Method for calculating effective temperature of multi-charged particle beam drawing area, multi-charged particle beam drawing device, readable recording medium on which program is non-temporarily recorded, and multi-charged particle beam drawing device

Abstract

The purpose of the invention is to provide a method that makes it possible, in multi-charged particle beam drawing, to correct resist heating without performing extensive calculations to accumulate the effects of temperature increase for individual shots and beams.　In the present invention, a method for calculating the effective temperature a multi-charged particle beam drawing area comprises, in each of a plurality of mesh areas in which a drawing area of a sample irradiated with a multi-charged particle beam is divided in the drawing progress direction and a direction linearly independent of the drawing progress direction: calculating a representative value of the dose of a beam directed in a mesh area as a dose representative value (S108); and calculating a representative value of an increasing temperature imparted to each of the plurality of mesh areas by heat generated via beam irradiation as the effective temperature of each of the plurality of mesh areas by convolutional processing of the dose representative value, and a kernel that is determined by the speed of a stage on which the sample is placed, and the size of a beam array area in the drawing progress direction on the surface of the sample of the multi-charged particle beam (S112).

Description

Method for calculating effective temperature of multi-charged particle beam writing region, multi-charged particle beam writing method, readable recording medium on which a program is non-temporarily recorded, and multi-charged particle beam writing device

[0001] The present invention relates to a method for calculating the effective temperature of a multi-charged particle beam writing region, a multi-charged particle beam writing device, a multi-charged particle beam writing method, and a program (or a readable recording medium on which the program is non-temporarily recorded), and relates to, for example, a method for correcting resist heating that occurs in multi-beam writing.

[0002] Lithography technology, which is responsible for the advancement of miniaturization of semiconductor devices, is an extremely important process in semiconductor manufacturing, as it is the only one that generates patterns. In recent years, with the increasing integration density of LSIs, the circuit line width required for semiconductor devices has become finer year by year. Here, electron beam (EB) lithography technology has inherently excellent resolution, and lithography is performed using an electron beam to draw on wafers, etc.

[0003] For example, there is a lithography system that uses multiple beams. Compared to lithography using a single electron beam, the use of multiple beams allows for the irradiation of many beams at once, thereby significantly improving throughput. In such a 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 of which is blanked, and the unblocked beams are reduced in size by an optical system, deflected by a deflector, and irradiated onto the desired position on the sample.

[0004] However, in electron beam lithography, if a higher-density electron beam is used for irradiation in a short time, the substrate temperature can overheat, causing changes in resist sensitivity and degrading linewidth accuracy, resulting in a phenomenon known as resist heating (see, for example, Patent Document 1). For example, in single-beam lithography, a method has been used in which the dose correction amount for the current shot is determined by accumulating the effects of temperature increases from each previous shot using a single beam. However, in multi-beam lithography, multiple beams are used, and accumulating the effects of temperature increases from each previous shot and beam requires a huge amount of calculation. Furthermore, in multi-beam lithography, multiple beams are shot simultaneously, so it is necessary to consider the effects of temperature increases from multiple beams located in a wide area that is simultaneously irradiated.

[0005] Special Publication No. 2003-503837

[0006] One aspect of the present invention provides an apparatus and method capable of correcting resist heating in multi-beam writing without accumulating the effects of temperature rise for each shot and each beam.

[0007] A method for calculating the effective temperature of a multi-charged particle beam writing region according to one aspect of the present invention is characterized in that, for each of a plurality of mesh regions in which the writing region of a sample irradiated with the multi-charged particle beam is divided in the writing progress direction and in a direction linearly independent of the writing progress direction, a representative value of the dose of the beam irradiating the mesh region is calculated as a representative dose value, and a kernel determined by the speed of the stage on which the sample is placed and the size of the beam array region of the multi-charged particle beam on the surface of the sample in the writing progress direction is convolved with the representative dose value to calculate and output a representative value of the temperature rise caused by the heat due to beam irradiation in each of the plurality of mesh regions as the effective temperature of each of the plurality of mesh regions.

[0008] A multi-charged particle beam writing method according to one embodiment of the present invention is a multi-charged particle beam writing method for writing a pattern on a sample using a correction amount calculated using an effective temperature obtained by the above-described effective temperature calculation method, characterized in that: the method calculates, using the effective temperature in each of a plurality of mesh regions, a correction amount for correcting the dose amount of a plurality of beams irradiating a mesh region of interest, which is one of the mesh regions, among the multi-charged particle beams, or pattern data of a figure to be written in the mesh region of interest; and writes a pattern on the sample using the correction amount.

[0009] A readable recording medium non-temporarily recording a program to be executed by a computer according to one aspect of the present invention has: a function of calculating, as a dose representative value, a representative value of the dose of the beam irradiating within each of a plurality of mesh regions obtained by dividing a drawing region of a sample irradiated with a multi-charged particle beam in the drawing progression direction and in a direction linearly independent of the drawing progression direction; and a function of calculating, as an effective temperature of each of the plurality of mesh regions, a representative value of the temperature rise caused by the heat due to beam irradiation, by convolution processing of the dose representative value and a kernel determined by the speed of a stage on which the sample is placed and the size of the beam array region of the multi-charged particle beam in the drawing progression direction on the surface of the sample.

[0010] Another aspect of the present invention is a readable recording medium non-temporarily recording a program to be executed by a computer, which non-temporarily records the above-mentioned functions, a function of calculating, using the effective temperature in each of the plurality of mesh regions, the dose amount of a plurality of beams irradiating a mesh region of interest, which is one of the plurality of mesh regions, of the multi-charged particle beam, or a correction amount for correcting pattern data of a figure to be drawn in the mesh region of interest, and a function of drawing a pattern on a sample using the correction amount.

[0011] A multi-charged particle beam writing apparatus according to one aspect of the present invention comprises: a dose representative value calculation circuit for calculating, as a dose representative value, a representative value of a dose of a beam irradiating a mesh region in each of a plurality of mesh regions obtained by dividing a writing region of a sample irradiated with the multi-charged particle beam in the writing proceeding direction and in a direction linearly independent of the writing proceeding direction; an effective temperature calculation circuit for calculating, as an effective temperature of each of the plurality of mesh regions, a representative value of a temperature rise caused by heat due to beam irradiation by the beam through a convolution process of the dose representative value and a kernel determined by the speed of a stage on which the sample is placed and the size of the beam array region of the multi-charged particle beam on the surface of the sample in the writing proceeding direction; a correction amount calculation circuit for calculating, using the effective temperature of each of the plurality of mesh regions, a correction amount for correcting the dose of a plurality of beams irradiating a mesh region of interest, which is one of the plurality of mesh regions, of the multi-charged particle beam, or pattern data of a figure to be written in the mesh region of interest; and a writing mechanism for writing a pattern on the sample using the calculated correction amount.

[0012] According to one aspect of the present invention, in multi-beam writing, resist heating can be corrected without accumulating the influence of temperature rise for each shot and each beam.

[0013] 1 is a conceptual diagram showing the configuration of a writing apparatus according to the first embodiment. FIG. 2 is a conceptual diagram showing the configuration of a shaping aperture array substrate according to the first embodiment. FIG. 3 is a cross-sectional view showing the configuration of a blanking aperture array mechanism according to the first embodiment. FIG. 4 is a conceptual top view showing a part of the configuration within a membrane region of the blanking aperture array mechanism according to the first embodiment. FIG. 5 is a diagram showing an example of an individual blanking mechanism according to the first embodiment. FIG. 6 is a conceptual diagram for explaining an example of a writing operation according to the first embodiment. FIG. 7 is a diagram showing an example of an irradiation region of multi-beams and a pixel to be written according to the first embodiment. FIG. 8 is a diagram for explaining an example of a multi-beam writing operation according to the first embodiment. FIG. 9 is a diagram showing an example of a relationship between temperature distribution and temperature caused by irradiation of one beam on an area equivalent to one beam pitch in a comparative example of the first embodiment. FIG. 10 is a diagram showing an example of a relationship between temperature and temperature caused by simultaneous irradiation of multiple beams according to the first embodiment. FIG. 11 is a flowchart showing an example of main steps of a writing method according to the first embodiment. FIG. 12 is a diagram showing an example of a processing mesh according to the first embodiment. FIG. 13 is a diagram for explaining a method of calculating an effective temperature according to the first embodiment. FIG. 14 is a diagram for explaining a part of a formula for calculating an effective temperature according to the first embodiment. FIG. 15 is a diagram for explaining an example of a formula for calculating a thermal spread function according to the first embodiment. FIG. 16 is a diagram for explaining another part of a formula for calculating an effective temperature according to the first embodiment. FIG. 10 is a diagram for explaining another part of the formula for calculating the effective temperature in embodiment 1. FIG. 11 is a diagram for explaining another part of the formula for calculating the effective temperature in embodiment 1. FIG. 12 is a diagram for explaining an example of a virtual model of the effective temperature in embodiment 1. FIG. 13 is a diagram for explaining an example of a process for deriving a kernel in embodiment 1. FIG. 14 is a diagram showing another example of a process for deriving a kernel in embodiment 1. FIG. 15 is a diagram showing another example of a process for deriving a kernel in embodiment 1. FIG. 16 is a diagram for explaining a kernel in embodiment 1. FIG. 17 is a diagram showing an example of a relationship between a stage speed and a kernel in embodiment 1. FIG. 18 is a diagram showing an example of a relationship between a size of a beam array in a movement direction and a kernel in embodiment 1. FIG. 19 is a diagram showing another example of a relationship between a size of a beam array in a movement direction and a kernel in embodiment 1. FIG. 19 is a diagram showing an example of a kernel defined as a table in embodiment 1.FIG. 1 is a diagram showing an example of a kernel equation defined as a continuous function in embodiment 1. FIG. 2 is a diagram for explaining a method for calculating an effective temperature in embodiment 1. FIG. 3 is a diagram showing an example of the relationship between a line width CD and a temperature in embodiment 1. FIG. 4 is a diagram showing an example of the relationship between a line width CD and a dose amount in embodiment 1. FIG. 5 is a diagram showing an example of the configuration of a writing apparatus in embodiment 2. FIG. 6 is a flowchart showing an example of main steps of a writing method in embodiment 2.

[0014] In the following embodiments, a configuration using an electron beam will be described as an example of a charged particle beam, but the charged particle beam is not limited to an electron beam and may be a beam using charged particles such as an ion beam.

[0015] [First Embodiment] FIG. 1 is a conceptual diagram showing the configuration of a lithography apparatus according to a first embodiment. In FIG. 1, the lithography apparatus 100 includes a lithography mechanism 150 and a control circuit 160. The lithography apparatus 100 is an example of a multi-charged particle beam lithography apparatus and also an example of a multi-charged particle beam exposure apparatus. The lithography mechanism 150 includes an electron lens barrel 102 (electron beam column) and a lithography chamber 103. The electron lens barrel 102 includes an electron gun 201, an illumination lens 202, a shaping 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. An XY stage 105 is located in the lithography chamber 103. A sample 101, such as a mask, which serves as a substrate to be lithographed during lithography (exposure) is placed on the XY stage 105. The sample 101 includes an exposure mask used in manufacturing a semiconductor device, a semiconductor substrate (silicon wafer) on which a semiconductor device is manufactured, and the like. The sample 101 is coated with resist. The sample 101 includes, for example, a mask blank coated with resist and on which nothing has yet been drawn. A mirror 210 for measuring the position of the XY stage 105 is also arranged on the XY stage 105.

[0016] The control system circuit 160 includes a control computer 110, a memory 112, a deflection control circuit 130, digital-to-analog conversion (DAC) amplifier units 132 and 134, a lens control circuit 136, a stage control mechanism 138, a stage position measurement device 139, and storage devices 140, 142, and 144 such as magnetic disk drives. The control computer 110, the memory 112, the deflection control circuit 130, the lens control circuit 136, the stage control mechanism 138, the stage position measurement device 139, and the storage devices 140, 142, and 144 are connected to one another via a bus (not shown). The deflection control circuit 130 is connected to the DAC amplifier units 132 and 134 and a 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 a corresponding DAC amplifier 134. A stage position measuring device 139 receives reflected light from a mirror 210 and measures the position of the XY stage 105 based on the principle of laser interferometry.

[0017] The control computer 110 includes a pattern density calculation unit 50, a dose calculation unit 52, a division unit 53, a dose representative value calculation unit 54, an acquisition unit 56, a kernel determination unit 57, an effective temperature calculation unit 58, a correction amount 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 writing control unit 80. Each of the "units" such as the pattern density calculation unit 50, the dose calculation unit 52, the division unit 53, the dose representative value calculation unit 54, an acquisition unit 56, the kernel determination unit 57, the effective temperature calculation unit 58, the correction amount calculation unit 60, the correction unit 62, the irradiation time data generation unit 72, the data processing unit 74, the transfer control unit 79, and the writing control unit 80 has a processing circuit. Such a processing circuit includes, for example, an electric circuit, a computer, a processor, a circuit board, a quantum circuit, or a semiconductor device. Each of the "~ units" may use a common processing circuit (the same processing circuit) or may use a different processing circuit (separate processing circuit). Information input to and output from the pattern density calculation unit 50, the dose calculation unit 52, the division unit 53, the dose representative value calculation unit 54, the acquisition unit 56, the kernel determination unit 57, the effective temperature calculation unit 58, the correction amount calculation unit 60, the correction unit 62, the irradiation time data generation unit 72, the data processing unit 74, the transfer control unit 79, and the writing control unit 80, and information being calculated are stored in the memory 112 each time.

[0018] The drawing operation of the drawing apparatus 100 is controlled by a 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 a transfer control unit 79.

[0019] Furthermore, chip data is input from outside the drawing apparatus 100 and stored in the storage device 140. The drawing data includes chip data and drawing condition data. The chip data defines, for each graphic pattern, for example, a graphic code, coordinates, size, etc. The drawing condition data also includes information indicating the degree of multiplicity and the stage speed.

[0020] The storage device 144 also stores correlation data, which will be described later, for calculating a modulation factor for correcting resist heating.

[0021] 1 shows the configuration necessary for explaining the first embodiment. The drawing device 100 may also include other configurations that are normally required.

[0022] FIG. 2 is a conceptual diagram showing the configuration of a shaping aperture array substrate in embodiment 1. In FIG. 2 , holes (openings) 22 are formed in a matrix of p columns (y direction) by q columns (x direction) (p, q≧2) at a predetermined arrangement pitch in the shaping aperture array substrate 203. The example in FIG. 2 shows, for example, a case where 500 columns and 500 rows of holes 22 are formed in the horizontal and vertical directions (x, y directions). The number of holes 22 is not limited to this. Each hole 22 is formed as a rectangle of the same size and shape. Alternatively, it may be a circle of the same diameter. A portion of the electron beam 200 passes through each of these multiple holes 22, thereby forming a multibeam 20. In other words, the shaping aperture array substrate 203 forms a multibeam 20.

[0023] FIG. 3 is a cross-sectional view showing the configuration of the blanking aperture array mechanism according to the first embodiment. FIG. 4 is a top view conceptual diagram showing a portion of the configuration within the membrane region of the blanking aperture array mechanism according to the first embodiment. Note that the positional relationships between the control electrodes 24, the counter electrodes 26, the control circuit 41, and the pads 343 are not shown in FIGS. 3 and 4 . As shown in FIG. 3 , the blanking aperture array mechanism 204 includes a blanking aperture array substrate 31, which is a semiconductor substrate made of silicon or the like, disposed on a support base 33. In a membrane region 330 in the center of the blanking aperture array substrate 31, passage holes 25 (openings) for passing each beam of the multibeam 20 are opened at positions corresponding to the holes 22 of the shaping aperture array substrate 203 shown in FIG. 2 . Furthermore, for each of the multiple passage holes 25, a pair of a control electrode 24 and a counter electrode 26 (blanker: blanking deflector) is disposed at a position facing each other across the passage hole 25. Furthermore, inside the blanking aperture array substrate 31 near each passage hole 25, a control circuit 41 (logic circuit; cell) is disposed, which applies a deflection voltage to the control electrode 24 for each passage hole 25. The opposing electrode 26 for each beam is connected to ground.

[0024] As shown in FIG. 4 , each control circuit 41 is connected to n-bit (e.g., 10-bit) parallel wiring for control signals. Each control circuit 41 is connected to n-bit parallel wiring for irradiation time control signals (data), as well as wiring for clock signals, load signals, shot signals, and power supplies. These wirings may be part of the parallel wiring. An individual blanking mechanism 47 is configured for each beam constituting the multibeam 20, consisting of a control electrode 24, a counter electrode 26, and a control circuit 41. In the first embodiment, a shift register system, for example, is used as the data transfer system. In the shift register system, the multibeam 20 is divided into multiple groups for each of the multiple beams, and multiple shift registers for multiple beams in the same group are connected in series. Specifically, the multiple control circuits 41 formed in an array in the membrane region 330 are grouped, for example, at a predetermined pitch in the same row or column. The control circuits 41 in the same group are connected in series, as shown in FIG. 4 . Signals from pads 343 arranged in each group are transmitted to the control circuits 41 in the group.

[0025] FIG. 5 is a diagram illustrating an example of an individual blanking mechanism according to the first embodiment. In FIG. 5, an amplifier 46 (an example of a switching circuit) is disposed within a control circuit 41. In the example of FIG. 5, a CMOS (Complementary MOS) inverter circuit serving as a switching circuit is disposed as an example of the amplifier 46. An input (IN) of the CMOS inverter circuit receives, as a control signal, either an L (low) potential (e.g., ground potential) that is lower than the threshold voltage or an H (high) potential (e.g., 1.5 V) that is equal to or higher than the threshold voltage. In the first embodiment, 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). The electric field resulting from the potential difference with the ground potential of the counter electrode 26 deflects the corresponding beam 20, and the beam is controlled to be turned OFF by being blocked by the limiting aperture substrate 206. On the other hand, when an H potential is applied to the input (IN) of the CMOS inverter circuit (active state), the output (OUT) of the CMOS inverter circuit becomes the ground potential, and there is no potential difference with the ground potential of the opposing electrode 26, so the corresponding beam 20 is not deflected, and the beam is controlled to be turned ON by passing through the limiting aperture substrate 206. Blanking control is performed by this deflection.

[0026] 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.

[0027] Next, a specific example of the operation of the drawing mechanism 150 will be described. An electron beam 200 emitted from an electron gun 201 (emission source) is illuminated almost perpendicularly by an illumination lens 202 onto the entire shaping aperture array substrate 203. A plurality of rectangular holes 22 (openings) are formed in the shaping aperture array substrate 203, and the electron beam 200 illuminates an area including all of the holes 22. Portions of the electron beam 200 irradiated onto the positions of the holes 22 pass through the holes 22 of the shaping aperture array substrate 203, thereby forming, for example, a rectangular multibeam (multiple electron beams) 20. The multibeam 20 passes through corresponding blankers (first deflectors: individual blanking mechanisms 47) of the blanking aperture array mechanism 204. Each blanker performs blanking control on the individual beams passing through it so that the beams are turned on for a set drawing time (irradiation time).

[0028] The multi-beams 20 that pass through the blanking aperture array mechanism 204 are reduced by a reduction lens 205 and travel toward a central hole formed in a limiting aperture substrate 206. Here, the electron beams deflected by the blankers of the blanking aperture array mechanism 204 are shifted from the central hole of the limiting aperture substrate 206 and are blocked by the limiting aperture substrate 206. On the other hand, the electron beams that are not deflected by the blankers of the blanking aperture array mechanism 204 pass through the central hole of the limiting aperture substrate 206 as shown in FIG. 1. In this way, the limiting aperture substrate 206 blocks each beam that has been deflected to a beam-off state by the individual blanking mechanisms 47. Then, each beam of one shot is formed by the beams that pass through the limiting aperture substrate 206 from when the beam is turned on until when the beam is turned off. The multibeams 20 that have passed through the limiting aperture substrate 206 are focused by the objective lens 207 to form a pattern image with the desired reduction ratio, and the entire multibeams 20 that have passed through the limiting aperture substrate 206 are deflected in the same direction by the main deflector 208 and the sub-deflector 209, and each beam is irradiated onto 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 multibeams 20 by the main deflector 208 so that the beam irradiation position follows the movement of the XY stage 105. Ideally, the multibeams 20 that are irradiated at one time are arranged at a pitch obtained by multiplying the arrangement pitch of the plurality of holes 22 in the shaping aperture array substrate 203 by the desired reduction ratio described above.

[0029] FIG. 6 is a conceptual diagram illustrating an example of the writing operation in the first embodiment. As shown in FIG. 6, the writing region 30 on the sample 101 is virtually divided into a plurality of stripe regions 32, each having a predetermined width in the y direction. First, the XY stage 105 is moved to adjust the irradiation region 34 that can be irradiated with one shot of the multi-beam 20 to the left end of the first stripe region 32, or further to the left, and writing begins. When writing the first stripe region 32, the XY stage 105 is moved, for example, in the −x direction, thereby relatively writing in the x direction. The XY stage 105 is moved continuously, for example, at a constant speed. After writing the first stripe region 32, the stage position is moved in the −y direction, and then the XY stage 105 is moved, for example, in the x direction, to similarly write in the −x direction. This operation is repeated to write each stripe region 32 in sequence. By alternately changing the direction of writing, the writing time can be shortened. However, the drawing is not limited to this case of alternately changing the direction, and drawing may proceed in the same direction when drawing each stripe region 32. When moving the XY stage 105 at a constant speed, the continuous movement speed may be different for each stripe. In one shot, multiple shot patterns, up to the same number as the number of holes 22, are formed at once by the multi-beams formed by passing through each hole 22 in the shaping aperture array substrate 203.

[0030] FIG. 7 shows an example of a multibeam irradiation area and a target pixel for drawing in the first embodiment. In FIG. 7 , the stripe area 32 is divided into a plurality of mesh areas, for example, based on the beam size of the multibeam 20. Each mesh area corresponds to a target pixel 36 (unit irradiation area, irradiation position, or drawing position). The size of the target pixel 36 is not limited to the beam size and may be any size regardless of the beam size. For example, the size may be 1 / a (a is an integer greater than or equal to 1) of the beam size. The example in FIG. 7 shows a case where the target pixel 30 on the sample 101 is divided, for example, in the y direction, into a plurality of stripe areas 32, each having a width substantially equal to the size of the irradiation area 34 (beam array area) that can be irradiated with one irradiation of the multibeam 20. The size of the rectangular irradiation area 34 in the x direction can be defined by the number of beams in the x direction multiplied by 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 multiplied by the beam pitch in the y direction. In the example of FIG. 7 , for example, a 500-column by 500-row multibeam is shown in an 8-column by 8-row multibeam arrangement. A plurality of pixels 28 (beam imaging positions) that can be irradiated with a single shot of the multibeam 20 are shown within the irradiation area 34. The pitch between adjacent pixels 28 on the sample surface is the pitch between each beam of the multibeam 20. A rectangular area surrounded by the beam pitch size in the x and y directions constitutes one sub-irradiation area 29 (pitch cell). Each sub-irradiation area 29 includes one pixel 28. In the example of FIG. 7 , for example, the pixel in the upper left corner of each sub-irradiation area 29 is shown as the pixel 28 that is the beam imaging position. Each sub-irradiation area 29 is composed of, for example, 10×10 pixels. In the example of FIG. 7 , each sub-irradiation area 29, for example, of 10×10 pixels, is shown in an abbreviated form to, for example, 4×4 pixels.

[0031] 8 is a diagram for explaining an example of a multi-beam writing operation in the first embodiment. The example of FIG. 8 shows a case where writing is performed with ten different beams in each sub-irradiation region 29 on the surface of the sample 101. The example of FIG. 8 also shows a writing operation in which the XY stage 105 continuously moves at a speed of, for example, a distance L of 25 beam pitches while writing 1 / 10 (one times the number of beams used for irradiation) of an area in each sub-irradiation region 29. In the writing operation shown in the example of FIG. 8, for example, while the XY stage 105 moves the distance L of 25 beam pitches, the sub-deflector 209 sequentially shifts the irradiation position (pixel 36) over a shot cycle time t ｔｒｋ－ｃｙｃｌｅ 1 shows a case where ten different pixels in the same sub-irradiation area 29 are written (exposed) by ten shots of the multibeam 20. While these ten pixels are written (exposed), the main deflector 208 deflects the entire multibeam 20 collectively so that the irradiation area 34 does not shift in relative position to the sample 101 due to 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 deflected collectively by the main deflector 208 during one tracking control is the tracking distance.

[0032] When one tracking cycle is completed, tracking is reset and the system returns to the previous tracking start position. Since the drawing of the first pixel row from the top of each sub-irradiation region 29 has been completed, after tracking reset, the sub-deflector 209 first deflects the beam in the next tracking cycle to adjust (shift) the drawing position of the beam so that the undrawn pixel row, for example, the second row from the top, of each sub-irradiation region 29 is drawn. In this way, the pixel row to be drawn next is changed for each tracking reset. During 10 tracking control operations, each pixel 36 in each sub-irradiation region 29 is drawn once. By repeating this operation during drawing of the stripe region 32, the position of the irradiation region 34 is moved sequentially from the irradiation region 34a to the irradiation region 34o, as shown in FIG. 6, and the drawing of the stripe region 32 is completed.

[0033] 8 , in the second tracking control, the sub-irradiation area 29 on the sample surface, which is located at the lower right corner of the irradiation area 34 having a width W, is moved a distance L to the left from the lower right corner of the irradiation area 34. Therefore, in the second tracking control, the sub-irradiation area 29, which is located at the lower right corner of the irradiation area 34 in the first tracking control, is written by another beam at a position that is a distance L to the left from the lower right corner of the irradiation area 34. Here, writing is performed by a beam that is, for example, 25 beams away in the −x direction from the beam at the lower right corner.

[0034] For example, in a writing process in which the multiplicity per stage pass is set to 2, each pixel 36 in each sub-irradiation area 29 can be written twice by 20 tracking controls.

[0035] FIG. 9 is a diagram showing an example of the relationship between temperature and temperature distribution resulting from irradiation of a single beam over an area corresponding to one beam pitch in a comparative example of the first embodiment. In FIG. 9, the vertical axis represents temperature, and the horizontal axis represents temperature distribution. As shown in FIG. 9, the temperature distribution resulting from irradiation of a single beam has a wide base region. Therefore, the effect is felt over a wide area. However, the effect on the base region is small, with the temperature rise due to a single beam being at most 0.01°C or less.

[0036] FIG. 10 is a diagram showing an example of the relationship between temperature and temperature distribution resulting from simultaneous irradiation of multiple beams in embodiment 1. In FIG. 10, the vertical axis represents temperature, and the horizontal axis represents temperature distribution. The temperature rise from a single beam is at most 0.01°C. However, if, for example, 500 x 500 = 250,000 beams are irradiated simultaneously, the temperature rises from each beam will overlap in the foot region, as shown in FIG. 10. As a result, if, for example, 500 x 500 = 250,000 beams are irradiated simultaneously, a significant temperature rise will occur in the foot region.

[0037] Although there are known techniques for predicting and correcting the heating effect in single-beam writing using a single beam, there has been no precedent for correcting the heating effect in multi-beam writing, where multiple beams, for example 250,000, are shot simultaneously multiple times per stage pass. Calculating the heat generated by each of the 250,000 beams, for example, in the same way as for a single beam, is not realistic due to the volume of calculations required.

[0038] With multi-beams, the current density J is extremely small compared to, for example, a single beam in the VSB system, so the temperature rises slowly. During this time, the temperature distribution due to one shot spreads over several tens of micrometers. Therefore, sufficient accuracy can be achieved even if the shot data and dose data within the stripe are divided and calculated together to some extent. Furthermore, as mentioned above, multi-beam writing uses a raster scan method, so the position is determined by the time. Therefore, once the dose data and writing speed (stage speed or tracking cycle time) are determined, the temperature rise is determined. This allows for simpler correction than with VSB writing, which requires both position and time.

[0039] Therefore, in the first embodiment, the dose information of the stripe region 32 is divided into pixel information of a certain Nx x Ny number of pixels including the mesh of interest for which the temperature is to be calculated. The temperature at each of the beam irradiations divided into multiple times is calculated for the mesh of interest. Then, the statistical value (for example, the average value) is used as the effective temperature for correction. A specific description will be given below.

[0040] Fig. 11 is a flowchart showing an example of main steps of the writing method according to Embodiment 1. In Fig. 11, the writing method according to Embodiment 1 carries out a series of steps, namely, a pattern density calculation step (S102), a dose calculation step (S104), a processing mesh division step (S106), a dose representative value calculation step (S108), a stage speed and beam array size input step (S109), a kernel determination step (S110), an effective temperature calculation step (S112), a correction amount calculation step (S114), a correction step (S118), an irradiation time data generation step (S120), a data processing step (S122), and a writing step (S124).

[0041] First, the drawing data is read from the storage device 140 for each stripe region 32 .

[0042] In the pattern density calculation step (S102), the pattern density calculation unit 50 calculates the pattern density ρ (pattern area density) for each pixel 36 in the target stripe region 32. The pattern density calculation unit 50 creates a pattern density map for each stripe region 32 using the calculated pattern density ρ for each pixel 36. The pattern density of each pixel 36 is defined as each element of the pattern density map. The created pattern density map is stored in the storage device 144.

[0043] In the dose calculation step (S104), the dose calculation unit 52 calculates, for each pixel 36, a dose (irradiation amount) to be applied to the pixel 36. The dose may be calculated, for example, by multiplying a preset reference irradiation amount Dbase by a proximity effect correction irradiation coefficient Dp and a pattern density ρ. In this manner, the dose is preferably calculated in proportion to the pattern area density calculated for each pixel 36. Regarding the proximity effect correction irradiation coefficient Dp, the writing region (e.g., the stripe region 32) is virtually divided into a plurality of proximity mesh regions (mesh regions for calculating proximity effect correction) of a predetermined size in a mesh pattern. The size of the proximity mesh region is preferably set to approximately 1 / 10 of the range of influence of the proximity effect, for example, approximately 1 μm. Then, the writing data is read from the storage device 140, and for each proximity mesh region, a pattern area density ρ′ of the pattern to be arranged within the proximity mesh region is calculated.

[0044] Next, a proximity effect correction irradiation coefficient Dp for correcting the proximity effect is calculated for each proximity mesh region. Here, the size of the mesh region for calculating the proximity effect correction irradiation coefficient Dp does not need to be the same as the size of the mesh region for calculating the pattern area density ρ'. Furthermore, the correction model for the proximity effect correction irradiation coefficient Dp and its calculation method may be the same as the method used in the conventional single-beam writing method.

[0045] Then, the dose calculation unit 52 creates a dose map (1) for each stripe region 32 using the calculated dose for each pixel 36. The dose for each pixel 36 is defined as each element of the dose map (1). In the above example, the dose is calculated as an absolute value multiplied by the reference dose Dbase, but this is not limiting. The dose may be calculated as a relative value to the reference dose Dbase, assuming that the reference dose Dbase is 1. In other words, the dose may be calculated as a coefficient value obtained by multiplying the proximity effect correction irradiation coefficient Dp by the pattern density ρ. The created dose map (1) is stored in the storage device 144.

[0046] In the processing mesh division step (S106), the division unit 53 (division processing circuit) divides the writing area of ​​the sample 101 into a plurality of processing meshes 39 (mesh areas) in the writing progress direction and in a direction linearly independent of the writing progress direction. In other words, the division unit 53 (division processing circuit) divides each of a plurality of stripe areas obtained by dividing the writing area of ​​the sample in the y direction by the size of the y direction (first direction) of the beam array area of ​​the multi-charged particle beam on the sample surface, into a plurality of mesh areas in the x direction (second direction) parallel to the y direction and the direction of movement of the stage along each stripe area (-x direction). Specifically, the division unit 53 (division processing circuit) divides each stripe region 32 into a plurality of processing meshes (mesh regions) each having a size of 1 / Ny of the size W of the beam array region in the y direction (first direction) and a size of 1 / Nx of the size W of the beam array region (Nx and Ny are both integers greater than or equal to 2) in the x direction (second direction) perpendicular to the y direction.

[0047] FIG. 12 is a diagram showing an example of a processing mesh in the first embodiment. As described above, the writing region 30 of the sample 101 is divided into, for example, a plurality of stripe regions 32 in the y direction by the size W of the irradiation region 34 (beam array region) of the multibeam 20 on the surface of the sample 101. Each stripe region 32 is then divided into a plurality of processing meshes (mesh regions) 39, each having a size 1 / Ny (Ny is an integer greater than or equal to 2) of the size W of the irradiation region 34 (beam array region) in the y direction and a size 1 / Nx (Nx is an integer greater than or equal to 2) of the size W of the irradiation region 34 (beam array region) in the x direction. 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 sub-irradiation regions 29 of the beam pitch size. In the example of FIG. 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.

[0048] In the first embodiment, 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 (k is a natural number) the inter-beam pitch size on the surface of the sample 101. In the example described above, the tracking distance L is set to, for example, 25 times the inter-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. In this way, the size s of the processing mesh 39 is larger than the inter-beam pitch size on the surface of the sample 101. Furthermore, the processing mesh 39 is an area sufficiently large relative to the pixel 36, which is the unit area irradiated by each beam.

[0049] In the dose representative value calculation step (S108), the dose representative value calculation unit 54 (dose statistical value calculation circuit) calculates, as a dose representative value D, a representative value of the dose of the beam irradiating each processing mesh 39, for each of a plurality of processing meshes 39 (mesh regions) obtained by dividing the writing region of the sample 101 irradiated with the multibeam 20 in the writing progress direction and in a direction linearly independent of the writing progress direction. In other words, the dose representative value calculation unit 54 (dose statistical value calculation circuit) calculates, for each divided processing mesh 39, a representative value of multiple doses of the multiple beams irradiating each processing mesh 39, as a dose representative value D. The processing mesh 39 includes multiple sub-irradiation regions 29. As described above, each sub-irradiation region 29 is irradiated with multiple different beams. In the above example, for example, the sub-irradiation region 29 is irradiated with 10 different beams spaced apart by 25 beam pitches in the x direction, and the processing mesh 39 includes multiple pixels 36. Here, a representative value of the dose (dose representative value Dij) defined for all pixels 36 within the processing mesh 39 is calculated. Examples of representative values ​​include an average value, a maximum value, a minimum value, or a median value. Here, for example, an average dose, which is an average value, is calculated as the dose representative value Dij. The dose representative value calculation unit 54 creates a dose representative value map using the calculated dose representative value Dij of each processing mesh 39. The dose of each processing mesh 39 is defined as each element of the dose representative value map. i indicates the index in the x direction of the processing mesh 39. j indicates the index in the y direction of the processing mesh 39. The created dose representative value map is stored in the storage device 144.

[0050] In the first embodiment, as will be explained in the effective temperature calculation step (S112) described later, the effective temperature within each processing mesh 39 is calculated. First, the effective temperature will be explained.

[0051] A calculation process is performed to calculate the temperature rise that occurs in a mesh region of interest, which is one of the processing meshes 39, due to the heat caused by beam irradiation on each processing mesh 39 in the processing region corresponding to the beam array region. This calculation process is performed by convolution processing using a representative dose value for each processing mesh 39 and a heat spread function that represents the heat spread created by the processing mesh 39.

[0052] The above-described calculation process is repeated while shifting the position of the processing region corresponding to the beam array region in the x direction on the stripe region, and this repetitive process is performed multiple times until the processing mesh 39 moves from one end of the processing region in the x direction to the other end, and a representative value of the multiple temperature increases obtained is calculated as the effective temperature of the mesh region of interest. Specifically, for each processing mesh 39, the effective temperature is calculated using the dose statistical value Dij for each processing mesh 39 and a thermal spread function PSF that represents the thermal spread created by each mesh. The thermal spread function PSF can be defined, for example, as the following equation (1) as a general thermal diffusion equation.

[0053]

[0054] A function representing the surface temperature of the quartz glass substrate obtained from Equation (1) can be used. Here, λ represents the thermal diffusivity of the material through which the temperature diffuses. An example of the solution of the above equation will be described later in the explanation of Equation (3-1). Using the dose representative value Dij and the thermal spread function PSF, a convolution process is performed to calculate the temperature rise in a mesh region of interest caused by heat irradiated with a beam on each processing mesh 39 within a processing region, which is, for example, a rectangular region of the same size as the beam array region composed of Nx × Ny processing meshes 39. This process is performed by shifting the rectangular region in the x direction on the target stripe region 32 by the size s of the processing mesh 39 until the mesh region of interest is included in the rectangular region. This process is performed N times, from when the mesh region of interest is positioned at one end of the rectangular region in the x direction to when it is positioned 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).

[0055] 13 is a diagram for explaining a method for calculating the effective temperature in the first embodiment. The effective temperature T(k, l) can be defined by equation (2) shown in FIG. 13. M processing meshes 39 are arranged in the x direction and N processing meshes 39 are arranged in the y direction within the stripe region 32. In equation (2), of the multiple processing meshes 39 within the stripe region 32, the processing mesh 39 located in the lth row in the y direction and the kth column in the x direction is shown as a mesh region of interest.

[0056] In equation (2), i indicates the index in the x direction of the dose statistical value map. It is defined as the index i=0 in the x direction of the processing mesh 39 at the left end of the stripe region 32. j indicates the index in the y direction of the dose statistical value map. It is defined as the index j=0 in the y direction of the processing mesh 39 at the bottom of the stripe region 32. N indicates the number of meshes in the vertical direction (y direction) of the input dose map used for calculating the effective temperature. M indicates the number of meshes in the horizontal direction (x direction) of the input dose map used for calculating the effective temperature. (k, l) indicates the index (reference number) of the processing mesh (mesh region of interest) for which the effective temperature T is calculated within the (M×N) processing meshes. Dij indicates the dose representative value of the processing mesh 39 assigned to index (k, l) in the dose representative value map. (μC / cm^2) m indicates the beam irradiation numbers from l-N+1 to l that are performed before the beam array area (N x N, where 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 corresponds to the tracking reset numbers from l-N+1 to l that are performed before the beam array area passes through the mesh of interest (k, l). When m = l-N+1, the mesh of interest is located at the right end of the (N x N) beam array area. When m = l, the mesh of interest is located at the left end. n indicates the beam irradiation numbers from 0 to m. When the processing mesh size s is set to the tracking distance L, n corresponds to the tracking reset numbers from 0 to m. In the first tracking control (tracking cycle), a tracking reset has not yet been performed, so the tracking reset number is zero. In the second tracking control, a tracking reset has been performed once, so the tracking reset number is one. PSF(n, m, ki, lj) denotes the thermal spread function.

[0057] FIG. 14 is a diagram illustrating a portion of the formula for calculating the effective temperature in the first embodiment. In FIG. 14, the portion enclosed by a dotted line in Equation (2) represents the calculation portion of the convolution process. In the calculation portion of Equation (2), a convolution process is performed to calculate the temperature rise that occurs in a mesh region of interest with index (k, l) due to heat generated by beam irradiation on each mesh region within a rectangular region 35 having the same size as the beam array region, which is composed of N×N processing meshes 39. 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 are arranged, corresponding to columns n to n+N-1 in the x direction and rows 0 to N-1 in the y direction.

[0058] FIG. 15 is a diagram illustrating an example of a formula for calculating the thermal spread function in the first embodiment. The thermal spread function PSF(n, m, ki, l-j) is defined by formula (3-1) shown in FIG. 15 . Formula (3-1) can be obtained by solving the heat conduction equation under the boundary conditions of infinity in the X and Y directions and semi-infinity in the Z direction along the substrate depth direction, under the initial condition that uniform heat is applied to the substrate surface by beam irradiation over a volume equal to the mesh size multiplied by Rg. Symbols in the thermal spread function PSF(n, m, ki, l-j) that overlap with those in formula (2) are the same as those in formula (2). The thermal spread function PSF(n, m, ki, l-j) shown in FIG. 15 is defined for the case where the XY stage 105 moves at a constant speed, for example, in the direction opposite to the x direction (-x direction), which is the drawing direction. As shown in FIG. 15, the thermal spread function PSF(n, m, ki, lj) is defined using a tracking cycle time determined from the velocity v of the XY stage 105 .

[0059] In equation (3-1), Rg represents the range of a 50 kV electron beam in quartz. For example, range Rg = (0.046 / ρ)E １．７５is used. ρ indicates the density of the substrate (quartz) (for example, 2.2 g / cm^3). σn,m indicates a function determined by the number of tracking resets (m-n) performed from the nth to the mth. The function σn,m is defined in equation (3-3). The function A is defined in equation (3-2). In equation (3-2), V indicates the acceleration voltage of the electron beam. Cp indicates the specific heat of the substrate (quartz) (for example, 0.77 J / g / K). In equation (3-3), λ indicates the thermal diffusivity of the substrate (quartz) (for example, 0.0081 cm^2 / sec). (m-n) indicates the number of tracking resets performed from the nth to the mth. t ｔｒｋ-ｃｙｃｌｅ indicates the tracking cycle time. The tracking cycle time t ｔｒｋ-ｃｙｃｌｅ is shown in equation (3-4). ｓｔａｇｅ indicates the stage velocity. In a normal multi-beam lithography system, the stage velocity v ｓｔａｇｅ = (constant), the tracking cycle time t ｔｒｋ-ｃｙｃｌｅ can be defined by equation (3-4).

[0060] FIG. 16 is a diagram illustrating another part of the formula for calculating the effective temperature in the first embodiment. The convolution process described in FIG. 14 is performed by shifting the rectangular region 35 in the x direction from the left end (n=0) of the stripe region 32 by the size s of the processing mesh 39 until the mesh region of interest with index (k, l) is included in the rectangular region 35 (where n=m). This process is illustrated by the calculation portion surrounded by a dotted line in equation (2) in FIG. 16. The example in FIG. 16 shows the case where the rectangular region 35 is moved until the mesh region of interest with index (k, l) is located at the right end of the rectangular region 35. In this state, the left end of the rectangular region 35 is located at the (k-N+1)th column, and the right end is located at the kth column.

[0061] FIG. 17 is a diagram for explaining another part of the formula for calculating the effective temperature in embodiment 1. FIG. 18 is a diagram for explaining another part of the formula for calculating the effective temperature in embodiment 1. FIG. 18 specifically illustrates the processing performed by the calculation portion of FIG. 17 using equations. As shown in FIG. 17, the processing shown in FIG. 16 is performed N times from when the mesh region of interest reaches the right end position, which is one end of the rectangular region 35 in the x direction, to when it reaches the left end position, which is the other end. In other words, as shown in equation (4) in FIG. 18, the processing shown in FIG. 16 from n=0 to n=m=k-N+1, the processing shown in FIG. 16 from n=0 to n=m=k-N+2, the processing shown in FIG. 16 from n=0 to n=m=k-N+3, ..., the processing shown in FIG. 16 from n=0 to n=m=k are performed N times, and the sum of these processings is calculated. Since N processing meshes 39 are arranged in the x direction in the rectangular region 35, N processing steps are required to move the mesh region of interest from the right end to the left end of the rectangular region 35. This processing is shown by the calculation portion surrounded by a dotted line in equation (2) in FIG. 17. The statistical value of the results of the N convolution steps is then calculated as the effective temperature T(k, l). This processing is shown by the calculation portion surrounded by a dotted line in equation (2) in FIG. 18. The example of equation (2) shows a case where the effective temperature T(k, l) is calculated by dividing the sum of N convolution steps by N. Note that the number of divisions of the rectangular region and the number of calculation steps do not necessarily have to match. That is, the rectangular region may be divided into N parts and the number of calculation steps may be smaller than N (downsampling). Alternatively, the rectangular region may be divided into N parts and distributed to a number of meshes greater than N (upsampling).

[0062] The effective temperature T(k, l) is not limited to the average value, but may be the maximum value, minimum value, or median value of the results of N convolution processes. The median value is more preferable, and the average value is even more preferable.

[0063] The position of the mesh region of interest is changed, and the effective temperature T(i, j) is found for each position (i, j) of the processing mesh 39 .

[0064] As described above, instead of calculating the temperature rise for each shot and each beam, the effective temperature T(i, j) is calculated for each processing mesh 39 using the representative dose value Dij for 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 is the unit area of ​​beam irradiation for each shot. This allows for a significant reduction in the amount of calculation.

[0065] Although it is preferable to calculate the effective temperature T each time using the above method, in the first embodiment, the method for calculating the effective temperature T is further improved.

[0066] 19 is a diagram for explaining an example of a virtual model of effective temperature in embodiment 1. In FIG. 19, when a point irradiation of 1 μC of charge at position coordinates (0, 0) is performed using a multi-beam writing method, the kernel is obtained by calculating the effective temperature (average temperature while the BAA region passes through the (x, y) region) observed at an arbitrary position (x, y). In the graph below the position coordinates (0, 0) in FIG. 19, the vertical axis indicates the amount of charge, and the horizontal axis indicates time t. Also, in the graph below the arbitrary position (x, y), the vertical axis indicates the temperature, and the horizontal axis indicates time t.

[0067] As shown in the graph below the position coordinate (0, 0) in Figure 19, it is assumed that a beam array region with a size Lx in the x-direction moves continuously and linearly at a stage speed Vstage while continuously and linearly irradiating electric charges. It is further assumed that irradiation begins at the right end of the beam array region and ends at the left end. Based on these two assumptions, the effective temperature at an arbitrary position (x, y) is approximately calculated. The graph below the position coordinate (0, 0) in Figure 19 shows the state in which irradiation is performed sequentially as the beam array region passes. As shown in the graph below the arbitrary position (x, y), a temperature rise occurs at the time (t = Lx / Vstage) when the beam array region performs point irradiation at the position coordinate (0, 0) and before and after that time. The effective temperature indicates the average temperature during the time the beam array region passes.

[0068] 20 is a diagram illustrating an example of the kernel derivation process in the first embodiment. Within the stripe 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 intermediate position in the y direction within the stripe region 32 is defined as j=0, then within the stripe region 32, processing meshes 39 ranging from −Ny / 2 to +Ny / 2 are arranged in the y direction. Furthermore, if the central position in the x direction within the stripe region 32 is defined as i=0, then within the stripe region 32, processing meshes 39 ranging from −∞ to M are arranged in the x direction. In equation (5), of the multiple processing meshes 39 within the stripe region 32, the coordinate processing mesh 39 located in the lth row in the y direction and the kth column in the x direction is shown as the mesh region of interest.

[0069] 20, the size sx of the processing mesh 39 in the x direction is the value obtained by dividing the beam array size Lx in the x direction by the number of meshes Nx in the x direction in the beam array, and the size sy of the processing mesh 39 in the y direction is the value obtained by dividing the beam array size Ly in the y direction by the number of meshes Ny in the y direction in the beam array.

[0070] Here, it is assumed that a 1 μC charge is point-irradiated onto the processing mesh at positions i = 0 and j = 0. In this case, the representative dose value Dij of the processing mesh at position (0, 0) is the average value per unit area, so that Dij = 1 / (sxsy), and the representative dose values ​​of the processing meshes other than i = 0 and j = 0 are set to 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 FIG. 20. Because the method of setting the indexes has been changed as described above, the integration range on the right side of equation (5) has been converted from the integration range on the right side of equation (2).

[0071] Here, it is assumed that Nx and Ny are infinity ∞. In other words, it is assumed that the size of the processing mesh is infinitely small.

[0072] FIG. 21 is a diagram showing another example of the kernel derivation process in the first embodiment. By making the processing mesh sizes sx and sy infinitesimal, Equation (5) can be transformed into Equation (6-1). However, function C is shown in Equation (6-2). Function E is shown in Equation (6-3). Here, the thermal spread function PSF is expressed by Equation (3-1) to Equation (3-3) above. The tracking cycle time ttrkcycle can be defined as the value obtained by dividing the processing mesh size sx in the x direction by the stage speed Vstage. Furthermore, 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 Nx in the x direction 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).

[0073] 22 is a diagram showing another example of the kernel derivation process in embodiment 1. As described above, it is assumed that the numbers of meshes Nx and Ny in the processing region overlapping with the beam array region are infinite. In other words, it is assumed that the size of the processing mesh 39 is infinitesimal. In FIG. 22 , the reference number i, which represents a mesh region in the beam propagation direction (x direction) in the processing region of the same size as the beam array region, is divided by the number Nx of mesh regions in the beam propagation direction in the processing region overlapping with the beam array region. This value is multiplied by the size Lx of the beam array region in the beam propagation direction, and the integral variable ω is defined as a value converted by taking Nx to the limit of infinity.

[0074] Also, in FIG. 22, the integral variable ξ is defined as the value obtained by dividing the reference number j, which represents a mesh area in the y direction within a processing area of ​​the same size as the beam array area, by the number Ny of mesh areas in the y direction within the processing area that overlaps with the beam array area, and multiplying this value by the size Ly of the beam array area in the y direction, with Ny being taken to the limit of infinity.

[0075] Also, in Figure 22, the beam irradiation number m of m = k - Nx + 1, k - Nx, ... k, which is performed sequentially Nx times until the processing area consisting of the size of Nx x Ny passes through the mesh of interest at coordinates (k, l), is divided by the number of mesh areas Nx, and multiplied by the size Lx of the beam array area in the beam traveling direction (x direction), and the converted value by taking Nx to the limit of infinity is defined as the integral variable u.

[0076] In addition, in Figure 22, the beam irradiation number n, which is performed sequentially as mth, m-1th, m-2th, etc., is divided by the number of mesh areas Nx, and the result is multiplied by the size Lx of the beam array area in the beam traveling direction (x direction). The value converted by taking Nx to the limit of infinity is defined as the integral variable v.

[0077] As a result, the convolution processing part of the term on the right 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 indicating an integral operation that integrates from v to v + Lx with the integral variable ω, as shown in equation (7-1).

[0078] Furthermore, the convolution processing part of the term on the right side of equation (6-1) that defines the kernel K(k, l) that sums Ly / Ny from j = -Ly / 2 to +Ly / 2 can be defined as a term component that indicates an integral operation that integrates from -Ly / 2 to +Ly / 2 with the integral variable ξ, as shown in equation (7-2).

[0079] Furthermore, the convolution processing part of the term on the right 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 indicating an integral operation that integrates with integral variable v from -∞ to u, as shown in equation (7-3).

[0080] Furthermore, the convolution processing part of the term on the right side 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 that indicates the integration operation of integrating from x - Lx to x with the integral variable u, as shown in equation (7-4).

[0081] Note that the term components integrated with integral variables ω and ξ are integration operations that represent the sum of the temperature rise contributed to position (x, y) by heat generated by a beam irradiated at a certain position (ω, ξ) within the beam array area when the beam array area is at a certain position v. Therefore, the integration range of ω and ξ is within the beam array area, with ω being from v to v + Lx, and ξ being from -Ly / 2 to +Ly / 2. The term components integrated with integral variable v are integration operations that further integrate the temperature rise contributed to position (x, y) by the temperature rise integrated by the above integration operation when the beam array area is at each position from infinity to position u. Therefore, the integration range of v is from -∞ to u. The term components integrated with integral variable u are integration operations that further integrate the temperature rise integrated by the above integration operation from when one end of the beam array area is at position (x, y) to when the other end is at position (x, y). Therefore, the integration range of u is from x - Lx to x.

[0082] Therefore, the kernel K(k, l) can be defined by an integral formula using the integral variables ω, ξ, u, and v. Specifically, the kernel K(k, l) includes a term component indicating an integral operation to integrate with the integral variable ω, a term component indicating an integral operation to integrate with the integral variable ξ, a term component indicating an integral operation to integrate with the integral variable v, a term component indicating an integral operation to integrate with the integral variable u, and a function A / (πσ ｕ，ｖ ２ ) erf(Rg / σ ｕ，ｖ )e^(-((x-ω) ２ +(y-ξ) ２ ) / σ ｕ，ｖ ) and the Dirac delta function δ(ω,ξ), which is a function that satisfies the formulas (8-2) and (8-3). ｕ，ｖ is defined by equation (8-4). In addition, by making the sizes sx and sy of the processing meshes infinitesimal, the differential equation of the error function can be defined by equation (8-5).

[0083] FIG. 23 is a diagram illustrating the kernel in the first embodiment. The kernel K(x, y) represents the average temperature (effective temperature) at any position during the passage of the beam array region when a 1 μC charge is continuously irradiated at (x, y) = (0, 0) while the beam passes through the region. The lower right diagram in FIG. 23 illustrates the continuous irradiation of 1 μC of charge while the beam passes through the region. The vertical axis represents the charge amount, and the horizontal axis represents time. In this case, as shown in the upper diagram in FIG. 23, a non-zero effective temperature appears at x > −Lx even behind the charge irradiation point at coordinates (0, 0). This is because the heat generated by irradiation at the right end of the beam array region contributes to a heating effect when the inside of the beam array region is irradiated, as shown in the lower left diagram in FIG. 23. In other words, the kernel depends on the size Lx of the beam array region.

[0084] FIG. 24 is a diagram showing an example of the relationship between the stage speed and the kernel in the first embodiment. In the example of FIG. 24, an example of four kernels with different stage speeds Vstage, vstage = v1 to v4, is shown, with the beam array size Lx in the x direction being constant. As shown in FIG. 24, the kernel has an asymmetric temperature distribution with different heights and shapes depending on the stage speed. In the example of FIG. 24, it can be seen that the temperature at the center of the temperature distribution increases as the stage speed increases.

[0085] Figure 25 is a diagram showing an example of the relationship between the size of the beam array in the movement direction and the kernel in embodiment 1. The example in Figure 25 shows an example of three kernels with different x-direction sizes Lx of the beam array, Lx = Lx1 to Lx3, when the stage speed is constant. As shown in Figure 25, the height and shape of the temperature distribution kernel vary depending on the x-direction size Lx of the beam array. In the example in Figure 25, it can be seen that the smaller the x-direction size Lx of the beam array, the higher the temperature at the center of the temperature distribution.

[0086] Fig. 26 is a diagram showing another example of the relationship between the kernel and the size in the movement direction of the beam array in embodiment 1. Fig. 26 shows an example of the temperature distribution in the x-direction size Lx of the three beam arrays in Fig. 25. The vertical axis represents temperature, and the horizontal axis represents position in the x-direction. As shown in the example of Fig. 26, the shapes of the rise and fall of the kernel temperature distribution differ depending on the size Lx of the beam array region.

[0087] Therefore, in the first embodiment, a plurality of kernels are created in advance according to the stage speed and the beam array size Lx.

[0088] 27 is a diagram showing an example of a kernel defined as a table in the first embodiment. In FIG. 27, the kernel K(x, y) is defined as a value for each position within a range larger than the beam array area. This is because of the influence of residual heat after the beam array passes through. For example, if the size Lx of the beam array area is set within a range of approximately 100 μm (maximum value) to 10 μm (minimum value), it is preferable to calculate the kernel within a range of approximately ±300 μm in each of the x and y directions.

[0089] In the example of Figure 27, the stage speed Vstage, the beam array size Lx in the x direction (opposite to the stage travel direction), the position (x, y), and the kernel value K(x, y) at each position are related and defined as a table. The value of the kernel K(x, y) at each position is based on the assumption that the beam array region moves continuously at a constant speed and a point charge of 1 μC is irradiated at the center of the kernel, and that the irradiation of the point charge begins at one end of the beam array region and ends at the other end. Under these two assumptions, the value represents a representative value of the temperature while the beam array region passes through that position. Note that the value is referenced based on the actual stage speed and size of the beam array region. If no consistent value is found, a linear interpolation value using the previous and next values ​​can be used.

[0090] FIG. 28 is a diagram showing an example of a kernel equation defined as a continuous function in the first embodiment. In the example of FIG. 28, an example of a function approximating five kernels with different stage velocities by adding together five Gaussian functions that are anisotropic in the x and y directions is shown in Equation (9). Note that a coefficient Ai is prepared for each stage velocity, and the velocity between the stage velocities defined in the table can be determined by using linearly interpolated coefficients Ai, σxi, and σyi. Then, for example, a kernel equation defined as a continuous function can be prepared for each beam array region size Lx. Alternatively, it is also preferable to prepare a function approximating multiple kernels with different stage velocities and beam array region sizes Lx.

[0091] As described above, in the first embodiment, a plurality of kernels that depend on the stage speed and the beam array area size Lx are prepared in advance. The plurality of kernels are stored in the storage device 144.

[0092] In the stage speed and beam array size input step (S109), the acquisition unit 56 acquires the stage speed Vstage and the beam array size Lx for the current drawing process. Specifically, the acquisition unit acquires the stage speed Vstage and the beam array size Lx set when setting drawing conditions (not shown). The drawing conditions are set by manual input by the user. Alternatively, it is preferable to set multiple drawing condition parameters, including the stage speed Vstage and the beam array size Lx, on an input screen (not shown) so that multiple conditions can be selected for each parameter, and the user can select each drawing condition parameter from the multiple conditions set. The beam array size Lx changes when, for example, a limited number of beams are used among the beam arrays that can be irradiated by the drawing apparatus 100. Specifically, this can be achieved by using only the central beam arrays of the beam arrays, which are less affected by aberration. This reduces the number of beams, thereby increasing the drawing time but improving the drawing position accuracy.

[0093] In the kernel determination step (S110), the kernel determination unit 57 determines a corresponding kernel from among a plurality of kernels in accordance with the acquired (input) stage velocity Vstage and beam array size Lx.

[0094] In the effective temperature calculation step (S112), the effective temperature calculation unit 58 calculates a representative value of the temperature rise caused by the heat from the beam irradiation on each of the multiple processing meshes 39 as the effective temperature T(k, l) of each of the multiple processing meshes 39 by convolution processing of a kernel determined by the speed of the stage 105 on which the sample 101 is placed and the size of the beam array area of ​​the multi-beam 20 on the surface of the sample 101 in the drawing progression direction, and a representative value of the dose amount. In other words, the effective temperature calculation unit 58 inputs the speed Vstage of the stage 105 and the size Lx of the beam array region in the x direction, and calculates, using a kernel determined by the speed Vstage of the stage 105 and the size Lx of the beam array region in the x direction and a representative dose value, a representative value of the temperature rise that is given to a mesh region of interest (k, l), which is one of the multiple processing meshes 39, by heat caused by beam irradiation into a processing region on the surface of the sample 101 that overlaps with the beam array region and is the same size as the beam array region, as the effective temperature T(k, l) of the mesh region of interest. The calculated effective temperature is output and stored in the memory 112 or the storage device 142, etc. Specifically, it operates as follows.

[0095] FIG. 29 is a diagram illustrating a method for calculating the effective temperature in the first embodiment. As shown in FIG. 29, the effective temperature calculation unit 58 performs a convolution process between the dose distribution of the dose amount representative 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) showing the convolution process. In the convolution process, the kernel center is shifted within the dose distribution, and the sum of the element products of elements at the same position is calculated. The sum of the element products when the kernel center is located at coordinates (k, l) becomes the effective temperature T(k, l).

[0096] In the above example, the stage 105 moves at a constant speed, but the present invention is not limited to this. The above-described formula (10) can also be applied when the stage 105 moves at a variable speed. In such a case, the stage speed distribution is stored in the storage device 144. The effective temperature calculation unit 58 acquires the stage speed at the position where the kernel center is located, and selects and uses the kernel corresponding to the stage speed at the position where the kernel center is located. This allows the effective temperature to be calculated using the above-described kernel even when the stage moves at a variable speed.

[0097] In the correction amount calculation step (S114), the correction amount calculation unit 60 uses the effective temperatures in each of the plurality of mesh regions to calculate the dose of a plurality of beams that irradiate a mesh region of interest, which is one of the plurality of mesh regions, among the multibeam 20. For example, the correction amount calculation unit 60 first calculates a modulation factor α(x) of the dose that depends on the effective temperature T.

[0098] FIG. 30 is a diagram showing an example of the relationship between line width CD and temperature in the first embodiment. In FIG. 30, the vertical axis represents line width CD (Critical Dimension), and the horizontal axis represents temperature. As shown in FIG. 30, it can be seen that as the resist temperature increases, the deviation in line width CD also increases. There is a linear relationship between the CD variation ΔCD / ΔT [nm / K] due to the heating effect. This value differs for each resist type and substrate type, so it is obtained by conducting experiments for those types. Therefore, an approximation formula that approximates the CD change ΔCD per unit temperature ΔT is obtained in advance. Such correlation data (1) is input from the outside and stored in the storage device 144.

[0099] FIG. 31 is a diagram showing an example of the relationship between line width CD and dose amount in the first embodiment. In FIG. 31, the vertical axis represents line width CD, and the horizontal axis represents dose amount. In the example of FIG. 31, the horizontal axis is plotted logarithmically. As shown in FIG. 31, the line width CD depends on the pattern density, and as the dose amount increases, the line width CD also increases. The relationship ΔCD / ΔD between CD fluctuations and dose amount, which depends on each resist / substrate type and pattern density, is obtained by conducting experiments. Then, an approximation formula that approximates the CD change amount ΔCD per unit dose is determined. Such correlation data (2) is input from the outside and stored in the storage device 144.

[0100] The correction amount calculation unit 60 reads out the correlation data (1) and (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, 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 The correction amount calculation unit 60 calculates the correction amount by multiplying the effective temperature T(i, j) by the modulation factor α(x).

[0101] In the correction step (S118), the correction unit 62 (an example of a dose correction circuit) corrects the dose of the multiple beams irradiating each mesh region of interest using the effective temperature T(i, j). The corrected dose D'(x) can be calculated using the following equation (12). x indicates the index of the pixel 36. (i, j) indicates the index of the processing mesh. Furthermore, the pattern density ρ can be calculated by using the pattern density of the target pixel 36. (12) D'(x) = D(x) - T(i, j) α(x)

[0102] Then, the correction unit 62 creates a dose map (2) for each stripe region 32 using the calculated corrected dose D'(x) for each pixel 36. The dose D'(x) for each pixel 36 is defined as each element of the dose map (2). This determines the corrected (modulated) dose distribution D'(x). In other words, the CD dimension corresponding to the temperature increase can be returned to the design dimension. The created dose map (2) is stored in the storage device 144.

[0103] In the irradiation time data generation step (S120), the irradiation time data generation unit 72 calculates, for each pixel 36, the irradiation time t of the electron beam for injecting the calculated corrected dose D'(x) into the pixel 36. The irradiation time t can be calculated by dividing the dose D'(x) by the current density J. If the uncorrected dose D(x) defined in the dose map (1) is a relative value (dose coefficient value) to the reference dose Dbase calculated assuming that the reference dose Dbase is 1, the dose statistical value Dij of each processing mesh 39 is also calculated as a relative value to the reference dose Dbase. Therefore, the effective temperature T(i, j) of each processing mesh 39 is also calculated as a relative value to the reference dose Dbase. Therefore, in such a case, the irradiation time t can be calculated by multiplying the dose D'(x) by the reference dose Dbase and dividing the result by the current density J. The irradiation time t of each pixel 36 is calculated as a value within the maximum irradiation time Ttr that can be irradiated with one shot of the multi-beam 20. The irradiation time t of each pixel 36 is converted into gradation value data of 0 to 1023 gradations, where the maximum irradiation time Ttr is, for example, 1023 gradations (10 bits). The gradated irradiation time data is stored in the storage device 142.

[0104] In the data processing step (S122), the data processing unit 74 rearranges the irradiation time data in the order of shots in accordance with the writing sequence, and also rearranges the irradiation time data in the order of data transfer taking into consideration the order of the shift registers in each group.

[0105] In the writing step (S124), under the control of the writing control unit 80, the transfer control unit 79 transfers the irradiation time data to the deflection control circuit 130 in the order of the shots. The deflection control circuit 130 outputs a blanking control signal to the blanking aperture array mechanism 204 in the order of the shots, and outputs a deflection control signal to the DAC amplifier units 132 and 134 in the order of the shots. Then, the writing mechanism 150 writes a pattern on the sample 101 using the multi-beams 20 with dose amounts D'(x) corrected using the effective temperatures T(i, j). In other words, the writing mechanism 150 writes a pattern on the sample 101 using the correction amount calculated using the effective temperatures obtained by the above-mentioned effective temperature calculation method.

[0106] In the above example, the case where writing processing is sequentially performed on the stripe regions 32 for which calculation of the dose D'(x) has been completed has been described. For example, while writing processing is being performed on a certain stripe region 32, calculation of the dose D'(x) of the stripe region 32 one stripe ahead of the stripe region 32 currently being written, or the stripe region 32 two stripes ahead of the stripe region 32 currently being written, is performed in parallel. In other words, the case where calculation of the dose D'(x) is performed simultaneously with the writing processing has been described. However, this is not limiting. As a preprocessing before starting the writing processing, calculation of the effective temperature T(i, j) and / or the dose D'(x) may be performed.

[0107] As described above, according to the first embodiment, in multi-beam writing, resist heating can be corrected without accumulating the influence of temperature rise for each shot and each beam. Furthermore, by preparing multiple kernels in advance, the volume of calculation processing during writing processing can be significantly reduced.

[0108] [Embodiment 2] In the first embodiment, a configuration was described in which resist heating is corrected by dose modulation based on the effective temperature obtained using a kernel. The method of correcting resist heating is not limited to this. In the second embodiment, a configuration will be described in which correction is performed by resizing the graphic pattern to be written based on the effective temperature obtained using a kernel. The following content may be the same as in the first embodiment except for the points that will be particularly described.

[0109] Fig. 32 is a diagram showing an example of the configuration of a drawing device according to embodiment 2. Fig. 32 is the same as Fig. 1 except that correction unit 63 is provided instead of correction unit 62.

[0110] 32 , each of the “units” such as the pattern density calculation unit 50, the dose calculation unit 52, the division unit 53, the dose representative value calculation unit 54, the acquisition unit 56, the kernel determination unit 57, the effective temperature calculation unit 58, the correction amount calculation unit 60, the correction unit 63, the irradiation time data generation unit 72, the data processing unit 74, the transfer control unit 79, and the writing control unit 80 has a processing circuit. Such a processing circuit includes, for example, an electric circuit, a computer, a processor, a circuit board, a quantum circuit, or a semiconductor device. Each of the “units” may use a common processing circuit (the same processing circuit) or different processing circuits (separate processing circuits). The information input and output to the pattern density calculation unit 50, dose calculation unit 52, division unit 53, dose representative value calculation unit 54, acquisition unit 56, kernel determination unit 57, effective temperature calculation unit 58, correction amount calculation unit 60, correction unit 63, irradiation time data generation unit 72, data processing unit 74, transfer control unit 79, and drawing control unit 80, as well as the information being calculated, are stored in memory 112 each time.

[0111] Fig. 33 is a flowchart showing an example of main steps of the writing method according to embodiment 2. Fig. 33 is the same as Fig. 11 except that a correction amount calculation step (S115) and a correction step (S117) are performed instead of the correction amount calculation step (S114) and the correction step (S118).

[0112] The details of each step from the pattern density calculation step (S102) to the effective temperature calculation step (S112) are the same as those in the first embodiment.

[0113] In the correction amount calculation step (S115), the correction amount calculation unit 60 uses the effective temperatures in each of the plurality of mesh regions to calculate a correction amount for correcting pattern data of a graphic to be drawn in a mesh region of interest, which is one of the plurality of mesh regions among the multi-beam 20. Specifically, the operation is as follows. The correction amount calculation unit 60 calculates the correction amount using the relationship between the effective temperature T(i, j) and the dimensional change amount (ΔCD / ΔT) of the drawn pattern. Furthermore, the correction amount calculation unit 60 refers to correlation data (1) stored in the storage device 144 that approximates the CD change amount ΔCD per unit temperature ΔT. Then, the correction amount calculation unit 60 calculates the value obtained by multiplying T(i, j) of each mesh region of interest by (ΔCD / ΔT).

[0114] In the correction step (S117), the correction unit 63 (an example of a resizing processing circuit) resizes the size of the graphic pattern to be drawn in each processing mesh using a correction amount calculated using the relationship between the effective temperature T(i, j) and the dimensional change amount (ΔCD / ΔT) of the pattern to be drawn. The corrected pattern dimension L'(x) can be calculated using the following equation (13). x indicates the index of the pixel 36. (i, j) indicates the index of the processing mesh. Furthermore, the initial pattern density of the target pixel 36 can be used as the pattern density ρ. (13) L'(x)=L(x)-T(i, j)·(ΔCD / ΔT)

[0115] The size L(y) in the y direction is also resized in the same manner. The resized data of each figure pattern is then stored in the storage device 144.

[0116] In the irradiation time data generation step (S120), the pattern density calculation unit 50 uses the data of the resized figure pattern to calculate the pattern density ρ (pattern area density) for each pixel 36 in the target stripe region 32. Then, a pattern density map is created.

[0117] In the dose calculation step (S104), the dose calculation unit 52 uses the recreated pattern density map to calculate, for each pixel 36, a dose D′(x) (irradiation amount) to irradiate the pixel 36. Then, the dose map is recreated.

[0118] The irradiation time data generation unit 72 calculates, for each pixel 36, the irradiation time t of the electron beam for making the calculated resize-corrected dose D'(x) incident on that pixel 36. The irradiation time t can be calculated by dividing the dose D'(x) by the current density J. The irradiation time t of each pixel 36 is calculated as a value within the maximum irradiation time Ttr that can be irradiated with one shot of the multi-beam 20. The irradiation time t of each pixel 36 is converted into gradation value data of 0 to 1023 gradations, for example, with the maximum irradiation time Ttr being 1023 gradations (10 bits). The gradated irradiation time data is stored in the storage device 142.

[0119] The contents of the data processing step (S122) and the writing step (S124) are the same as those in the embodiment 1. In the writing step (S124), the writing mechanism 150 writes the resized pattern on the sample 101 using the multi-beam 20.

[0120] As described above, according to the second embodiment, in multi-beam writing, resist heating can be corrected by resizing without accumulating the influence of temperature rise for each shot and each beam. Furthermore, by preparing multiple kernels in advance, the volume of calculation processing during writing processing can be significantly reduced.

[0121] The above describes the embodiments with reference to specific examples. However, the present invention is not limited to these specific examples. Furthermore, the processing functions described in the first and second embodiments may be executed by a computer. Furthermore, a program for causing a computer to execute such processing functions may be stored in a non-transitory, tangible, readable recording medium, such as a magnetic disk device.

[0122] Although the description of the device configuration, control method, and other parts not directly necessary for the explanation of the present invention have been omitted, the required device configuration and control method can be appropriately selected and used. For example, the description of the control unit configuration that controls the drawing device 100 has been omitted, but it goes without saying that the required control unit configuration can be appropriately selected and used.

[0123] In addition, all methods for calculating the effective temperature of a multi-charged particle beam drawing area, multi-charged particle beam drawing devices, multi-charged particle beam drawing methods, and programs (or readable recording media on which programs are non-temporarily recorded) that include elements of the present invention and that can be appropriately modified by a person skilled in the art are included in the scope of the present invention.

[0124] The present invention relates to a method for calculating the effective temperature of a multi-charged particle beam drawing region, a multi-charged particle beam drawing device, a multi-charged particle beam drawing method, and a program (or a readable recording medium on which the program is non-temporarily recorded), and can be used, for example, as a method for correcting resist heating that occurs in multi-beam drawing.

[0125] 20 Multi-beam 22 Hole 24 Control electrode 25 Passage hole 26 Counter electrode 28, 36 Pixel 29 Sub-irradiation area 30 Writing area 32 Stripe area 34 Irradiation area 35 Rectangular area 39 Processing mesh 41 Control circuit 46 Amplifier 47 Individual blanking mechanism 50 Pattern density calculation unit 52 Dose amount calculation unit 53 Dividing unit 54 Dose amount representative value calculation unit 56 Acquisition unit 57 Kernel determination unit 58 Effective temperature calculation unit 60 Correction amount calculation unit 62, 63 Correction unit 72 Irradiation time data generation unit 74 Data processing unit 79 Transfer control unit 80 Writing control unit 100 Writing device 101 Sample 102 Electron lens column 103 Writing chamber 105 XY stage 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 device 140, 142, 144 Storage device 150 Drawing mechanism 160 Control system circuit 200 Electron beam 201 Electron gun 202 Illumination lens 203 Shaping 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 region 343 Pad

Claims

1. A method for calculating an effective temperature in a multi-charged particle beam drawing area, comprising the steps of: calculating a representative value of the dose of the beam irradiating within each of a plurality of mesh areas into which a drawing area of ​​a sample irradiated with a multi-charged particle beam is divided in the drawing progress direction and in a direction linearly independent of the drawing progress direction, as a representative dose value; and calculating and outputting a representative value of the increase in temperature caused by heat due to beam irradiation to each of the plurality of mesh areas by convolution processing of the representative dose value and a kernel determined by the speed of a stage on which the sample is placed and the size of the beam array area of ​​the multi-charged particle beam on the surface of the sample in the drawing progress direction.

2. The method for calculating the effective temperature of a multi-charged particle beam drawing area as described in claim 1, characterized in that the kernel is defined as values ​​for each position within a predetermined range, and the values ​​at each position of the kernel represent representative values ​​of the temperature while the beam array area passes through the position under the assumption that the beam array area moves continuously at a constant speed and irradiates a point charge at the center position of the kernel, and that the irradiation of the point charge starts at one end of the beam array area and ends at the other end.

3. The kernel is an integral variable ω converted by dividing a reference number i representing a mesh area in the beam traveling direction within a processing area of ​​the same size as the beam array area by the number Nx of mesh areas in the beam traveling direction within the processing area that overlaps with the beam array area, and multiplying the result by the size Lx of the beam array area in the beam traveling direction, and taking Nx to the limit of infinity; and an integral variable ξ converted by dividing a reference number j representing a mesh area in the first direction within the processing area of ​​the same size as the beam array area, by the number Ny of mesh areas in the first direction within the processing area that overlaps with the beam array area, and multiplying the result by the size Ly of the beam array area in the first direction, and taking Ny to the limit of infinity.

2. The method for calculating an effective temperature in a multi charged particle beam writing region according to claim 1, wherein the effective temperature is defined by an integral equation using: an integral variable u converted by taking the limit of infinity to obtain a value obtained by dividing a beam irradiation number m of m=k-Nx+1, k-Nx, ..., k, which is sequentially performed Nx times until the processing region having a size of Nx x Ny passes through a mesh of interest at coordinates (k, l), by the number of mesh regions Nx, and multiplying the result by the size Lx of the beam array region in the beam traveling direction, and taking Nx to the limit of infinity; and an integral variable v converted by taking the limit of infinity to obtain a value obtained by dividing a beam irradiation number n of m-th, m-1-th, m-2-th, ..., which is sequentially performed, by the number of mesh regions Nx, and multiplying the result by the size Lx of the beam array region in the beam traveling direction, and taking Nx to the limit of infinity.

4. A multi-charged particle beam drawing method for drawing a pattern on the sample using a correction amount calculated using the effective temperature obtained by the effective temperature calculation method described in claim 1, comprising the steps of: calculating, using the effective temperature in each of the plurality of mesh regions, a correction amount for correcting dose amounts of a plurality of beams of the multi-charged particle beam irradiating a mesh region of interest, which is one of the plurality of mesh regions, or pattern data of a figure to be drawn within the mesh region of interest; and drawing a pattern on the sample using the correction amount.

5. A readable recording medium non-temporarily recording thereon a program for causing a computer to execute the following functions: a function for calculating, in each of a plurality of mesh regions in which a drawing region of a sample irradiated with a multi-charged particle beam is divided in the drawing progression direction and in a direction linearly independent of the drawing progression direction, a representative value of the dose of the beam irradiating within the mesh region as a representative dose value; and a function for calculating, by convolution processing of a kernel determined by the speed of a stage on which the sample is placed and the size of the beam array region of the multi-charged particle beam in the drawing progression direction on the surface of the sample, and the representative dose value, a representative value of the temperature rise caused by heat due to beam irradiation to each of the plurality of mesh regions as an effective temperature of each of the plurality of mesh regions.

6. A readable recording medium non-temporarily recording thereon a program for causing a computer to execute the functions set forth in claim 5; a function for calculating, using the effective temperature in each of the plurality of mesh regions, a correction amount for correcting dose amounts of a plurality of beams irradiating the mesh region of interest, which is one of the plurality of mesh regions, of the multi-charged particle beam, or pattern data of a figure to be drawn within the mesh region of interest; and a function for drawing a pattern on the sample using the correction amount.

7. A dose representative value calculation circuit for calculating a representative value of the dose of the beam irradiating within each of a plurality of mesh regions obtained by dividing a drawing region of a sample irradiated with a multi-charged particle beam in the drawing progress direction and in a direction linearly independent of the drawing progress direction as a dose representative value; an effective temperature calculation circuit for calculating a representative value of the temperature rise caused by heat due to beam irradiation to each of the plurality of mesh regions as an effective temperature of each of the plurality of mesh regions by convolution processing of a kernel determined by the speed of a stage on which the sample is placed and the size of the beam array region of the multi-charged particle beam on the surface of the sample in the drawing progress direction and the dose representative value; a correction amount calculation circuit for calculating a correction amount for correcting the dose of a plurality of beams irradiating a mesh region of interest, which is one of the plurality of mesh regions, of the multi-charged particle beam or pattern data of a figure to be drawn within the mesh region of interest, using the effective temperature in each of the plurality of mesh regions; and a drawing mechanism for drawing a pattern on the sample using the calculated correction amount. A multi-charged particle beam drawing apparatus comprising:

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