the artificial background dose, this is sufficient and can save writing time by not affecting all passes. The other passes, as in the embodiment shown in FIG. 10A, have a reduced peak dose of pixels or a reduced peak dose density of the region without the additional writing time required for the artificial background dose.

[0064] In some embodiments, relatively isolated patterns are intentionally surrounded by an artificial background dose that causes an increase in backscattering. PEC, which is a correction for backscattering, is achieved by reducing the dose of pixels or shots - less reduction when the exposure concentration is low and greater reduction when the exposure density is high. However, reducing the dose deteriorates the dose margin.

[0065] The acceptable dose margin can be determined by the amount of size variation caused by the dose reduction. In one embodiment, an isolated pattern exposed at a normal dose can be fired using a reduced dose to a larger pattern and an acceptable level without adding an artificial background dose.

[0066] For example, when using charged particle beam lithography to expose a pattern repeated on a surface, the size of each instance of the pattern measured on the finally manufactured surface will vary slightly due to manufacturing variations. The amount of size variation is an important manufacturing optimization criterion. In particular, if the variation of the smallest size features is too large, their shape may not be printed at all, and as a result, the circuit may malfunction. Manufacturing variations such as line edge roughness and corner rounding also exist in the actual pattern on the surface. Furthermore, the greater the size variation, the greater the variation in circuit performance, the greater the required margin design, and the more difficult it becomes to design a faster and lower power integrated circuit. This variation is called critical dimension (CD) variation. Low CD variation, especially uniformly low CD variation across all shapes on the mask, is desirable, indicating that manufacturing variations result in relatively small size variations on the final manufactured surface. On a small scale, the effects of large CD variation may be observed as line edge roughness (LER). LER occurs because the manufacturing method for each part of the line edge is slightly different, causing some undulation in a line intended to have a straight edge. CD variation is inversely proportional to the slope of the dose curve at the resist threshold, called the edge slope. Therefore, the edge slope and its inverse, the dose margin, are important optimization factors for particle beam writing on the surface. In this disclosure, edge slope and dose margin are terms used interchangeably.

[0067] In some embodiments, the method includes suggesting an appropriate amount of artificial background dose through the use of the slope of the edge that meets the target level. That is, it is the slope of an "adequately good" edge. Since the resilience to manufacturing variations is a statistical concept, what is meant by an "adequately good" edge slope is not an exact mathematical formula of a strict inequality. In some embodiments of the present method, the amount of artificial background dose where the slope of the edge exceeds an "adequately good" level is determined. For example, adjusting a particular mask manufacturing process to produce reliable manufacturing results for 100 nm × 2 μm lines written in 75% of the exposure density region, generating a greater amount of backscattering, and thus having a minimal amount of PEC post-dose per shot / pixel, and thus being able to have a relatively gentle edge slope. In some embodiments, the edge slope of that line after PEC is referred to as "adequately good". Despite other shapes, in the mask manufacturing process, even those where the edge slope is relatively poor, such as a 40 nm × 200 nm space written in a 75% density region where the edge slope is "not adequately good", can still be determined to be manufacturable in terms of the overall trade-off of economy, time, and manufacturing reliability. The function of the "adequately good" edge slope of the present embodiment indicates that it takes an excessive amount of time to cast that dose when compared to the additive benefit of resilience to variations in manufacturing, which is much better than "adequately good". Since the conventional teaching is to maximize the edge slope, it is counterintuitive to lower the edge slope below the optimal level, i.e., below the target level.

[0068] In some embodiments, the maximum dose before PEC and the artificial background dose are automatically calculated. In one embodiment, the maximum dose before PEC and the artificial background dose It can be calculated to achieve an acceptable level of contrast (contrast reduction). In another embodiment, the maximum dose before PEC and the artificial background dose can be calculated to achieve a dose margin below the target minimum dose margin. The minimum allowable dose margin can be determined by calculating the dose margin at a predetermined edge position of a predetermined pattern in a predetermined backscattering region.

[0069] In some embodiments, the artificial background dose is added before PEC to shorten the write time by reducing the dose during PEC, and the slope of the edge associated with the dose reduction can fall below the target level. In some embodiments, the target or "good enough" level can be calculated by simulating the slope of the edge of a feature known to function well enough for manufacturing purposes in a manufacturing process. For example, in advanced photomask manufacturing, when exposed at a normal dose before PEC, the repetition pattern of 100 nm wide wires separated by 100 nm wide spaces stabilizes. The simulation of the slope of the edge of a 100 nm wide wire in the context of a 100 nm line and space pattern can be considered a "good enough" dose margin. To calculate the artificial background dose, in a 100 nm line and space pattern, there is 50% exposure density in the surrounding area. The natural backscattering resulting from 50% exposure concentration is calculated as the minimum backscattering amount. The sum of the natural backscattering already present in a region and the artificial background dose is evenly distributed and contributes to the overall background exposure to a uniform minimum backscattering across the mask. The 50% exposure density may not produce the lowest allowable dose margin after PEC, but can be declared as a good practical goal to achieve for the purpose of calculating the amount of the minimum allowable dose for which the artificial background dose is calculated.

[0070] FIG. 16 is a diagram 1600 of a conceptual flow for creating a surface, such as a reticle or other surface, using charged particle beam lithography, as is known in the art. In a first step 1602, a physical design, such as a physical design of an integrated circuit, is created. This includes determining logical gates, transistors, metal layers, and other items that need to be found in a physical design such as a physical design of an integrated circuit. Next, in step 1604, optical proximity correction (OPC) is determined for the physical design of step 1602 or for a portion of the physical design desired on the wafer to create the mask design 1606. OPC calculates the shape of the mask necessary to optimally generate the shape of the target wafer across the entire variant of the manufacturing. OPC modifies the physical design to compensate for distortions caused by effects such as optical diffraction and the optical interaction between adjacent features that generate the mask design 1106.

[0071] Mask process correction (MPC) may optionally be performed on the mask design 1606. MPC changes the pattern written on the reticle to correct for non-linear effects such as effects associated with patterns less than about 100 nm in conventional optical lithography masks. MPC can also be used to correct for non-linear effects that affect EUV masks. In some embodiments of the present invention, MPC may be performed as part of a fragmentation or other mask data preparation (MDP) operation.

[0072] Mask data preparation (MDP) operations, which may include fragmentation operations, shot placement operations, dose assignment operations, or shot sequence optimization, in step 1608. In some embodiments for multi-beam mask writing, the MDP step 1608 may include generating a plurality of multi-beam shots, each multi-beam shot including one or more beamlets, in which case a dose region is determined and the dose region is assigned to the beamlets at each dose. In some embodiments, the dose of the beamlets may vary within the dose region.

[0073] The Proximity Effect Correction (PEC) improvement is performed at step 1618, where the dose is adjusted considering backscattering, fogging, and loading effects, and exposure information is created at step 1620 for the adjusted dose. The adjusted dose of the exposure information at step 1620 is used to generate a surface in a mask writing step 1622 using a charged particle beam writer such as an electron beam lithography system. Depending on the type of charged particle beam writer being used, the PEC improvement 1618 can be performed by the charged particle beam writer. The mask writing step 1622 can include a single exposure pass or multiple exposure passes. The electron beam lithography system projects an electron beam through a stencil or aperture plate onto the surface to form a mask image 1624 that includes a pattern on the surface. Next, the finished surface, such as a reticle, can be used in an optical lithography machine shown at step 1626.

[0074] FIG. 17 shows a flow 1700 representing a method for exposing a pattern onto a region on a surface, according to some embodiments, where a dynamic maximum dose and an artificial background dose can be calculated and applied. At step 1706, a set of original exposure information for the pattern is input. In some embodiments, the set of original exposure information is a set of pixels and their doses. In another embodiment, the set of original exposure information is a set of shapes that potentially include curves or fully non-polygonal descriptions (such as circles or splines). In yet another embodiment, the set of original exposure information is a set of shots of the dose before PEC that are assigned or implied (e.g., VSB), or a set of shapes of the dose before PEC that are assigned or implied (e.g., multi-beam writing). Generally, the input at step 1706 describes a shape or a dose.

[0075] The maximum dose after PEC is input at step 1708, which functions as the target or desired maximum dose after PEC. In some embodiments, step 1708 includes inputting the maximum dose after target proximity effect correction, in which case the target maximum dose after PEC is based on the maximum write time. In some embodiments, a threshold for the artificial background dose is also input. In other embodiments, a target dose margin is input and used to determine the target maximum dose after PEC. That is, the target dose margin can be used as a factor in selecting the maximum dose after PEC, such as to achieve a dose margin below the target dose margin. In such embodiments, flow 1700 may include a step of calculating the dose margin of the pattern to be exposed, for example, calculating the target minimum dose margin at a predetermined edge position in a predetermined pattern in a predetermined backscatter region, in which case the maximum dose before PEC is determined to achieve the dose margin of the pattern exposed below the target minimum dose margin. The maximum dose after PEC, the artificial background dose threshold, and / or the target dose margin can be input, for example, by a user. In yet another embodiment, the maximum dose after PEC can be selected based on the desired write time, such as by shortening the write time by a certain amount compared to the normal dose or remaining below a threshold limited by the maximum machine write time. In another embodiment, the maximum dose after PEC can be based on the size of features such as the smallest feature. In another embodiment, the maximum dose after PEC can be based on other measures of printability or based on some other method.

[0076] The local pattern density is determined (i.e., calculated) at step 1710 based on the set of original exposure information. In one embodiment, the calculation of the local pattern density at step 1710 includes an initial determination by the PEC that creates an initial map of backscatter. The PEC is an iterative process in which the dose is adjusted to print the target size in the presence of backscatter. The initial map of backscatter from the first PEC determination is an excellent relative indicator of the local pattern density. That is, the local pattern density can be calculated by calculating the amount of backscatter. In some embodiments, regions where the backscatter is below a predetermined threshold are identified at step 1710.

[0077] The maximum dose before PEC of the local pattern density is dynamically determined (i.e., calculated) at step 1712 based on the maximum dose after PEC of the target at step 1708. That is, the maximum dose before PEC is dynamic in that it can vary according to a particular set of exposure information (local pattern density), the target dose margin, the desired maximum write time, and / or other target parameters. In some embodiments, the maximum dose before PEC is pre-calculated for various region pattern densities and the maximum dose before PEC is supplied accordingly for the local pattern density. In some embodiments, the maximum dose before PEC calculated for the local pattern density is input into a linearity correction algorithm.

[0078] At step 1716, the original exposure information is modified to include the maximum dose before PEC of step 1712 to create a modified set of exposure information. In some embodiments, the modified set of exposure information is improved by the PEC, resulting in an adjusted dose that is less than (i.e., does not exceed) the maximum dose after PEC of step 1708. In some embodiments, flow 1700 may also include exposing the surface with the modified set of exposure information.

[0079] In some embodiments, the calculation includes determining an artificial background dose for a region at step 1714, the artificial background dose including additional exposure information. In some embodiments, step 1714 is performed on a region having a local pattern density where backscatter less than a predetermined threshold is identified at step 1710. In some embodiments, flow 1700 includes calculating backscatter for a region based on a set of original exposure information, and step 1714 adds an artificial background dose only if the calculated backscatter is less than a predetermined threshold (i.e., is less than). That is, the artificial background dose is the difference between the predetermined threshold and the calculated backscatter. In some embodiments, at step 1714, a dose margin or edge slope for a desired pattern within the region is calculated, and the artificial background dose is determined to maintain a "sufficiently good" edge slope or contrast for the desired pattern within the region. In some embodiments, step 1714 adds an artificial background dose to maintain a "sufficiently good" edge slope of a pattern within the region that meets certain criteria, such as the minimum target size of a "sufficiently good" edge slope. For example, a smaller-sized shape for an SRAF may be excluded from a "sufficiently good" edge slope. As another example, a smaller-sized shape for an SRAF may have a different "sufficiently good" edge slope to achieve when determining the artificial background dose to add. In some embodiments, these calculations may result in creating an artificial background dose that includes additional patterns with exposure below a threshold so that no additional patterns are printed. The additional pattern(s) are combined with the set of modified exposure information. In some embodiments, the artificial background dose is applied only beyond a predetermined distance from the edge of the pattern on the surface. In some embodiments, the set of original exposure information includes information for a plurality of exposure passes, and the artificial background dose is added only in the exposure pass.

[0080] In some embodiments, the calculation of the maximum dose before PEC and the creation of additional patterns are performed as part of the MDP step (e.g., step 1608 of flow 1600, FIG. 16), and the additional patterns overlap with the geometrically desired patterns in the mask design (e.g., step 1606 of flow 1600, FIG. 16). The set of modified exposure information at step 1716, which can be adjusted with the maximum dose before PEC or combined with additional exposure information (i.e., additional patterns), includes the original set of exposure information and is subject to proximity effect correction (PEC) improvement step (e.g., step 1618 of flow 1600, FIG. 16), and can generate the modified exposure information at step 1716, which includes an artificial background dose and may also include backscatter resulting from the artificial background dose. In some embodiments, the set of modified exposure information shortens the overall write time compared to the original set of exposure information. In some embodiments, the set of modified exposure information is improved by PEC, resulting in an adjusted dose for the set of modified exposure information. Next, the surface is exposed with the set of modified exposure information using the exposure information. In some embodiments, the dose of a pixel or shot is changed to add an artificial background dose. In some embodiments, a pixel or shot casts an artificial background dose into an otherwise empty region (a pixel starting with a zero dose), and the amount of the dose is relatively similar for the pixel in, for example, a number of adjacent pixels of 3×3 or more.

[0081] In some embodiments, some or all of steps 1710, 1712, 1714, and 1716 of FIG. 17 follow steps 1618 and 1620 of FIG. 16 and are executed simultaneously with mask writing step 1622 of flow 1600 of FIG. 16, involving in-line processing to perform data operations while the mask is being exposed. That is, in some embodiments, mask exposure is executed in-line for one or more steps selected from the group consisting of determining (i.e., calculating) local (i.e., regional) pattern density and determining the maximum dose before PEC for that region, calculating backscatter, determining regions where the calculated backscatter is below a predetermined threshold, determining artificial background dose, and creating a set of modified exposure information. In other embodiments, the calculations may be performed in a pipelined manner during the exposure of another surface. In a pipelined system, while the previous surface is being written on the machine, the next surface to be written on the machine is calculated. A pipelined system is effective in improving the throughput of many surfaces when the write time and calculation time of the surfaces are similar. An in-line (real-time) system is effective in improving the throughput and turn-around time of each surface.

[0082] This method can be used offline, in a pipeline, or inline. It is most desirable to be fast enough to be processed inline. Inline processing is most desirable especially when the total number of pixels that need to be written is very large. For example, in a semiconductor device manufactured for multi-beam eBeam writing of a mask, more than 500 TB of data is required to store all pixel data. Since a multi-beam eBeam machine needs to write pixels very fast, storing such data on a hard disk or even on a solid state disk may not be practical in terms of cost. In inline processing, unlike offline or pipeline processing, there is no need to store the data because the machine consumes the data and writes the pixels immediately after the data is calculated. This is another reason why the inline processing enabled by this method is valuable. As described above, the same methodology can be used to adjust the pixel dose and improve the dose margin (i.e., the slope of the edge).

[0083] The creation of mask data, the calculation of the maximum dose, the calculation of the artificial background dose, and the proximity effect correction described in this disclosure can be implemented using a general-purpose computer that uses a central processing unit (CPU) equipped with appropriate computer software as a computing device. Since a large amount of calculation is required, multiple computers or processor cores of the CPU can also be used in parallel. In one embodiment, the calculation can be subdivided into a plurality of two-dimensional geometric regions for one or more computationally intensive steps of the flow in order to support parallel processing. In another embodiment, using a dedicated hardware device used alone or in plurality, it is faster than using a general-purpose computer or processor core, and one or can perform calculations in multiple steps. Special computing hardware devices or processors may include, for example, field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), or digital signal processor (DSP) chips. In one embodiment, the dedicated hardware device can be a graphics processing unit (GPU). In another embodiment, the optimization and calculation processes described in this disclosure may include an iterative process that modifies and recalculates possible solutions to minimize the total charged particle beam writing time or other parameters. In yet another embodiment, the process can be a deterministic calculation without iteration.

[0084] FIG. 18 shows an example of a computing hardware device 1800 that may be used to perform the calculations described in this disclosure. The computing hardware device 1800 includes a central processing unit (CPU) 1802 to which a main memory 1804 is connected. The CPU includes, for example, eight processing cores, thereby improving the performance of any part of the multithreaded computer software. The size of the main memory 1804 may be, for example, 64 gigabytes. The CPU 1802 is connected to a peripheral component interconnect express (PCIe) bus 1820. Also, a graphics processing unit (GPU) 1814 is connected to the PCIe bus. In the computing hardware device 1800, the GPU 1814 may or may not be connected to a graphics output device such as a video monitor. When not connected to a graphics output device, the GPU 1814 can be used purely as a high-speed parallel computing engine. Computing software can achieve significantly higher performance by using the GPU for a portion of the calculations compared to using the CPU 1802 for all calculations. The CPU 1802 communicates with the GPU 1814 via the PCIe bus 1820. In other embodiments (not shown), the GPU 1814 may be integrated with the CPU 1802 rather than connected to the PCIe bus 1820. Also, a disk controller 1808 may be connected to the PCIe bus, and for example, two disks 1810 are connected to the disk controller 1808. Finally, a local area network (LAN) controller 1812 may also be connected to the PCIe bus, providing gigabit Ethernet (registered trademark) (GbE) connectivity to other computers. In some embodiments, computer software and / or design data are stored on the disk 1810. In other embodiments, either the computer program or the design data, or both the computer program and the design data, can be accessed from other computers or file providing hardware via GbE Ethernet (registered trademark).

[0085] Although this specification has been described in detail with respect to particular embodiments, those of ordinary skill in the art will understand that, upon obtaining an understanding of the foregoing, various changes, modifications, and equivalents to these embodiments can be readily conceived. These and other changes and modifications to the present method for creating mask data can be implemented by those of ordinary skill in the art without departing from the scope of the subject matter specifically recited by the appended claims. Further, those of ordinary skill in the art will understand that the foregoing description is by way of example only and is not intended to be limiting. Steps can be added to, obtained from, or modified from the steps of this specification without departing from the scope of the present invention. Generally, any flowchart presented is intended only to show one possible sequence of basic operations for achieving a function, and many variations are possible. Accordingly, it is intended that the subject matter cover such changes and modifications that fall within the scope of the appended claims and their equivalents.

Claims

Claim 1 A method for exposing a pattern in a region on a surface using a charged particle beam system, comprising: determining a local pattern density of the region based on a set of original exposure information; determining a maximum dose before proximity effect correction (PEC) for the local pattern density based on a predetermined target maximum dose after PEC; modifying the set of original exposure information with the maximum dose before PEC to create a modified set of exposure information. Claim 2 The method according to claim 1, wherein the modified set of exposure information is improved by PEC and an adjusted dose less than the target maximum dose after PEC is obtained. Claim 3 The method according to claim 1, further comprising determining an artificial background dose of the region, wherein the artificial background dose includes additional patterns with exposures below a threshold, and the additional patterns are combined with the modified set of exposure information. Claim 4 The method according to claim 3, wherein the artificial background dose is applied only beyond a predetermined distance from an edge of the pattern on the surface. Claim 5 The method according to claim 3, wherein the set of original exposure information includes information on a plurality of exposure passes, and the artificial background dose is added only to the exposure passes. Claim 6 The method according to claim 3, further comprising calculating a backscattering of the region based on the set of original exposure information, and wherein in the region where the calculated backscattering is less than a predetermined threshold, the artificial background dose is the difference between the predetermined threshold and the calculated backscattering. Claim 7 The method according to claim 3, wherein the region is subdivided into partitions and the artificial background dose is determined for each partition. Claim 8 The method according to claim 7, wherein the artificial background dose at any location within an individual partition is interpolated across the entire partition. Claim 9 The method according to claim 8, wherein the interpolation is based on the artificial background doses of adjacent partitions. Claim 10 The method according to claim 3, wherein the mask exposure is performed inline for one or more steps selected from the group consisting of determining the local pattern density, determining the maximum dose before the PEC, determining the artificial background dose, and creating the set of modified exposure information.

11. The method according to claim 1, further comprising inputting a target dose margin, wherein the target dose margin is used to determine the maximum dose after the PEC of the target.

12. The method according to claim 1, further comprising calculating a dose margin of the pattern to be exposed.

13. The method further comprises calculating a target minimum dose margin at a predetermined edge position of a predetermined pattern in a predetermined backscatter region, The method according to claim 12, wherein the maximum dose before the PEC is determined to achieve the dose margin of the pattern exposed below the target minimum dose margin.

14. The method according to claim 1, further comprising exposing the surface with the set of modified exposure information.

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