A charged particle beam lithography apparatus, a charged particle beam lithography method, and a readable recording medium that stores the program permanently.

Abstract

The objective is to provide an apparatus and method capable of reducing correction residuals when correcting resist heating in charged particle beam lithography. The charged particle beam lithography apparatus is characterized by comprising: an effective temperature calculation circuit (59) that calculates a representative value of the temperature rise that the heat from beam irradiation to the sample surface imparts to the mesh area of ​​interest, which is the mesh area of ​​interest, as the effective temperature of the mesh area of ​​interest, for each mesh area in which the mesh area is divided by a first direction and a second direction corresponding to the movement direction of the stage which is linearly independent of the first direction; and a modulation dose amount calculation unit (62) that calculates the modulation dose amount for each position by correcting the dose amount for each position defined in the dose map, using a function that uses an effective temperature distribution map in which the effective temperature is defined for each mesh area, an area density map for each position, and a backscattering coefficient for proximity effect correction.

Description

[Technical Field]

[0001] The present invention relates to a charged particle beam lithography apparatus, a charged particle beam lithography method, and a readable recording medium that stores a program rather than temporarily, and for example, to a method for correcting resist heating that occurs in charged particle beam lithography. [Background technology]

[0002] Lithography technology, which drives the miniaturization of semiconductor devices, is an extremely important process in semiconductor manufacturing, being the only process that generates patterns. In recent years, with the increasing integration of LSIs, the circuit line width required for semiconductor devices has been decreasing year by year. Electron beam lithography technology inherently possesses superior resolution, and is used to draw patterns on wafers and other materials.

[0003] For example, there are lithography systems that use multiple beams. Compared to lithography with a single electron beam, using multiple beams allows for the irradiation of many beams at once, significantly improving throughput. In such a multi-beam lithography system, for example, an electron beam emitted from an electron gun is passed through a mask with multiple holes to form multiple beams. Each beam is then blanked, and the unshielded beams are reduced by an optical system, deflected by a deflector, and irradiated to the desired position on the sample.

[0004] In electron beam lithography, attempting to irradiate with a higher density electron beam for a shorter time can lead to a problem called resist heating, where the substrate temperature overheats, changing the resist sensitivity and degrading linewidth accuracy. For example, in single-beam lithography, a method was used to determine the dose correction amount for the current shot by accumulating the effects of the temperature rise from each past shot by a single beam. However, in multi-beam lithography, multiple beams are used, so accumulating the effects of the temperature rise from each past shot and each beam becomes computationally intensive. Furthermore, in multi-beam lithography, since multiple beams are fired simultaneously, it is necessary to consider the effects of temperature rise from multiple other beams located in a wide area that is irradiated simultaneously.

[0005] Here, if heating correction is performed by dose modulation, the corrected dose amount will deviate from the correction conditions of the proximity effect correction performed before the heating correction. As a result, problems such as correction residuals in the proximity effect correction may occur. Regarding this point, although it is not a heating correction, a method has been disclosed for re-determining the proximity effect correction coefficient of the dose amount that takes into account edge and corner correction by dose variables (see, for example, Patent Document 1). [Prior art documents] [Patent Documents]

[0006] [Patent Document 1] Patent No. 6523767 [Overview of the project] [Problems that the invention aims to solve]

[0007] One aspect of the present invention provides an apparatus and method capable of reducing correction residuals when correcting resist heating in charged particle beam lithography. [Means for solving the problem]

[0008] A charged particle beam lithography apparatus according to one aspect of the present invention is A dose map creation circuit creates a dose map that defines the amount of dose incident at each of multiple locations within each of multiple stripe regions, which are formed by dividing the drawing area on the sample surface irradiated with a charged particle beam in a first direction. An effective temperature calculation circuit calculates a representative value of the temperature rise that the heat from beam irradiation on the sample surface imparts to the mesh region of interest, which is the mesh region of interest, for each of the multiple mesh regions in which each stripe region is divided by a first direction and a second direction corresponding to the movement direction of the stage which is linearly independent of the first direction, as the effective temperature of the mesh region of interest. A modulation dose calculation unit calculates the modulated dose amount for each position by correcting the dose amount for each position defined in the dose map, using a function that uses an effective temperature distribution map in which the effective temperature is defined for each mesh region, an area density map for each position, and a backscattering coefficient for proximity effect correction. A drawing mechanism that draws a pattern on the sample using a modulated dose of charged particle beam, It is characterized by having the following features.

[0009] A charged particle beam lithography method according to one aspect of the present invention is: For each of the multiple stripe regions within each stripe region, where the drawing area on the sample surface irradiated with a charged particle beam is divided in a first direction, a dose map is created that defines the amount of dose incident at that position. Within each stripe region, a representative value of the temperature rise imparted to the mesh region of interest by the heat generated by beam irradiation on the sample surface is calculated as the effective temperature of the mesh region of interest, for each of the multiple mesh regions divided by a first direction and a second direction corresponding to the linearly independent movement direction of the stage. Using a function that employs an effective temperature distribution map with defined effective temperatures for each mesh region, an area density map for each location, and a backscattering coefficient for proximity effect correction, the modulated dose amount for each location is calculated by correcting the dose amount for each location defined in the dose map. Drawing a pattern on a sample using a charged particle beam with a modulated dose amount characterized by comprising

[0010] A readable recording medium that temporarily stores the program of one aspect of the present invention For each position of a plurality of positions within each stripe region of a plurality of stripe regions into which a drawing region on a sample surface irradiated with a charged particle beam is divided in a first direction, creating a dose map in which the dose amount incident on that position is defined For each mesh region of a plurality of mesh regions into which each stripe region is divided by a first direction and a second direction corresponding to the moving direction of a stage linearly independent of the first direction, calculating, as the effective temperature of the target mesh region, a representative value of the rising temperature given to the target mesh region, which is the mesh region, by heat due to beam irradiation on the sample surface Function of storing an effective temperature distribution map in which the effective temperature is defined for each mesh region in a storage device Reading the effective temperature distribution map from the storage device and calculating the modulated dose amount for each position obtained by correcting the dose amount for each position defined in the dose map using a function using the effective temperature distribution map, the area density map for each position, and the backscattering coefficient for proximity effect correction Function of drawing a pattern on a sample using a charged particle beam with a modulated dose amount Temporarily stores a program for causing a computer to execute

Advantages of the Invention

[0011] According to one aspect of the present invention, in charged particle beam lithography, when correcting resist heating, the correction residual can be reduced.

Brief Description of the Drawings

[0012] [Figure 1] It is a conceptual diagram showing the configuration of a drawing apparatus in Embodiment 1. [Figure 2] It is a conceptual diagram showing the configuration of a shaping aperture array substrate in Embodiment 1. [Figure 3] It is a cross-sectional view showing the configuration of the blanking aperture array mechanism in Embodiment 1. [Figure 4] It is a top conceptual view showing a part of the configuration within the membrane region of the blanking aperture array mechanism in Embodiment 1. [Figure 5] It is a diagram showing an example of the individual blanking mechanism of Embodiment 1. [Figure 6] It is a conceptual diagram for explaining an example of the drawing operation in Embodiment 1. [Figure 7] It is a diagram showing an example of the irradiation region of the multi-beam and the drawing target pixel in Embodiment 1. [Figure 8] It is a diagram for explaining an example of the multi-beam drawing operation in Embodiment 1. [Figure 9] It is a diagram showing an example of the relationship between the temperature distribution and temperature caused by the irradiation of one beam to the region of one beam pitch in the comparative example of Embodiment 1. [Figure 10] It is a diagram showing an example of the relationship between the temperature distribution and temperature caused by the simultaneous irradiation of the multi-beam in Embodiment 1. [Figure 11] It is a diagram for explaining an example of proximity effect correction in the state without resist heating in the comparative example of Embodiment 1. [Figure 12] It is a diagram for explaining the relationship between the pattern area density, proximity effect correction dose amount, and resolution threshold in the comparative example of Embodiment 1. [Figure 13] It is a diagram showing an example of the accumulation energy distribution and an example of the CD distribution in the state without resist heating and the state with resist heating in Embodiment 1. [Figure 14] It is a diagram showing an example of the accumulation energy distribution and an example of the CD distribution in the state after heating correction in Embodiment 1. [Figure 15] It is a diagram showing an example of the accumulation energy distribution of the pattern after the influence of the heating effect before and after the heating effect correction in Embodiment 1. [Figure 16]This figure illustrates an example of the process for deriving the correction term in Embodiment 1. [Figure 17] This figure illustrates another example of the process for deriving the correction term in Embodiment 1. [Figure 18] This is a flowchart illustrating an example of the main steps of the drawing method in Embodiment 1. [Figure 19] This is a block diagram showing an example of the internal configuration of the effective temperature calculation processing unit in Embodiment 1. [Figure 20] This figure shows an example of the processing mesh in Embodiment 1. [Figure 21] This is a diagram illustrating the method for calculating the effective temperature in Embodiment 1. [Figure 22] This figure illustrates a part of the formula for calculating the effective temperature in Embodiment 1. [Figure 23] This figure illustrates an example of a formula for calculating the heat spreading function in Embodiment 1. [Figure 24] This figure illustrates another part of the formula for calculating the effective temperature in Embodiment 1. [Figure 25] This figure illustrates another part of the formula for calculating the effective temperature in Embodiment 1. [Figure 26] This figure illustrates another part of the formula for calculating the effective temperature in Embodiment 1. [Figure 27] This figure illustrates an example of a virtual model of the effective temperature in Embodiment 1. [Figure 28] This is a diagram illustrating an example of the kernel derivation process in Embodiment 1. [Figure 29] This figure shows another example of the kernel derivation process in Embodiment 1. [Figure 30] This figure shows another example of the kernel derivation process in Embodiment 1. [Figure 31] This is a diagram illustrating the kernel in Embodiment 1. [Figure 32] This figure shows an example of the relationship between stage speed and kernel in Embodiment 1. [Figure 33] This figure shows an example of the relationship between the movement direction size of the beam array and the kernel in Embodiment 1. [Figure 34] This figure shows another example of the relationship between the movement direction size of the beam array and the kernel in Embodiment 1. [Figure 35] This figure shows an example of a kernel defined as a table in Embodiment 1. [Figure 36] This figure shows an example of a kernel expression defined as a continuous function in Embodiment 1. [Figure 37] This is a diagram illustrating the method for calculating the effective temperature in Embodiment 1. [Figure 38] This figure shows an example of the relationship between line width CD and temperature in Embodiment 1. [Figure 39] This figure shows an example of the relationship between line width CD and dose amount in Embodiment 1. [Figure 40] This figure shows an example of the stored energy distribution and CD distribution after heating effect correction in Embodiment 1. [Figure 41] This is a conceptual diagram showing the configuration of the drawing device in Embodiment 2. [Figure 42] This is a flowchart illustrating an example of the main steps of the drawing method in Embodiment 2. [Figure 43] This figure shows an example of the stored energy distribution when the maximum effective temperature is varied and the heating effect is corrected using the method of Embodiment 1. [Figure 44] This figure illustrates an example of the process for deriving the correction term in Embodiment 2. [Figure 45] This figure shows an example of the stored energy distribution when the maximum effective temperature in Embodiment 2 is varied and the heating effect is corrected. [Modes for carrying out the invention]

[0013] In the following embodiments, an electron beam configuration will be described as an example of a charged particle beam. However, the charged particle beam is not limited to an electron beam; it may also be a beam using charged particles such as an ion beam.

[0014] [Embodiment 1] Figure 1 is a conceptual diagram showing the configuration of a lithography apparatus in Embodiment 1. In Figure 1, the lithography apparatus 100 includes a lithography mechanism 150 and a control system circuit 160. The lithography apparatus 100 is an example of a multi-charged particle beam lithography apparatus and an example of a multi-charged particle beam exposure apparatus. The lithography mechanism 150 includes an electron tube 102 (electron beam column) and a lithography chamber 103. Inside the electron tube 102 are an electron gun 201, an illumination lens 202, a shaped aperture array substrate 203, a blanking aperture array mechanism 204, a reduction lens 205, a limiting aperture substrate 206, an objective lens 207, a main deflector 208, and a sub-deflector 209. Inside the lithography chamber 103 is an XY stage 105. On the XY stage 105 is a sample 101, such as a mask, which will be the substrate to be lithographed during lithography (exposure). Sample 101 includes an exposure mask used in the manufacturing of a semiconductor device, or a semiconductor substrate (silicon wafer) on which a semiconductor device is manufactured. Sample 101 is also coated with resist. Sample 101 includes, for example, a mask blank with resist coated but no drawing yet. A mirror 210 for position measurement of the XY stage 105 is also placed on the XY stage 105.

[0015] The control system circuit 160 includes a control computer 110, memory 112, deflection control circuit 130, digital-to-analog converter (DAC) amplifier units 132 and 134, lens control circuit 136, stage control mechanism 138, stage position measuring instrument 139, and storage devices 140, 142, and 144 such as magnetic disk drives. The control computer 110, memory 112, deflection control circuit 130, lens control circuit 136, stage control mechanism 138, stage position measuring instrument 139, and storage devices 140, 142, and 144 are connected to each other via a bus (not shown). The deflection control circuit 130 is connected to the DAC amplifier units 132 and 134 and the blanking aperture array mechanism 204. The sub-deflector 209 is composed of four or more electrodes, and each electrode is controlled by the deflection control circuit 130 via its respective DAC amplifier 132. The main deflector 208 is composed of four or more electrodes, and each electrode is controlled by the deflection control circuit 130 via its respective DAC amplifier 134. The stage position measuring instrument 139 measures the position of the XY stage 105 using the principle of laser interferometry by receiving reflected light from the mirror 210.

[0016] The control computer 110 includes a pattern density calculation unit 50, a dose calculation unit 52, an effective temperature calculation processing unit 59, a modulation rate calculation unit 60, a correction unit 62, an irradiation time data generation unit 72, a data processing unit 74, a transfer control unit 79, and a drawing control unit 80. Each of these "~units" has a processing circuit. Such processing circuits include, for example, electrical circuits, computers, processors, circuit boards, quantum circuits, or semiconductor devices. Each of these "~units" may use a common processing circuit (the same processing circuit) or different processing circuits (separate processing circuits). Information input to and output to the pattern density calculation unit 50, dose amount calculation unit 52, effective temperature calculation processing unit 59, modulation rate calculation unit 60, correction unit 62, irradiation time data generation unit 72, data processing unit 74, transfer control unit 79, and drawing control unit 80, as well as information being calculated, are stored in the memory 112 each time.

[0017] The drawing operation of the drawing device 100 is controlled by the drawing control unit 80. Furthermore, the transfer process of the irradiation time data for each shot to the deflection control circuit 130 is controlled by the transfer control unit 79.

[0018] Furthermore, chip data is input from outside the drawing device 100 and stored in the storage device 140. The drawing data includes chip data and drawing condition data. For each graphic pattern, the chip data defines, for example, a graphic code, coordinates, and size. The drawing condition data includes information indicating the multiplicity and the stage speed.

[0019] Furthermore, the storage device 144 stores correlation data, which will be described later, for calculating the modulation rate used to correct the resist heating.

[0020] Here, Figure 1 shows the configuration necessary to explain Embodiment 1. The drawing device 100 may also have other configurations that are normally necessary.

[0021] Figure 2 is a conceptual diagram showing the configuration of a molded aperture array substrate in Embodiment 1. In Figure 2, the molded aperture array substrate 203 has holes (openings) 22 formed in a matrix with a predetermined arrangement pitch, arranged in p columns vertically (y direction) and q columns horizontally (x direction) (p,q≧2). In the example in Figure 2, for example, it shows a case where 500 columns × 500 rows of holes 22 are formed in the horizontal and vertical (x,y directions). The number of holes 22 is not limited to this. Each hole 22 is formed as a rectangle of the same dimensions and shape. Alternatively, they may be circles of the same diameter. A portion of the electron beam 200 passes through each of these multiple holes 22, thereby forming a multi-beam 20. In other words, the molded aperture array substrate 203 forms a multi-beam 20.

[0022] Figure 3 is a cross-sectional view showing the configuration of the blanking aperture array mechanism in Embodiment 1. Figure 4 is a top-view conceptual diagram showing a part of the configuration within the membrane region of the blanking aperture array mechanism in Embodiment 1. Note that the positional relationships of the control electrode 24, counter electrode 26, control circuit 41, and pad 343 are not shown in the same way in Figures 3 and 4. As shown in Figure 3, the blanking aperture array mechanism 204 has a blanking aperture array substrate 31 made of a semiconductor substrate such as silicon placed on a support base 33. In the membrane region 330 in the center of the blanking aperture array substrate 31, through holes 25 (openings) for the passage of each beam of the multi-beam 20 are opened at positions corresponding to each hole 22 of the molded aperture array substrate 203 shown in Figure 2. Then, for each of the multiple through holes 25, a set of control electrode 24 and counter electrode 26 (blanker: blanking deflector) is placed at a position opposite to the through hole 25. Furthermore, a control circuit 41 (logic circuit; cell) that applies a deflection voltage to the control electrode 24 for each through hole 25 is arranged inside the blanking aperture array substrate 31 near each through hole 25. The counter electrode 26 for each beam is connected to ground.

[0023] Furthermore, as shown in Figure 4, each control circuit 41 is connected to an n-bit (e.g., 10-bit) parallel wiring for control signals. In addition to the n-bit parallel wiring for irradiation time control signals (data), each control circuit 41 is also connected to wiring for clock signals, load signals, shot signals, and power supply. These wirings may utilize some of the wiring of the parallel wiring. For each beam constituting the multi-beam 20, an individual blanking mechanism 47 is configured, consisting of a control electrode 24, a counter electrode 26, and a control circuit 41. In Embodiment 1, for example, a shift register method is used as the data transfer method. In the shift register method, the multi-beam 20 is divided into multiple groups for each of the multiple beams, and multiple shift registers for multiple beams within the same group are connected in series. Specifically, the multiple control circuits 41 formed in an array on the membrane region 330 are grouped, for example, at a predetermined pitch within the same row or column. The groups of control circuits 41 within the same group are connected in series, as shown in Figure 4. Signals from the pads 343 arranged for each group are transmitted to the control circuits 41 within the group.

[0024] Figure 5 shows an example of the individual blanking mechanism of Embodiment 1. In Figure 5, an amplifier 46 (an example of a switching circuit) is arranged within the control circuit 41. In the example of Figure 5, a CMOS (Complementary MOS) inverter circuit, which is a switching circuit, is arranged as an example of the amplifier 46. Either an L (low) potential (e.g., ground potential) that is lower than the threshold voltage or an H (high) potential (e.g., 1.5V) that is higher than the threshold voltage is applied as a control signal to the input (IN) of the CMOS inverter circuit. In Embodiment 1, when an L potential is applied to the input (IN) of the CMOS inverter circuit, the output (OUT) of the CMOS inverter circuit applied to the control circuit 41 becomes a positive potential (Vdd), and the electric field due to the potential difference with the ground potential of the counter electrode 26 deflects the corresponding beam 20, which is then shielded by the limiting aperture substrate 206 to control it to the OFF state. On the other hand, when a high potential is applied to the input (IN) of the CMOS inverter circuit (active state), the output (OUT) of the CMOS inverter circuit becomes ground potential, and the potential difference with the ground potential of the counter electrode 26 disappears, so the corresponding beam 20 is not deflected, and the control is made so that the beam turns ON when it passes through the limiting aperture substrate 206. Blanking control is performed by this deflection.

[0025] Then, each individual blanking mechanism 47 controls the irradiation time of the shot individually for each beam using a counter circuit (not shown) in accordance with the irradiation time control signal transferred for each beam.

[0026] Next, a specific example of the operation of the drawing mechanism 150 will be described. The electron beam 200 emitted from the electron gun 201 (emission source) illuminates the entire molded aperture array substrate 203 almost vertically by the illumination lens 202. Multiple rectangular holes 22 (openings) are formed in the molded aperture array substrate 203, and the electron beam 200 illuminates the area containing all of the multiple holes 22. Each portion of the electron beam 200 irradiated at the location of the multiple holes 22 passes through each of the multiple holes 22 in the molded aperture array substrate 203, thereby forming, for example, a rectangular multi-beam (multiple electron beams) 20. These multi-beams 20 pass through their respective blankers (first deflectors: individual blanking mechanisms 47) of the blanking aperture array mechanism 204. Each of these blankers individually controls the blanking of the passing beam so that the beam remains ON for a set drawing time (irradiation time).

[0027] The multi-beam 20 that has passed through the blanking aperture array mechanism 204 is reduced by the reduction lens 205 and travels toward the central hole formed in the limiting aperture substrate 206. Here, the electron beam deflected by the blanker of the blanking aperture array mechanism 204 is moved away from the central hole in the limiting aperture substrate 206 and is shielded by the limiting aperture substrate 206. On the other hand, the electron beam that was not deflected by the blanker of the blanking aperture array mechanism 204 passes through the central hole in the limiting aperture substrate 206 as shown in Figure 1. In this way, the limiting aperture substrate 206 shields each beam that has been deflected by the individual blanking mechanism 47 to the beam-OFF state. Then, each beam of one shot is formed by the beams that have passed through the limiting aperture substrate 206 from the time the beam is turned ON until it is turned OFF. The multi-beams 20 that have passed through the limiting aperture substrate 206 are focused by the objective lens 207 to form a pattern image with a desired reduction ratio. The main deflector 208 and sub-deflector 209 then deflect the entire multi-beams 20 that have passed through the limiting aperture substrate 206 in the same direction, illuminating each beam at its respective irradiation position on the sample 101. Furthermore, for example, when the XY stage 105 is moving continuously, tracking control is performed by deflecting the multi-beams 20 with the main deflector 208 so that the irradiation position of the beams follows the movement of the XY stage 105. Ideally, the multi-beams 20 irradiated at one time will be arranged at a pitch obtained by multiplying the arrangement pitch of the multiple holes 22 in the molded aperture array substrate 203 by the desired reduction ratio described above.

[0028] Figure 6 is a conceptual diagram illustrating an example of the drawing operation in Embodiment 1. As shown in Figure 6, the drawing area 30 of the sample 101 is virtually divided into multiple stripe-shaped areas 32 with a predetermined width in the y direction, for example. First, the XY stage 105 is moved to adjust the position of the irradiation area 34 that can be irradiated with a single shot of the multi-beam 20 to the left end of the first stripe area 32, or further to the left, and drawing is started. When drawing the first stripe area 32, the drawing is advanced relatively in the x direction by moving the XY stage 105, for example, in the -x direction. The XY stage 105 is moved continuously at a constant speed, for example. After the drawing of the first stripe area 32 is completed, the stage position is moved in the -y direction, and then the XY stage 105 is moved, for example, in the x direction, to perform drawing in the same way in the -x direction. This operation is repeated to draw each stripe area 32 in order. Drawing time can be shortened by drawing while alternating directions. However, drawing is not limited to alternating directions; when drawing each stripe region 32, drawing may proceed in the same direction. When the XY stage 105 is moved at a constant speed, the continuous movement speed may differ for each stripe. In a single shot, multiple shot patterns, up to the same number as each hole 22, are formed at once by the multi-beam formed by passing through each hole 22 of the molded aperture array substrate 203.

[0029] Figure 7 shows an example of the multi-beam irradiation area and the pixels to be drawn in Embodiment 1. In Figure 7, the stripe area 32 is divided into multiple mesh areas, for example, by the beam size of the multi-beam 20. Each of these mesh areas becomes the pixels 36 to be drawn (unit irradiation area, irradiation position, or drawing position). The size of the pixels 36 to be drawn is not limited to the beam size, and may be composed of any size regardless of the beam size. For example, it may be composed of a size of 1 / a (where a is an integer of 1 or more) of the beam size. In the example in Figure 7, the drawing area 30 of the sample 101 is shown as being divided into multiple stripe areas 32 with substantially the same width size as the irradiation area 34 (beam array area) that can be irradiated with one irradiation of the multi-beam 20 in the y direction. The size of the rectangular irradiation area 34 in the x direction can be defined by the number of beams in the x direction × the beam pitch in the x direction. The size of the rectangular irradiation area 34 in the y direction can be defined by the number of beams in the y direction × the beam pitch in the y direction. In the example in Figure 7, for example, a 500x500 multibeam is shown as an 8x8 multibeam. Within the irradiation area 34, multiple pixels 28 (beam drawing positions) that can be irradiated in one shot of the multibeam 20 are shown. The pitch between adjacent pixels 28 on the sample surface becomes the pitch between each beam of the multibeam 20. A rectangular area enclosed by the beam pitch size in the x,y directions constitutes one sub-irradiation area 29 (pitch cell). Each sub-irradiation area 29 contains one pixel 28. In the example in Figure 7, for example, the pixel at the upper left corner of each sub-irradiation area 29 is shown as the pixel 28 that will be the beam drawing position. Each sub-irradiation area 29 consists of, for example, 10x10 pixels. In the example in Figure 7, for example, each sub-irradiation area 29 of 10x10 pixels is shown as, for example, 4x4 pixels.

[0030] Figure 8 is a diagram illustrating an example of multi-beam lithography operation in Embodiment 1. The example in Figure 8 shows a case where each sub-irradiation area 29 on the surface of sample 101 is lithographed with 10 different beams. Furthermore, the example in Figure 8 shows a lithography operation in which the XY stage 105 moves continuously at a speed of, for example, a distance L equivalent to 25 beam pitches while lithographing 1 / 10 (1 / 2 the number of beams used for irradiation) of each sub-irradiation area 29. In the lithography operation shown in the example in Figure 8, for example, while the XY stage 105 moves a distance L equivalent to 25 beam pitches, the irradiation position (pixel 36) is sequentially shifted by the sub-deflector 209 while the shot cycle time t trk-cycle This shows a case where 10 different pixels within the same sub-irradiation area 29 are drawn (exposed) by firing the multi-beam 20 10 times. While drawing (exposing) these 10 pixels, the entire multi-beam 20 is deflected collectively by the main deflector 208 so that the irradiation area 34 does not shift relative to the sample 101 due to the movement of the XY stage 105, thereby causing the irradiation area 34 to follow the movement of the XY stage 105. In other words, tracking control is performed. Therefore, the distance L that is deflected collectively by the main deflector 208 during each tracking control is the tracking distance.

[0031] Once a tracking cycle is completed, the tracking is reset and returned to the previous tracking start position. Since the first row of pixels from the top of each sub-irradiation area 29 has already been drawn, after the tracking reset, the sub-deflector 209 first deflects the beam to adjust (shift) its drawing position so that it can draw the undrawn pixel column, for example, the second row from the top, in each sub-irradiation area 29 in the next tracking cycle. In this way, the pixel column to be drawn next is changed with each tracking reset. During 10 tracking control cycles, each pixel 36 within each sub-irradiation area 29 is drawn once. By repeating this operation while drawing the stripe area 32, the position of the irradiation area 34 moves sequentially, such as irradiation area 34a to 34o, as shown in Figure 6, and the stripe area 32 is drawn accordingly.

[0032] In the example shown in Figure 8, the sub-irradiation area 29 on the sample surface, located at the lower right corner of the irradiation area 34 with width W, moves to a position L to the left of the lower right corner of the irradiation area 34 during the second tracking control. Therefore, the sub-irradiation area 29, located at the lower right corner of the irradiation area 34 during the first tracking control, is drawn by another beam located at a distance L to the left of the lower right corner of the irradiation area 34 during the second tracking control. In this case, it is drawn by a beam located, for example, 25 beams away in the -x direction from the beam at the lower right corner.

[0033] For example, in a drawing process where the multiplicity is set to 2 per stage pass, each pixel 36 within each sub-illumination area 29 can be drawn twice through 20 tracking controls.

[0034] Figure 9 shows an example of the relationship between the temperature distribution and temperature in a comparative example of Embodiment 1, caused by irradiation of a region the size of one beam pitch with a single beam. In Figure 9, the vertical axis shows temperature, and the horizontal axis shows the temperature distribution. As shown in Figure 9, the temperature distribution caused by irradiation with a single beam has a wide base region. Therefore, it affects a wide area. However, the temperature rise from a single beam is small, at most 0.01°C or less, as an effect on the base region.

[0035] Figure 10 shows an example of the relationship between temperature and temperature resulting from simultaneous irradiation of multiple beams in Embodiment 1. In Figure 10, the vertical axis shows temperature and the horizontal axis shows temperature distribution. The temperature rise from a single beam is at most 0.01°C or less, but for example, when 500 × 500 = 250,000 beams are irradiated simultaneously, the temperature rises from each beam will overlap in the lower region, as shown in Figure 10. As a result, for example, when 500 × 500 = 250,000 beams are irradiated simultaneously, a significant temperature rise occurs in the lower region.

[0036] While techniques for predicting and correcting heating effects in single-beam lithography are known, there has been no precedent for correcting heating effects in multi-beam lithography systems where, for example, 250,000 beams are fired simultaneously multiple times per stage pass. Calculating the heat generated by each of the 250,000 beams, as in a single-beam system, is not practical due to the computational volume involved.

[0037] In multi-beam lithography, the current density J is extremely small compared to, for example, a single-beam VSB system, so the temperature rises slowly. During this time, the temperature distribution per shot is diffused by several tens of micrometers. Therefore, even if the shot data and dose data within the stripe are divided and calculated together to some extent, sufficient accuracy can be obtained. Also, as mentioned above, since multi-beam lithography uses a raster scan method, the position is determined by time. Therefore, if the dose data and lithography speed (stage speed or tracking cycle time) are determined, the temperature rise can be determined. This allows for simpler correction than VSB lithography, which requires both position and time.

[0038] Therefore, in Embodiment 1, dose information of the stripe region 32 is distributed to Nx × Ny pixel information containing the mesh of interest for which the temperature should be determined. The temperature rise during each of the multiple beam irradiations is calculated for the mesh of interest. Then, a statistical value (e.g., the average value) of this temperature rise is used as the effective temperature (effective temperature T) for heating correction. This will be explained in detail below.

[0039] Figure 11 illustrates an example of proximity effect correction without resist heating in a comparative example of Embodiment 1. Figure 11 shows the case where a line and space pattern with an area density of 30% and a line and space pattern with an area density of 50% are drawn. The proximity effect correction dose Dpec can be defined by equations (1-1) to (1-3) using the function dn(x), proximity effect density U(x), V(x), distribution function g(x), and reference irradiation dose Db. Note that the proximity effect density U(x) is defined by equation (1-4). Equation (1-4) shows the convolution integral of the pattern area density ρ′(x) and the distribution function g(x) within the proximity mesh. The proximity effect density V(x) is defined by equation (1-5). An example of the distribution function g(x) is defined by equation (1-6).

[0040] Figure 11 shows graphs of the proximity-corrected stored energy distribution for line-and-space patterns with 30% area density and 50% area density. The vertical axis represents stored energy, and the horizontal axis represents the position in the x-direction. The stored energy distribution shows the sum of the energy due to backscattering ηUDpec, defined using the proximity-corrected dose Dpec and the backscattering coefficient η.

[0041] Figure 12 is a diagram illustrating the relationship between pattern area density, proximity effect correction dose, and resolution threshold in a comparative example of Embodiment 1. In proximity effect correction, the resolution threshold is modeled so that the ISO-FOCAL level, which is the inflection point position of the energy distribution where the line width CD does not change even if the blur changes, becomes the resolution threshold. In an ideal state without resist heating, the ISO-FOCAL level is a dose amount equal to half of the proximity effect correction dose amount Dpec plus the accumulated energy ηUDpec due to backscattering. The proximity effect correction dose amount Dpec depends on the pattern area density. Therefore, as shown in Figure 12, there is a difference in the proximity effect correction dose amount Dpec between a line and space pattern with an area density of 30% and a line and space pattern with an area density of 50%. The proximity effect correction dose amount Dpec for the line and space pattern with a smaller area density of 30% is larger than the proximity effect correction dose amount Dpec for the line and space pattern with a 50% area density.

[0042] Figure 13 shows an example of the stored energy distribution and CD distribution in Embodiment 1, under conditions without resist heating and with resist heating. In the stored energy distribution of Figure 13, the portion above and below the ISO-FOCAL dose level is shown in different colors. Therefore, the boundary between the two colors indicates the ISO-FOCAL dose level. In the stored energy distribution where dose modulation is performed by proximity effect correction in the ideal state without resist heating, as shown in Figure 13, the resolution threshold Dth is obtained by adding the stored energy ηUDpec due to backscattering to half of the proximity effect correction dose amount Dpec. However, in reality, for example, resist heating (heating effect) occurs due to the effective temperature T(x) defined in the effective temperature distribution shown in Figure 13. Specifically, due to the heating effect, the stored energy increases by αT(x)Dpec, which is obtained by multiplying the modulation rate α by the effective temperature T(x) and the proximity effect correction dose amount Dpec. Therefore, as shown in the distribution with heating in Figure 13, the ISO-FOCAL dose level exceeds the resolution threshold. Consequently, as shown in the CD distribution, the line width CD of the pattern changes by the amount of increase in stored energy. In other words, the dose for pattern formation becomes (1+αT(x)) times the expected (1+αT(x))Dpec, resulting in a non-uniform CD distribution.

[0043] Figure 14 shows an example of the stored energy distribution and CD distribution in the state after heating correction in Embodiment 1. In the stored energy distribution of Figure 14, the portion above and below the ISO-FOCAL dose level is shown in different colors. Therefore, the boundary between the two colors indicates the ISO-FOCAL dose level. As described above, the stored energy increases by αT(x)Dpec due to the heating effect, so in the heating effect correction, this amount is subtracted from the dose amount before correction. In other words, the heating effect can be corrected by setting the heating effect correction dose amount Dtec = (1 - αT(x))Dpec. However, as shown in Figure 14, the stored energy distribution after heating effect correction results in overcorrection, where the ISO-FOCAL dose level falls below the resolution threshold. Consequently, as shown in the CD distribution, the pattern line width CD deviates from the design value by the amount of overcorrection.

[0044] One factor contributing to the CD shift in the CD distribution is the dose modulation caused by heating effect correction, which deviates from the proximity effect correction conditions before heating effect correction. Another factor is the discrepancy between the effective temperature used for heating effect correction and the actual effective temperature during beam irradiation after correction.

[0045] Figure 15 shows an example of the stored energy distribution of the pattern after the influence of the heating effect, before and after the heating effect correction in Embodiment 1. As shown in equation (1-7) of Figure 15, in the state before the heating effect correction, the resolution threshold Dth is the level obtained by adding the stored energy ηUDpec due to backscattering to half of the proximity effect correction dose Dpec. When the heating effect is introduced into this state, the stored energy of the pattern after the influence of the heating effect can be approximated as Dpec(1+αTpec) using the effective temperature Tpec calculated in the state before the heating effect correction.

[0046] On the other hand, after correcting for the heating effect, the dose becomes the corrected dose Dtec. Since the corrected dose Dtec is smaller than the corrected dose Dpec, the level obtained by adding the backscattered storage energy ηUDtec to half of the corrected dose Dtec is smaller than the resolution threshold Dth. Furthermore, when the heating effect is present in this state, the actual storage energy can be approximated as Dtec(1+αTtec) using the effective temperature Ttec calculated in the state after correcting for the heating effect. Therefore, in order to satisfy the proximity effect correction condition after the heating effect, as shown in equation (1-8), the level obtained by adding the backscattered storage energy ηUDtec to half of Dtec(1+αTtec) must match the resolution threshold Dth. Therefore, the dose should be corrected so that equation (1-9) is satisfied, where the value obtained by adding the backscattered stored energy ηUDtec to half of Dtec(1+αTtec) matches the value obtained by adding the backscattered stored energy ηUDpec to half of the proximity effect corrected dose Dpec.

[0047] Figure 16 is a diagram illustrating an example of the process for deriving the correction term in Embodiment 1. Figure 17 is a diagram illustrating another example of the process for deriving the correction term in Embodiment 1. The effective temperature Ttec can be defined by equation (1-10), which involves convolving kernel K(x) and Dtec(x) / PASS using the kernel K(x) described later. Here, the value obtained by dividing Dtec by the number of passes is used as the dose amount per drawing process (1 pass) when performing multiple drawing. Therefore, equation (1-9) can be transformed into equation (1-11).

[0048] Here, we define the difference ΔD between Dtec and Dpec as shown in equation (1-12). By substituting equation (1-12) into equation (1-11), we can obtain equation (1-13). Here, we approximate that the difference ΔD is infinitesimal, and furthermore, due to the characteristics of the heating effect in multi-beam systems, its change within the integral range is also infinitesimal and can be ignored, so we take it outside the integral. Then, rearranging with respect to ΔD, we can obtain equation (1-14).

[0049] The difference ΔD is small, and ΔD in equation (1-14) 2 Ignoring the first term, the difference ΔD can be defined by equation (1-15). Substituting the obtained ΔD into equation (1-12) and transforming it, Dtec can be transformed into equation (1-16). The correction term function β(x) is defined using the effective temperature Tpec(x), proximity density U(x), backscattering coefficient η, and modulation index α(x). The function β(x) can be defined by equation (1-17).

[0050] By plotting with a beam whose heating effect correction dose Dtec(x) is obtained by correcting the proximity effect correction dose Dpec(x) using the function β(x), the correction residual of the pattern line width CD due to the heating effect correction can be eliminated or reduced. The plotting method using the function β(x) will be described below.

[0051] Figure 18 is a flowchart showing an example of the main steps of the drawing method in Embodiment 1. In Figure 18, the drawing method in Embodiment 1 performs a series of steps: pattern density calculation step (S102), dose amount calculation step (S104), effective temperature calculation step (S112), modulation rate calculation step (S114), correction step (S130), irradiation time data generation step (S140), data processing step (S142), and drawing step (S144).

[0052] First, drawing data is read from the storage device 140 for each stripe area 32.

[0053] In the pattern density calculation step (S102), the pattern density calculation unit 50 calculates the pattern density ρ (area density of the pattern) for each pixel 36 within the target stripe region 32. For each stripe region 32, the pattern density calculation unit 50 creates a pattern density map using the calculated pattern density ρ of each pixel 36. The pattern density of each pixel 36 is defined as an element of the pattern density map. The created pattern density map is stored in the storage device 144.

[0054] As a dose calculation step (S104), the dose calculation unit 52 (an example of a dose map creation circuit) creates a dose map that defines the dose amount incident on each pixel 36 at each of the multiple pixels 36 (positions) within each of the multiple stripe regions 32. The dose amount corrected for proximity effect is used as the dose amount defined in the dose map. Each stripe region 32 represents one of the multiple stripe regions 32 whose drawing area on the surface of the sample 101 irradiated by the multibeam 20 is divided in the y direction by the size of the beam array area of ​​the multibeam 20 on the surface of the sample 101, for example in the y direction (first direction). Specifically, it operates as follows: The dose calculation unit 52 calculates the dose amount (irradiation amount) to irradiate each pixel 36. Here, it is sufficient to calculate the value obtained by multiplying the proximity effect corrected dose amount Dpec for each proximity mesh by the pattern density ρ for each pixel 36. For the proximity effect correction dose Dpec for each nearby mesh, the drawing area (here, for example, the stripe area 32) is virtually divided into multiple nearby mesh areas (mesh areas for proximity effect correction calculation) of a predetermined size. The size of the nearby mesh area is preferably set to about 1 / 10 of the area affected by the proximity effect, for example, about 1 μm. Then, the drawing data is read from the storage device 140, and for each nearby mesh area, the pattern area density ρ' of the pattern placed within that nearby mesh area is calculated.

[0055] Next, for each adjacent mesh region, a proximity effect correction dose amount Dpec is calculated to correct for the proximity effect. Here, the size of the mesh region for which the proximity effect correction dose amount Dpec is calculated does not need to be the same as the size of the mesh region for which the pattern area density ρ' is calculated. Furthermore, the correction model and calculation method for the proximity effect correction dose amount Dpec can be the same as the method used in conventional single-beam lithography. For example, it can be calculated using equations (1-1) to (1-6) described above.

[0056] The dose calculation unit 52 then creates a dose map (1) for each stripe region 32 using the calculated proximity effect corrected dose amount Dpec(x) for each pixel 36. The proximity effect corrected dose amount Dpec(x) for each pixel 36 is defined as the value obtained by multiplying the proximity effect corrected dose amount Dpec for each nearby mesh by the pattern density ρ for each pixel 36. The proximity effect corrected dose amount Dpec(x) for each pixel 36 may also be calculated as a relative value to the reference irradiation dose Db, normalized by assuming the reference irradiation dose Db is 1. The created dose map (1) is stored in the storage device 144.

[0057] In the effective temperature calculation step (S112), the effective temperature calculation processing unit 59 (effective temperature calculation processing circuit) calculates a representative value of the temperature rise that the heat from beam irradiation on the surface of the sample 101 imparts to the mesh of interest, which is the processing mesh, for each processing mesh (mesh region) of which the stripe region 32 is divided into multiple processing meshes (mesh regions) in the y direction (first direction) and the x direction (second direction) which corresponds to the linearly independent movement direction of the stage in the y direction. In other words, the effective temperature calculation processing unit 59 (effective temperature calculation processing circuit) calculates a representative value of the temperature rise that the heat from beam irradiation on the processing mesh (mesh region) of which is the processing mesh, imparts to the mesh of interest, which is the processing mesh, for each processing mesh (mesh region) of which the stripe region 32 is divided into multiple processing meshes (mesh regions) in the x direction and the y direction, which is the processing mesh The x-direction (second direction) is parallel to the direction of movement of the stage 105 along each stripe region 32. The method for calculating the effective temperature will be explained in detail below.

[0058] Figure 19 is a block diagram showing an example of the internal configuration of the effective temperature calculation processing unit in Embodiment 1. In Figure 19, the effective temperature calculation processing unit 59 contains a division unit 53, a dose amount representative value calculation unit 54, an acquisition unit 56, a kernel determination unit 57, and an effective temperature calculation unit 58.

[0059] Each of the "~ section," such as the pattern density calculation section 50, dose amount calculation section 52, effective temperature calculation processing section 59 (dividing section 53, dose amount representative value calculation section 54, acquisition section 56, kernel determination section 57, and effective temperature calculation section 58), modulation rate calculation section 60, correction section 62, irradiation time data generation section 72, data processing section 74, transfer control section 79, and drawing control section 80, has a processing circuit. Such a processing circuit includes, for example, an electrical circuit, a computer, a processor, a circuit board, a quantum circuit, or a semiconductor device. Each of the "~ section" may use a common processing circuit (the same processing circuit) or different processing circuits (separate processing circuits). Information input to and output to the pattern density calculation unit 50, dose amount calculation unit 52, effective temperature calculation processing unit 59 (dividing unit 53, dose amount representative value calculation unit 54, acquisition unit 56, kernel determination unit 57, and effective temperature calculation unit 58), modulation rate calculation unit 60, correction unit 62, irradiation time data generation unit 72, data processing unit 74, transfer control unit 79, and drawing control unit 80, as well as information being calculated, is stored in the memory 112 each time.

[0060] The division unit 53 divides the sample drawing area into multiple stripe regions, each of which is divided in the y direction by the size of the beam array region of the multi-charged particle beam on the sample surface in the y direction (first direction). Within each stripe region, the division unit 53 divides the area into multiple mesh regions in the y direction and in the x direction (second direction) parallel to the direction of movement of the stage along each stripe region (-x direction). Specifically, the division unit 53 (division processing circuit) divides each stripe region 32 into multiple processing meshes (mesh regions) for example in the y direction (first direction) by a size of 1 / Ny of the size W of the beam array region, and in the x direction (second direction) perpendicular to the y direction by a size of 1 / Nx of the size W of the beam array region (Nx and Ny are both integers of 2 or more).

[0061] Figure 20 shows an example of a processing mesh in Embodiment 1. As described above, the drawing area 30 of the sample 101 is divided into multiple stripe areas 32 in the y direction, for example, by the size W of the irradiation area 34 (beam array area) of the multi-beam 20 on the surface of the sample 101. Each stripe area 32 is then divided into multiple processing meshes (mesh areas) 39 in the y direction with a size of 1 / Ny (where Ny is an integer of 2 or more) of the size W of the irradiation area 34 (beam array area), and in the x direction with a size of 1 / Nx (where Nx is an integer of 2 or more) of the size W of the irradiation area 34 (beam array area). The size sx in the x direction and the size sy in the y direction of each processing mesh 39 are configured to be larger than the beam pitch size of the sub-irradiation area 29. In the example in Figure 12, the size sx in the x direction and the size sy in the y direction of each processing mesh 39 are shown as the same size s.

[0062] In Embodiment 1, the size s of the processing mesh 39 is preferably set to, for example, the tracking distance L. The tracking distance L is k times the beam pitch size on the surface of the sample 101 (where k is a natural number). In the example described above, the tracking distance L is set to, for example, 25 times the beam pitch size. Therefore, the size s of the processing mesh 39 is preferably set to, for example, a size equivalent to 25 beam pitches. Thus, the size s of the processing mesh 39 is larger than the beam pitch size on the surface of the sample 101. Moreover, the processing mesh 39 is a sufficiently large area relative to the pixel 36, which is the unit area irradiated by each beam.

[0063] Next, the dose quantity representative value calculation unit 54 calculates a representative value of multiple dose quantities from multiple beams irradiating within each divided processing mesh 39 as the dose quantity representative value Dij. The processing mesh 39 contains multiple sub-irradiation areas 29. As described above, each sub-irradiation area 29 is irradiated with multiple different beams. In the example above, for example, it is irradiated with 10 different beams spaced 25 beam pitches apart in the x direction, and the processing mesh 39 contains multiple pixels 36. Here, a representative value of the dose quantity (dose quantity representative value Dij) defined for all pixels 36 in the processing mesh 39 is calculated. Examples of representative values ​​include the mean, maximum, minimum, or median. Here, the average dose quantity, which is the mean value, is calculated as the dose quantity representative value Dij. The dose quantity representative value calculation unit 54 creates a dose quantity representative value map using the calculated dose quantity representative value Dij for each processing mesh 39. The dose quantity of each processing mesh 39 is defined as an element of the dose quantity representative value map. i represents the x-axis index of the processing mesh 39. j represents the y-axis index of the processing mesh 39. The created dose quantity representative value map is stored in the storage device 144.

[0064] The process calculates the temperature rise in a particular mesh region, which is one of multiple processing meshes 39, due to the heat generated by beam irradiation to each processing mesh 39 within the processing region corresponding to the beam array region. This calculation is performed by a convolution process using a representative dose value for each processing mesh 39 and a heat spreading function that represents the heat spreading created by the processing mesh 39.

[0065] The above calculation process is repeated while shifting the position of the processing area corresponding to the beam array area in the x direction on the stripe area. This iterative process is performed multiple times until the processing mesh 39 is located from one end in the x direction of the processing area to the other end. The representative values ​​of the multiple temperature increases obtained are then calculated as the effective temperature of the mesh area of ​​interest. Specifically, for each processing mesh 39, the effective temperature is calculated using the dose statistic Dij for each processing mesh 39 and the thermal diffusion function PSF, which represents the thermal diffusion created by each mesh. The thermal diffusion function PSF can be defined, for example, as a general thermal diffusion equation by the following equation (1-18).

[0066]

number

[0067] A function representing the surface temperature of the quartz glass substrate, obtained from equation (1-18), can be used. Here, λ represents the thermal diffusivity of the material through which the temperature diffuses. An example of a solution to the above equation will be explained later as an explanation of equation (3-1). Using the dose quantity representative value Dij and the thermal spreading function PSF, a convolution process is performed to calculate the temperature rise in the mesh of interest due to the heat generated by beam irradiation to each processing mesh 39 within a processing area that is the same size as a beam array area composed of Nx × Ny processing meshes 39. This process is carried out on the target stripe area 32, shifting the position of the rectangular area in the x-direction by the size s of the processing meshes 39 until the mesh of interest is included in the rectangular area. This process is performed N times, from when the mesh of interest is at one end of the rectangular area in the x-direction until it is at the other end. The statistical value of the results of these N convolution processes is then calculated as the effective temperature T(k,l).

[0068] Figure 21 is a diagram illustrating the method for calculating the effective temperature in Embodiment 1. The effective temperature T(k,l) can be defined by equation (2) shown in Figure 21. Within the stripe region 32, M processing meshes 39 are arranged in the x direction and N processing meshes 39 in the y direction. In equation (2), among the multiple processing meshes 39 within the stripe region 32, the processing mesh 39 in the l-th row in the y direction and the k-th column in the x direction is indicated as the mesh region of interest.

[0069] In equation (2), i represents the x-direction index of the dose statistics map. It is defined as the x-direction index i=0 of the processing mesh 39 at the leftmost end of the striped region 32. j represents the y-direction index in the dose statistics map. It is defined as the y-direction index j=0 for the processing mesh 39 at the bottom of the striped region 32. N represents the number of vertical (y-direction) meshes in the input dose map used for the effective temperature calculation. M represents the number of horizontal (x-direction) meshes in the input dose map used for the effective temperature calculation. (k,l) indicates the index (reference number) of the processing mesh (area of ​​interest) for which the effective temperature T within (M×N) processing meshes is calculated. Dij represents the representative dose value for processing mesh 39 assigned to index (k,l) in the dose representative value map. (μC / cm^2) m represents the l-N+1 to lth beam irradiation numbers that occur before the beam array region (N×N, here Nx=Ny=N) passes through the mesh of interest (k,l). When the processing mesh size s is set to the tracking distance L, m coincides with the l-N+1 to lth tracking reset numbers that occur before the beam array region passes through the mesh of interest (k,l). When m=l-N+1, the mesh of interest is located at the right edge of the (N×N) beam array region. When m=l, the mesh of interest is located at the left edge. n represents the beam irradiation number from the 0th to the mth. When the processing mesh size s is set to the tracking distance L, n corresponds to the tracking reset number from the 0th to the mth. The first tracking control (tracking cycle) has not yet performed a tracking reset, so the tracking reset number is zero. The second tracking control has performed one tracking reset, so the tracking reset number is 1. PSF(n,m,ki,lj) represents the heat spreading function.

[0070] Figure 22 is a diagram illustrating a part of the formula for calculating the effective temperature in Embodiment 1. In Figure 22, the portion of equation (2) enclosed by the dotted line shows the calculation part of the convolution process. The calculation part of the convolution process in equation (2) performs a convolution process to calculate the temperature rise that the heat from beam irradiation to each mesh region within a rectangular region 35 of the same size as the beam array region composed of N×N processing meshes 39 exerts on the mesh region of interest at index (k,l). A rectangular region 35 is used in which the left end of the rectangular region 35 is the nth column of the processing mesh 39 and the right end is the n+N-1th column of the processing mesh 39. Therefore, within the rectangular region 35, N×N processing meshes 39 corresponding to the nth column to the n+N-1th column in the x direction and the 0th row to the N-1th row in the y direction are arranged.

[0071] Figure 23 is a diagram illustrating an example of the calculation formula for the heat spreading function in Embodiment 1. The heat spreading function PSF(n,m,ki,lj) is defined by equation (3-1) shown in Figure 23. Equation (3-1) can be obtained by solving the heat conduction equation under initial conditions where uniform heat is applied to the substrate surface in a volume equal to the mesh size multiplied by Rg by beam irradiation, with boundary conditions of infinity in the XY direction and semi-infinity in the Z direction in the substrate depth direction. Symbols in the thermal spreading function PSF(n,m,ki,lj) that overlap with equation (2) indicate the same symbols as in equation (2). The thermal spreading function PSF(n,m,ki,lj) shown in Figure 23 defines the case where the XY stage 105 moves at a constant velocity in the opposite direction to the drawing direction, for example, the x-direction (-x-direction). As shown in Figure 23, the thermal spreading function PSF(n,m,ki,lj) is defined using the tracking cycle time obtained from the velocity v of the XY stage 105.

[0072] In equation (3-1), Rg represents the range of a 50kV electron beam within quartz. For example, range Rg = (0.046 / ρ)E 1.75 Use this. ρ represents the density of the substrate (quartz) (e.g., 2.2 g / cm³). σn,m represents a function determined by the number of tracking resets (mn) performed from the nth to the mth step. The function σn,m is defined by equation (3-3). Function A is defined by equation (3-2). In equation (3-2), V represents the acceleration voltage of the electron beam. Cp represents the specific heat of the substrate (quartz) (e.g., 0.77 J / g / K). In equation (3-3), λ represents the thermal diffusivity of the substrate (quartz) (e.g., 0.0081 cm² / sec). (mn) indicates the number of tracking resets performed from the nth to the mth instance. t trk-cycle This indicates the tracking cycle time. Tracking cycle time between t trk-cycle This is shown by equation (3-4). v stage This indicates the stage speed. In a typical multibeam lithography system, the stage velocity v is within the stage path. stage =(constant) The system is optimized so that the shot (10 shots in the previous example) is completed within the time between tracking intervals. Since the tracking distance L (=W / N) is chased at the stage speed, the tracking cycle time t trk-cycle This can be defined by equation (3-4).

[0073] Figure 24 is a diagram illustrating another part of the formula for calculating the effective temperature in Embodiment 1. Regarding the convolution process described in Figure 22, the rectangular region 35 is shifted in the x-direction by the size s of the processing mesh 39, starting from the left edge (n=0) of the striped region 32, until the target mesh region of index (k,l) is included in the rectangular region 35 (n=m). This process is represented by the calculation portion enclosed by the dotted line in formula (2) shown in Figure 24. The example in Figure 24 shows the case where the rectangular region 35 has been moved to the right edge of the rectangular region 35 where the target mesh region of index (k,l) is located. In this state, the left edge of the rectangular region 35 is in column k-N+1, and the right edge is in column k.

[0074] Figure 25 is a diagram illustrating another part of the formula for calculating the effective temperature in Embodiment 1. Figure 26 is a diagram illustrating another part of the formula for calculating the effective temperature in Embodiment 1. In Figure 26, the process performed by the calculation part in Figure 25 is specifically shown in formula form. The process shown in Figure 22 is performed N times, as shown in Figure 25, from the rightmost position (one end) to the leftmost position (the other end) of the rectangular region 35 in the x-direction. In other words, as shown in equation (4) in Figure 26, the process shown in Figure 24 from n=0 to n=m=k-N+1, the process shown in Figure 24 from n=0 to n=m=k-N+2, the process shown in Figure 24 from n=0 to n=m=k-N+3, ..., the process shown in Figure 24 from n=0 to n=m=k, and so on, N times, and their sum is calculated. Since the rectangular region 35 has N processing meshes 39 arranged in the x-direction, N processing is performed until the mesh region of interest moves from the rightmost to the leftmost position of the rectangular region 35. This process is shown in the calculation part enclosed by the dotted line in equation (2) in Figure 25. The statistical value of the result of the N convolution processes is then calculated as the effective temperature T(k,l). This process is shown in the calculation portion enclosed by the dotted line in equation (2) in Figure 26. The example in equation (2) shows the case where the effective temperature T(k,l) is calculated by dividing the sum of N convolution operations by N and taking the average value obtained. Note that the number of divisions in the rectangular region and the number of calculations do not necessarily have to be the same. That is, it may be divided into N parts and the number of calculations may be less than N (downsampling). Alternatively, it may be divided into N parts and distributed to a number of meshes greater than N (upsampling).

[0075] The effective temperature T(k,l) is not limited to the average value; it can also be the maximum, minimum, or median value obtained from N convolution operations. The median is preferable, and the average value is even preferable.

[0076] The position of the area of ​​interest in the mesh region is changed, and the effective temperature T(i,j) is calculated for each position (i,j) of the processed mesh 39.

[0077] As described above, instead of calculating the temperature rise for each shot and each beam, the effective temperature T(i,j) is calculated per processing mesh 39 using the representative dose value Dij of the processing mesh 39. The effective temperature T(i,j) can be calculated for each processing mesh 39, which is sufficiently larger than the pixel 36 that constitutes the unit area of ​​beam irradiation for each shot. Therefore, the amount of computation can be significantly reduced.

[0078] Alternatively, the effective temperature T(x) can be calculated using the kernel K(x) as follows. This will be explained in detail below.

[0079] Figure 27 is a diagram illustrating an example of a virtual model of the effective temperature in Embodiment 1. In Figure 27, when a point irradiation of a 1 μC charge is performed at position coordinate (0,0) using a multibeam lithography method, the kernel is obtained by calculating the effective temperature observed at an arbitrary position (x,y) (the average temperature while the BAA region passes through the (x,y) region). In the graph below position coordinate (0,0) in Figure 27, the vertical axis shows the amount of charge, and the horizontal axis shows time t. Also, in the graph below arbitrary position (x,y), the vertical axis shows the temperature, and the horizontal axis shows time t.

[0080] As shown in the graph below the position coordinate (0,0) in Figure 27, we assume that a beam array region of size Lx in the x-direction moves continuously and linearly at stage velocity Vstage, while continuously irradiating charges linearly. Furthermore, we assume that irradiation starts at the right end of the beam array region and ends at the left end. Under these two assumptions, we approximate the effective temperature at an arbitrary position (x,y). The graph below the position coordinate (0,0) in Figure 19 shows the state where irradiation occurs sequentially over the time it takes for the beam array region to pass. As shown in the graph below the arbitrary position (x,y), a temperature rise occurs during the time (t=Lx / Vstage) when the beam array region is performing point irradiation at position coordinate (0,0) and before and after this time. The effective temperature represents the temperature average during the time the beam array region is passing.

[0081] Figure 28 is a diagram illustrating an example of the kernel derivation process in Embodiment 1. Within the striped region 32, M processing meshes 39 are arranged in the x direction and Ny processing meshes 39 are arranged in the y direction. If the midpoint in the y direction within the striped region 32 is set to j=0, then processing meshes 39 from -Ny / 2 to +Ny / 2 are arranged within the striped region 32 in the y direction. Also, if the central position in the x direction within the striped region 32 is set to i=0, then processing meshes 39 from, for example, -∞ to M are arranged within the striped region 32 in the x direction. In equation (5), among the multiple processing meshes 39 within the striped region 32, the coordinate processing mesh 39 at the l-th row in the y direction and the k-th column in the x direction is shown as the mesh region of interest.

[0082] Furthermore, in Figure 28, the x-direction size sx of the processing mesh 39 is the value obtained by dividing the x-direction beam array size Lx by the number of meshes in the x-direction within the beam array Nx. Similarly, the y-direction size sy of the processing mesh 39 is the value obtained by dividing the y-direction beam array size Ly by the number of meshes in the y-direction within the beam array Ny.

[0083] Here, we assume that a charge of 1 μC is applied to the processing mesh at positions i=0 and j=0. In this case, the representative dose value Dij for the processing mesh at position (0,0) is given by Dij = 1 / (sxsy) as the average value per unit area, and the representative dose values ​​for processing meshes other than i=0 and j=0 are assumed to be zero. The effective temperature T(k,l) in this case is defined as the kernel T(k,l). The kernel T(k,l) can be defined by equation (5) shown in Figure 28. As described above, the method of setting the index has been changed, so the integration range on the right side of equation (5) has been transformed from the integration range on the right side of equation (2).

[0084] Here, we assume that Nx and Ny are infinite. In other words, we assume that the size of the processing mesh is infinitesimally small.

[0085] Figure 29 shows another example of the kernel derivation process in Embodiment 1. By making the processing mesh sizes sx and sy infinitesimally small, equation (5) can be transformed as shown in equation (6-1). However, the function C is given in equation (6-2). The function E is given in equation (6-3). Here, the thermal spreading function PSF is given by equations (3-1) to (3-3) above. The tracking cycle time ttrkcycle can be defined as the processing mesh size sx in the x direction divided by the stage speed Vstage. The processing mesh size sx is the value obtained by dividing the x-direction size Lx of the beam array region by the number of meshes in the x direction Nx within the beam array region. In other words, this means that a virtual tracking distance Lx / Nx is defined. Therefore, the functions σn and m in equation (3-3) can be transformed into equation (6-4).

[0086] Figure 30 shows another example of the kernel derivation process in Embodiment 1. As described above, we assume that the number of meshes Nx,Ny in the processing region overlapping with the beam array region is infinite. In other words, we assume that the size of the processing mesh 39 is infinitesimally small. Then, in Figure 30, the integral variable ω is defined as the value obtained by taking the limit of Nx as Nx approaches infinity, which is the value obtained by dividing the reference number i, which represents the mesh region in the beam propagation direction (x direction) within a processing region of the same size as the beam array region, by the number of mesh regions in the beam propagation direction within the processing region that overlaps with the beam array region Nx, and multiplying this value by the size Lx of the beam array region in the beam propagation direction.

[0087] Furthermore, in Figure 30, the integral variable ξ is defined as the value obtained by taking the limit of Ny as Ny approaches infinity, which is the value obtained by dividing the reference number j, representing the mesh region in the y direction within a processing region of the same size as the beam array region, by the number of mesh regions in the y direction Ny within the processing region overlapping with the beam array region, and multiplying this value by the size Ly of the beam array region in the y direction.

[0088] Furthermore, the integral variable u is defined as the value obtained by taking the limit of Nx as Nx approaches infinity, which is obtained by dividing the beam irradiation number m (m = k - Nx + 1, k - Nx, ... k), which is sequentially performed Nx times until the processing region, consisting of a size of Nx × Ny, passes through the target mesh at coordinate (k, l). This process is performed sequentially.

[0089] Furthermore, in Figure 30, the integral variable v is defined as the value obtained by taking the value obtained by dividing the beam irradiation number n, which is sequentially performed as the mth, m-1th, m-2nd, ... by the number of mesh regions Nx, and multiplying this by the size Lx of the beam array region in the beam propagation direction (x direction), and taking Nx to the limit.

[0090] As a result, the convolution operation part of the right-hand side of equation (6-1) that defines the kernel K(k,l), which sums Lx / Nx from i=n to n+Nx-1, can be defined as a term component representing an integral operation that integrates with respect to the integral variable ω from v to v+Lx, as shown in equation (7-1).

[0091] Furthermore, the convolution operation portion of the right-hand side term of equation (6-1) that defines the kernel K(k,l), which sums Ly / Ny from j=-Ly / 2 to +Ly / 2, can be defined as a term component representing an integral operation that integrates with respect to the integral variable ξ from -Ly / 2 to +Ly / 2, as shown in equation (7-2).

[0092] Furthermore, the convolution part of the right-hand side of equation (6-1) that defines the kernel K(k,l), which sums Lx / Nx from n=-∞ to m, can be defined as a term component representing an integral operation that integrates with respect to the integral variable v from -∞ to u, as shown in equation (7-3).

[0093] Furthermore, the convolution part of the right-hand side term of equation (6-1) that defines the kernel K(k,l), which sums Lx / Nx from m=k-Nx+1 to k, can be defined as a term component representing an integral operation that integrates with respect to the integral variable u from x-Lx to x, as shown in equation (7-4).

[0094] Note that the integral components with respect to the integration variables ω and ξ represent the integral operation that represents the cumulative temperature rise at position (x, y) due to the heat generated by the beam irradiated at a certain position (ω, ξ) within the beam array region, when the beam array region is at a certain position v. Therefore, the integration range for ω and ξ is within the beam array region, with ω going from v to v+Lx and ξ going from -Ly / 2 to +Ly / 2. The term component integrated with respect to the integration variable v: This integral operation further integrates the temperature increase that contributes to the position (x,y) from the temperature increase accumulated by the above integration operation, for each position from infinity to position u. Therefore, the integration range for v is from -∞ to u. The term component integrated with respect to the integration variable u: This integral operation further accumulates the temperature rise accumulated by the above integration operation, from the point where one end of the beam array region is at position (x,y) to the point where the other end is at position (x,y). Therefore, the integration range for u is from x-Lx to x.

[0095] Therefore, the kernel K(k, l) can be defined by an integral formula using the integration variables ω, ξ, u, and v. Specifically, the kernel K(k, l) includes a term component indicating an integration operation with respect to the integration variable ω, a term component indicating an integration operation with respect to the integration variable ξ, a term component indicating an integration operation with respect to the integration variable v, a term component indicating an integration operation with respect to the integration variable u, and the function A / (πσ u,v 2 ) erf(Rg / σ u,v ) e^(-((x - ω) 2 + (y - ξ) 2 ) / σ u,v ), and is defined by Equation (8-1) multiplied by the Dirac delta function δ(ω, ξ). Note that the Dirac delta function δ(ω, ξ) is a function that satisfies Equations (8-2) and (8-3). Also, the function σ u,v is defined by Equation (8-4). Also, by making the sizes sx and sy of the processing mesh infinitesimal, the differential formula of the error function can be defined by Equation (8-5).

[0096] FIG. 31 is a diagram for explaining the kernel in Embodiment 1. The kernel K(x, y) represents the average temperature (effective temperature) during the passage of the beam array region when a charge of 1 μC is continuously irradiated at (x, y) = (0, 0). The lower right diagram of FIG. 31 shows the state of continuously irradiating a charge of 1 μC during the passage of the beam array region. The vertical axis represents the charge amount, and the horizontal axis represents time. In such a case, as shown in the upper diagram of FIG. 31, an effective temperature that is not zero appears at x > -Lx even behind the charge irradiation point at the coordinate (0, 0). This is because the heat generated by irradiation at the right end of the beam array region contributes as a heating effect when the inside of the beam array region is irradiated, as shown in the lower left diagram of FIG. 31. That is, the kernel depends on the size Lx of the beam array region.

[0097] Figure 32 shows an example of the relationship between stage speed and kernel in Embodiment 1. In the example in Figure 32, under the condition that the x-direction size Lx of the beam array is constant, four examples of kernels with different vstages (v1 to v4) and stage speeds (Vstage) are shown. As shown in Figure 32, the kernels have asymmetrical temperature distributions with different heights and shapes for each stage speed. In the example in Figure 32, it can be seen that the temperature in the center of the temperature distribution increases as the stage speed increases.

[0098] Figure 33 shows an example of the relationship between the beam array's movement direction size and the kernel in Embodiment 1. In the example in Figure 33, under constant stage speed, three examples of kernels with different beam array x-direction sizes Lx (Lx1 to Lx3) are shown. As shown in Figure 33, each beam array x-direction size Lx results in a kernel with a different temperature distribution, height, and shape. In the example in Figure 25, it can be seen that the smaller the beam array x-direction size Lx, the higher the temperature in the center of the temperature distribution.

[0099] Figure 34 shows another example of the relationship between the beam array's movement direction size and the kernel in Embodiment 1. Figure 34 shows an example of the temperature distribution for the three beam arrays in Figure 33 at an x-direction size Lx. The vertical axis shows temperature, and the horizontal axis shows the position in the x-direction. As shown in the example in Figure 34, the rise and fall shapes of the kernel's temperature distribution differ depending on the beam array region size Lx.

[0100] Therefore, in Embodiment 1, multiple kernels corresponding to the stage speed and beam array size Lx are created in advance.

[0101] Figure 35 shows an example of a kernel defined as a table in Embodiment 1. In Figure 35, the kernel K(x,y) is defined as the values ​​at each position within a range larger than the beam array region. This is because of the effect of residual heat after the beam array has passed. For example, if the size Lx of the beam array region is set in a range of approximately 100 μm (maximum value) to 10 μm (minimum value), it is preferable to calculate the kernel in a range of approximately ±300 μm in the x and y directions, respectively.

[0102] In the example shown in Figure 35, the stage velocity Vstage, the beam array size Lx in the x-direction (opposite direction of stage movement), the position (x,y), and the kernel value K(x,y) at each position are defined in relation to each other as a table. The value of kernel K(x,y) at each position represents a typical temperature during the time the beam array region passes over that position, under the assumption that the beam array region moves continuously at a constant velocity while a point charge of 1 μC is irradiated at the center of the kernel, and that the irradiation of the point charge starts at one end of the beam array region and ends at the other end. Furthermore, the actual stage speed and beam array area size used should be referenced, and if no matching value is available, a linearly interpolated value using the preceding and succeeding values ​​can be used.

[0103] Figure 36 shows an example of a kernel equation defined as a continuous function in Embodiment 1. In the example in Figure 36, equation (9) shows an example of a function that approximates five kernels with different stage velocities by summing five Gaussian functions that are anisotropic in the x and y directions. Note that a coefficient Ai is prepared for each stage velocity, and the velocities between the stage velocities defined in the table can be obtained by using linearly interpolated coefficients Ai, σxi, and σyi. For example, a kernel equation defined as a continuous function can be prepared for each beam array area size Lx. Alternatively, it is also preferable to prepare a function that approximates multiple kernels with different stage velocities and beam array area sizes Lx.

[0104] As described above, in Embodiment 1, multiple kernels are prepared in advance, depending on the stage speed and the beam array area size Lx. These multiple kernels are stored in the memory device 144.

[0105] The acquisition unit 56 acquires the stage speed Vstage and beam array size Lx for the current drawing process. Specifically, it acquires the stage speed Vstage and beam array size Lx, which are set when setting drawing conditions (not shown). The drawing conditions are set by manual input by the user. Alternatively, it is preferable to set up an input screen (not shown) that allows the user to select from multiple conditions for each of the multiple drawing condition parameters, including the stage speed Vstage and beam array size Lx, and allow the user to select each drawing condition parameter from the multiple conditions set. The beam array size Lx changes when, for example, the number of beams used is limited from the beam array that can be irradiated by the drawing device 100. Specifically, this includes cases where only the central beam array, which has a small effect of aberration, is used. As a result, the number of beams is reduced, so the drawing time is longer, but the accuracy of the drawing position can be improved.

[0106] The kernel determination unit 57 determines a corresponding kernel from among multiple kernels according to the acquired (input) stage velocity Vstage and beam array size Lx.

[0107] The effective temperature calculation unit 58 receives the velocity Vstage of the stage 105 and the size Lx of the beam array region in the x-direction, and uses the kernel determined by the velocity Vstage of the stage 105 and the size Lx of the beam array region in the x-direction, and the representative dose value, to calculate the representative value of the temperature rise that the heat from beam irradiation into a processing region of the same size as the beam array region that overlaps with the beam array region on the surface of the sample 101 imparts to the mesh region of interest (k,l), which is one of the multiple processing meshes 39, as the effective temperature T(k,l) of the mesh region of interest. Specifically, it operates as follows.

[0108] Figure 37 is a diagram illustrating the method for calculating the effective temperature in Embodiment 1. As shown in Figure 37, the effective temperature calculation unit 58 performs a convolution operation between the dose distribution of the representative dose value Dij and the kernel K(xk,yl). (xk,yl) indicates the position within the kernel. This allows the effective temperature T(k,l) of the mesh of interest to be calculated. The effective temperature T(k,l) of the mesh of interest can be defined by equation (10), which shows the convolution operation. In the convolution operation, the kernel center is shifted within the dose distribution, and the sum of the element products of elements whose positions coincide is calculated. The sum of the element products at the position of the kernel center at coordinate (k,l) becomes the effective temperature T(k,l).

[0109] In the example described above, the case where stage 105 moves at a constant speed was explained, but it is not limited to this case. The calculation formula (10) described above can also be applied when stage 105 moves at a variable speed. In such a case, the stage speed distribution is stored in the memory device 144. The effective temperature calculation unit 58 can obtain the stage speed at the position where the kernel center is located and select and use the kernel corresponding to the stage speed at the position where the kernel center is located. This makes it possible to calculate the effective temperature using the kernel described above even in the case of variable speed movement.

[0110] As described above, in Embodiment 1, the effective temperature Tpec(x) before heating effect correction is calculated.

[0111] As part of the modulation rate calculation process (S114), the modulation rate calculation unit 60 calculates the modulation rate α(x) of the dose amount, which depends on the effective temperature Tpec(x).

[0112] Figure 38 shows an example of the relationship between line width CD and temperature in Embodiment 1. In Figure 38, the vertical axis shows the line width CD (Critical Dimension), and the horizontal axis shows the temperature. As shown in Figure 38, it can be seen that the line width CD also deviates as the temperature of the resist increases. The CD variation ΔCD / ΔT [nm / K] due to the heating effect has a linear relationship. This value differs depending on the type of resist and substrate, so experiments are conducted to obtain it. Therefore, an approximate formula is obtained to approximate the amount of CD change ΔCD per unit temperature ΔT. Such correlation data (1) is input from an external source and stored in the storage device 144.

[0113] Figure 39 shows an example of the relationship between line width CD and dose amount in Embodiment 1. In Figure 39, the vertical axis shows line width CD, and the horizontal axis shows dose amount. In the example in Figure 39, the horizontal axis is shown using a logarithmic scale. As shown in Figure 39, the line width CD increases as the dose amount increases, depending on the pattern density. The relationship between CD fluctuation and dose amount ΔCD / ΔD, which depends on the resist / substrate type and pattern density, is obtained through experiments. Then, an approximate formula is obtained that approximates the amount of CD change ΔCD per unit dose. This correlation data (2) is input from an external source and stored in the storage device 144.

[0114] The modulation rate calculation unit 60 reads the correlation data (1)(2) from the storage device 144 and calculates the dose change amount ΔD per unit temperature ΔT, which depends on the pattern density, as the modulation rate α(x) of the dose amount which depends on the effective temperature T. The modulation rate α(x) which depends on the pattern density ρ is defined by the following equation (11). (11) α(x)=(ΔCD / ΔT) / (ΔCD / ΔD) ρ =(ΔD / ΔT) ρ

[0115] As a correction step (S130), the correction unit 62 (an example of a modulation dose amount calculation unit) calculates the modulation dose amount for each position by correcting the dose amount for each position defined in the dose map, using a function that uses an effective temperature distribution map in which the effective temperature is defined for each mesh region, an area density map for each position, and a backscattering coefficient for proximity effect correction. In other words, the correction unit 62 (an example of a modulation dose amount calculation unit) uses the function β(x) to calculate the heating effect correction dose amount Dtec(x) for each position, which is the modulation dose amount for each position corrected for the heating effect due to irradiation by the multi-beam 20, with respect to the dose amount for each position defined in the dose map (here, the proximity effect correction dose amount Dpec(x) for each of the 36 pixels). The heating effect correction dose amount Dtec(x) can be obtained by the above equation (1-16). The function β(x), as shown in equation (1-17), is a function that uses an effective temperature distribution map in which the effective temperature Tpec(x) is defined for each mesh region, an area density map in which the area density at each location is defined, and a backscattering coefficient η and modulation rate α(x) for proximity effect correction. The proximity density U(x), which is the value obtained by convolution integral of the area density ρ′(x) and the distribution function g(x), is used as the area density defined in the area density map.

[0116] The correction unit 62 then creates a dose map (2) for each stripe region 32 using the calculated heating effect correction dose amount Dtec(x) for each pixel 36 after heating effect correction. The heating effect correction dose amount Dtec(x) for each pixel 36 is defined as an element of the dose map (2). This allows the heating effect correction dose amount Dtec(x) to be determined. In other words, it is possible to obtain a dose amount that can draw CD dimensions with the correction residual of the heating effect correction eliminated or reduced. The created dose map (2) is stored in the storage device 144.

[0117] As part of the irradiation time data generation process (S140), the irradiation time data generation unit 72 calculates the irradiation time t of the electron beam for each pixel 36 to inject the calculated heating effect correction dose amount Dtec(x) into the pixel 36. The irradiation time t can be calculated by dividing the heating effect correction dose amount Dtec(x) by the current density J. If the heating effect correction dose amount Dtec(x) is a relative value normalized with the reference irradiation dose Db as 1, the irradiation time t can be calculated by multiplying the heating effect correction dose amount Dtec(x) by the reference irradiation dose Db and dividing the result by the current density J. The irradiation time t for each pixel 36 is calculated as a value within the maximum irradiation time Ttr that can be irradiated in one shot of the multi-beam 20. The irradiation time t for each pixel 36 is converted into gradation value data of 0 to 1023 levels, for example, with 1023 levels (10 bits) for the maximum irradiation time Ttr. The graded irradiation time data is stored in the storage device 142.

[0118] As a data processing step (S142), the data processing unit 74 rearranges the irradiation time data in shot order according to the drawing sequence, and also rearranges it in a data transfer order that takes into account the order of the shift registers in each group.

[0119] As part of the drawing process (S144), under the control of the drawing control unit 80, the transfer control unit 79 transfers the irradiation time data to the deflection control circuit 130 in shot order. The deflection control circuit 130 outputs blanking control signals to the blanking aperture array mechanism 204 in shot order, and also outputs deflection control signals to the DAC amplifier units 132 and 134 in shot order.

[0120] The drawing mechanism 150 then uses a multi-beam 20 with a heating effect correction dose Dtec(x) (modulated dose) to draw a pattern on the sample 101.

[0121] Figure 40 shows an example of the stored energy distribution and CD distribution after heating effect correction in Embodiment 1. In the stored energy distribution in Figure 40, the portion above and below the ISO-FOCAL dose level is shown in different colors. Therefore, the boundary between the two colors indicates the ISO-FOCAL dose level. By dose modulation using the function β(x) in Embodiment 1, the stored energy distribution after heating effect correction can be made to approximately match the ISO-FOCAL dose level to the resolution threshold, as shown in Figure 40. Therefore, as shown in the CD distribution, the distribution of the pattern line width CD approximately matches the design value.

[0122] As described above, according to Embodiment 1, when correcting resist heating in multibeam lithography, the correction residual can be reduced.

[0123] [Embodiment 2] In Embodiment 1, the difference ΔD in equation (1-14) 2 Although we have described a configuration for calculating the function β(x) while ignoring the term, this is not the only configuration. Embodiment 2 describes a configuration that uses the function β'(x) including such term. The following is the same as Embodiment 1, except for the points specifically mentioned.

[0124] Figure 41 is a conceptual diagram showing the configuration of the drawing device in Embodiment 2. In Figure 41, the configuration is the same as in Figure 1, except that an effective temperature calculation processing unit 64, an effective temperature change amount calculation unit 66, and a correction unit 68 are further added to the control computer 110. Each of the "~ section," such as the pattern density calculation section 50, dose amount calculation section 52, effective temperature calculation processing section 59, modulation rate calculation section 60, correction section 62, effective temperature calculation processing section 64, effective temperature change amount calculation section 66, correction section 68, irradiation time data generation section 72, data processing section 74, transfer control section 79, and drawing control section 80, has a processing circuit. Such a processing circuit includes, for example, an electrical circuit, a computer, a processor, a circuit board, a quantum circuit, or a semiconductor device. Each of the "~ section" may use a common processing circuit (the same processing circuit) or may use different processing circuits (separate processing circuits). Information input to and output to the pattern density calculation unit 50, dose amount calculation unit 52, effective temperature calculation processing unit 59, modulation rate calculation unit 60, correction unit 62, effective temperature calculation processing unit 64, effective temperature change amount calculation unit 66, correction unit 68, irradiation time data generation unit 72, data processing unit 74, transfer control unit 79, and drawing control unit 80, as well as information being calculated, is stored in the memory 112 each time.

[0125] Figure 42 is a flowchart showing an example of the main steps of the drawing method in Embodiment 2. Figure 42 is the same as Figure 18 except that the intermediate modulation dose calculation step (S120), the effective temperature calculation step (S122), and the effective temperature change calculation step (S124) are added between the modulation rate calculation step (S114) and the correction step (S130).

[0126] Figure 43 shows an example of the stored energy distribution when the maximum effective temperature is varied and heating effect correction is performed using the method of Embodiment 1. In the example in Figure 43, the stored energy distribution when the effective temperature Tpec is a maximum of 100°C, a maximum of 150°C, and a maximum of 175°C is shown. The boundary between the two colors in the stored energy distribution indicates the ISO-focal dose level. In Figure 43, the effective temperature distribution graph is shown above the stored energy distribution graph for each maximum temperature. In the effective temperature distribution for each maximum temperature, the effective temperature Tpec calculated under the conditions before heating effect correction is shown by a solid line. The effective temperature Ttec calculated under the conditions after heating effect correction is shown by a dotted line. It can be seen that as the maximum temperature increases, the deviation of the ISO-focal dose level from the resolution threshold becomes larger. This is thought to be because the change in effective temperature ΔT (=Ttec-Tpec) becomes larger before and after heating effect correction.

[0127] Therefore, in Embodiment 2, a correction is made that takes into account the change in effective temperature ΔT.

[0128] Figure 44 is a diagram illustrating an example of the process for deriving the correction term in Embodiment 2. The difference ΔD in equation (1-14) 2 The integral part of the first term, which is the term, can be transformed into equation (13-1) by substituting the difference ΔD = Dtec - Dpec obtained by rearranging equation (1-12). Therefore, the difference ΔD in equation (1-14) 2 The integral part of the first term, which is the term of , is Ttec(x)-Tpec(x)(=ΔT(x)). Therefore, equation (1-14) can be transformed into equation (13-2).

[0129] Here, the difference ΔD is infinitesimal, and furthermore, due to the characteristics of the heating effect in multi-beam systems, we approximate that its change within the integral range is also infinitesimal and can be ignored, and take it outside the integral. Then, rearranging with respect to ΔD, we can transform it into equation (13-3).

[0130] Substituting the calculated ΔD into equation (13-2) and transforming it, Dtec'(x) (=Dtec(x)) can be transformed into equation (13-4). Therefore, the function β′(x) which is the correction term in Embodiment 2 is defined using the effective temperature Tpec(x), the proximity density U(x), the backscattering coefficient η, the modulation index α(x), and the change in effective temperature ΔT(x). In other words, the function β′(x) in Embodiment 2 includes, in addition to the parameters used in the function β(x) of Embodiment 1, the change in effective temperature ΔT(x) before and after correction of the dose amount at each position as a correction term. In other words, the function β′(x) in Embodiment 2 includes, in addition to the parameters used in the function β(x) of Embodiment 1, the change in effective temperature ΔT(x) before and after correction of the heating effect as a correction term. The function β′(x) can be defined by equation (13-5).

[0131] By plotting with a beam whose heating effect-corrected dose Dtec'(x) is obtained by correcting the proximity effect-corrected dose Dpec(x) using the function β'(x), the correction residual of the pattern line width CD due to the heating effect correction can be eliminated or reduced even when the maximum effective temperature Tpec(x) is high. The plotting method using the function β'(x) for correction will be described below.

[0132] The contents of each step up to the modulation rate calculation step (S114) are the same as in Embodiment 1. In the effective temperature calculation step (S112), the effective temperature calculation processing unit 59 (first effective temperature calculation circuit) calculates the effective temperature Tpec(x) (first effective temperature) using the dose amount before correction of the heating effect, as described above.

[0133] As an intermediate modulation dose calculation step (S120), the correction unit 62 (an example of a modulation dose calculation unit) uses the function β(x) shown in equation (1-17) used in Embodiment 1 to calculate the heating effect correction dose amount Dtec(x) for each position, which is the modulation dose amount for each position corrected for the heating effect due to irradiation by the multi-beam 20, for each position defined in the dose map (here, the proximity effect correction dose amount Dpec(x) for each pixel 36). The heating effect correction dose amount Dtec(x) can be obtained by the above-mentioned equation (1-16). In Embodiment 2, the calculated heating effect correction dose amount Dtec(x) becomes the intermediate modulation dose amount.

[0134] In the effective temperature calculation step (S122), the effective temperature calculation processing unit 64 (second effective temperature calculation circuit) calculates the effective temperature Ttec(x) (second effective temperature) using a modulation dose amount corrected using the effective temperature Tpec(x) (first effective temperature). In other words, the effective temperature calculation processing unit 64 (second effective temperature calculation circuit) calculates the effective temperature Ttec(x) (second effective temperature) after heating effect correction using an intermediate modulation dose amount Dtec(x) that has been corrected for the heating effect using the effective temperature Tpec(x) (first effective temperature). The internal configuration of the effective temperature calculation processing unit 64 may be the same as the internal configuration of the effective temperature calculation processing unit 59 shown in Figure 19. Furthermore, the method for calculating the effective temperature Ttec(x) after heating effect correction is the same as the method for calculating the effective temperature Tpec(x) before heating effect correction described above. However, the typical dose value Dij is calculated using the intermediate modulation dose amount Dtec(x).

[0135] As part of the effective temperature change calculation process (S124), the effective temperature change calculation unit 66 calculates the change ΔT(x) (=Ttec(x)-Tpec(x)) between the effective temperature Tpec(x) and the effective temperature Ttec(x).

[0136] As a correction step (S130), the correction unit 68 (another example of the modulation dose amount calculation unit) uses the function β'(x) in Embodiment 2 to calculate the heating effect correction dose amount Dtec'(x) for each position, which is the modulation dose amount for each position corrected for the heating effect due to irradiation by the multi-beam 20, for each position defined in the dose map (here, the proximity effect correction dose amount Dpec(x) for each pixel 36). The heating effect correction dose amount Dtec'(x) can be obtained by the above-described equation (13-4). The function β'(x) is a function that uses an effective temperature distribution map in which the effective temperature Tpec(x) is defined for each mesh region, an area density map in which the proximity density U(x) for each position is defined, and the backscattering coefficient η, modulation rate α(x), and effective temperature change amount ΔT(x) for proximity effect correction, as shown in equation (13-5).

[0137] The correction unit 68 then creates a dose map (2) for each stripe region 32 using the calculated heating effect correction dose amount Dtec'(x) for each pixel 36 after heating effect correction. The heating effect correction dose amount Dtec'(x) for each pixel 36 is defined as an element of the dose map (2). This allows the heating effect correction dose amount Dtec'(x) to be determined. In other words, it is possible to obtain a dose amount that can draw CD dimensions with the correction residual of the heating effect correction eliminated or reduced. The created dose map (2) is stored in the storage device 144.

[0138] The process from the irradiation time data generation step (S140) onward is the same as in Embodiment 1. However, the irradiation time t can be calculated by dividing the heating effect correction dose amount Dtec'(x) by the current density J. If the heating effect correction dose amount Dtec'(x) is a relative value normalized with the reference irradiation dose Db as 1, the irradiation time t can be calculated by multiplying the heating effect correction dose amount Dtec'(x) by the reference irradiation dose Db and dividing the result by the current density J. The drawing mechanism 150 then uses a multi-beam 20 with a heating effect correction dose Dtec'(x) (modulated dose) to draw a pattern on the sample 101.

[0139] Figure 45 shows an example of the stored energy distribution when the maximum effective temperature is varied and heating effect correction is performed in Embodiment 2. In the example in Figure 45, the stored energy distribution when the effective temperature Tpec is a maximum of 100°C, a maximum of 150°C, and a maximum of 175°C is shown. The boundary between the two colors in the stored energy distribution indicates the ISO-focal dose level. The effective temperature distribution is also shown above the stored energy distribution for each maximum temperature. In the effective temperature distribution for each maximum temperature, the effective temperature Tpec calculated under the conditions before heating effect correction is shown by a solid line. The effective temperature Ttec calculated under the conditions after heating effect correction is shown by a dotted line. In Embodiment 2, by including the change in effective temperature ΔT(x) as a correction term in the function β′(x), even when the maximum temperature is high, the amount of deviation of the ISO-focal dose level from the resolution threshold can be kept small.

[0140] The embodiments have been described above with reference to specific examples. However, the present invention is not limited to these specific examples. It is not limited to multi-charged particle beam lithography apparatuses or multi-charged particle beam lithography methods, but can also be applied to charged particle beam lithography apparatuses or charged particle beam lithography methods using raster beams. Furthermore, the processing functions described in Embodiments 1 and 2 may be made to be executed by a computer. The program for causing the computer to execute such processing functions may be stored, for example, in a tangible, non-temporary, readable recording medium such as a magnetic disk drive.

[0141] Furthermore, while descriptions of the device configuration, control methods, and other parts not directly necessary for explaining the present invention have been omitted, it goes without saying that the necessary device configuration and control methods can be appropriately selected and used. For example, although the control unit configuration for controlling the drawing device 100 has been omitted, it goes without saying that the necessary control unit configuration can be appropriately selected and used.

[0142] Furthermore, all charged particle beam lithography apparatuses, charged particle beam lithography methods, and programs (or readable recording media on which the program is recorded, not temporarily) that incorporate elements of the present invention and can be appropriately modified by those skilled in the art are included within the scope of the present invention. [Industrial applicability]

[0143] The present invention relates to a charged particle beam lithography apparatus, a charged particle beam lithography method, and a program (or a readable recording medium on which the program is stored, not temporarily), and can be used, for example, as a method for correcting resist heating that occurs in charged particle beam lithography. [Explanation of Symbols]

[0144] 20 Multibeam 22 holes 24 control electrodes 25 Passing hole 26 Counter electrode 28,36 pixels 29 Sub-irradiation area 30 drawing area 32 Stripe Area 34 Irradiation area 35 rectangular area 39 processing mesh 41 Control circuits 46 Amplifier 47 Individual blanking mechanism 50 Pattern density calculation unit 52 Dose calculation unit 53 Split part 54 Dose quantity representative value calculation unit 56 Acquisition Department 57 Kernel decision-making unit 58 Effective temperature calculation unit 59 Effective temperature calculation processing unit 60 Modulation Rate Calculation Unit 62 Correction section 64 Effective temperature calculation processing unit 66 Effective temperature change calculation unit 68 Correction section 72 Irradiation time data generation unit 74 Data Processing Department 79 Transfer Control Unit 80 Drawing Control Unit 100 drawing device 101 samples 102 Electronic Microscope Tube 103 Drawing room 105 XY Stages 110 Control Computer 112 memory 130 Deflection control circuit 132,134 DAC Amplifier Unit 136 Lens control circuit 138 Stage control mechanism 139 Stage position measuring instrument 140,142,144 Storage device 150 Drawing mechanism 160 Control System Circuits 200 electron beam 201 Electron Gun 202 Illumination Lens 203 Molded aperture array substrate 204 Blanking Aperture Array Mechanism 205 Reduction Lens 206 Limiting Aperture Substrate 207 Objective lens 208 Main deflector 209 Sub deflector 210 Mirror 330 Membrane area 343 pads

Claims

1. A dose map creation circuit creates a dose map that defines the amount of dose incident at each of multiple locations within each of multiple stripe regions, which are formed by dividing the drawing area on the sample surface irradiated with a charged particle beam in a first direction. An effective temperature calculation circuit calculates, for each mesh region in which multiple mesh regions are divided by a first direction and a second direction corresponding to the linearly independent movement direction of the stage, the effective temperature of the mesh region of interest, which is the mesh region in question, from the temperature rise that the heat from beam irradiation on the sample surface imparts to the mesh region of interest, while the multi-beam irradiable beam array region passes through the mesh of interest, and defines the effective temperature of the mesh region of interest as the effective temperature of the mesh region of interest. A modulation dose calculation unit calculates the modulated dose amount for each position by correcting the dose amount for each position defined in the dose map, using a function that uses an effective temperature distribution map in which the effective temperature is defined for each mesh region, an area density map for each position, and a backscattering coefficient for proximity effect correction. A drawing mechanism that draws a pattern on the sample using the modulated dose of charged particle beam, A charged particle beam lithography apparatus characterized by comprising the following features.

2. The charged particle beam lithography apparatus according to claim 1, characterized in that the function further includes as a correction term the change in effective temperature before and after correction of the dose amount at each of the positions.

3. The effective temperature calculation circuit, as a first effective temperature calculation circuit, calculates the first effective temperature as the effective temperature using the dose amount before correction. A second effective temperature calculation circuit that calculates a second effective temperature using the modulation dose amount corrected using the first effective temperature, An effective temperature change calculation circuit that calculates the amount of change between the first effective temperature and the second effective temperature, The charged particle beam lithography apparatus according to claim 2, further comprising the above.

4. The charged particle beam lithography apparatus according to claim 1, characterized in that each dose amount defined in the dose map is a dose amount corrected for proximity effects.

5. The charged particle beam lithography apparatus according to claim 1, characterized in that the area density defined in the area density map is the value obtained by convolution and integral of the area density and the distribution function.

6. For each of the multiple stripe regions within each of the multiple positions in the sample surface irradiated with a charged particle beam, a dose map is created that defines the amount of dose incident at that position. For each mesh region, which is divided within each stripe region by a first direction and a second direction corresponding to the linearly independent movement direction of the stage, a representative value of the temperature rise that the heat from beam irradiation on the sample surface imparts to the mesh region of interest is calculated as the effective temperature of the mesh region of interest, while the multi-beam irradiable beam array region passes through the mesh of interest. Using a function that employs an effective temperature distribution map in which the effective temperature is defined for each mesh region, an area density map for each location, and a backscattering coefficient for proximity effect correction, the modulated dose amount for each location is calculated by correcting the dose amount for each location defined in the dose map. A pattern is drawn on the sample using the charged particle beam with the aforementioned modulated dose. A charged particle beam lithography method characterized by comprising the following:

7. A function to create a dose map that defines the dose amount incident at each of multiple locations within each of multiple stripe regions, which are formed by dividing the drawing area on the sample surface irradiated with a charged particle beam in a first direction, and Each stripe region is divided into multiple mesh regions by a first direction and a second direction corresponding to the linearly independent movement direction of the stage. For each mesh region, the function calculates a representative value of the temperature rise that occurs while the multi-beam irradiable beam array region passes through the mesh region of interest, out of the temperature rise that occurs when heat from beam irradiation to the sample surface is applied to the mesh region of interest, as the effective temperature of the mesh region of interest. A function to store in a memory device an effective temperature distribution map in which the effective temperature is defined for each mesh region, A function to read the effective temperature distribution map from the storage device, and to calculate the modulated dose amount for each position by correcting the dose amount for each position defined in the dose map using a function that uses the effective temperature distribution map, the area density map for each position, and the backscattering coefficient for proximity effect correction, The function of drawing a pattern on the sample using the modulated dose of charged particle beam, A readable recording medium that permanently stores, rather than temporarily stores, a program used to execute a computer.

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