Operating method of electronic device for semiconductor memory manufacture

Abstract

The present invention relates to a method of operation of an electronic device for manufacturing a semiconductor device. The method of operation of the present invention includes the steps of receiving a layout image of a semiconductor device, generating auxiliary features based on main features of the layout image to generate an intermediate image, performing a simulation based on a first image to evaluate a process result, and modifying the intermediate image by modifying the shapes of the main features and / or auxiliary features of the intermediate image based on the process result.

Description

Technology Field

[0001] The present invention relates to a method of operation of an electronic device, and more specifically, to a method of operation of an electronic device for manufacturing a semiconductor device that prevents defects without post-processing during Optical Proximity Correction (OPC). Background Technology

[0002] Optical Proximity Correction (OPC) can pre-correct deviations between the shapes of generated mask patterns and target mask patterns caused by process characteristics or errors during the photolithography process. During optical proximity correction, the shapes of the photomask patterns used in the process can be corrected to differ from the target mask patterns so that the shapes of the generated mask patterns conform to the target mask patterns.

[0003] Various defects may occur during optical proximity correction. These defects can render the photomask obtained through optical proximity correction unusable. If the photomask becomes unusable, the time and costs incurred for optical proximity correction may be unrecoverable. The problem to be solved

[0004] The purpose of this description is to provide an apparatus or method for performing optical proximity correction to prevent defects from occurring. means of solving the problem

[0005] A method of operating an electronic device for manufacturing a semiconductor device comprises the steps of receiving a layout image of the semiconductor device, generating auxiliary features based on main features of the layout image to generate an intermediate image, performing a simulation based on the intermediate image to evaluate the process results, and modifying the intermediate image by modifying the shapes of the main features and / or auxiliary features of the intermediate image based on the process results.

[0006] A method for operating an electronic device for manufacturing a semiconductor device comprises, based on a simulation and evaluation result based on a layout image including main features and auxiliary features, a step of calculating a change in the target slope of the change in light intensity with respect to a change in a photoresist image from a target slope of the change in light intensity at each boundary line of the main features; a step of calculating a change in the target slope of the change in light intensity with respect to a change in an optical image from a change in the target slope of the change in light intensity with respect to a change in a photoresist image; a step of calculating a change in the target slope of the change in light intensity with respect to a change in a mask image from a change in the target slope of the change in light intensity with respect to a change in an optical image from a change in the target slope of the change in light intensity with respect to a change in a mask image from a change in the target slope of the change in light intensity with respect to a change in a mask image from a change in the target slope of the change in light intensity with respect to a change in a curvilinear image; and a step of calculating modification information of the layout image from a change in the target slope of the change in light intensity with respect to a change in a curvilinear image.

[0007] A method of operation of an electronic device for manufacturing a semiconductor device comprises the steps of: receiving a layout image of a semiconductor device; generating an intermediate image by generating auxiliary features based on main features of the layout image; generating a curvilinear image from the intermediate image; pixelating the curvilinear image to generate a mask image; performing an optical simulation on the mask image to generate an optical image; performing a photoresist simulation on the optical image to generate a photoresist image; calculating the slope of the change in light intensity at each boundary line of the main features; calculating the change in the target slope of the change in light intensity with respect to the change in the photoresist image from the target slope of the change in light intensity at each boundary line of the main features; calculating the change in the target slope of the change in light intensity with respect to the change in the optical image from the change in the target slope of the change in light intensity with respect to the change in the photoresist image; calculating the change in the target slope of the change in light intensity with respect to the change in the mask image from the change in the target slope of the change in light intensity with respect to the change in the optical image; and the light with respect to the change in the mask image It includes the step of calculating the change in the target slope of the change in light intensity for the change in a curvilinear image from the change in the target slope of the change in intensity, and the step of calculating the modification information of the layout image from the change in the target slope of the change in light intensity for the change in the curvilinear image. Effects of the invention

[0008] According to this description, photomask patterns are represented in the form of curves, and the photomask patterns are modified by directly modifying the curves. Therefore, since the modification of the curves is not performed in a pixelated state, the occurrence of various defects such as consistency defects, Mask Rule Constraints (MRC) defects, and boundary defects is prevented. Brief explanation of the drawing

[0009] FIG. 1 is a block diagram showing an electronic device according to an embodiment of the present invention. FIG. 2 shows a method of operation of an electronic device according to an embodiment of the present invention. Figure 3 shows an example of an implementation of an OPC module. Figure 4 shows an example of a layout image. Figure 5 shows an example of an intermediate image. Figure 6 shows an example of the process in which pixelation is performed. Figure 7 shows an example where pixelation is completed. Figure 8 shows the change in the target gradient of the change in light intensity with respect to the change in the mask image in the form of an image. Figure 9 shows modification information for modifying an intermediate image in the form of an image. FIG. 10a shows a first embodiment in which a curved shape image is defined. Figure 10b shows an example in which an intermediate image is modified based on a curved image defined as in Figure 10a. FIG. 11a shows a second embodiment in which a curved shape image is defined. Figure 11b shows an example in which an intermediate image is modified based on a curved image defined as in Figure 11a. FIG. 12 shows a third embodiment in which a curved shape image is defined. FIG. 13 shows a fourth embodiment in which a curved shape image is defined. Specific details for implementing the invention

[0010] In the following, embodiments of the present invention will be described clearly and in detail so that a person skilled in the art can easily practice the present invention. In the following, the term 'and / or' is interpreted to include any one of the items listed in association with the term, and a combination of some or all of the items listed in association.

[0011] FIG. 1 is a block diagram showing an electronic device (100) according to an embodiment of the present invention. Referring to FIG. 1, the electronic device (100) may include processors (110), random access memory (120), device driver (130), storage device (140), modem (150), and user interfaces (160).

[0012] The processors (110) may include at least one general-purpose processor, such as, for example, a central processing unit (111) (CPU), an application processor (AP), etc. The processors (110) may also include at least one special-purpose processor, such as a neural processing unit (113), a neuromorphic processor (114), a graphics processing unit (115) (GPU), etc. The processors (110) may include two or more processors of the same type.

[0013] At least one of the processors (110) can drive an Optical Proximity Correction (OPC) module. For example, the OPC module (200) can be implemented in the form of instructions (or codes) executed by at least one of the processors (110). At this time, at least one processor can load the instructions (or codes) of the OPC module (200) into a random access memory (120).

[0014] As another example, at least one (or at least one other) of the processors (110) may be manufactured to implement the OPC module (200). For example, at least one processor may be a dedicated processor that implements the functions of the OPC module (200) in hardware.

[0015] Random access memory (120) is used as operating memory for processors (110) and can be used as main memory or system memory for electronic devices (100). Random access memory (120) may include volatile memory such as dynamic random access memory or static random access memory, or non-volatile memory such as phase change random access memory, ferroelectric random access memory, magnetic random access memory, or resistive random access memory.

[0016] The device driver (130) can control peripheral devices such as a storage device (140), a modem (150), and user interfaces (160) at the request of the processors (110). The storage device (140) may include a fixed storage device such as a hard disk drive, a solid-state drive, or a removable storage device such as an external hard disk drive, an external solid-state drive, or a removable memory card.

[0017] The modem (150) can provide remote communication with an external device. The modem (150) can perform wireless or wired communication with an external device. The modem (150) can communicate with an external device through at least one of various forms of communication such as Ethernet, Wi-Fi, LTE, 5G mobile communication, etc.

[0018] User interfaces (160) can receive information from a user and provide information to the user. User interfaces (160) may include at least one user output interface such as a display (161), a speaker (162), etc., and at least one user input interface such as a mouse (163), a keyboard (164), a touch input device (165), etc.

[0019] The commands (or codes) of the OPC module (200) can be received via the modem (150) and stored in the storage device (140). The commands (or codes) of the OPC module (200) can be stored in a removable storage device and coupled to the electronic device (100). The commands (or codes) of the OPC module (200) can be loaded from the storage device (140) into the random access memory (120) and executed.

[0020] FIG. 2 illustrates a method of operation of an electronic device (100) according to an embodiment of the present invention. For example, FIG. 2 illustrates an example in which an OPC module (200) performs OPC. Referring to FIG. 1 and FIG. 2, in step S110, the electronic device (100) or the OPC module (200) may receive a layout image. For example, the layout image may include target patterns to be formed on a semiconductor wafer, such as semiconductor patterns, conductor patterns, or insulator patterns. The target patterns on the layout image may be referred to as main features.

[0021] In step S120, the electronic device (100) or the OPC module (200) may generate assist features from the layout image. The assist features may be used to help generate the main features. At locations corresponding to the assist features, a pattern may not be formed on the semiconductor wafer. The electronic device (100) or the OPC module (200) may generate an intermediate image by adding the assist features to the layout image. The intermediate image may be a shape-shape image containing the shapes of the main features and the shapes of the assist features. The intermediate image may be a candidate to be used as a photomask.

[0022] For example, an example of a layout image is illustrated in FIG. 4, and an example of an intermediate image is illustrated in FIG. 5. Referring to FIG. 4, the layout image (LI) is divided into multiple regions, and each of the multiple regions may include main features (MF). An electronic device (100) or an OPC module (200) may perform OPC on each of the multiple regions.

[0023] Referring to FIG. 5, the intermediate image (p) is divided into multiple regions, and each of the multiple regions may include main features (MF) and auxiliary features (AF). The main features (MF) may correspond to a target pattern. The auxiliary features (AF) may be added in the form of a curve surrounding the main features (MF).

[0024] Referring again to FIGS. 1, FIGS. 2 and FIGS. 3, at step S130, the electronic device (100) or OPC module (200) can evaluate the process results. The electronic device (100) or OPC module (200) can calculate the process results through simulation when the semiconductor manufacturing process is performed using an intermediate image as a photomask.

[0025] In step S140, the electronic device (100) or the OPC module (200) can determine whether the process result is acceptable. For example, when the electronic device (100) or the OPC module (200) performs a semiconductor manufacturing process using an intermediate image as a photomask, it can calculate the intensities of the light projected onto the semiconductor wafer through simulation. It can determine whether the intensities of the light projected onto the semiconductor wafer can generate patterns similar to target patterns on the semiconductor wafer.

[0026] If the process result is unacceptable, in step S150, the electronic device (100) or the OPC module (200) may modify the main features and / or auxiliary features of the intermediate image. For example, the electronic device (100) or the OPC module (200) may reverse the evaluation process of step S130 to calculate control information for at least one of the main features and / or at least one of the auxiliary features. Subsequently, the electronic device (100) or the OPC module (200) may repeat steps S130 and S140.

[0027] If the process result is acceptable, at step S160, the electronic device (100) or the OPC module (200) can finalize the OPC result image. For example, the electronic device (100) or the OPC module (200) can finalize the current intermediate image as the image of the photomask.

[0028] As described above, the electronic device (100) or OPC module (200) according to the embodiment of the present invention can repeatedly perform simulation evaluation (e.g., forward operation of step S130) and modification of an intermediate image (e.g., reverse operation of step S150) and modify an intermediate image that is a candidate for a photomask.

[0029] In some OPCs, image modification may be performed in a pixelated state. Pixelation of the image may include lowering the image resolution to reduce computational complexity. Once the modification of the pixelated image is complete, post-processing to increase the resolution may be required.

[0030] During the post-processing stage, a consistency defect may occur where non-identical auxiliary features are generated when main features of the same form are repeated. Additionally, during the post-processing stage, a Mask Rule Constraints (MRC) defect may occur, where auxiliary features or main features that are unacceptable in the semiconductor manufacturing process are generated.

[0031] OPC can divide a single semiconductor die into multiple regions and be performed sequentially on these regions. Post-processing to increase resolution can also be performed sequentially on multiple regions. A specific main feature may span two or more regions. During the post-processing stage, boundary defects may occur where the boundary of a specific feature in one region does not coincide with the boundary of a part in another region.

[0032] According to an embodiment of the present description, the electronic device (100) or the OPC module (200) performs modifications on an intermediate image rather than in a pixelated state. Accordingly, the occurrence of various defects, including the defects described above, is prevented.

[0033] FIG. 3 shows an example of an implementation of an OPC module (200). Referring to FIG. 1, FIG. 2 and FIG. 3, the OPC module (200) may include a forward unit (210) that performs a forward operation and a reverse unit (220) that performs a reverse operation. For example, a component that generates an intermediate image from a layout image is omitted in FIG. 3.

[0034] The forward unit (210) can receive an intermediate image (p). The forward unit (210) can generate a slope (q) by performing simulation and evaluation on the intermediate image (p). For example, the slope (q) can represent the slope of the change in light intensities reaching the semiconductor wafer when the intermediate image (p) is used as a photomask. For example, the slope (q) can represent the slope of the change in light intensity at each boundary line of the main features.

[0035] The greater the slope (q) of the change in light intensity at each boundary of the main features, the greater the difference between the light intensity irradiated on the area where photoresist is to be formed and the light intensity irradiated on the area where photoresist is not to be formed. In other words, the greater the slope (q), the sharper and more accurately photoresist patterns are formed, and the process margin can be improved.

[0036] The reverse unit (220) can receive a target slope (e.g., 1). Based on the target slope (e.g., 1), the reverse unit (220) performs the forward operation of the forward unit (210) in reverse, for example, can perform a reverse operation. The reverse unit (220) performs the reverse operation to obtain correction information (▽) for correcting the intermediate image. p q) can be calculated.

[0037] The electronic device (100) or OPC module (200) can optimize the shape of the photomask and increase the process margin by repeating the forward operation of the forward unit (210), the reverse operation of the reverse unit (220), and the modification of the intermediate image.

[0038] The forward unit (210) may include a curve shape generator (211), a mask image generator (212), an optical simulation block (213), a photoresist simulation block (214), and a target evaluation block (215). The curve shape generator (211), the mask image generator (212), the optical simulation block (213), the photoresist simulation block (214), and / or the target evaluation block (215) may be implemented in hardware, software, or a combination of hardware and software.

[0039] The curve shape generator (211) can calculate a curve shape image (Ω) from an intermediate image (p). For example, depending on the implementation method, the curve shape generator (211) can generate a curve shape image (Ω) using various methods.

[0040] The mask image generator (212) can generate a mask image (M) by pixelating a curved image (Ω). An example of the process of performing pixelation is illustrated in FIG. 6. Referring to FIG. 6, the curved image (Ω) is divided into a plurality of regions, and pixelation can be performed on each of the main features and auxiliary features of the plurality of regions.

[0041] Each of the multiple regions of the curved image (Ω) can be divided into pixels (PX). The pixels (PX) can have the same size. The resolution of the pixels (PX) can be lower than the resolution of the data of the layout image (LI) or the resolution of the data of the curved image (Ω).

[0042] Each of the pixels (PX) may have a value between 0 and 1 (e.g., a normalized value). The mask image generator (212) can calculate the values ​​of the pixels (PX) of the mask image (M) based on Equation 1.

[0043]

[0044] In mathematical formula 1, x' and x represent positions on the pixels of the intermediate image and can each have values ​​in a two-dimensional coordinate system based on pixels (PX). can be a filter function. When the mask image (M) is a thin (e.g., 2D) mask, the filter function ( ) can be an anti-aliasing filter. When the mask image (M) is a thick (e.g., 3D) mask, the filter function ( ) can be an edge filter or a coupling filter.

[0045] An example of completed pixelation is illustrated in FIG. 7. Referring to FIG. 7, the mask image (M) generated after pixelation is completed can be reduced.

[0046] Referring again to FIGS. 1, 2 and 3, the optical simulation block (213) can perform an optical simulation based on a mask image (M) to calculate an optical image (I) projected onto a semiconductor wafer. The photoresist simulation block (214) can perform a photoresist simulation based on the optical image (I) to calculate a photoresist image (R) formed on a semiconductor wafer. The target evaluation block (Q) can perform an evaluation based on the photoresist image (R) to calculate a slope (q).

[0047] The reverse unit (220) may include a first block (221), a second block (222), a third block (223), a fourth block (224), and a fifth block (225).

[0048] The first block (221) calculates the Prechet derivative (Q') based on the target slope (e.g., 1) and the calculation of the target evaluation block (215). * Calculate ) and the change in the target slope of the change in light intensity with respect to the change in the photoresist image ( ) can be output as an adjoint variable.

[0049] The second block (222) is a change in the target slope of the change in light intensity for the change in the photoresist image ( ) and based on the calculation of the photoresist simulation block (214), the Prechet derivative (R' * Calculate ) and the change in the target slope of the change in light intensity with respect to the change in the optical image ( ) can be output as an AddJoint Variable.

[0050] The third block (223) is a change in the target slope of the change in light intensity for the change in the optical image ( Based on the calculations of the ) and optical simulation blocks, the Fréchet derivative (I' * Calculate ) and the change in the target slope of the change in light intensity with respect to the change in the mask image ( ) can be output as an AddJoint Variable.

[0051] For example, changes in the mask image ( ), for example, the shape derivative of the mask image (M) The shape derivative can be derived as Equation 2 based on Equation 1.

[0052]

[0053] In mathematical formula 2, can refer to the boundary line of a curved image (Ω). can be the normal vector of each point (or pixel) belonging to the boundary line of the curved image (Ω). can represent the positional displacement of each point (or pixel) belonging to the boundary line of the curved image (Ω). As illustrated in Equation 2, the shape derivative of the mask image (M) ) can be calculated at the boundary of the curved image (Ω) (or at the pixels (PX) of the boundary).

[0054] Change in the target gradient of the change in light intensity ( ), that is, the objective derivative( ) can be defined by mathematical formula 3 based on the chain rule.

[0055]

[0056] If the order of integration in Equation 3 is changed, Equation 3 can be changed to Equation 4.

[0057]

[0058] Change in the target gradient of the change in light intensity with respect to the change in the mask image ( ) can be represented in the form of an image as shown in Fig. 8. In Fig. 8, as the boundary line of the main features or auxiliary features moves toward a bright area, the slope (q) of the change in light intensity increases, and as the boundary line of the main features or auxiliary features moves toward a dark area, the slope (q) of the change in light intensity decreases.

[0059] Referring again to FIGS. 1, 2, and 3, the fourth block (224) is a change in the target slope of the change in light intensity with respect to the change in the mask image ( Based on the operation of the ) and the mask image generator (212), the Prechet derivative (M' * Calculate ) and the change in the target slope of the change in light intensity with respect to the change in the curve-shaped image ( )(e.g., shape gradient) can be output as an adjoint variable. The change in the target gradient of the change in light intensity with respect to the change in the curved image ( ) can be calculated using mathematical formula 5.

[0060]

[0061] The fifth block (225) is a change in the target slope of the change in light intensity for the change in the curved shape image ( Based on the calculation of ) and the curve shape generator (211), the Prechet derivative (x' * Calculate ), and correction information for modifying the intermediate image (▽ p q) can be output as an adjoint variable. Modification information for modifying the intermediate image (▽ p q) can be calculated using mathematical formula 6.

[0062]

[0063] Modification information for modifying the intermediate image (▽ p q) can be represented in the form of an image as shown in FIG. 9. In FIG. 9, circular shapes represent points defining a curved image (Ω). Lines extending from the circular shapes represent the modified locations of the points defining the curved image (Ω).

[0064] The electronic device (100) or OPC module (200) provides modification information (▽) for modifying an intermediate image. p Based on q), the points defining the curved image (Ω) can be modified. The modification of the intermediate image is based on gradient descent and can be calculated using Equation 7.

[0065]

[0066] In mathematical formula 7, i is a positive integer and may represent the number of times a loop is performed, including the forward operation of the forward unit (210), the reverse operation of the reverse unit (220), and the modification of the intermediate image. is a constant and can be determined arbitrarily or based on process characteristics.

[0067] FIG. 10a shows a first embodiment in which a curved shape image (Ω) is defined. Referring to FIG. 3 and FIG. 10a, an electronic device (100) or an OPC module (200) can set first points (P1) on the boundary line of the main feature of an intermediate image (p). The electronic device (100) or the OPC module (200) can parameterize the intermediate image (p) with the first points (P1). A curved shape generator (211) can generate a curved shape image (Ω) that is inscribed in the boundary line connecting the first points (P1).

[0068] FIG. 10b shows an example in which an intermediate image (p) is modified based on a curved shape image (Ω) defined as in FIG. 10a. Referring to FIG. 3, FIG. 10a and FIG. 10b, an electronic device (100) or an OPC module (200) can modify the locations of first points (P1) to second points (P2). A curved shape generator (211) can generate a curved shape image (Ω) that is inscribed in the boundary line connecting the second points (P2).

[0069] FIG. 11a shows a second embodiment in which a curved shape image (Ω) is defined. Referring to FIG. 3 and FIG. 11a, the electronic device (100) or OPC module (200) can set third points (P3) on the boundary line of the main feature of the intermediate image (p). The electronic device (100) or OPC module (200) can parameterize the intermediate image (p) with the third points (P3). The curved shape generator (211) can generate a curve connecting the third points (P3) as the curved shape image (Ω).

[0070] FIG. 11b shows an example in which an intermediate image (p) is modified based on a curved shape image (Ω) defined as in FIG. 11a. Referring to FIG. 3, FIG. 11a and FIG. 11b, an electronic device (100) or an OPC module (200) can modify the locations of the third points (P3) to the fourth points (P4). A curved shape generator (211) can generate a curved shape image (Ω) that connects the fourth points (P4).

[0071] FIG. 12 shows a third embodiment in which a curved shape image (Ω) is defined. Referring to FIG. 3 and FIG. 12, an electronic device (100) or an OPC module (200) can set fifth points (P5) from the boundary line of the main feature of an intermediate image (p). The electronic device (100) or the OPC module (200) can parameterize the intermediate image (p) with the fifth points (P5). A curved shape generator (211) can generate a curved shape image (Ω) based on the fifth points (P5) and a spline curve function.

[0072] As described with reference to FIGS. 10a, 10b, 11a, and 11b, the electronic device (100) or OPC module (200) can modify the positions of the fifth points (P5). The curve shape generator (211) can generate a curve shape image (Ω) based on the modified fifth points (P5) and a spline curve function (spline).

[0073] FIG. 13 shows a fourth embodiment in which a curved image (Ω) is defined. Referring to FIG. 3 and FIG. 13, the electronic device (100) or OPC module (200) may set sixth points (e.g., including P6_i and P6_j) at the center inside the boundary lines of auxiliary features of the intermediate image (p). The electronic device (100) or OPC module (200) may parameterize the intermediate image (p) with the sixth points (e.g., including P6_i and P6_j).

[0074] The electronic device (100) or the OPC module (200) can tag each of the six points with width information (W_i based on P6_i or W_j based on P6_j) and at least one point identifier information (C_i1, C_i2 based on P6_i). The at least one point identifier information may represent at least one point forming the most adjacent and continuous auxiliary feature. The width information may include information on the width in the normal direction toward the boundary of the auxiliary feature at each point. The curve shape generator (211) can generate a curve shape image (Ω) based on the width information and point identifier information of the six points.

[0075] As described with reference to FIGS. 10a, FIGS. 10b, FIGS. 11a, and FIGS. 11b, the electronic device (100) or OPC module (200) can modify the positions of the sixth points (P6). Additionally, the electronic device (100) or OPC module (200) can modify the width information tagged at the sixth points (P6). The curve shape generator (211) can generate a curve shape image (Ω) based on the width information of the sixth points and the point identifier information.

[0076] For example, to optimize the intermediate image (p), the movement of the positions of the sixth points (P6) may be constrained in the normal direction. Explanation of the symbols

[0078] 100: Electronic device 110: Processors 111: Central Processing Unit 112: Application processor 113: Neural Processing Unit 114: Neuromorphic processor 115: Graphics Processing Unit 120: Random access memory 130: Device driver 140: Storage device 150: Modem 160: User Interfaces 200: OPC Module

Claims

Claim 1 A method of operation of an electronic device for manufacturing a semiconductor device, comprising: receiving a layout image of the semiconductor device; generating auxiliary features based on main features of the layout image to generate an intermediate image; performing a simulation based on the intermediate image to evaluate a process result; and modifying the intermediate image by modifying the shapes of the main features and / or auxiliary features of the intermediate image based on the process result, wherein the step of modifying the intermediate image includes calculating modification information of the intermediate image from a target slope of the change in light intensity at each boundary line of the main features and a slope of the change in light intensity. Claim 2 In claim 1, the method of operation in which the evaluating step and the modifying step are repeated until the modified result of the intermediate image matches the layout image. Claim 3 A method of operation according to claim 1, wherein the evaluating step comprises: generating a curvilinear image from the intermediate image; pixelating the curvilinear image to generate a mask image; performing an optical simulation on the mask image to generate an optical image; performing a photoresist simulation on the optical image to generate a photoresist image; and evaluating the process result based on the photoresist image. Claim 4 In paragraph 3, the step of generating the curved shape image comprises: generating a curve inscribed in the outline connecting each point of the main features as an element of the curved shape image corresponding to each of the main features. Claim 5 In paragraph 4, the step of modifying the intermediate image comprises: a method of operation including the step of adjusting the position of at least one of the points. Claim 6 A method of operation according to paragraph 3, comprising the step of generating a curve connecting each point of the main features as an element of the curve-shaped image corresponding to each of the main features. Claim 7 In claim 6, the step of modifying the intermediate image comprises: a method of operation including the step of adjusting the position of at least one of the points. Claim 8 In paragraph 3, the step of generating the curved shape image comprises: generating a curve based on a spline curve function from each point of the main features as an element of the curved shape image corresponding to each of the main features. Claim 9 A method of operation of an electronic device for manufacturing a semiconductor device, comprising: a step of calculating, based on a simulation and evaluation result based on a layout image including main features and auxiliary features, a change in the target slope of the change in light intensity with respect to a change in a photoresist image from a target slope of the change in light intensity at each boundary line of the main features; a step of calculating a change in the target slope of the change in light intensity with respect to a change in an optical image from a change in the target slope of the change in light intensity with respect to a change in the photoresist image; a step of calculating a change in the target slope of the change in light intensity with respect to a change in a mask image from a change in the target slope of the change in light intensity with respect to a change in the optical image; a step of calculating a change in the target slope of the change in light intensity with respect to a change in a curvilinear image from a change in the target slope of the change in light intensity with respect to a change in the mask image; and a step of calculating modification information of the layout image from a change in the target slope of the change in light intensity with respect to a change in the curvilinear image. Claim 10 A method of operation of an electronic device for manufacturing a semiconductor device, comprising: receiving a layout image of the semiconductor device; generating auxiliary features based on main features of the layout image to generate an intermediate image; generating a curvilinear image from the intermediate image; pixelating the curvilinear image to generate a mask image; performing an optical simulation on the mask image to generate an optical image; performing a photoresist simulation on the optical image to generate a photoresist image; calculating the slope of the change in light intensity at each boundary line of the main features; calculating the change in the target slope of the change in light intensity with respect to the change in the photoresist image from the target slope of the change in light intensity at each boundary line of the main features; calculating the change in the target slope of the change in light intensity with respect to the change in the optical image from the change in the target slope of the change in light intensity with respect to the change in the photoresist image; and calculating the change in the target slope of the change in light intensity with respect to the change in the mask image from the change in the target slope of the change in light intensity with respect to the change in the optical image. A method of operation comprising: a step of calculating; a step of calculating a change in the target slope of the change in light intensity for a change in a curvilinear image from a change in the target slope of the change in light intensity for a change in the mask image; and a step of calculating modification information of the layout image from a change in the target slope of the change in light intensity for a change in the curvilinear image.

Images