WO2018061960A1

WO2018061960A1 - Method and device for obtaining exposure intensity distribution in multibeam electron beam lithography device

Info

Publication number: WO2018061960A1
Application number: PCT/JP2017/034033
Authority: WO
Inventors: 剛哉下村; 洋平大川
Original assignee: 大日本印刷株式会社
Priority date: 2016-09-29
Filing date: 2017-09-21
Publication date: 2018-04-05

Abstract

The purpose of the present invention is to obtain, in a highly accurate manner and in a short period of time, the exposure intensity distribution on a layer to be shaped. The exposure intensity distribution, when lithography data in which pixels P(i, j) having pixel values represented by the intensity of an electron beam at each respective irradiation position are arranged at a pitch d is inputted into a multibeam electron beam lithography device, is computationally obtained. Each of the pixels P (i, j) is split vertically and horizontally into five parts and cells (m, n) having a width g are defined. An irradiation intensity matrix representing the electron beam irradiation intensity distribution is created by an aggregation of a large number of the cells C (m, n). A representative cell, which is at the center of each of the pixels, is imparted with a pixel value of the pixel in question, and the other cells are imparted with a value of zero. A point spread matrix, which corresponds to a point spread function psf representing the distribution of the degree of effect from the center position to the surroundings, is created. The exposure intensity distribution is obtained by convolution integration using the two matrices. A function that has a flat section H having a width corresponding to the opening size of the aperture of the electron beam lithography device is used as the point spread function psf.

Description

Method and apparatus for determining exposure intensity distribution in multi-beam electron beam lithography system

The present invention relates to a method and apparatus for obtaining an exposure intensity distribution in a multi-beam electron beam drawing apparatus, and in particular, relates to an exposure intensity distribution when a predetermined pattern is exposed and drawn on a molding layer using the multi-beam electron beam drawing apparatus. It relates to the technology required by simulation.

2. Description of the Related Art Patterning methods using an electron beam drawing apparatus are widely used in fields where it is necessary to perform fine patterning on a specific material layer, such as a semiconductor device manufacturing process. When an electron beam drawing apparatus is used, a fine pattern can be exposed on the layer to be molded based on given drawing data, so that an extremely thin linear pattern can be formed. For example, the following Patent Document 1 discloses an electron beam drawing apparatus of a single beam method (VSB method: Variable Shape Beam) and a drawing method of drawing a desired pattern using the device.

On the other hand, recently, a multi-beam type electron beam drawing apparatus capable of simultaneously irradiating a plurality of electron beams has been put into practical use. For example, in Patent Document 2, a plurality of electron beams are generated by passing an expanded electron beam through an aperture plate having a plurality of openings, and these are individually controlled ON / OFF using a blanking plate. A multi-beam electron beam drawing apparatus for drawing a predetermined pattern on the surface is disclosed. Further, Patent Document 3 draws a grayscale pattern with gradation by performing beam exposure a plurality of times on the same portion of the sample surface using such a multi-beam type electron beam drawing apparatus. A method is disclosed.

However, it is known that in the patterning method using this electron beam drawing apparatus, the dimension of the pattern to be actually formed varies due to a factor called the proximity effect. This proximity effect is caused by the phenomenon that electrons with a small mass spread while being scattered by molecules in the resist (forward scattering) when the molding layer composed of a resist layer or the like is irradiated with an electron beam. This is explained as a phenomenon (backscattering) in which electrons scattered and bounced near the surface of a metal substrate or the like underneath are diffused in the resist layer.

Therefore, in order to perform patterning with high accuracy, it is necessary to correct the drawing data given to the electron beam drawing apparatus in consideration of the proximity effect. In order to perform such correction, it is effective to estimate the exposure intensity distribution that would actually occur when electron beam drawing is performed on the molding layer using specific drawing data by computer simulation. . If there is an error in the exposure intensity distribution as a result of the simulation, an appropriate correction can be applied to the drawing data so as to eliminate the error. For example, Patent Document 4 discloses a method of obtaining an exposure intensity distribution that will actually occur by computer simulation in consideration of the proximity effect.

JP 2009-253124 A JP 2014-003279 A JP 2010-123966 A Japanese Patent No. 5864424

As described above, in order to perform highly accurate patterning using an electron beam drawing apparatus, it is necessary to correct the drawing data in consideration of the proximity effect of the electron beam. And in order to perform such correction | amendment, the method of estimating correctly the exposure intensity distribution formed in a to-be-molded layer is required. Patent Document 4 described above discloses a method for obtaining such an exposure intensity distribution by computer simulation. This method assumes that the electrons irradiated to the resist layer are distributed according to the intensity distribution indicated by the Gaussian error function, and performs a convolution operation to obtain the exposure intensity distribution for the entire resist layer. Is executed.

As described above, in recent years, multi-beam electron beam drawing apparatuses have become widespread. However, the conventional method disclosed in the above-mentioned Patent Document 4 is basically a method suitable for a single beam type electron beam drawing apparatus, and the method is directly applied to a multi-beam type electron beam drawing apparatus. In this case, the exposure intensity distribution cannot be estimated accurately. In the case of the multi-beam method, the number of beams becomes enormous. Therefore, if the conventional method is applied as it is, the calculation burden becomes heavy and a large calculation time is required for the simulation.

Therefore, the present invention provides a simulation method capable of obtaining the exposure intensity distribution on the electron beam irradiation surface with high accuracy in a multi-beam electron beam lithography apparatus, and exposure intensity distribution calculation capable of implementing the method. An object is to provide an apparatus. It is another object of the present invention to provide a simulation method capable of performing such a calculation for obtaining the exposure intensity distribution in a short time, and to provide an exposure intensity distribution calculating apparatus capable of performing the method. .

(1) A first aspect of the present invention is a simulation method for obtaining an exposure intensity distribution when a predetermined pattern is exposed and drawn on a molding layer using a multi-beam electron beam drawing apparatus.
For each of a number of reference points defined in the electron beam irradiation region, individual evaluation is performed by performing convolution integration of a function indicating the electron beam irradiation intensity and a point spread function indicating the degree of influence of the reference point on the surroundings. Calculate the total exposure intensity at the point,
As the point spread function, a function including an aperture size parameter determined based on the aperture size of the aperture of the electron beam drawing apparatus is used.

(2) According to a second aspect of the present invention, in the simulation method according to the first aspect described above,
Define an xy plane of a two-dimensional xy orthogonal coordinate system as an electron beam irradiation surface,
The influence of the reference point T (x ′, y ′) positioned at the coordinates (x ′, y ′) on the evaluation point V (x, y ′) positioned at the coordinates (x, y) is referred to as the reference point T A function D (x ′, y ′) indicating the electron beam irradiation intensity with respect to (x ′, y ′) and a point spread function psf (X, y defined as X = x′−x, Y = y′−y) Y) and a convolution integral with respect to the x-axis direction and the y-axis direction for
As the point spread function psf (X, Y), in addition to the variables X and Y, a function including an aperture size parameter B determined based on the aperture size of the aperture of the electron beam drawing apparatus is used.

(3) According to a third aspect of the present invention, in the simulation method according to the second aspect described above,
As the point spread function psf (X, Y), a function in which the width of the flat portion of the graph is influenced by the aperture size parameter B is used.

(4) According to a fourth aspect of the present invention, in the simulation method according to the third aspect described above,
As the point spread function psf (X, Y), in addition to the aperture size parameter B, a function including a parameter σ that affects the inclination of the inclined portion of the graph is used.

(5) According to a fifth aspect of the present invention, in the simulation method according to the fourth aspect described above,
Including error function erf as point spread function,
psf (X, Y) = 1/4 · (erf ((B / 2−X) / σ) −erf ((− B / 2−X) / σ)) · (erf ((B / 2−Y) / Σ) −erf ((− B / 2−Y) / σ)).

(6) According to a sixth aspect of the present invention, in the simulation method according to the fourth aspect described above,
Including the inverse trigonometric function arctan as the point spread function,
psf (X, Y) = 1/4 · (arctan ((B / 2−X) / σ) −arctan ((− B / 2−X) / σ)) · (arctan ((B / 2−Y) / Σ) −arctan ((− B / 2−Y) / σ)).

(7) According to a seventh aspect of the present invention, in the simulation method according to the fourth aspect described above,
As a point spread function, an error function erf, a predetermined constant C, a backscattering parameter β, and a proximity effect correction parameter η are included.
psf (X, Y) = C / (1 + η) · (1 / 4σ ² · (erf ((B / 2−X) / σ) −erf ((− B / 2−X) / σ)) · (erf ((B / 2−Y) / σ) −erf ((− B / 2−Y) / σ)) + η / β ² · exp (− (X ² + Y ² ) / β ² ))
This function is used.

(8) An eighth aspect of the present invention is the simulation method according to the first to seventh aspects described above,
When the aperture of the electron beam lithography system has a circular shape, the diameter of the circle is the aperture size of the aperture, and when the aperture has a square shape, the length of one side of the square is the aperture The aperture size is obtained by multiplying the aperture size by the reduction magnification of the projection lens of the electron beam drawing apparatus and used as an aperture size parameter determined based on the aperture size of the aperture.

(9) According to a ninth aspect of the present invention, in the simulation method according to the first to eighth aspects described above,
A drawing data input stage for inputting drawing data consisting of an array of pixels having data representing a pattern drawn by the electron beam drawing apparatus and having a pixel value indicating the irradiation intensity at each irradiation position of the beam;
A parameter setting stage in which a computer sets an aperture size parameter determined based on the aperture size of the aperture of the electron beam lithography apparatus;
A computer prepares two sets of empty calculation matrices made up of a set of calculation cells obtained by dividing each pixel of drawing data into a plurality of cells, and each cell of the first calculation matrix includes By giving a predetermined cell value based on the pixel value of the pixel including the cell, an irradiation intensity matrix showing a planar distribution of the electron beam irradiation intensity is created, and an aperture size parameter is set for each cell of the second calculation matrix. A calculation matrix creation stage for creating a point spread matrix indicating a plane distribution of the degree of influence indicated by the point spread function by giving a cell value according to a predetermined point spread function including:
A computer performs a convolution integral using an irradiation intensity matrix and a point spread matrix to obtain a total exposure intensity at each evaluation point;
Is to do.

(10) According to a tenth aspect of the present invention, in the simulation method according to the ninth aspect described above,
When creating an irradiation intensity matrix in the computation matrix creation stage, a predetermined value determined based on the pixel value of the pixel only for a specific representative cell among a plurality of computation cells included in the same pixel The cell value 0 is given to other non-representative cells.

(11) An eleventh aspect of the present invention is the simulation method according to the tenth aspect described above,
When creating an irradiation intensity matrix in the computation matrix creation stage, one or more computation cells located at the center of the pixel are selected as representative cells among the plurality of computation cells included in the same pixel, and the others The calculation cell is a non-representative cell.

(12) A twelfth aspect of the present invention is the simulation method according to the eleventh aspect described above,
When creating the irradiation intensity matrix at the stage of creating the calculation matrix, each pixel of the drawing data is divided into odd and vertical numbers, and one calculation cell located at the center of each pixel is used as a representative cell. The cell is a non-representative cell, the pixel value of the pixel including the representative cell is given to the representative cell as the cell value, and the cell value 0 is given to the non-representative cell.

(13) According to a thirteenth aspect of the present invention, in the simulation method according to the eleventh aspect described above,
When creating the irradiation intensity matrix in the calculation matrix creation stage, each pixel of the drawing data is divided into an even number for each of the vertical and horizontal directions, and the four calculation cells located at the center of each pixel are used as representative cells. The cell is a non-representative cell, and a value of ¼ of the pixel value of the pixel including the representative cell is given to the representative cell as the cell value, and a cell value of 0 is given to the non-representative cell.

(14) According to a fourteenth aspect of the present invention, in the simulation method according to the tenth aspect described above,
When creating an irradiation intensity matrix in the computation matrix creation stage, among the plurality of computation cells included in the same pixel, a computation cell that exists at a position displaced from the center of the pixel by a predetermined offset amount in a predetermined direction As a representative cell, and other calculation cells as non-representative cells,
When creating a point spread matrix in the calculation matrix creation stage, a point spread matrix showing a plane distribution of the degree of influence indicated by the point spread function corrected by the offset amount in the direction opposite to the predetermined direction is created. It is a thing.

(15) According to a fifteenth aspect of the present invention, in the simulation methods according to the ninth to fourteenth aspects described above,
In the convolution operation stage,
A first calculation step of creating an irradiation intensity frequency matrix by Fourier transforming the irradiation intensity matrix;
A second stage of creating a point spread frequency matrix by Fourier transforming the point spread matrix;
A third calculation stage for creating an exposure intensity frequency matrix having a cell value as a product of the corresponding calculation cells of the irradiation intensity frequency matrix and the point spread frequency matrix;
A fourth calculation stage for creating an exposure intensity matrix showing a planar distribution of the total exposure intensity at each evaluation point by performing an inverse Fourier transform on the exposure intensity frequency matrix;
Is to be executed.

(16) A sixteenth aspect of the present invention includes a drawing data input stage, a parameter setting stage, a calculation matrix creation stage, and a convolution calculation stage in the simulation methods according to the ninth to fifteenth aspects described above. A program is built into a computer and executed.

(17) According to a seventeenth aspect of the present invention, in an exposure intensity distribution calculation device that performs an operation for obtaining an exposure intensity distribution when a predetermined pattern is exposed and drawn on a molding layer using a multi-beam electron beam drawing apparatus.
A drawing data input unit for inputting drawing data composed of an array of pixels having pixel values indicating the irradiation intensity at each irradiation position of the beam, which is data indicating a pattern drawn by the electron beam drawing apparatus;
A parameter setting unit for setting an aperture size parameter determined based on the aperture size of the aperture of the electron beam lithography apparatus;
Prepare an empty calculation matrix consisting of a set of calculation cells obtained by dividing each pixel of drawing data into a plurality of cells, and each calculation cell has a predetermined cell based on the pixel value of the pixel including the cell By providing a value, an irradiation intensity matrix creating unit for creating an irradiation intensity matrix indicating a planar distribution of electron beam irradiation intensity,
A point spread matrix showing a plane distribution of the degree of influence indicated by the point spread function by giving a cell value corresponding to a predetermined point spread function including an aperture size parameter to each calculation cell of the empty calculation matrix. A point spread matrix creation part for creating
A convolution operation execution unit that performs convolution integration using an irradiation intensity matrix and a point spread matrix, and calculates a total exposure intensity at each evaluation point;
Is provided.

(18) According to an eighteenth aspect of the present invention, in the exposure intensity distribution calculating apparatus according to the seventeenth aspect described above,
The point spread matrix creation unit uses a function in which the width of the flat portion of the graph is influenced by the opening size parameter B as the point spread function.

(19) According to a nineteenth aspect of the present invention, in the exposure intensity distribution calculating apparatus according to the eighteenth aspect described above,
The point spread matrix creation unit uses a function including a parameter σ that affects the slope of the slope of the graph in addition to the aperture size parameter B as the point spread function.

(20) According to a twentieth aspect of the present invention, in the exposure intensity distribution calculating apparatus according to the seventeenth to nineteenth aspects described above,
The irradiation intensity matrix creation unit gives a predetermined value determined based on the pixel value of the pixel only for a specific representative cell among a plurality of calculation cells included in the same pixel as a cell value, and other non-representatives The cell value 0 is given for the cell.

(21) According to a twenty-first aspect of the present invention, in the exposure intensity distribution calculating apparatus according to the twentieth aspect described above,
The irradiation intensity matrix creation unit uses one or a plurality of calculation cells located at the center of the pixel as a representative cell among a plurality of calculation cells included in the same pixel, and sets the other calculation cells as non-representative cells. It is made to do.

(22) According to a twenty-second aspect of the present invention, in the exposure intensity distribution calculating apparatus according to the twenty-first aspect described above,
The irradiation intensity matrix creation unit divides each pixel of the drawing data into an odd number in the vertical and horizontal directions. One calculation cell located at the center of each pixel is set as a representative cell, and the other calculation cells are set as non-representative cells. In the cell, the pixel value of the pixel including the representative cell is given as the cell value, and the cell value 0 is given to the non-representative cell.

(23) According to a twenty-third aspect of the present invention, in the exposure intensity distribution calculating apparatus according to the twenty-first aspect described above,
The irradiation intensity matrix creation unit divides each pixel of the drawing data into an even number, both vertically and horizontally, and sets the four calculation cells located at the center of each pixel as representative cells and the other calculation cells as non-representative cells. In the cell, a value of 1/4 of the pixel value of the pixel including the representative cell is given as the cell value, and a cell value of 0 is given to the non-representative cell.

(24) According to a twenty-fourth aspect of the present invention, in the exposure intensity distribution calculating apparatus according to the twentieth aspect described above,
The irradiation intensity matrix creation unit uses, as a representative cell, a calculation cell that exists at a position displaced by a predetermined offset amount in a predetermined direction from the center of the pixel among a plurality of calculation cells included in the same pixel. The calculation cell is a non-representative cell,
The point spread matrix creating unit creates a point spread matrix indicating a plane distribution of the degree of influence indicated by the point spread function corrected in the opposite direction to the predetermined direction by the offset amount.

(25) According to a twenty-fifth aspect of the present invention, in the exposure intensity distribution calculating apparatus according to the seventeenth to twenty-fourth aspects described above,
The convolution operation part
A first calculation unit that creates an irradiation intensity frequency matrix by performing Fourier transform on the irradiation intensity matrix;
A second arithmetic unit for creating a point spread frequency matrix by performing Fourier transform on the point spread matrix;
A third calculation unit for creating an exposure intensity frequency matrix having a cell value that is a product of the corresponding calculation cells of the irradiation intensity frequency matrix and the point spread frequency matrix;
A fourth calculation unit that creates an exposure intensity matrix indicating a planar distribution of the total exposure intensity at each evaluation point by performing inverse Fourier transform on the exposure intensity frequency matrix;
It is made to have.

(26) According to a twenty-sixth aspect of the present invention, the exposure intensity distribution calculation apparatus according to the above-described seventeenth to twenty-fifth aspects is configured by incorporating a program into a computer.

According to the exposure intensity distribution simulation method and the exposure intensity distribution calculation device according to the present invention, the irradiation intensity distribution function of the electron beam generated based on the drawing data, the point spread function indicating the degree of the influence on the surroundings, By performing the convolution integral, it is possible to obtain the exposure intensity distribution generated in the molding layer. Moreover, since a function including an aperture size parameter determined based on the aperture size of the aperture of the electron beam lithography apparatus is used as the point spread function, it is possible to perform an optimum simulation for a multi-beam electron beam lithography apparatus, It becomes possible to obtain the exposure intensity distribution with high accuracy.

In addition, if the calculation is performed using a matrix in which cell values other than the representative cell are set to 0 as the irradiation intensity matrix indicating the irradiation intensity distribution of the electron beam, the calculation burden of convolution integration can be greatly reduced. The calculation for obtaining the exposure intensity distribution can be performed in a short time.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a front view showing a basic structure of a general multi-beam type electron beam drawing apparatus and its drawing principle (partly a sectional view). It is a graph which shows distribution of the energy density (intensity) of a general electron beam. FIG. 6 is a plan view (upper (a)) and a graph (lower (b)) showing the relationship between the two-dimensional pixel array constituting the drawing data and the intensity distribution of the electron beam irradiated based on the drawing data. It is a graph which shows the principle which controls stepwise exposure intensity by performing beam irradiation as many times as a pixel value. A plan view (upper (a)) showing an example of a state in which overlapping exposure occurs due to the relationship between the pixel pitch d and the spot diameter φ of each electron beam, and a graph (lower (b )). FIG. 6 is a plan view (upper stage (a)) of a pattern having a width Da in the x-axis direction and a graph (lower stage (b)) showing the principle of exposing the pattern with multi-beams. FIG. 6 is a plan view (upper (a)) of a linear pattern having a width Da = 25 nm in the x-axis direction and a diagram (lower (b)) showing a pixel arrangement constituting drawing data for exposing the linear pattern. . FIG. 6 is a plan view (upper (a)) of a linear pattern having a width Da = 27 nm in the x-axis direction and a diagram (lower (b)) showing a pixel arrangement constituting drawing data for exposing the linear pattern. . It is a figure which compares the procedure (Drawing (a)) which draws the same pattern with a single beam method, and the drawing procedure (Drawing (b)) with a multi-beam method. It is a top view which shows the calculation principle of the total exposure intensity in the arbitrary evaluation points V (x, y) at the time of drawing by a single beam system. It is a figure which shows an example of the calculating formula used for the calculating principle shown in FIG. It is a top view which shows the calculation principle of the total exposure intensity in the arbitrary evaluation points V (x, y) at the time of drawing by a multi-beam system. It is a figure which shows an example of the calculating formula used for the calculating principle shown in FIG. It is a figure which shows an example of the computing equation used for the calculation which calculates | requires exposure intensity distribution with the simulation method which concerns on this invention, when drawing by a multi-beam system. 15 is a one-dimensional graph showing an example of a point spread function psf (X, Y) shown in Expression (3) of FIG. It is a figure which shows the type | formula of another point spread function psf (X, Y) suitable for using for Formula (3) of FIG. It is a figure which shows the type | formula of another point spread function psf (X, Y) suitable for using for Formula (3) of FIG. It is a flowchart which shows the basic procedure of the simulation method which concerns on this invention. It is a figure which shows the specific example of creation of the irradiation intensity matrix D (x ', y') by step S30 of FIG. FIG. 19 is a diagram illustrating a correspondence relationship between the irradiation intensity matrix D (x ′, y ′) created in step S30 of FIG. 18 and the point spread matrix psf (X, Y). It is a figure which shows the concept of the process which performs the convolution operation by step S40 of FIG. 18 based on the drawing data shown to FIG. It is a figure which shows the modification of irradiation intensity matrix D (x ', y') and point spread matrix psf (X, Y) produced by step S30 of FIG. It is a figure which shows the concept of the process which performs the convolution operation by FIG.18 S40 about the example shown in FIG. It is a figure which shows another modification of the irradiation intensity matrix D (x ', y') produced by step S30 of FIG. It is a figure which shows another modification of the irradiation intensity matrix D (x ', y') produced by step S30 of FIG. It is a figure which shows the principle which performs the convolution operation by step S40 of FIG. 18 using Fourier transformation. It is a figure which shows the principle by which the calculation burden is eased by determining the representative cell and performing the convolution calculation using Fourier transform. It is a block diagram which shows the basic composition of the exposure intensity distribution calculating apparatus which concerns on this invention. It is a figure which shows the 1st example of exposure intensity distribution obtained by the simulation method which concerns on this invention. It is a figure which shows the 2nd example of exposure intensity distribution obtained by the simulation method which concerns on this invention.

Hereinafter, the present invention will be described based on the illustrated embodiment.

<<< §1. Drawing principle with multi-beam electron beam drawing system >>
The present invention is premised on a technique for obtaining an exposure intensity distribution in a multi-beam electron beam lithography apparatus. Therefore, for the convenience of explanation, the drawing principle by a general multi-beam electron beam drawing apparatus will be briefly described first. FIG. 1 is a front view showing a basic structure of a multi-beam electron beam drawing apparatus and its drawing principle (partly a sectional view).

As shown in the figure, the electron beam 20 irradiated from the electron gun 10 is expanded by a condenser lens 30 that performs an electromagnetic action, and is irradiated to an aperture plate 40 (shown as a sectional view in the figure). A large number of openings 41 are formed in the aperture plate 40, and only the electron beam 21 that has passed through the openings 41 is reduced and projected onto the lower sample substrate 60 through the projection lens 50 that also performs an electromagnetic action. Then, the surface to be exposed of a layer to be molded (usually a resist layer) 61 formed on the upper surface is irradiated. The sample substrate 60 is placed on the moving stage 70, and can be moved in the horizontal direction in the figure and in the depth direction in the figure.

Recently, an aperture plate 40 having openings 41 arranged in a 512 × 512 two-dimensional matrix is used, and the upper surface of the molding layer 61 is simultaneously exposed by 250,000 or more electron beams 21 to form a fine pattern. An apparatus having a drawing function has been put into practical use. Usually, a blanking plate (not shown) is disposed on the lower surface of the aperture plate 40, and a function of individually turning on / off each electron beam 21 that has passed through the opening 41 is provided.

The individual openings 41 formed in the aperture plate 40 usually have a circular cross section, and the cross sections of the individual electron beams 21 that have passed through the openings 41 are circular. In some cases, an opening having a rectangular cross section may be used. Hereinafter, it is assumed that the opening 41 has a circular cross section, and one electron beam is formed on the upper surface (exposed surface) of the layer 61 to be molded. The description will be made assuming that a circular irradiation spot is formed by the irradiation of 21. For example, if the opening 41 is a circle having a diameter of 4 μm and the reduction magnification of the projection lens 50 is 1/200, a circular irradiation spot (strictly, a slightly larger spot) having a diameter of about 20 nm is formed on the exposure target surface. Formed).

It is said that the energy density of a general electron beam has a distribution according to a Gaussian error function with its central axis as a peak. As will be described later, in the present invention, a special function is used instead of a Gaussian error function as a function indicating the energy density of one electron beam 21 that has passed through the opening 41. The following description will be given on the assumption that the energy density of the electron beam 21 has a distribution corresponding to a Gaussian error function.

Under such a premise, the energy density E (irradiation intensity of the electron beam) of the circular irradiation spot formed on the exposure target surface of the molding target layer 61 by one electron beam 21 is as shown in the graph M of FIG. Distribution according to the Gaussian error function. The horizontal axis of this graph indicates the position in the one-dimensional direction expressed in units of nm, and the position of the numerical value 0 on the horizontal axis corresponds to the position where the central axis of one electron beam 21 is irradiated. . Actually, a circular irradiation spot having a two-dimensional spread is formed on the exposure target surface, and the graph showing the energy density E is obtained by rotating the graph M shown in FIG. 2 around its central axis. Become a rotating body.

The dimension φ on the horizontal axis in the graph of FIG. 2 corresponds to the diameter of the circular irradiation spot thus formed on the exposure target surface. Therefore, when one electron beam having an energy density E as shown in FIG. 2 is irradiated, the inside of a circle with a diameter φ is exposed on the surface to be exposed, and the irradiation intensity of each part is from the center to the periphery. It decreases with a distribution according to the Gaussian error function. Normally, the beam size is shown as a beam diameter indicating the half width value of the graph of FIG. 2, but for convenience of explanation, the dimension φ shown in FIG. 2 is referred to as a spot diameter, and a numerical value corresponding to the beam diameter. Will be treated as

In the case of an electron beam drawing apparatus of a single beam method (VSB method: Variable Shape Beam), since only one electron beam is irradiated on the sample substrate 60, its cross-sectional shape is processed into an arbitrary shape such as a rectangle, and an arbitrary shape is obtained. Irradiation can be performed with the intensity adjusted. However, the multi-beam type electron beam drawing apparatus has an advantage that drawing can be performed at a very high speed using a large number of electron beams 21, but the cross-sectional shape of each beam can be controlled individually. It is difficult to individually control the intensity of each beam. In fact, in the case of an apparatus that generates as many as 250,000 beams, it is not possible to provide a mechanism for individually shaping or individually adjusting the intensity of each electron beam that has passed through the opening 41 of the fine aperture plate.

In the end, a general multi-beam electron beam lithography system currently used can form a large number of circular irradiation spots having a diameter φ on the surface to be exposed, but the irradiation spots can be formed in any shape. Therefore, it is necessary to adopt a method of performing drawing by ON / OFF control of individual electron beams. Therefore, in order to perform drawing control of the multi-beam type electron beam drawing apparatus, drawing data (also referred to as a quantization map) configured by a two-dimensional pixel array is used.

FIG. 3 (a) （is a plan view (upper (a)) and graph (lower) showing the relationship between the two-dimensional pixel array constituting the drawing data and the intensity distribution of the electron beam irradiated based on the drawing data. (b)). Now, an xy two-dimensional coordinate system is defined on the exposure target surface, and a square pixel P as shown in FIG. 3 (a) is hatched in the upper right corner of FIG. Define an array. Here, it is assumed that the width of each pixel P in the horizontal direction (x-axis direction) and the vertical direction (y-axis direction) is d. This width d corresponds to the horizontal and vertical pitches of the pixels P.

Here, an irradiation reference point Q is defined at the center position of each pixel P, and a value indicating the intensity of the electron beam to be irradiated to the irradiation reference point Q is given as the pixel value of the pixel P. If drawing data having such a pixel array is supplied to a multi-beam electron beam drawing apparatus, the drawing apparatus performs electron beam exposure having a predetermined intensity distribution on the exposure target surface based on the drawing data. It can be performed. For example, exposure with a circular irradiation spot S1 is performed on the exposure target surface (xy plane) by the electron beam irradiated to the irradiation reference point Q1 defined at the center of the pixel P1 shown in FIG. The exposure by the circular irradiation spot S2 is performed on the exposure target surface (xy plane) by the electron beam irradiated to the irradiation reference point Q2 defined at the center of the.

In this case, the exposure intensity by the irradiation spot S1 is determined based on the pixel value E1 of the pixel P1, and the exposure intensity by the irradiation spot S2 is determined by the pixel value E2 of the pixel P2. For example, assuming that the individual pixel values E1 and E2 indicate the peak value of the distribution according to the Gaussian error function, the exposure intensity distribution in the x-axis direction by the irradiation spots S1 and S2 shown in FIG. Is as shown in the graph of FIG. That is, the exposure intensity distribution by the electron beam irradiated around the irradiation reference point Q1 is a mountain having a width φ as shown in the graph M1, and the exposure intensity distribution by the electron beam irradiated around the irradiation reference point Q2 is It becomes a mountain having a width φ as in the graph M2. Here, the width φ is the diameter of the circular irradiation spot as described above.

3 shows a state in which the irradiation spots S1 and S2 are formed for the irradiation reference points Q1 and Q2 of the two pixels P1 and P2, respectively, for convenience of explanation. An irradiation reference point Q is defined at the center position of P, and each irradiation reference point Q is irradiated with an electron beam. Here, the vertical and horizontal arrangement pitch of the irradiation reference point Q is the pitch d as in the vertical and horizontal arrangement pitch of the pixels P.

By the way, in the multi-beam type electron beam drawing apparatus, the intensity of a large number of electron beams cannot be individually controlled. Therefore, in the example shown in FIG. 3, the electron beam irradiated to the irradiation reference point Q1 and the electron beam irradiated to the irradiation reference point Q2 must be electron beams having the same intensity. However, it is possible to individually turn on / off individual electron beams by controlling the blanking plate. Therefore, for each irradiation reference point Q, a method of changing the exposure intensity by individually controlling ON / OFF of the irradiated electron beam and changing the exposure time is adopted. In the case of the above example, by setting the irradiation time to the irradiation reference point Q1 longer than the irradiation time to the irradiation reference point Q2, an exposure intensity distribution as shown in the graph of FIG. .

Such control of the exposure time is actually performed in the form of control of the number of exposures. As shown in FIG. 1, in practice, a large number of electron beams 21 are two-dimensionally formed on the molding layer 61 while moving the moving stage 70 in two dimensions (left and right direction and depth direction in FIG. 1). This is because the drawing is performed while scanning.

For example, an exposure time of several nanoseconds is set as a unit exposure time for one electron beam irradiation, and the moving stage 70 is moved in the x-axis direction by a pitch d each time one electron beam irradiation is completed. If the next electron beam irradiation is performed, a specific irradiation reference point Q is exposed for a unit exposure time by a different electron beam (adjacent electron beam) each time. . At this time, if individual ON / OFF control is performed for each individual electron beam each time, it is possible to set a specific exposure intensity for each irradiation reference point Q although it is stepwise.

Specifically, for example, if an exposure intensity distribution like the graph M1 in FIG. 3B is obtained by performing exposure 10 times on the irradiation reference point Q1, the irradiation reference point Q2 By performing the exposure five times, an exposure intensity distribution like the graph M2 in FIG. 3B is obtained.

FIG. 4 is a graph showing the principle of controlling the exposure intensity in 16 steps by changing the number of exposures for each irradiation reference point Q as described above. Here, for convenience of illustration, only examples of four

stages

0, 5, 10, and 15 are shown, but in reality, intermediate stages between them are also set and stages 0 to 15 are set. All 16 stages are set. The exposure intensity distribution graphs M (15), M (10), and M (5) shown in FIG. 4 have peak intensities E (15), E (10), and E (5), respectively, and have the same spot diameter φ. The graph is a distribution according to a Gaussian error function with a spread.

For example, if the pixel values p of the pixels P (15), P (10), P (5), and P (0) are p = 15, p = 10, p = 5, and p = 0, respectively In the vicinity of the irradiation reference points Q (15), Q (10), Q (5), Q (0) defined at the center position of the pixel, exposure intensity distribution graphs M (15), M ( 10), M (5), and exposure having an intensity distribution corresponding to M (0) are performed. The peak value of each exposure intensity distribution graph is a value corresponding to the number of exposures (= pixel value p) at each irradiation reference point position.

That is, the irradiation reference point Q (0) corresponding to the pixel value p = 0 is never irradiated with an electron beam, and the graph M (0) is actually a substantial mountain-shaped graph. Don't be. On the other hand, the irradiation reference point Q (5) corresponding to the pixel value p = 5 is irradiated with the electron beam five times, and the graph M (5) becomes a mountain having the peak intensity E (5). Similarly, the irradiation reference point Q (10) corresponding to the pixel value p = 10 is irradiated with the electron beam ten times, and the graph M (10) becomes a mountain having the peak intensity E (10). The irradiation reference point Q (15) corresponding to the pixel value p = 15 is irradiated with the electron beam 15 times, and the graph M (15) becomes a mountain having the peak intensity E (15).

Incidentally, in FIG. 3, an example is described in which the two pixels P1 and P2 that are sufficiently separated from each other are each irradiated with a separate electron beam. As in this example, the electron beams irradiated to the two irradiation reference points Q1 and Q2 that are separated by the spot diameter φ or more do not interfere with each other. However, the electron beams irradiated to a plurality of irradiation reference points arranged close to each other at a distance less than the spot diameter φ cause mutual interference. Usually, the pixel pitch d (the pitch of the irradiation reference point Q) is set to a value smaller than the spot diameter φ of the electron beam. In this case, the exposure target surface is subjected to superimposed exposure by a plurality of electron beams.

FIG. 5A is a plan view showing an example of a state in which superimposed exposure occurs on the exposure target surface due to the relationship between the pixel pitch d and the spot diameter φ of each electron beam, and FIG. It is a graph which shows exposure intensity distribution about each electron beam in case such superposition exposure has arisen. The example shown here is an example in the case where a relationship of φ = 4d is set between the pixel pitch d (the pitch of the irradiation reference point Q) and the spot diameter φ of the electron beam. In FIG. 5 (a), the five pixels P1 to P5 arranged adjacent to each other in the x-axis direction and the five irradiation reference points Q1 to Q5 defined at the center positions of these pixels are irradiated. Five circular irradiation spots S1 to S5 formed by the electron beam are shown. As shown in the figure, the circular irradiation spots S1 to S5 are overlapped with each other, and each part of the exposure target surface is subjected to superposition exposure by a plurality of irradiation spots.

The exposure intensity distribution graphs M1 to M5 shown in FIG. 5B show the exposure intensity distributions in the x-axis direction for the irradiation spots S1 to S5, respectively. Since the individual irradiation spots S1 to S5 are partially overlapped, the individual exposure intensity distribution graphs M1 to M5 are also partially overlapped. This is given as the sum of the exposure intensity distribution graphs M1 to M5. For example, the irradiation reference point Q3 in the pixel P3 indicated by a bold line in the drawing is irradiated with an electron beam that generates a circular irradiation spot S3. The exposure intensity distribution of the circular irradiation spot S3 is a mountain as shown by the graph M3. However, as shown in the figure, the ridges of the other adjacent graphs M1, M2, M4, and M5 are also located in the pixel P3. Therefore, after all, the total exposure intensity in the pixel P3 is an intensity obtained by superimposing all these peaks.

Based on such a principle, the multi-beam type electron beam drawing apparatus can draw a gray scale pattern with gradation on the molding layer, and develop the exposed molding layer by developing it. A pattern having a desired shape can be formed.

FIG. 6A is a plan view of a pattern having a width Da in the x-axis direction, and FIG. 6B is a graph showing the principle of exposing the pattern by multi-beams. The x-axis shown as a horizontal axis in FIG. 6 (b) corresponds to the x-axis indicating the horizontal direction of FIG. 6 (a), and the graph of FIG. 6 (b) is shown in FIG. 6 (a). The exposure intensity distribution in the x-axis direction when drawing the pattern shown in FIG.

FIG. 6B shows nine exposure intensity distribution graphs M1 to M9 (hereinafter referred to as “small mountains”) composed of small peaks and one exposure intensity distribution graph MM (hereinafter referred to as “large mountains”) composed of large peaks. It is shown. Koyama M1 to M9 show exposure intensity distributions based on individual electron beams irradiated to the irradiation reference points Q1 to Q9, respectively, and overlap each other at the base as in the example shown in FIG. ing. The irradiation reference points Q1 to Q9 are points defined as center points of the pixels P1 to P9 (not shown), and are arranged at a predetermined pitch d. The height (peak intensity) of each of the small mountains M1 to M9 is a value corresponding to the pixel value of each of the pixels P1 to P9.

In the case of the example shown in FIG. 4, the pixel value p is expressed in 16 steps from 0 to 15, that is, 4 bits of data, and by setting p = 0 to 15, 16 kinds of mounds M ( p) can be defined. Then, a total of p exposures are performed to form an intensity distribution according to the small mountain M (p). The hills M1 to M9 shown in FIG. 6 (b) are one of these 16 stages. For example, when the pixel values of the pixels P1 and P9 at both ends are p = 7 and the pixel values of the intermediate pixels P2 to P8 are p = 15, the small mountains M1 and M9 at both ends are at a medium height as shown in the figure. Mountains M2 to M8 in the middle are the mountains with the highest height.

On the other hand, Oyama MM shown in FIG. 6 (b) is a graph showing the distribution of the total exposure intensity obtained when all the mounds M1 to M9 are superimposed, and is a graph corresponding to the sum of the mounds M1 to M9. (For convenience of illustration, it does not indicate an exact sum). Eventually, when exposure is performed for the irradiation reference points Q1 to Q9 by the number of times corresponding to the pixel values of the pixels P1 to P9, the total exposure intensity indicated by Oyama MM in the x-axis direction on the exposure target surface. A distribution will be obtained.

When the electron beam irradiation process for performing such exposure on the molding layer 61 is completed, a developing process for the molding layer 61 is subsequently performed. The molding layer 61 is composed of a resist layer that changes in composition when irradiated with an electron beam. In the case of a general resist, when the energy density to be irradiated exceeds a predetermined critical value, the composition layer suddenly changes nonlinearly. It has sex. Therefore, even when a gentle total exposure intensity distribution is obtained as shown in the illustrated Oyama MM, an area where the total exposure intensity in the molding layer 61 is equal to or greater than a predetermined threshold Eth is defined as an exposure area a and a total exposure. If the region where the intensity is less than the predetermined threshold Eth is defined as the non-exposed region b, the composition of the exposed region a changes greatly compared to the composition of the non-exposed region b. For this reason, when the developing process is performed on the layer 61, pattern formation based on the difference between the exposed area a and the non-exposed area b can be performed.

Specifically, when a positive resist material is used as the resist layer, only the exposed area a of the molding layer 61 is dissolved in the developer by the development process, and the pattern is formed by the remaining molding layer in the non-exposed area b. When a negative resist material is used as the resist layer, only the non-exposed area b of the molding layer 61 is dissolved in the developer by the development process, and the pattern is formed by the remaining molding layer in the exposed area a. Formation takes place. FIG. 6 shows an example in which an exposure region a having a width corresponding to the width Da when the Oyama MM is cut at a level corresponding to the threshold Eth is shown.

Of course, the scaling of the vertical axis of the graph and the value of the threshold Eth vary depending on the exposure conditions such as the intensity (energy density) of the irradiating electron beam and the single exposure time, and the development conditions such as the type of resist material and developer used. However, if these conditions are fixed, the threshold Eth on the vertical axis of the graph also becomes a fixed value. Therefore, the obtained pattern width Da can be controlled by the shape of Oyama MM. As described above, the Oyama MM is obtained as the sum of the Oyama M1 to M9, so that the pattern width Da can be controlled by the drawing data defining the pixel values of the individual pixels P1 to P9. .

In the description so far, for the sake of convenience, the principle of patterning in the x-axis direction with respect to the layer to be molded has been described. However, the actual patterning process is performed on the layer to be molded spreading on the xy plane, The same patterning will be performed. That is, Oyama MM shown in FIG. 6 (b) represents an exposure intensity distribution in the x-axis direction, but since drawing data is given as a two-dimensional pixel array, the same exposure intensity distribution in the y-axis direction is also provided. Will be obtained. Then, the vertical width of the pattern shown in FIG. 6A is determined based on the exposure intensity distribution in the y-axis direction.

As described above, the drawing principle by the general multi-beam electron beam drawing apparatus conventionally used has been described. Of course, the above description is an explanation using an example of the multi-beam electron beam drawing apparatus, and the present invention is implemented. The multi-beam electron beam drawing apparatus used for this is not limited to the example used in the above description.

<<< §2. Drawing data for drawing linear patterns >>
Here, specific drawing data used when drawing a linear pattern based on the drawing principle described in §1 will be described. FIG. 7A is a plan view of a linear pattern having a width Da = 25 nm in the x-axis direction, and FIG. 7B shows a pixel array constituting drawing data for exposing the linear pattern. FIG. In the manufacturing process of a semiconductor device, it is necessary to form a large number of linear patterns having a minute line width such as a wiring layer. A linear pattern (hatched portion) shown in FIG. 7A is an elongated pattern having a minute line width used in such a process. Note that the actual linear pattern has an extremely large line length (length in the y-axis direction in the figure) compared to the line width (width in the x-axis direction in the figure), and is literally understood as “one line”. In this application, for the sake of illustration, in this application, a linear pattern with a greatly reduced line length (a pattern grasped as a “rectangle” like the hatched portion in FIG. 7A) is taken as an example. I will explain.

The drawing data shown in FIG. 7 (b) is data given to the multi-beam electron beam drawing apparatus to form a linear pattern as shown in FIG. 7 (a) on the layer to be molded. It is configured by a two-dimensional pixel array in which a predetermined pixel value p is defined. As already described in §1, the individual pixels P constituting this two-dimensional pixel array irradiate a number of irradiation reference points Q arranged at predetermined pitches d vertically and horizontally on the exposure target surface on the molding layer. It has a pixel value p indicating the power electron beam intensity. Hereinafter, an example in which the vertical and horizontal pixel pitch d of this two-dimensional pixel array is set to d = 5 nm will be described. Accordingly, the vertical and horizontal pitches d of the irradiation reference point Q are also set to d = 5 nm.

The drawing data shown in FIG. 7 (b) is obtained by defining such a two-dimensional pixel array on the exposure target surface (xy plane) and giving each pixel a predetermined pixel value. In this example, as the individual pixel values p, numbers in the range of p = 0 to 15 are assigned, so that the drawing data is so-called grayscale image data having 4-bit gradation values. Each pixel serves to designate one of 16 exposure intensity distributions as shown in FIG. 4 by its pixel value p.

In the case of the drawing data shown in FIG. 7B, the pixel value p of each pixel takes either p = 0 (minimum value) or p = 15 (maximum value), and the intermediate pixel value. There is no pixel that takes p = 1-14. This is because the outline of the linear pattern shown in FIG. 7A corresponds to the outline of the pixel, so that the linear pattern can be formed without using an intermediate pixel value. . That is, in the case of the illustrated example, a pixel value p = 15 (maximum value) is given to a pixel that is completely included in the linear pattern, and a pixel value p = 0 (minimum value) is given to a pixel that does not include any linear pattern. ), The drawing data is configured.

When such drawing data is given to the electron beam drawing apparatus, the irradiation reference point position corresponding to the pixel having the pixel value p = 0 is not irradiated with the electron beam once, and the pixel having the pixel value p = 15. The irradiation of the electron beam is performed 15 times at the irradiation reference point position corresponding to. As a result, the small mountain M (15) shown in FIG. 4 is added to form a large mountain MM, and the exposure as shown in FIG. 7 (a) is performed on the exposure target surface with a predetermined threshold value Eth as a reference. Region a (region where the total exposure intensity is greater than or equal to the threshold Eth) and non-exposure region b (region where the total exposure intensity is less than the threshold Eth) are formed.

When the design is made such that the outline of the linear pattern coincides with the outline of the pixel as in the example shown in FIG. 7A, the linear pattern is obtained when the linear pattern is arranged on the two-dimensional pixel array. Only two types of pixels are defined: pixels that are completely included in the pattern (hereinafter referred to as complete pixels) and pixels that do not include any linear pattern (hereinafter referred to as empty pixels). Therefore, a pixel value p = 15 (maximum value: a pixel value indicating that the electron beam is irradiated the maximum number of times) is given for the complete pixel, and a pixel value p = 0 (minimum value: the electron beam is applied once) for the empty pixel. If a pixel value indicating that no irradiation is performed) is given, drawing data as shown in FIG. 7B is obtained.

In the case of a patterning process using a general multi-beam electron beam lithography system, an accurate pattern with no dimensional error is usually given when drawing data showing a linear pattern whose contour line matches the pixel contour is given. An operation is performed in which standard patterning conditions are set so as to form. Therefore, in general, when forming a linear pattern in which the line width Da is an integer multiple of the pixel line width direction pitch d, alignment is performed so that the outline of the linear pattern matches the outline of the pixel. If the design is performed, accurate pattern formation without dimensional errors can be performed under standard patterning conditions.

In the case of the example shown in FIG. 7, since the pixel pitch d = 5 nm and the line width Da of the linear pattern is 25 nm, the line width Da is exactly five times the pixel pitch d. Therefore, when designing a linear pattern, it is possible to design such that the contour lines on both the left and right sides match the contour of the pixel. If such a design is performed and pattern formation processing (exposure processing and development processing) is performed under the standard patterning conditions, a physical pattern having dimensions as designed can be obtained. That is, the line width depends on the molding layer remaining as the exposure region a (when the molding layer is a negative resist) or the molding layer remaining as the non-exposure region b (when the molding layer is a positive resist). A physical pattern with 25 nm can be formed.

On the other hand, when forming a linear pattern having a line width of a fractional dimension at a sub-pixel level that is less than the pixel pitch d, an intermediate pixel is used for pixels corresponding to the fractional dimension in the innermost portion of the contour line. A value should be given. FIG. 8A is a plan view of a linear pattern having a width Da = 27 nm in the x-axis direction, and FIG. 8B is a pixel array that constitutes drawing data for exposing the linear pattern. FIG. Whereas the line width Da of the linear pattern shown in FIG. 7 is Da = 25 nm, the line width Da of the linear pattern shown in FIG. 8 is Da = 27 nm, which is wider by 2 nm. In the case of the illustrated example, since the pixel pitch d is 5 nm, the increase in width of 2 nm is a fractional dimension at a sub-pixel level that is less than the pixel pitch d.

Therefore, in the drawing data shown in FIG. 8B, this 2 nm width increase is compensated by providing a pixel row having an intermediate gradation value of p = 6 as the pixel value p. That is, in the case of the example shown in FIG. 8, since the left side contour line of the linear pattern having a line width of Da = 27 nm is designed to match the pixel contour, As for the pixel columns up to the seventh column, the pixel value p = 15 (maximum value) is given as in the example shown in FIG. 7, but the pixel value p = 6 is assigned to the eighth pixel column. Is granted. This is because the pixel column of the eighth column is a pixel partially including a linear pattern (hereinafter referred to as an incomplete pixel), and therefore a gradation value determined according to the content rate of the linear pattern is set. This is a result given as a pixel value p.

As described above, in the case of the example shown here, the maximum pixel value p = 15 is given to the complete pixels (pixels from the third column to the seventh column) that are completely included in the linear pattern, and the linear pattern For empty pixels (pixels in the first, second, ninth, and tenth columns) that do not contain any pixel number, the minimum pixel value p = 0 is given. For an incomplete pixel (a pixel in the eighth column) partially including the linear pattern, the product 6 obtained by multiplying the maximum pixel value p = 15 by the linear pattern content “4/10”. Is given as a pixel value.

If the drawing data shown in FIG. 8B is given to the electron beam drawing apparatus, the irradiation reference point position corresponding to the pixel having the pixel value p = 0 is not irradiated with the electron beam even once, and the pixel value p The irradiation reference point position corresponding to the pixel having = 6 and p = 15 is irradiated with the electron beam 6 times and 15 times, respectively. Then, with respect to the large mountain MM obtained by adding the small peaks of the exposure intensity distribution formed by each of these exposure processes, the classification based on the predetermined threshold Eth is performed, as shown in FIG. An exposure area a (area where the total exposure intensity is greater than or equal to the threshold Eth) and a non-exposure area b (area where the total exposure intensity is less than the threshold Eth) are formed, and if development is actually performed, the line width Da = 27 nm is obtained. A physical linear pattern is formed.

<<< §3. Estimation principle of exposure intensity distribution in the present invention >>
As already described, in patterning using an electron beam drawing apparatus, a dimensional variation occurs in a pattern to be actually formed due to the proximity effect. Therefore, in practice, when electron beam drawing is performed on a layer to be molded using specific drawing data, the exposure intensity distribution that would actually be obtained is estimated by computer simulation, and the original result is based on the result. It is necessary to correct the drawing data.

The above-mentioned Patent Document 4 discloses a method suitable for a single beam electron beam lithography apparatus as an example of such an exposure intensity distribution estimation method. Therefore, here, the basic principle of the exposure intensity distribution estimation method according to the present invention will be described while comparing the single beam method and the multi-beam method.

FIG. 9 is a diagram comparing the procedure for drawing the same pattern by the single beam method and the procedure for drawing by the multi-beam method, and FIG. 9A shows the procedure for drawing by the single beam method. b) shows the procedure for drawing by the multi-beam method. In either case, the procedure for drawing the “L-shaped” pattern on the exposure target surface is shown.

First, in the procedure of drawing by the single beam method shown in FIG. 9 (a), it is only necessary to perform a total of two exposure operations. The single beam method is also called VSB method (Variable Shape Beam), which employs a method in which exposure is performed by irradiating one shaped electron beam with an arbitrary intensity. The region of the shape (usually an arbitrary rectangular shape) can be exposed. In the example shown in FIG. 9 (a), an exposure operation is performed on the rectangular area A1 using one electron beam formed into a square, and then the rectangular area A2 is processed using one electron beam formed into a rectangle. It is the example which performed the exposure operation | work.

In the case of this example, if evaluation points V1 and V2 as shown by x in the figure are defined, the evaluation point V1 included in the rectangular area A2 is a point that has been directly irradiated with an electron beam during the second exposure operation. Thus, the evaluation point V2 is a point where no direct irradiation of the electron beam was received. Naturally, the exposure intensity at the evaluation point V1 is higher than the exposure intensity at the evaluation point V2. However, due to the influence of the proximity effect, some energy is accumulated at the evaluation point V1 even during the first exposure operation for the rectangular area A1. Similarly, some energy is accumulated in the evaluation point V2 during a total of two exposure operations.

Therefore, the total exposure intensity at the evaluation point V1 is the sum of the energy accumulated by the proximity effect in the first exposure operation and the energy accumulated by the direct irradiation in the second exposure operation. Similarly, the total exposure intensity at the evaluation point V2 is the sum of the energy accumulated by the proximity effect during the total two exposure operations. Since such a proximity effect occurs, the exposure intensity distribution actually obtained on the exposure target surface is not a simple “L-shaped” pattern as shown in FIG. It will be spread to.

For this reason, when actually performing the exposure operation twice, it is necessary to correct the shape and irradiation intensity of the electron beam in consideration of the proximity effect. For example, if there is no proximity effect, the exposure work may be performed with the irradiation intensity set to 255 for both the rectangular areas A1 and A2. In practice, the irradiation is performed during the first exposure work for the rectangular area A1. Correction processing is performed such that the intensity is set to 255 and the irradiation intensity is set to 230 in the second exposure operation for the rectangular area A2.

On the other hand, FIG. 9 (b) shows the drawing data given to the electron beam drawing apparatus when the “L-shaped” pattern shown in FIG. 9 (a) is exposed using a multi-beam electron beam drawing apparatus. Is shown. This drawing data is constituted by a two-dimensional pixel array, similarly to the drawing data shown in FIG. 7B and FIG. 8B. Each pixel of the drawing data corresponds to an individual electron beam irradiated by the multi-beam electron beam drawing apparatus, and each pixel value indicates the irradiation intensity of the electron beam.

The outline indicated by the broken line in FIG. 9 (a) 輪郭 corresponds to the outline of the two-dimensional pixel array shown in FIG. 9 (b). In consideration of the role of the drawing data described in §2, a pattern similar to the “L-shaped” pattern shown in FIG. 9A can be formed by using the drawing data shown in FIG. Easy to understand. As described in §2, the irradiation position corresponding to the pixel having the pixel value p = 15 is irradiated with the electron beam 15 times, and the irradiation position corresponding to the pixel having the pixel value p = 7 is irradiated with the electron beam. Irradiation is performed seven times, and irradiation with an electron beam is performed four times at an irradiation position corresponding to a pixel having a pixel value p = 4, and energy corresponding to the number of irradiations is accumulated at each irradiation position. The

Of course, one electron beam does not irradiate only the region corresponding to one pixel, and as shown in FIG. One evaluation point defined on the surface accumulates energy from multiple electron beams. In addition, since the energy is supplied by the proximity effect from the electron beam irradiated at a position far from the evaluation point, the final stored energy is determined for each evaluation point defined on the exposure target surface. The process for determining the amount (total exposure intensity) must be quite complicated.

Here, for convenience of explanation, the basic concept of the exposure intensity distribution estimation method disclosed in the above-mentioned Patent Document 4 will be briefly described. This estimation method is suitable for a single-beam electron beam lithography system, assuming that the electron irradiated to the exposure target surface spreads around in the intensity distribution indicated by the Gaussian error function. By performing the calculation, the exposure intensity distribution for the entire resist layer is calculated.

FIG. 10 is a plan view showing the calculation principle of the total exposure intensity at an arbitrary evaluation point V (x, y) when drawing by the single beam method. Here, let us consider the amount of energy stored at an arbitrary evaluation point V (x, y) when the first exposure operation is performed on the rectangular area A1 shown in FIG. 9A. Assume that an xy two-dimensional orthogonal coordinate system is defined on the exposure target surface and the rectangular area A1 is arranged at a regular position on the coordinate system as shown in the figure. Specifically, the left side of the rectangular area A1 is arranged at the position of the coordinate value x = 1 (meaning left), the right side is arranged at the position of the coordinate value x = r (meaning right), and the upper side is the coordinate value y. = T (meaning top), and the lower side is located at the position of coordinate value y = b (meaning bottom).

In the first exposure operation, one rectangular electron beam is irradiated onto the rectangular area A1, and each part in the rectangular area A1 is irradiated with electrons. However, as shown in the illustrated evaluation point V (x, y), electrons reach the position outside the rectangular area A1 due to proximity effects such as forward scattering and backscattering, so that the energy is affected by the influence. Will be accumulated. Therefore, here, the reference point T (x ′, y ′) is defined at the position of the coordinate (x ′, y ′) in the rectangular area A1 to be irradiated with the electron beam, and in the first exposure operation, Consider how much the amount of energy stored in the evaluation point V (x, y) is affected by the electrons irradiated to the reference point T (x ′, y ′).

In this case, the degree of influence of electrons irradiated to the reference point T (x ′, y ′) on the surroundings is a function depending on the distance from the reference point T (x ′, y ′), and the evaluation point V The closer (x, y) is to the reference point T (x ′, y ′), the greater the influence received from the electrons irradiated to the reference point T (x ′, y ′). Therefore, in the example shown in FIG. 10, the degree of influence of the evaluation point V (x, y) from the reference point T (x ′, y ′) is a function of the distance R between the two points. Of course, the stored energy value of the evaluation point V (x, y) is influenced not only by the illustrated reference point T (x ′, y ′) but also by electrons irradiated to all points in the rectangular area A1. It will be. Actually, the exposure operation is repeated in order for a plurality of N areas (in the case of the example shown in FIG. 9, N = 2 and two areas of the rectangular areas A1 and A2). .

Therefore, v (x, y) which is the final stored energy amount (total exposure intensity) at an arbitrary evaluation point V (x, y) shown in FIG. 10 is obtained by the equation (1-1) in FIG. (In this application, the evaluation point is indicated by a capital letter V and the amount of stored energy is indicated by a small letter v.)
. Here, the function psf (R) is a function generally called a point spread function, and is a function indicating the degree of influence of a reference point T on the surroundings. Usually, the degree of influence tends to decrease as the distance R from the reference point T increases.

The term of the double integral on the right side of the equation (1-1) indicates that the point spread function psf (R) for the reference point T (x ′, y ′) shown in FIG. This is a term for integration from the left end of the area A1 to the right end) and from y coordinate values b to t (from the lower end to the upper end of the rectangular area A1), and Di is an exposure operation for the i-th rectangular area Ai. This is the irradiation intensity (dose amount) of the electron beam. Further, σ is a forward scattering parameter determined by the electron acceleration voltage of the electron beam lithography apparatus, the resist material, and the like.

The summation Σ at the beginning of the right side of the equation (1-1) is for adding the results of the exposure work performed on a plurality of N areas. In the case of the example shown in FIG. 9A, the energy amount accumulated by the first exposure operation (exposure operation performed on the rectangular area A1 with i = 1) is set to N = 2, and the second The sum of the amount of energy accumulated by the first exposure operation (exposure operation performed on the rectangular area A2 with i = 2) is referred to as the total exposure intensity v (x, y) of the evaluation point V (x, y). It will be.

As shown in FIG. 10, since R = √ ((x′−x) ² + (y′−y) ² ), the expression (1-1) in FIG. 11 becomes as shown in the expression (1-2) Can be rewritten. Here, if x′−x = X, y′−y = Y, the point spread function psf (R) can be expressed as psf (X, Y) as a function of X and Y. 2) can be expressed as in formula (1-3). The point spread function psf (X, Y) is a function indicating the degree of influence at the evaluation point V at a position away from the specific reference point T by the distance X in the x-axis direction and by the distance Y in the y-axis direction. is there. The above-mentioned Patent Document 4 shows an example in which a two-dimensional Gaussian error function is used as the point spread function psf (X, Y).

Therefore, here, first, let us consider applying the exposure intensity distribution calculation method based on the single beam method shown in the equations of FIG. 11 to the multi-beam method. FIG. 12 is a plan view showing the calculation principle of the total exposure intensity at an arbitrary evaluation point V (x, y) when drawing by the multi-beam method. Compared to the single beam system shown in FIG. 10, the difference is that the rectangular area A1 is replaced with a pixel P (i, j).

In the calculation in the single beam method shown in FIG. 10, the calculation for performing the convolution by moving the reference point T (x ′, y ′) within the range of the i-th rectangular area Ai is performed for i = 1 to N. Thus, the process of calculating the total exposure intensity v (x, y) at the evaluation point V (x, y) is performed based on the equation of FIG. Therefore, in the calculation in the multi-beam method shown in FIG. 12, the calculation is performed by moving the reference point T (x ′, y ′) within the range of the pixel P (i, j) in the i-th row and j-th column. Is performed for all the pixels constituting the drawing data, thereby calculating the total exposure intensity v (x, y) at the evaluation point V (x, y).

FIG. 13 is a diagram showing an example of an arithmetic expression used for the arithmetic principle shown in FIG. The final stored energy amount (total exposure intensity) at an arbitrary evaluation point V (x, y) shown in FIG. 12 can be obtained by equation (2-1) in FIG. . This equation (2-1) corresponds to the equation (1-1) in FIG. 11, and is obtained by replacing the summation Σ in the equation (1-1) with an integral. As described above, recently, a multi-beam electron beam drawing apparatus capable of irradiating 250,000 or more electron beams has been used, and drawing data given to such an electron beam drawing apparatus includes 250,000 or more pixels. It has a pixel array. Therefore, in the equation (1-1) in FIG. 11, N is an enormous value of 250,000 or more.

Therefore, in equation (2-1) in FIG. 13, the summation intensity v (x, y) is calculated in a form in which the summation Σ is replaced by integration and integration is performed for all pixels constituting the drawing data. Here, the function psf (R) is a point spread function as described above, and indicates the degree of influence of a reference point T on the surroundings. On the other hand, D (x ′, y ′) is the irradiation intensity (dose amount) of the electron beam at the position of the reference point T (x ′, y ′) indicated by the coordinates (x ′, y ′). The value is determined based on the pixel value p of (i, j). The integration range is in the range from minus infinity to plus infinity in both the x-axis direction and the y-axis direction. This is because the entire exposure target surface is a calculation target.

As a result, the equation (2-1) in FIG. 13 is obtained from the function D (x ′, y ′) indicating the electron beam irradiation intensity for a number of reference points T (x ′, y ′) defined in the electron beam irradiation region. ) And the point spread function psf (R) indicating the degree of influence of the reference point T (x ′, y ′) on the surroundings, the total at each evaluation point V (x, y) is obtained. It can be said that the exposure intensity v (x, y) is calculated.

Again, as shown in FIG. 12, since R = √ ((x′−x) ² + (y′−y) ² ), the equation (2-1) in FIG. Can be rewritten as Here, if x′−x = X, y′−y = Y, the point spread function psf (R) can be expressed as psf (X, Y) as a function of X and Y. 2) can be expressed as in formula (2-3). Again, the point spread function psf (X, Y) indicates the degree of influence at the evaluation point V at a position away from the specific reference point T by the distance X in the x-axis direction and by the distance Y in the y-axis direction. It is a function to show.

<<< §4. Features of the simulation method according to the present invention >>
The present invention proposes a new simulation method for obtaining an exposure intensity distribution when a predetermined pattern is exposed and drawn on a molding layer using a multi-beam electron beam drawing apparatus. Here, the characteristics of this new simulation method will be described.

First, the first feature is that, based on the equation (2-3) shown in FIG. 13, the total exposure intensity v (x, y) at an arbitrary evaluation point V (x, y) located at the coordinates (x, y). ) Is calculated. The second feature is that a function including an aperture size parameter determined based on the aperture size of the aperture of the electron beam lithography apparatus is used as the point spread function psf (X, Y) in the equation (2-3). is there.

FIG. 14 is a diagram showing an example of an arithmetic expression used for calculating the exposure intensity distribution by the simulation method according to the present invention when drawing is performed by the multi-beam method. Hereinafter, the equations (3), (4), and (5) illustrated will be described.

First, equation (3) is exactly the same as equation (2-3) shown in FIG. 13, and is the basic equation used in the simulation method according to the present invention. As described above, v (x, y) on the left side is the total exposure intensity at an arbitrary evaluation point V (x, y) located at the coordinates (x, y), and the value v (x, y) for all coordinate positions. If y) is calculated, an exposure intensity distribution on the exposure target surface can be obtained. As described above, this equation (3) is a function D (x ′, y ′) indicating the electron beam irradiation intensity for the reference point T (x ′, y ′) defined in the electron beam irradiation region, It is an expression showing a convolution integral of a point spread function psf (X, Y) indicating the degree of influence of the reference point T (x ′, y ′) on the surroundings. As described above, X = x′−x and Y = y′−y.

After all, in the simulation method according to the present invention, when the xy plane of the two-dimensional xy orthogonal coordinate system is defined as the electron beam irradiation surface, the evaluation point V (x, y) located at the coordinates (x, y) is defined. Thus, the effect of the reference point T (x ′, y ′) located at the coordinates (x ′, y ′) is expressed as a function D (x indicating the electron beam irradiation intensity at the reference point T (x ′, y ′). ′, Y ′) and the point spread function psf (X, Y) defined as X = x′−x, Y = y′−y, are calculated by the convolution integral in the x-axis direction and the y-axis direction. Processing will be performed. Moreover, as the point spread function psf (X, Y), a function including an aperture size parameter B determined based on the aperture size K of the aperture of the electron beam drawing apparatus is used in addition to the variables X and Y.

Equation (4) is an equation showing a specific example of the point spread function psf (X, Y) used in Equation (3). The function erf included in the equation (4) is a Gaussian error function erf (ξ) shown in the equation (5), but the variable ξ part is replaced with an equation using the parameters B and σ. Yes. Here, the parameter B is an aperture size parameter related to the above-described second feature of the present invention, and is a value determined based on the aperture size K of the aperture 41 of the electron beam lithography apparatus. On the other hand, the parameter σ is a forward scattering parameter, and is a value determined by the electron acceleration voltage of the electron beam lithography apparatus, the resist material, and the like.

FIG. 15 is a one-dimensional graph showing an example of the point spread function psf (X, Y) shown in Equation (4) of FIG. 14, where the horizontal axis represents the X axis and the vertical axis represents the energy density E. This graph shows the degree of influence of the electron beam irradiated around the position of X = 0 on the surroundings. 2 is the same kind of graph, but the graph of FIG. 2 is a pure Gaussian error function graph, whereas the graph of FIG. 15 is a point spread function graph including the aperture size parameter B. The feature is a trapezoidal shape in which a flat portion H having a width w is formed in the central portion.

The opening size parameter B in the equation (4) is a parameter that affects the width w of the flat portion H of the graph shown in FIG. 15. On the other hand, the forward scattering parameter σ in Expression (4) is a parameter that affects the slopes of the left and right inclined portions U1 and U2 in the graph shown in FIG. become. FIG. 15 shows a one-dimensional distribution graph in which the horizontal axis is the X axis. Actually, a distribution graph having the same shape is also obtained in the Y-axis direction. Therefore, the graph of the point spread function psf (X, Y) shown in Expression (4) is actually a three-dimensional plateau-like graph that rises on the XY plane, and the vertical and horizontal widths are w at the top. Flat portion H is formed, and an inclined portion is formed around the flat portion H.

In short, in the simulation method according to the present invention, a function including the aperture size parameter B and the forward scattering parameter σ is used as the point spread function psf (X, Y). Here, the aperture size parameter B is a parameter that determines the width of the flat portion H of the graph, and the forward scattering parameter σ is a parameter that determines the inclination of the inclined portions U1 and U2 of the graph.

The simulation method disclosed in the above-mentioned Patent Document 4 is based on the premise of a single beam type electron beam drawing apparatus, and is expressed as a point spread function psf (X, Y) shown in Expression (1-3) of FIG. A general Gaussian error function as shown in the graph of FIG. 2 is used. However, according to various experiments conducted by the inventor of the present application, a simulation using a point spread function psf as shown in the graph of FIG. When it is assumed that a multi-beam type electron beam drawing apparatus is used, it has been found preferable to use a point spread function psf having a flat portion H as shown in the graph of FIG.

In addition, it is preferable to set the width w of the flat portion H to a value corresponding to the aperture size K of the aperture of the electron beam drawing apparatus to be used. In other words, it is preferable to use a point spread function psf that increases the width w of the flat portion H if the aperture 41 of the aperture is large. This is because, in the case of a multi-beam electron beam lithography apparatus as shown in FIG. 1, the energy density distribution of the cross section of the electron beam 20 generated by the electron gun 10 is a general Gaussian error as shown in the graph of FIG. Although the distribution depends on the function, when an individual electron beam passing through the aperture 41 of the aperture is irradiated onto the molding layer 61, the exposure intensity distribution in consideration of the proximity effect in the molding layer 61 is shown in FIG. This is probably because the distribution has a flat portion H as shown in the graph.

Here, the aperture size K of the aperture has a value that affects the cross-sectional size of each electron beam that has passed through the aperture 41 (diameter in the case of a circular cross-section, length of one side in the case of a square cross-section). As the point spread function psf (X, Y) used in Equation (3), a function represented by a graph having a flat portion H having a width w corresponding to the cross-sectional size of each electron beam passing through the opening 41 is used. It is preferable to use

Therefore, when carrying out the present invention, if the aperture 41 of the aperture of the electron beam lithography apparatus has a circular shape, the diameter of the circle is used as the aperture size K of the aperture, and the aperture 41 has a square shape. If it is, the length of one side of the square may be used as the aperture size of the aperture. Then, a value obtained by multiplying the aperture size K by the reduction ratio m by the projection lens 50 of the electron beam drawing apparatus may be used as the aperture size parameter B determined based on the aperture size of the aperture.

Specifically, in the case of the electron beam drawing apparatus shown in FIG. 1, the aperture size parameter B is set to B = m based on a value m · K obtained by multiplying the aperture size K of the aperture by the reduction ratio m by the projection lens 50.・ It may be defined by the expression K. For example, if the aperture 41 of the aperture has a circular shape with a diameter of 4 μm and the reduction magnification of the projection lens 50 is 1/200, the value can be set to B = 20 nm. In this case, the aperture size parameter B is a value corresponding to the beam diameter or spot diameter φ of one electron beam formed on the exposure target surface. Therefore, for example, the term “erf ((B / 2−X) / σ)” in Equation (4) is a value obtained by dividing the difference between the radius B / 2 of the electron beam and the distance X by the forward scattering parameter σ. Corresponds to a Gaussian error function as a variable.

Thus, since the expression (4) includes the forward scattering parameter σ in addition to the aperture size parameter B, it is necessary to determine the value of the parameter σ when performing the calculation. As described above, the forward scattering parameter σ is a value determined by the electron acceleration voltage of the electron beam lithography system, the resist material, and the like. Therefore, in practice, electrons are applied at a specific acceleration voltage to a resist of a specific material. If the exposure distribution at the time of skipping is actually measured and the value of the forward scattering parameter σ for the combination of the resist of the specific material and the specific acceleration voltage is determined by back calculation based on the actual measurement result, Good.

Expression (4) in FIG. 14 is an example of a point spread function psf (X, Y) including an aperture size parameter B determined based on the aperture size K of the aperture, and psf (X, Y) = 1/4 · ( erf ((B / 2−X) / σ) −erf ((− B / 2−X) / σ)) · (erf ((B / 2−Y) / σ) −erf ((− B / 2− Y) / σ)) and an error function erf. The graph of this function is a plate-like graph having a flat portion H having a width w corresponding to the spot size φ of the irradiated electron beam, as shown in FIG. However, the point spread function psf (X, Y) having such characteristics is not limited to the function represented by the equation (4) in FIG.

For example, equation (6) in FIG. 16 is a diagram illustrating an example of another function suitable for use as the point spread function psf (X, Y) in equation (3) in FIG. 14, and psf (X, Y ) = 1/4 · (arctan ((B / 2−X) / σ) −arctan ((− B / 2−X) / σ)) · (arctan ((B / 2−Y) / σ) −arctan This function includes the inverse trigonometric function arctan ((−B / 2−Y) / σ)). In the equation (4) in FIG. 14, the Gaussian error function erf is used. However, the equation (6) in FIG. 16 uses the inverse trigonometric function arctan instead. Although the shapes are slightly different, essentially, as shown in FIG. 15, a flat portion H having a width w corresponding to the aperture size parameter B and an inclined portion U1, having an inclination corresponding to the forward scattering parameter σ. A graph having U2 is obtained.

Also, equation (7) in FIG. 17 is a diagram showing another example of a function suitable for use as the point spread function psf (X, Y) in equation (3) in FIG. Psf (X, Y) = C / (1 + η) · (1 / 4σ ² · (erf ((B / 2−X) / σ) including predetermined constant C, backscattering parameter β, and proximity effect correction parameter η −erf ((− B / 2−X) / σ)) · (erf ((B / 2−Y) / σ) −erf ((− B / 2−Y) / σ)) + η / β ² · exp A function (− (X ² + Y ² ) / β ² )) is shown.

In the equation (7) of FIG. 17, the Gaussian error function erf is used as in the equation (4) of FIG. 14, but in addition to the aperture size parameter B and the forward scattering parameter σ as parameters, A backscattering parameter β and a proximity effect correction parameter η are used. The backscattering parameter β is the degree of backscattering in which the electrons scattered and bounced near the surface of the sample substrate 60 under the layer to be molded (resist layer) 61 in FIG. The proximity effect correction parameter η is a parameter indicating the ratio between the resist exposure due to forward scattering of the electron beam and the resist exposure due to back scattering. C is a predetermined constant. The parameters β and η are well-known parameters disclosed in, for example, the above-mentioned Patent Document 4 and so on, and thus detailed description thereof is omitted here.

The formula (7) in FIG. 17 is also a formula showing a graph having a flat portion H having a width w corresponding to the opening size parameter B as shown in FIG. , An expression showing an example of a function suitable for use as the point spread function psf (X, Y).

<<< §5. Procedure of simulation method according to the present invention >>
The simulation method according to the present invention is actually executed by arithmetic processing using a computer. Here, a specific procedure for executing this simulation method using a computer will be described.

FIG. 18 is a flowchart showing the basic procedure of the simulation method according to the present invention. As shown in the figure, this basic procedure includes steps of a drawing data input step S10, a parameter setting step S20, a calculation matrix creation step S30, and a convolution calculation step S40. Each step is executed by a computer based on a dedicated program.

First, in the drawing data input stage of step S10, processing for inputting drawing data is performed. The drawing data is data indicating a pattern drawn by the electron beam drawing apparatus. For example, as illustrated in FIG. 9B, from the array of pixels having pixel values indicating the irradiation intensity at each irradiation position of the beam. It becomes the data that becomes. The purpose of the simulation performed here is to expose the layer to be molded that is supposed to be obtained when it is assumed that such drawing data is given to the electron beam drawing apparatus and the exposure process is performed on the layer to be molded. It is to obtain an intensity distribution.

Subsequently, in the parameter setting stage of step S20, an aperture size parameter B determined based on the aperture size of the aperture of the electron beam drawing apparatus is set. For example, if the aperture 41 of the aperture has a circular shape with a diameter of 4 μm and the reduction magnification by the projection lens 50 is 1/200 as in the example described above, a value of B = 20 nm is set. The aperture size parameter B corresponds to the beam diameter or spot diameter φ of one electron beam formed on the exposure target surface, and is used in an arithmetic expression in the convolution calculation stage of step S40. .

When simulating an electron beam drawing apparatus in which the reduction ratio of the aperture 41 of the aperture and the projection lens 50 is fixed, a fixed value may be set as the value of the aperture size parameter B, but these are variable electron beams. Each time the simulation of the drawing apparatus is performed, it is necessary to input and set the value of the opening size parameter B.

The calculation matrix creation stage of step S30 is a preparation stage of the convolution calculation stage of step S40, and here, an operation of creating an irradiation intensity matrix and a point spread matrix is performed. These matrices are matrix data used by the computer to execute the calculation of the equation (3) in FIG. 14, and the irradiation intensity matrix corresponds to D (x ′, y ′) in the equation (3). The matrix data indicates the planar distribution of the irradiation intensity. On the other hand, the point spread matrix corresponds to psf (X, Y) in the equation (3), and is matrix data indicating a planar distribution of the degree of influence indicated by a predetermined point spread function. Hereinafter, for convenience of explanation, the same symbol “D (x ′, y ′)” as the function D (x ′, y ′) of the equation (3) is used for the irradiation intensity matrix, and the point spread matrix is expressed by the equation The same symbol “psf (X, Y)” as the function psf (X, Y) in (3) is used.

Expression (3) in FIG. 14 is a theoretical expression showing the convolution integral of the function D (x ′, y ′) and the function psf (X, Y), and is based on this theoretical expression in the convolution operation stage of step S40. An operation is performed. However, since the calculation is performed by a computer, in practice, calculation using discrete values is inevitably performed instead of calculation using continuous variables. The irradiation intensity matrix D (x ′, y ′) is a calculation matrix indicating the value of the function D (x ′, y ′) when a predetermined discrete value is adopted as the variable x ′, y ′. The matrix psf (X, Y) is a calculation matrix indicating values of the function psf (X, Y) when a predetermined discrete value is adopted as the variables X and Y. The actual calculation is performed using these two sets of calculation matrices.

The sample intervals as discrete values of the variables x ′ and y ′ and the variables X and Y may be determined according to the resolution of the exposure intensity distribution obtained by calculation. As described with reference to FIG. 12, in the present invention, the accumulated energy amount at a predetermined evaluation point V (x, y) on the exposure plane is influenced by the influence from a large number of reference points T (x ′, y ′). Calculated as an integrated value of degree. The spatial distribution of the stored energy amount obtained for a large number of evaluation points V (x, y) is the finally obtained exposure intensity distribution. Therefore, for example, when it is desired to obtain an exposure intensity distribution having a resolution in which the evaluation points V (x, y) are defined at intervals of 1 nm in the vertical and horizontal directions, 1 nm in the vertical and horizontal directions as discrete values of the variables x ′ and y ′ and the variables X and Y It is necessary to set a value sampled at intervals of. In this case, as the irradiation intensity matrix D (x ′, y ′) and the point spread matrix psf (X, Y), it is necessary to prepare a matrix assuming the vertical and horizontal pitches of the cells to be 1 nm.

The exposure intensity distribution obtained by the simulation method according to the present invention is used for correcting drawing data used in actual exposure processing. For example, the drawing data shown in FIG. 8B is drawing data prepared for forming a linear pattern having a width of Da = 27 nm as shown in FIG. 8A. Accordingly, as a result of simulation, an exposure intensity distribution (a distribution in which a portion having a width of Da = 27 nm is assumed to remain when developed) is obtained in which a linear pattern having a width of Da = 27 nm is formed. If this happens, no correction is required. However, when an exposure intensity distribution is obtained in which the width of the formed linear pattern is assumed to be, for example, Da = 28 nm, the pixel value “6” of the pixels in the eighth column needs to be slightly reduced. There is.

In the case of the embodiment shown in FIG. 8, the pitch d of the pixels constituting the drawing data is d = 5 nm, but the expected value of the line width Da is smaller than the pixel pitch d (for example, in units of 1 nm). It is necessary to ask for. That is, the resolution of the exposure intensity distribution obtained by the simulation needs to be set smaller than the pixel pitch d, and the cell pitch g constituting the calculation matrix created in step S30 is set smaller than the pixel pitch d. Must. Therefore, an embodiment in which the calculation cell pitch g is set to 1 / integer of the pixel pitch d will be described below.

In the case of the embodiment described here, in the calculation matrix creation stage of step S30, first, calculation cells are defined by dividing each pixel of the drawing data into a plurality of sets, and two sets of sets of calculation cells are formed. Prepare an empty calculation matrix. Each cell of the first calculation matrix is given a predetermined cell value based on the pixel value of the pixel including the cell, thereby providing an irradiation intensity matrix D (x ′, y ′) is created. On the other hand, by giving each cell of the second calculation matrix a cell value corresponding to a predetermined point spread function including the aperture size parameter B set in step S20, the degree of influence indicated by the point spread function A point spread matrix psf (X, Y) indicating the plane distribution of the.

Here, a specific procedure for creating the irradiation intensity matrix D (x ′, y ′) will be described with reference to FIG. Consider an example in which a simulation based on simple drawing data having a pixel array of 5 rows and 5 columns is performed as shown in FIG. Each pixel constituting the drawing data is given a predetermined pixel value p (12 or 15 in the illustrated example), and each pixel value p is an electron irradiated to the position of each pixel. The irradiation intensity of the beam is shown. Here, it is assumed that the pitch d of the pixels constituting the drawing data is d = 5 nm, and the pitch g of the computation cells constituting each computation matrix is set to g = 1 nm.

As described above, when the calculation cell pitch g is set to g = 1 nm, as shown in the lower right of FIG. 19A, the vertical direction of each evaluation point V (x, y) defined on the exposure target surface. Directional and lateral pitches can also be set to 1 nm. That is, the interval between the evaluation points V11 and V12 arranged adjacent to the horizontal direction (x-axis direction) is 1 nm, and the interval between the evaluation points V11 and V21 arranged adjacent to the vertical direction (y-axis direction) is also set. 1 nm. Accordingly, in the case of the embodiment shown in FIG. 19, the total exposure intensity can be obtained for the evaluation points arranged in a grid at intervals of 1 nm in the vertical and horizontal directions, and an exposure intensity distribution having a resolution of 1 nm can be obtained.

In FIG. 19B, the pixel P (i, j) in the i-th row and j-th column of the pixel array constituting the drawing data shown in FIG. The state where the calculation cell C (m, n) is generated is shown. Since a pixel having a size of 5 × 5 nm is divided into 25 to define 25 calculation cells, the size of each cell is 1 × 1 nm. Thus, after defining 25 empty calculation cells, a predetermined cell value based on the pixel value of the pixel including the cell is given to each cell. In the case of the example shown on the left side of FIG. 19B, the pixel value “12” of the pixel P (i, j) including the cell is given as it is as the cell value to all 25 calculation cells. The cell values of all the calculation cells are “12”.

Actually, since all of the 25 pixels P shown in FIG. 19A are divided into 25, the calculation matrix corresponding to the drawing data is composed of 625 calculation cells. Each calculation cell is given the pixel value of the pixel including the cell (12 or 15 in the illustrated example). That is, in the case of the illustrated example, the irradiation intensity matrix D (x ′, y ′) is composed of an array of calculation cells in 25 rows and 25 columns, and calculation cells C (m, n) in the m-th row and the n-th column. ) Is given a predetermined cell value based on the pixel value of the pixel including the cell. Eventually, the irradiation intensity matrix D (x ′, y ′) is matrix data indicating the plane distribution of the electron beam irradiation intensity on the exposure target surface with the resolution of the calculation cell pitch g (in this example, g = 1 nm). It turns out that.

Of course, in principle, as in the example shown on the left side of FIG. 19B, the pixel values of the pixels including the cell are given to all the cells as cell values as they are, and the irradiation intensity matrix D (x ′, y ′ However, in practice, it is preferable to devise a device for reducing the calculation burden in step S40. The example shown on the right side of FIG. 19 (b) is an example of such a device.

Specifically, in the case of the example shown on the right side of FIG. 19B, 24 cells other than the central one cell indicated by a bold frame in the figure out of the 25 cells of the matrix shown on the left side of FIG. 19B. The cell value is corrected to 0 for these cells. Here, the central cell is referred to as a representative cell, and the other 24 cells are referred to as non-representative cells. For the representative cell, the pixel value “12” of the pixel P (i, j) including the cell is directly given as the cell value, and for the non-representative cell, the cell value “0” is given. The reason why the calculation burden in step S40 is reduced by such a device will be described later.

On the other hand, the point spread matrix psf (X, Y) is matrix data indicating the plane distribution of the degree of influence indicated by the point spread function psf (X, Y) on the exposure target surface by the resolution of the pitch g of the operation cells. In the case of the embodiment described here, g is set to 1 nm, and it is constituted by a set of operation cells arranged at a pitch of 1 nm in length and width. The cell value of each calculation cell is determined based on the formula (4) in FIG. 14 according to the position of the cell (vertical position X and horizontal position Y) (of course, the formula in FIG. 16). (6) or equation (7) in FIG. 17 may be used). The cell value distribution corresponds to the graph of FIG. 15, and generally, a cell closer to the center of the matrix is given a larger cell value.

Thus, when the irradiation intensity matrix D (x ′, y ′) and the point spread matrix psf (X, Y) are generated in the calculation matrix creation stage of step S30, the irradiation intensity is set in the convolution calculation stage of step S40. Convolution integration using the matrix D (x ′, y ′) and the point spread matrix psf (X, Y) is performed, and the total exposure at each evaluation point V (x, y) located at the coordinates (x, y). Strength (amount of stored energy) v (x, y) is obtained.

As described above, in the embodiment described here, a matrix in which the pitch g of each cell is set to 1 nm is prepared as the irradiation intensity matrix D (x ′, y ′) and the point spread matrix psf (X, Y). Therefore, an exposure intensity distribution indicating the distribution of the total exposure intensity v (x, y) of each evaluation point V (x, y) can be obtained with a resolution of 1 nm in the vertical and horizontal pitches. Actually, based on the exposure intensity distribution thus obtained, the size of the pattern that will remain when the molding layer 61 (resist layer) is developed is estimated, and if necessary, the original drawing data Correction for each pixel value is performed. Here, description of such a correction method is omitted.

<<< §6. Specific processing of convolution calculation >>>
Here, specific processing in the convolution calculation stage in step S40 in the flowchart of FIG. 18 will be described. As described above, this process is a convolution integral process using two sets of calculation matrices, that is, an irradiation intensity matrix D (x ′, y ′) and a point spread matrix psf (X, Y). Thus, the convolution operation based on the arithmetic expression shown in Expression (3) in FIG. 14 is performed. Note that the calculation matrix is an aggregate of discretely defined calculation cells (cells arranged at a pitch of 1 nm in the vertical and horizontal directions in the above example), and strictly speaking, is performed in step S40. The calculation is not a “convolution integration” but an operation for obtaining a “convolution sum”, but in practice it is an operation using a large number of calculation cells. I will use the wording.

FIG. 20 is a diagram showing a correspondence relationship between the irradiation intensity matrix D (x ′, y ′) created in step S30 of FIG. 18 and the point spread matrix psf (X, Y). The upper part of FIG. 20 shows the arrangement of calculation cells constituting the irradiation intensity matrix D (x ′, y ′) created based on the drawing data shown in FIG. A region surrounded by a thick line frame shown in the drawing indicates one pixel P (i, j) constituting the drawing data, and a region surrounded by the thin line frame indicates one calculation cell C (m, n). Show.

As described above, the pixel P (i, j) is a square having a side of 5 nm, and the calculation cell C (m, n) is a square having a side of 1 nm. Therefore, one pixel P (i, j) includes 25 calculation cells C (m, n), and the irradiation intensity matrix D (x ′, y ′) includes a total of 625 cells. The calculation cell is included. Each calculation cell is given a predetermined cell value based on the pixel value of the pixel including the cell (in FIG. 20, display of the cell value of each calculation cell is omitted).

However, in the case of the embodiment described here, as a device for reducing the calculation burden, only a specific representative cell among a plurality of calculation cells included in the same pixel is determined based on the pixel value of the pixel. Is given as a cell value, and a cell value of 0 is given to other non-representative cells.

The example shown in FIG. 20 is an example in which one calculation cell located at the center of each pixel is a representative cell, and the other calculation cells are non-representative cells. Only the representative cell is shown in black. is there. Therefore, the representative cell shown in black in the figure is given the same value as the pixel value (12 or 15) of the pixel at the corresponding position in FIG. All of the non-representative cells shown are given a cell value of 0. Eventually, the irradiation intensity matrix D (x ′, y ′) created in step S30 gives a cell value of 12 or 15 to the black cells shown in the upper part of FIG. 20, and 0 to the white cells. This is a cell array given the cell value.

On the other hand, the graph psf shown in the lower part of FIG. 20 shows the cell values of the operation cells arranged in a specific row (for example, the row located in the center in the vertical direction) of the point spread matrix psf (X, Y). ing. As shown in FIG. 15, the point spread function psf (X, Y) used in the present invention has a flat portion H having a width w corresponding to the aperture size parameter B and an inclination having an inclination corresponding to the forward scattering parameter σ. It becomes a trapezoidal function having the parts U1 and U2. Therefore, the graph psf shown in the lower part of FIG. 20 is also a graph having a flat portion H and inclined portions U1 and U2. After all, the point spread matrix psf (X, Y) created in step S30 is a cell array having cell value distributions in the X-axis direction and the Y-axis direction according to the graph psf shown in the lower part of FIG. become.

The convolution operation shown in the equation (3) in FIG. 14 has a cell value distribution corresponding to the graph psf in the lower part of FIG. 20 with respect to the irradiation intensity matrix D (x ′, y ′) shown in the upper part of FIG. The spread matrix psf (X, Y) can be moved by two-dimensionally moving at a pitch of 1 nm while accumulating the product of cell values of cells at corresponding positions in both matrices. The lower part of FIG. 20 shows a point spread matrix psf at the center position of the calculation cell C (m, n) of the irradiation intensity matrix arranged at the center of the pixel P (i, j) in the i-th row and j-th column. A graph psf when the center positions of (X, Y) are superimposed is drawn.

FIG. 21 is a diagram showing a concept of a process for performing a convolution operation based on the drawing data shown in FIG. Hereinafter, the basic process of the convolution operation will be described with reference to FIG. First, FIG. 21A is a graph showing the pixel values D of the five pixels in the third row of the drawing data shown in FIG. 19A. The horizontal axis is the x axis, and the vertical axis is the pixel value. D is taken. As shown in the figure, a pixel value D = 12 is given to the pixels P (3, 1) and P (3, 5) at both ends, and three pixels P (3, 2) and P (3, sandwiched between them are provided. The pixel value D = 15 is given to 3) and P (3, 4). Here, each pixel value D indicates the irradiation intensity of the electron beam irradiated to the pixel position.

FIG. 21B is a graph showing the cell value of each calculation cell obtained by dividing one pixel into 25, and the x-axis is taken on the horizontal axis and the cell value D is taken on the vertical axis. . On the horizontal axis, 25 calculation cells are arranged. Each of these cells is a cell obtained by cutting five pixels in the third row of the drawing data shown in FIG. Yes, it corresponds to the cells C (13, 1) to C (13, 25) in the first to 25th columns of the 13th row in the cell array of all 25 rows and 25 columns. This example corresponds to the example shown on the left side of FIG. 19 (b), and for all cells, the pixel value D of the pixel including the cell (the pixel at the corresponding position in FIG. 21 (a)). Is given the same cell value (ie 12 or 15).

On the other hand, FIG. 21 (c) 例 corresponds to the example shown on the right side of FIG. 19 (b) and is located at the center of each pixel among the 25 cells arranged in the 13th row. Only the representative cell is given the same cell value as the pixel value D of the pixel including the cell, and the other non-representative cells are given the cell value 0. Specifically, for the representative cells C (13, 3), C (13, 8), C (13, 13), C (13, 18), C (13, 23) in the 13th row The

cell value

12 or 15 is given, and the cell value 0 is given to other non-representative cells.

On the other hand, FIG. 21 (d) shows one arrangement of the graph f of the point spread function pfs corresponding to the point spread matrix psf (X, Y). In the convolution calculation, the graph f is moved two-dimensionally in units of a calculation cell pitch g (g = 1 nm in this example), and two sets of cells at the corresponding positions (cells of the irradiation intensity matrix and point spread). The product of the cell values of the matrix cells) is cumulatively added. The graph f (13, 13) shown in FIG. 21 (d) shows a state where the graph f is arranged so that the center thereof coincides with the center position of the representative cell C (13, 13) shown in FIG. 21 (c). Show. In such an arrangement, the cell values (12 or 15) of the five representative cells shown in FIG. 21 (c) and the same coordinate position as each representative cell of the graph f (13, 13) shown in FIG. 21 (d). The product with the function value f is obtained.

FIG. 21 (e) shows the total exposure intensity obtained by accumulating the product of cell values at each position while moving the graph f (13, 13) shown in FIG. 21 (d) to the left and right. A distribution graph F is shown. Here, a graph f (13, 3) indicated by a broken line indicates a state in which the graph f is arranged so as to coincide with the center position of the representative cell C (13, 3), and a graph f (13, 8) indicated by a one-dot chain line. ) Shows a state in which the graph f is arranged so as to coincide with the center position of the representative cell C (13, 8), and the graph f (13, 13) indicated by a solid line indicates the graph f as the representative cell C (13, 13). The graph f (13, 18) indicated by the alternate long and short dash line indicates a state in which the graph f is arranged so as to match the center position of the representative cell C (13, 18). A graph f (13, 23) indicated by a broken line indicates a state in which the graph f is arranged so as to coincide with the center position of the representative cell C (13, 23).

A graph F shown in FIG. 21 (e) is a distribution graph of the total exposure intensity obtained by performing such a convolution operation, and the total exposure intensity v (x, y) shown in the equation (3) of FIG. It corresponds to the graph shown. As shown in FIG. 21 (b) IV, when the irradiation intensity matrix D (x ′, y ′) is created by giving the same cell value as the pixel value D to all the cells, the product for all the cells is obtained. However, as shown in FIG. 21C, only the representative cell located at the center of each pixel is given the same cell value as the pixel value D, and the irradiation intensity matrix D (x ′, y When ') is created, the product for the non-representative cell is 0, so that the operation for the non-representative cell can be substantially omitted.

The embodiment shown in FIGS. 20 and 21 is an example in which the calculation cell located at the center of each pixel constituting the drawing data is the representative cell, but the representative cell is not necessarily located at the cell located at the center of each pixel. It is not necessary to set any cell as a representative cell. FIG. 22 is a diagram illustrating a modification example in which a calculation cell located at the lower left of each pixel is a representative cell.

FIG. 22 (a) shows the arrangement of calculation cells constituting the irradiation intensity matrix D (x ′, y ′) as in the upper diagram of FIG. A square region having a size of one side d = 5 nm surrounded by a thick line frame shown in the drawing indicates one pixel P (i, j) constituting the drawing data, and one side d = 1 nm surrounded by a thin line frame. A square region having a size of 1 represents one arithmetic cell C (m, n). Here, the cells shown in black in the figure are representative cells, and the cells shown in white in the figure are non-representative cells. In the embodiment shown in the upper part of FIG. 20, a black representative cell is arranged at the center of each pixel. However, in the modification shown in FIG. 22A, a black representative cell is arranged at the lower left of each pixel. Has been.

In FIG. 22 (b), a calculation cell is defined by dividing one pixel P (i, j) shown in FIG. 22 (a) 、 into 25, and a predetermined cell value is given to each calculation cell. FIG. Since the lower left cell indicated by a bold frame in the figure is a representative cell, this representative cell is given a cell value “12” (pixel value of the pixel P (i, j)), and other non-representative cells A cell value of “0” is given. If the embodiment shown on the right side of FIG. 19B is compared with the modification shown in FIG. 22B, in the latter case, the position of the representative cell is the lower left position from the center position of the pixel P (i, j). It can be seen that it is displaced by a predetermined offset amount (in this example, 2√2 nm).

In other words, in the modification shown in FIG. 22, when the irradiation intensity matrix D (x ′, y ′) is created in the computation matrix creation stage in step S30, a plurality of computation cells included in the same pixel are created. Among them, the calculation cell existing at a position displaced by a predetermined offset amount in the predetermined direction from the center of the pixel is a representative cell, and the other calculation cells are non-representative cells. It can be said that the pixel value of the pixel including the cell is directly given as the cell value, and the cell value 0 is given to each non-representative cell.

In this way, when the irradiation intensity matrix D (x ′, y ′) is created, if a modification example is adopted in which the position of the representative cell is displaced from the center of the pixel in a predetermined direction by a predetermined offset amount, When creating the spread matrix psf (X, Y), it is preferable to perform correction in consideration of the offset amount. This is because each electron beam is irradiated with the center of each pixel as an irradiation target. As shown in the lower graph of FIG. 20, the center of the graph of the point spread function psf coincides with the center of each pixel. This is because it is preferable to arrange them as described above.

Therefore, when the representative cell is set at a position displaced by a predetermined offset amount from the center of the pixel in a predetermined direction as in the modification shown in FIG. 22, a point spread matrix psf (X, Y) is created. In this case, a point spread function psf (X, Y) corrected by the offset amount in a direction opposite to the predetermined direction is defined, and a point spread matrix indicating a plane distribution of the degree of influence indicated by the point spread function is defined. Just create it.

Specifically, instead of the point spread function psf (X, Y) shown in equation (4) in FIG. 14, a point spread function psf (X, Y) shown in equation (4 ′) in FIG. Use it to create a point spread matrix. The right side of Expression (4 ′) is obtained by replacing the variable X on the right side of Expression (4) with the variable “X + Δx” and replacing the variable Y with the variable “Y + Δy”. Here, Δx is an offset amount in the x-axis direction, and Δy is an offset amount in the y-axis direction. In the example shown in FIG. 22, Δx = 2 nm and Δy = 2 nm.

FIG. 23 is a diagram showing a concept of a process for performing a convolution operation when the modified example shown in FIG. 22 is adopted. Here, FIG. 23A is the same diagram as FIG. 21A and is a graph showing the pixel values D of the five pixels constituting the drawing data. FIG. 23 (b) is the same diagram as FIG. 21 (b), and is a graph showing an example in which the pixel values of the pixels including the cell are given as they are to the cell for calculation.

On the other hand, in FIG. 23 (c), as shown in FIGS. 22 (a) and (b), the lower left cell of each pixel is a representative cell, and only for this representative cell, the pixel of the pixel including the cell is displayed. The same cell value as the value D is given, and the cell value 0 is given for the other non-representative cells. Specifically, for the representative cells C (15, 1), C (15, 6), C (15, 11), C (15, 16), C (15, 21) in the 15th row The

cell value

12 or 15 is given, and the cell value 0 is given to other non-representative cells. Comparing FIG. 21C and FIG. 23C, in the latter, the position of the bar indicating the cell value of the representative cell is shifted to the left by two cells (offset amount Δx in the x-axis direction). I understand that.

On the other hand, FIG. 23 (d) shows one arrangement of the graph f of the point spread function pfs corresponding to the point spread matrix psf (X, Y), similarly to FIG. 21 (d). A graph f (15, 11) shown in FIG. 23 (d) shows a state where the center of the graph f is arranged at a position corresponding to the representative cell C (15, 11) shown in FIG. 23 (c). . However, the center position of the graph f (15, 11) does not coincide with the center position of the representative cell C (15, 11), but is shifted to the right by the offset amount Δx in the x-axis direction. Although not shown in the figure, the offset amount Δy is also shifted in the y-axis direction. As a result, the center position of the graph f (15, 11) coincides with the center position of the non-representative cell (13, 13).

Eventually, the position of the graph f (15, 11) shown in FIG. 23 (d) coincides with the position of the graph f (13, 13) shown in FIG. 21 (d), and the graph f (15, 11). Is an appropriate graph as a graph of the point spread function psf indicating the degree of influence of the electron beam irradiated with the center of the pixel P (3, 3) as the irradiation target from the irradiation point to the surroundings. In the equation (4 ′) in FIG. 22 (c), the correction using the offset amounts Δx and Δy is performed by convolution using the point spread matrix psf (X, Y) arranged at appropriate positions. This is so that the calculation is performed.

FIG. 23 (e) shows the process of accumulating the product of cell values at each position while moving the graph f (15, 11) to the left and right as in FIG. 21 (e). Further, a distribution graph F of the total exposure intensity finally obtained by the process is shown. Since the irradiation intensity matrix D (x ′, y ′) is created by giving the same cell value as the pixel value D only for the representative cell located at the lower left of each pixel, the product for the non-representative cell is 0. Substantially, the calculation for the non-representative cell can be omitted.

As described above, among a plurality of calculation cells included in each pixel, a cell value corresponding to the pixel value of the pixel is given only to a specific representative cell, and a cell value of 0 is given to other non-representative cells. When the method is employed, many calculation processes can be omitted and the calculation time can be shortened.

In the embodiments described so far, only one of a plurality of calculation cells included in one pixel is set as a representative cell, and the remaining cells are set as non-representative cells. A plurality of representative cells can be set for the pixel. Therefore, when creating the irradiation intensity matrix in the computation matrix creation stage, if the basic policy of setting the cell located at the center of each pixel as the representative cell is taken, multiple computations included in the same pixel Of the cells, one or more calculation cells located at the center of the pixel may be designated as representative cells, and the other calculation cells may be non-representative cells.

In general, when creating the irradiation intensity matrix in the computation matrix creation stage, if each pixel of the drawing data is divided into odd and vertical numbers, one computation cell located at the center of each pixel is used as the representative cell, Other calculation cells may be non-representative cells, the pixel value of the pixel including the representative cell may be given to the representative cell, and the cell value 0 may be given to the non-representative cell. The embodiment shown in FIG. 20 is an example in which each pixel is divided into five vertically and horizontally, and one arithmetic cell located at the center of each pixel is set as a representative cell.

On the other hand, when each pixel of the drawing data is divided into even numbers in the vertical and horizontal directions, four calculation cells are arranged at the center of each pixel. In such a case, these four calculation cells may be set as representative cells, and the other calculation cells may be non-representative cells. Then, a value of ¼ of the pixel value of the pixel including the representative cell may be given to the four representative cells, and a cell value of 0 may be given to the non-representative cell.

FIG. 24 (a) divides each pixel P (i, j) into 10 parts vertically and horizontally for drawing data composed of a pixel array of 9 pixels arranged in 3 rows and 3 columns at a vertical and horizontal pitch d = 10 nm. This is an example in which a calculation cell C (m, n) is created. Since each pixel is divided into even numbers in the vertical and horizontal directions, four calculation cells are arranged at the center of each pixel. Therefore, all the four calculation cells are set as representative cells for the pixel. That is, the cells shown in black in FIG. 24A are representative cells, and the cells shown in white in the figure are non-representative cells. Each representative cell is given a value that is ¼ of the pixel value of the pixel including the representative cell, and a cell value of 0 is given to the non-representative cell.

24 (b) (gives a predetermined cell value to each of a total of 100 operation cells C (m, n) included in one pixel P (i, j) shown in FIG. 24 (a). It is a figure which shows a state. The cell values “3” are assigned to the four sets of representative cells indicated by the bold frame in the figure, respectively, when the pixel value p of the pixel P (i, j) is “12”. It is an example. That is, a value “3” that is a quarter of the pixel value “12” of the pixel including the representative cell is given to each representative cell as the cell value. Also, cell values of 0 are given to all non-representative cells.

As described above, when a plurality of representative cells are set for one pixel, calculation for each of the plurality of representative cells is required. However, since calculation for non-representative cells can be omitted, the calculation time is reduced. The effect of shortening is obtained. Of course, even when a plurality of representative cells are set for one pixel in this way, the position of each representative cell may be displaced from the center of the pixel by a predetermined offset amount in a predetermined direction.

However, in the case of even division, it is not always necessary to set a plurality of representative cells, and only a single representative cell may be set for one pixel. In the case of even division, a single representative cell cannot be arranged at the center of the pixel, so that the representative cell is always arranged at a position offset by a predetermined offset amount in a predetermined direction from the center of the pixel. Become. In this case, as in the example shown in FIG. 22, when creating the point spread matrix psf (X, Y), the function psf (X, Y) corrected in the reverse direction by the offset amount is defined. Good.

In the example shown in FIG. 24B, one pixel is evenly divided into 100 cells, and four representative cells are defined in the vicinity of the center, and each pixel is 1/4 of the pixel value “12”. The value “3” is given as the cell value. This is a consideration for arranging the representative cell at the center of the pixel. As in the example shown in FIG. 22, if a method of correcting the function psf (X, Y) by a predetermined offset amount is employed, It is also possible to arrange a single representative cell at an arbitrary position.

For example, the example shown in FIG. 25 (a) is an example in which one pixel is divided into an even number of 100 cells, as in the example shown in FIG. 24 (a) 、. This is an example in which only the cell in the lower left corner shown in FIG. 6 is a single representative cell (the black cell is omitted for the convenience of drawing an arrow indicating the offset amount for the representative cell of the upper right pixel). 25 (b) b gives a predetermined cell value to each of a total of 100 operation cells C (m, n) included in one pixel P (i, j) shown in FIG. 25 (a). It is a figure which shows a state. The cell value “12” is given to the representative cell in the lower left corner indicated by the bold frame in the figure. This is because the pixel value p of the pixel P (i, j) is “12”. It is an example. The remaining 99 non-representative cells are all given a cell value of 0.

As indicated by an arrow for the upper right pixel in FIG. 25 (a), the center of the representative cell in the lower left corner is a predetermined offset amount (Δx = 4.5 nm horizontally, Δy vertically) from the pixel center to the lower left direction. = 4.5 nm), the function psf (X, Y) may be corrected by the same offset amount in the upper right direction. Specifically, instead of the point spread function psf (X, Y) shown in equation (4) in FIG. 14, a point spread function psf (X, Y) shown in equation (4 ′) in FIG. Use it to create a point spread matrix. The right side of the equation (4 ′) is obtained by replacing the variable X on the right side of the equation (4) with the variable “X + Δx” and replacing the variable Y with the variable “Y + Δy”. Equation (4 ′) may be applied with Δx = −4.5 nm and Δy = −4.5 nm.

<<< §7. Convolution calculation using Fourier transform >>>
In §6, as specific processing in the convolution calculation stage of step S40 in the flowchart of FIG. 18, two sets of calculation matrices, that is, an irradiation intensity matrix D (x ′, y ′) and a point spread matrix psf (X, Y) Explained the procedure of the convolution integration using. Here, the calculation which performs this convolution integral using Fourier transform is demonstrated.

Generally, it is known that the calculation time can be shortened by applying a calculation method using Fourier transform to the calculation for calculating the convolution integral of two functions f (A) and f (B). In principle, first, functions f (A) and f (B) are obtained by performing Fourier transform on the functions f (A) and f (B), respectively, to obtain the functions f ′ (A) and f ′ (B) having the spatial frequency values as variables. , Function f ′ (C) = f ′ (A) × f ′ (B) is calculated, and finally the function f ′ (C) is obtained by performing inverse Fourier transform on the function f ′ (C). (C) shows the convolution integral of the two functions f (A) and f (B).

Therefore, when implementing the present invention, it is preferable in practice to perform a convolution operation using Fourier transform. Step S40 in FIG. 18 describes four steps of processing, that is, a first calculation step S41, a second calculation step S42, a third calculation step S43, and a fourth calculation step S44. This is nothing but a process for performing a convolution operation using the Fourier transform described in §7.

FIG. 26 is a diagram showing the principle of performing the convolution operation in step S40 of FIG. 18 using Fourier transform. Expression (8) in FIG. 26 is exactly the same as expression (3) shown in FIG. 14, and is an expression showing the essence of the convolution operation performed in step S40. When the convolution operation using the Fourier transform described here is used, an operation equivalent to the equation (8) is performed by the following procedure to calculate the exposure intensity distribution v (x, y).

First, in the first calculation step S41, an irradiation intensity frequency matrix D ′ (f, g) is created by performing Fourier transform on the irradiation intensity matrix D (x ′, y ′) as shown in Equation (9). To do. The irradiation intensity matrix D (x ′, y ′) is a matrix showing a spatial distribution of irradiation intensity values in the horizontal direction (x′-axis direction) and the vertical direction (y′-axis direction). The intensity frequency matrix D ′ (f, g) is a matrix in which the f-axis indicating the spatial frequency in the x′-axis direction in the horizontal direction and the g-axis indicating the spatial frequency in the y′-axis direction in the vertical direction. The matrix D is a complex matrix indicating spatial frequency components in the x′-axis direction and the y′-axis direction of the matrix D (x ′, y ′).

Next, in the second calculation step S42, as shown in Expression (10), the point spread matrix psf (X, Y) is Fourier-transformed to create a point spread frequency matrix psf '(f, g). . The point spread matrix psf (X, Y) is a matrix indicating a spatial distribution of the degree of influence in the horizontal direction (X-axis direction) and the vertical direction (Y-axis direction), whereas the point spread frequency matrix psf. ′ (F, g) is a matrix in which the f-axis indicating the spatial frequency in the X-axis direction in the horizontal direction and the g-axis indicating the spatial frequency in the Y-axis direction in the vertical direction, and the point spread matrix psf (X, Y ) Of the complex numbers indicating the spatial frequency components in the X-axis direction and the Y-axis direction.

Subsequently, in the third calculation step S43, as shown in the equation (11), the corresponding calculation is performed for the irradiation intensity frequency matrix D ′ (f, g) and the point spread frequency matrix psf ′ (f, g), respectively. A product of complex numbers of the cells for use is obtained, and an exposure intensity frequency matrix v ′ (f, g) having the product as a cell value is created.

Then, in the final fourth calculation step S44, the exposure intensity matrix v (x, y) is created by performing inverse Fourier transform on the exposure intensity frequency matrix v ′ (f, g) obtained by the equation (11). . This exposure intensity matrix v (x, y) is a matrix indicating a planar distribution of the total exposure intensity at each evaluation point indicated by coordinates (x, y), that is, an exposure intensity distribution to be obtained by simulation according to the present invention. It becomes the matrix shown.

As described in §6, when the irradiation intensity matrix D (x ′, y ′) is created in the calculation matrix creation stage of step S30, only the representative cell is given a cell value corresponding to the pixel value, If a method of giving a cell value of 0 is adopted for non-representative cells, the computational burden of Fourier transform processing shown in equations (9) and (10) can be greatly reduced, and the computation time can be shortened.

FIG. 27 is a diagram for explaining the principle of reducing the computational burden of the Fourier transform process, and shows a specific procedure of the Fourier transform process shown in Equation (9). First, FIG. 27 (a) is a diagram showing a cell arrangement of the irradiation intensity matrix D (x ′, y ′). Each cell contains a cell value corresponding to the pixel value of the original drawing data.

In order to obtain the irradiation intensity frequency matrix D ′ (f, g) by performing Fourier transform on the irradiation intensity matrix D (x ′, y ′) according to the equation (9), first, the horizontal direction (x ′ axis The cell values arranged in the (direction) are subjected to Fourier transform, the spatial frequency is obtained, and processing for creating an irradiation intensity intermediate matrix D ″ (f, y) as shown in FIG. The irradiation intensity intermediate matrix D ″ (f, y) has a frequency f axis on the horizontal axis and a y ′ axis on the vertical axis, and x for each cell value of the original irradiation intensity matrix D (x ′, y ′). A matrix indicating spatial frequency components in the axial direction.

For example, each cell in the first row shown in FIG. 27 (a) surrounded by a thick line frame extending in the horizontal direction contains predetermined cell values. If the spatial frequency components are extracted and the values of the extracted components are arranged as cell values on the frequency f axis, a cell in the first row shown in FIG. 27 (b) is surrounded by a thick line frame extending in the horizontal direction. It is done. The cell in the first row is a one-dimensional array along the frequency f axis, and the value of the higher component of the spatial frequency f is accommodated as the cell value from the left to the right.

Subsequently, with respect to the irradiation intensity intermediate matrix D ″ (f, y), a Fourier transform is performed on the cell values arranged in the vertical direction (y′-axis direction), and the spatial frequency is obtained. ) An irradiation intensity frequency matrix D '(f, g) as shown in (9) is obtained. In this irradiation intensity frequency matrix D ′ (f, g), the horizontal axis is the frequency f axis and the vertical axis is the frequency g axis, and x for each cell value of the original irradiation intensity matrix D (x ′, y ′). This is a matrix indicating spatial frequency components in the ′ -axis direction and the y′-axis direction.

For example, each cell in the second column shown in FIG. 27 (b) surrounded by a bold line extending in the vertical direction contains predetermined cell values. If spatial frequency components are extracted and the values of the extracted components are arranged as cell values on the frequency g axis, the cells in the second column shown in FIG. 27 (c) are surrounded by a thick line frame extending in the vertical direction. It is done. The cells in the second column are one-dimensional arrays along the frequency g axis, and values of higher components of the spatial frequency g are accommodated as cell values from the top to the bottom.

A specific process for extracting the spatial frequency component of a one-dimensional array of cell values by performing a Fourier transform is known in the art because FFT (Fast Fourier Transform) is a well-known method. Although omitted, the irradiation intensity matrix D (x ′, y ′) may have a cell value corresponding to the pixel value only for a specific representative cell, and a cell value 0 for other non-representative cells. For example, the calculation load of the Fourier transform process is greatly reduced. This is because when the irradiation intensity matrix D (x ′, y ′) shown in FIG. 27A is converted into the irradiation intensity intermediate matrix D ″ (f, y) shown in FIG. This is because an operation can be omitted for a line that only includes the line.

For example, in the matrix shown on the right side of FIG. 19 (b) 、, the matrix shown in FIG. 22 (b), and the matrix shown in FIG. 24 (b), the cell values of the cells in the first and second rows are all 0. It has become. Thus, the result of Fourier transform of a row containing only the value 0 (row along the x′-axis) becomes a row (row along the f-axis) that also contains only the value 0. In fact, the Fourier transform process can be omitted for such a row. For this reason, if a method of giving a substantial cell value only for the representative cell and setting the cell value of the non-representative cell to 0 is adopted, the calculation burden of the Fourier transform process can be greatly reduced. The calculation time can be shortened.

<<< §8. Exposure intensity distribution calculation apparatus according to the present invention >>
So far, the present invention has been described as a method invention in the form of a simulation method for obtaining an exposure intensity distribution in a multi-beam electron beam lithography apparatus. Here, the present invention will be described as an apparatus invention in the form of an exposure intensity distribution calculation apparatus used in a multi-beam electron beam drawing apparatus.

FIG. 28 is a block diagram showing a basic configuration of an exposure intensity distribution calculation apparatus according to the present invention. This exposure intensity distribution calculation device is a device having a function for obtaining an exposure intensity distribution when a predetermined pattern is exposed and drawn on a molding layer using a multi-beam electron beam drawing device. A unit 110, an irradiation intensity matrix creation unit 120, a parameter setting unit 130, a point spread matrix creation unit 140, and a convolution calculation execution unit 150. Actually, each of these components is realized by a cooperative operation of a computer and a program incorporated in the computer, and this exposure intensity distribution calculation device incorporates a dedicated program in the computer. Can be configured.

The drawing data input unit 110 is a component for inputting drawing data Din. As described above, the drawing data Din is data indicating a pattern drawn by the electron beam drawing apparatus, and is data including an array of pixels having pixel values indicating the irradiation intensity at each irradiation position of the beam.

The parameter setting unit 130 is a component that sets an aperture size parameter B that is determined based on the aperture size of the aperture of the electron beam drawing apparatus. As illustrated, the aperture size K of the aperture is a value defined as the size of the aperture 41 formed in the aperture plate 40. As described above, when the aperture 41 has a circular shape, Is used as the aperture size K of the aperture, and when the aperture 41 has a square shape, the length of one side of the square may be used as the aperture size of the aperture. As the aperture size parameter B, a value obtained by multiplying the aperture size K by the reduction magnification m by the projection lens 50 of the electron beam drawing apparatus can be used.

When simulating an electron beam drawing apparatus in which the aperture size K of the aperture 41 of the aperture and the reduction magnification m by the projection lens 50 are fixed, the parameter setting unit 130 sets the value of the fixed value m · K to the aperture size parameter B. Set it as a value. When simulating an electron beam drawing apparatus in which these are variable, the parameter setting unit 130 is provided with a function for inputting the aperture size K and the reduction magnification m each time, and based on the input values, m · K May be set as the value of the aperture size parameter B.

The irradiation intensity matrix creation unit 120 prepares an empty calculation matrix composed of a collection of calculation cells obtained by dividing each pixel of the drawing data input by the drawing data input unit 110 into a plurality of pieces. This is a component that creates an irradiation intensity matrix D (x ′, y ′) indicating a planar distribution of electron beam irradiation intensity by giving a predetermined cell value based on the pixel value of a pixel including the cell to the cell. A specific method of creating the irradiation intensity matrix D (x ′, y ′) is as already described in Section 5 with reference to FIG.

Note that, in order to reduce the calculation burden, the irradiation intensity matrix creation unit 120 has a predetermined value determined based on the pixel value of the pixel only for a specific representative cell among a plurality of calculation cells included in the same pixel. It is preferable to give a value as a cell value and give a cell value of 0 for other non-representative cells. Specifically, among a plurality of calculation cells included in the same pixel, one or more calculation cells located at the center of the pixel are designated as representative cells, and the other calculation cells are designated as non-representative cells. That's fine.

When the irradiation intensity matrix creation unit 120 divides each pixel of the drawing data into odd and vertical numbers to define a calculation cell, one calculation cell located at the center of each pixel is used as a representative cell, and the others The calculation cell is a non-representative cell, the pixel value of the pixel including the representative cell is given to the representative cell as a cell value, and the cell value 0 can be given to the non-representative cell. On the other hand, when the irradiation intensity matrix creation unit 120 divides each pixel of the drawing data into an even number in each of the vertical and horizontal directions to define the calculation cell, the four calculation cells positioned at the center of each pixel are represented. A non-representative cell is set as a cell, and a non-representative cell is given to the representative cell as a cell value that is 1/4 of the pixel value of the pixel including the representative cell, and a cell value of 0 is given to the non-representative cell. be able to. The details of both are as already described in §6.

On the other hand, the point spread matrix creating unit 140 is a cell corresponding to a predetermined point spread function psf (X, Y) including the opening size parameter B set by the parameter setting unit 130 in each calculation cell of the empty calculation matrix. By giving a value, this is a component that creates a point spread matrix psf (X, Y) indicating a plane distribution of the degree of influence indicated by the point spread function psf. As the point spread function psf, as illustrated in FIG. 15, the width w of the flat portion H of the graph is influenced by the aperture size parameter B, and the inclinations of the inclined portions U1 and U2 of the graph are influenced by the forward scattering parameter σ. Use functions. Specific examples of the point spread function psf (X, Y) are as illustrated as Expression (4) in FIG. 14, Expression (6) in FIG. 16, and Expression (7) in FIG.

22 and FIG. 23, the irradiation intensity matrix creation unit 120 is displaced by a predetermined offset amount in a predetermined direction from the center of the pixel among a plurality of calculation cells included in the same pixel. The irradiation intensity matrix D (x ′, y ′) can also be created using the calculation cell existing at the position as a representative cell and the other calculation cells as non-representative cells. In this case, the point spread matrix creating unit 140 creates a point spread matrix psf (X, Y) indicating a plane distribution of the degree of influence indicated by the point spread function corrected by the offset amount in the direction opposite to the predetermined direction. (See FIG. 22 (c) IV).

The convolution operation execution unit 150 includes an irradiation intensity matrix D (x ′, y ′) created by the irradiation intensity matrix creation unit 120, a point spread matrix psf (X, Y) created by the point spread matrix creation unit 140, and the like. Is a component that performs a calculation to obtain a total exposure intensity at each evaluation point.

In the illustrated embodiment, the convolution operation execution unit 150 has a function of performing convolution integration using Fourier transform. Therefore, the convolution calculation execution unit 150 performs a Fourier transform on the irradiation intensity matrix D (x ′, y ′), thereby creating a first calculation unit 151 (FIG. 15) that creates the irradiation intensity frequency matrix D ′ (f, g). 26) and a second arithmetic unit that creates a point spread frequency matrix psf ′ (f, g) by performing Fourier transform on the point spread matrix psf (X, Y). 152 (means for executing the processing of the equation (10) in FIG. 26), the product of the calculation cells corresponding to the irradiation intensity frequency matrix D ′ (f, g) and the point spread frequency matrix psf ′ (f, g). A third calculation unit 153 (means for executing the processing of the expression (11) in FIG. 26) for creating an exposure intensity frequency matrix v ′ (f, g) having a cell value as a cell value; A fourth operation unit 154 that generates an exposure intensity matrix v (x, y) indicating a planar distribution of the total exposure intensity at each evaluation point by performing inverse Fourier transform on ′ (f, g). ing.

The specific processing procedure of the convolution integral using the Fourier transform is as described in §7. Thus, the exposure intensity matrix v (x, y) created by the fourth calculation unit 154 is output as exposure intensity distribution data Dout.

<<< §9. Example of exposure intensity distribution obtained using the present invention >>>
Finally, an actual example of the exposure intensity distribution obtained by using the present invention will be shown. FIG. 29 is a view showing a first example of the exposure intensity distribution obtained by the simulation method according to the invention. FIG. 29 (a) is a diagram showing drawing data prepared for drawing a linear pattern having a width of 50 nm as a gray-tone image. On the left side of the figure, pixel values corresponding to the gray tone densities are shown as legends. As shown in the figure, the pixel value 15 is given to the pixels inside the linear pattern, and the pixel value 0 is given to the external pixels. The pixel pitch d is set to d = 5 nm, and 10 pixels having the pixel value 15 are arranged in the horizontal width direction of the linear pattern.

FIG. 29 (b) shows the irradiation intensity matrix D (x ′, y ′) created based on the drawing data shown in FIG. 29 (a) as a gray-tone image. This irradiation intensity matrix is composed of a collection of operation cells arranged at a pitch g. This example is an example in which a calculation cell is defined by dividing one pixel vertically and horizontally as in the example shown in FIG. 20, and the cell pitch g is set to g = 1 nm. A small black dot shown in the figure is a representative cell located at the center of each pixel, and the same 15 as the pixel value is given as the cell value.

FIG. 29 (c) is obtained by a convolution integral operation for the irradiation intensity matrix D (x ′, y ′) shown in FIG. 29 (b) and a predetermined point spread matrix psf (X, Y) not shown. It is a figure which shows the obtained exposure intensity matrix v (x, y), ie, exposure intensity distribution, as a gray tone image. On the left side of the figure, cell values (calculated values of v (x, y)) corresponding to the gray tone densities are shown as legends. The closer to black, the higher the exposure intensity (accumulated energy amount). The two white lines in the figure indicate the outline of the linear pattern shown in FIG. 29 (a). As described above, the result shown in FIG. 29C shows the appropriate exposure intensity distribution obtained when the exposure process is performed based on the drawing data shown in FIG.

On the other hand, FIG. 30A is a diagram showing another drawing data prepared for drawing a linear pattern having a width of 50 nm as a gray-tone image. Pixel values corresponding to the respective densities are shown as legends. In the case of this example, the pixel pitch d is set to d = 10 nm, and a total of 6 pixels are arranged in the horizontal width direction of the linear pattern. Each of the four pixels arranged in the horizontal direction near the center of the linear pattern is given a pixel value of 15; however, each of the one pixel arranged on the left side and the one pixel arranged on the right side has both A pixel value of 7 is given.

FIG. 30B is a diagram showing an irradiation intensity matrix D (x ′, y ′) created based on the drawing data shown in FIG. 30A as a gray-tone image. This irradiation intensity matrix is composed of a collection of operation cells arranged at a pitch g. This example is an example in which a calculation cell is defined by dividing one pixel vertically and horizontally as in the example shown in FIG. 24, and the cell pitch g is set to g = 1 nm. Shown as small gray dots in the figure are four representative cells located at the center of each pixel, and a value corresponding to 1/4 of the pixel value 15 is given as the cell value.

30 (c) c is obtained by a convolution integral operation on the irradiation intensity matrix D (x ′, y ′) shown in FIG. 30 (b) and a predetermined point spread matrix psf (X, Y) not shown. It is a figure which shows the obtained exposure intensity matrix v (x, y), ie, exposure intensity distribution, as a gray tone image. On the left side of the figure, cell values (calculated values of v (x, y)) corresponding to the gray tone densities are shown as legends. The closer to black, the greater the exposure intensity (accumulated energy amount). The two white lines in the figure indicate the outline of the linear pattern shown in FIG. 30 (a). As described above, the result shown in FIG. 30C also shows an appropriate exposure intensity distribution obtained when the exposure process is performed based on the drawing data shown in FIG.

The example shown in FIG. 29 and the example shown in FIG. 30 both show the results obtained by performing the convolution operation using the Fourier transform described in §7, and the calculation time until the result is obtained is greatly increased. Has been shortened to.

A method and apparatus for obtaining an exposure intensity distribution in a multi-beam electron beam lithography apparatus according to the present invention provides an exposure intensity distribution in a field where a specific material layer needs to be finely patterned, such as a semiconductor device manufacturing process. Can be widely used as a technique for estimating by computer simulation.

10: Electron gun 20: Expanded electron beam 21: Individual electron beam 30 constituting a multi-beam 30: Condenser lens 40: Aperture plate 41: Aperture 50: Projection lens 60: Sample substrate 61: Molded layer (resist layer )
70: Movement stage 110: Drawing data input unit 120: Irradiation intensity matrix creation unit 130: Parameter setting unit 140: Point spread matrix creation unit 150: Convolution calculation execution unit 151: First calculation unit 152: Second calculation unit 153 : Third computing unit 154: fourth computing unit A1, A2: rectangular area a: exposure area B: aperture size parameter b: non-exposure area C: constant C (m, n) used for point spread function: m rows Calculation cell Da in the n-th column: width Di in the x-axis direction of the pattern: irradiation intensity (dose amount) of the electron beam at the i-th exposure operation
Din: drawing data Dout: exposure intensity distribution data D (x ′, y ′): dose amount / irradiation intensity matrix D ′ (f, g) at reference point T (x ′, y ′): irradiation intensity frequency matrix D ′ '(F, y): irradiation intensity intermediate matrix d: pixel pitch E, E1, E2: electron beam intensity (energy density)
E (5), E (10), E (15): Electron beam intensity (energy density)
Eth: Threshold value of total exposure intensity F: Distribution graph of total exposure intensity f: Frequency axis f (m, n): Graph of point spread function psf g: Pitch / frequency axis of calculation cell H: Flat part K of graph: Aperture aperture size M, M1 to M9: Exposure intensity distribution graph (Oyama)
M (5), M (10), M (15): Exposure intensity distribution graph (Oyama)
MM: Total exposure intensity distribution graph (Oyama)
N: number of exposure operations P, P1 to P5: individual pixels P (i, j) of the two-dimensional pixel array constituting the drawing data: pixel psf in the i-th row and j-th column: point spread function
psf (X, Y): Point spread matrix psf ′ (f, g): Point spread frequency matrix Q, Q1 to Q9: Individual irradiation reference points Q (0), Q (5) defined on the exposure target surface , Q (10), Q (15): Individual irradiation reference points R defined on the exposure target surface: Distances between reference points T and evaluation points V S1 to S5: Electron beam irradiation spots S10 to S44: Flow chart Steps T (x ′, y ′): reference points U1, U2 located at coordinates (x ′, y ′): slopes V1, V2, V11, V12, V21 of the graph: evaluation points V (x, y) ): Evaluation point v (x, y) located at coordinates (x, y): Accumulated energy amount (total exposure intensity) / exposure intensity matrix v ′ (f, g) at evaluation point V (x, y): Exposure Intensity frequency matrix w: width of flat portion H of graph X: between reference point T and evaluation point V Directional distance x, x ′: Horizontal coordinate axis / horizontal coordinate value defined on the exposure target surface Y: Vertical distance y, y ′ between the reference point T and the evaluation point V: Defined on the exposure target surface Longitudinal coordinate axis / longitudinal coordinate value β: backscattering parameter Δx, Δy: offset amount η: proximity effect correction parameter φ: beam spot diameter σ: forward scattering parameter

Claims

A simulation method for obtaining an exposure intensity distribution (MM) when a predetermined pattern is exposed and drawn on a molding layer (61) using a multi-beam electron beam drawing apparatus,
For a number of reference points (T (x ′, y ′)) defined in the electron beam irradiation region, a function (D (x ′, y ′)) indicating the electron beam irradiation intensity and the reference points affect the surroundings. Including a process of calculating the total exposure intensity (v (x, y)) at each evaluation point (V (x, y)) by performing convolution integration with a point spread function (psf) indicating the degree of influence. ,
An exposure intensity in a multi-beam electron beam lithography system using a function including an aperture size parameter (B) determined based on the aperture size of the aperture (40) of the electron beam lithography system as the point spread function (psf) A simulation method for obtaining the distribution.
The simulation method according to claim 1,
Define an xy plane of a two-dimensional xy orthogonal coordinate system as an electron beam irradiation surface,
The influence of the reference point T (x ′, y ′) positioned at the coordinates (x ′, y ′) on the evaluation point V (x, y ′) positioned at the coordinates (x, y) is referred to as the reference point T A function D (x ′, y ′) indicating the electron beam irradiation intensity with respect to (x ′, y ′) and a point spread function psf (X, y defined as X = x′−x, Y = y′−y) Y) and a convolution integral with respect to the x-axis direction and the y-axis direction for
A multi-beam electron beam using a function including an aperture size parameter B determined based on the aperture size of the aperture of the electron beam drawing apparatus in addition to the variables X and Y as the point spread function psf (X, Y) A simulation method for obtaining an exposure intensity distribution in a drawing apparatus.
The simulation method according to claim 2,
A simulation method for obtaining an exposure intensity distribution in a multi-beam electron beam drawing apparatus, wherein a function in which a width of a flat portion of a graph is influenced by an aperture size parameter B is used as the point spread function psf (X, Y).
In the simulation method according to claim 3,
Exposure intensity distribution in a multi-beam electron beam drawing apparatus using a function including a parameter σ that affects the inclination of the inclined portion of the graph in addition to the aperture size parameter B as the point spread function psf (X, Y) Simulation method to find out.
The simulation method according to claim 4,
Including error function erf as point spread function,
psf (X, Y) = 1/4 · (erf ((B / 2−X) / σ) −erf ((− B / 2−X) / σ)) · (erf ((B / 2−Y) / Σ) −erf ((− B / 2−Y) / σ)). A simulation method for obtaining an exposure intensity distribution in a multi-beam electron beam imaging apparatus.
The simulation method according to claim 4,
Including the inverse trigonometric function arctan as the point spread function,
psf (X, Y) = 1/4 · (arctan ((B / 2−X) / σ) −arctan ((− B / 2−X) / σ)) · (arctan ((B / 2−Y) / Σ) -arctan ((−B / 2−Y) / σ)) is used. A simulation method for obtaining an exposure intensity distribution in a multi-beam electron beam imaging apparatus.
The simulation method according to claim 4,
As a point spread function, an error function erf, a predetermined constant C, a backscattering parameter β, and a proximity effect correction parameter η are included.
psf (X, Y) = C / (1 + η) · (1 / 4σ 2 · (erf ((B / 2−X) / σ) −erf ((− B / 2−X) / σ)) · (erf ((B / 2−Y) / σ) −erf ((− B / 2−Y) / σ)) + η / β 2 · exp (− (X 2 + Y 2 ) / β 2 ))
A simulation method for obtaining an exposure intensity distribution in a multi-beam electron beam apparatus characterized by using the function
The simulation method according to any one of claims 1 to 7,
When the opening (41) of the aperture (40) of the electron beam drawing apparatus is circular, the diameter of the circle is the aperture size of the aperture, and when the opening (40) is square, The length of one side of the square is the aperture size of the aperture, and a value obtained by multiplying this aperture size by the reduction ratio of the projection lens (50) of the electron beam drawing apparatus is determined based on the aperture size of the aperture (B And a simulation method for obtaining an exposure intensity distribution in a multi-beam electron beam imaging apparatus.
The simulation method according to any one of claims 1 to 8,
A drawing data input stage in which a computer inputs drawing data (Din) consisting of an array of pixels having pixel values indicating the irradiation intensity at each irradiation position of the beam, which is data indicating a pattern drawn by the electron beam drawing apparatus. S10)
A parameter setting step (S20) in which the computer sets an aperture size parameter (B) determined based on the aperture size of the aperture (40) of the electron beam lithography apparatus;
Two sets of empty calculation matrices comprising a set of calculation cells (C (m, n)) obtained by the computer dividing each pixel (P (i, j)) of the drawing data into a plurality of pieces. And a predetermined cell value based on the pixel value of the pixel including the cell is given to each cell of the first calculation matrix, whereby an irradiation intensity matrix (D ( x ′, y ′)) and a cell value corresponding to a predetermined point spread function (psf) including the aperture size parameter is given to each cell of the second calculation matrix, thereby the point spread. A calculation matrix creation step (S30) for creating a point spread matrix (psf (X, Y)) indicating a plane distribution of the degree of influence indicated by the function;
A computer performs convolution integration using the irradiation intensity matrix (D (x ′, y ′)) and the point spread matrix (psf (X, Y)), and calculates the total exposure intensity (v ( x, y)) to obtain a convolution operation step (S40);
A simulation method for obtaining an exposure intensity distribution in a multi-beam electron beam imaging apparatus.
The simulation method according to claim 9, wherein
When the irradiation intensity matrix (D (x ′, y ′)) is created in the computation matrix creation stage (S30), a plurality of computation cells (C (m) included in the same pixel (P (i, j)) are created. , N)), a predetermined value determined based on the pixel value of the pixel is given as a cell value only for a specific representative cell, and a cell value of 0 is given to other non-representative cells. A simulation method for obtaining an exposure intensity distribution in a multi-beam electron beam imaging apparatus.
The simulation method according to claim 10, wherein
When the irradiation intensity matrix (D (x ′, y ′)) is created in the computation matrix creation stage (S30), a plurality of computation cells (C (m) included in the same pixel (P (i, j)) are created. , N)), one or a plurality of calculation cells located at the center of the pixel are designated as representative cells, and the other calculation cells are designated as non-representative cells. A simulation method for obtaining an exposure intensity distribution.
The simulation method according to claim 11,
When the irradiation intensity matrix (D (x ′, y ′)) is created in the calculation matrix creation stage (S30), each pixel of the drawing data is divided into odd and vertical numbers, and each pixel (P (i, j)) ) Is set as a representative cell, the other calculation cells are set as non-representative cells, and the pixel value of the pixel including the representative cell is given to the representative cell as a cell value. A simulation method for obtaining an exposure intensity distribution in a multi-beam electron beam imaging apparatus, wherein a cell value of 0 is given to a representative cell.
The simulation method according to claim 11,
When the irradiation intensity matrix (D (x ′, y ′)) is created in the calculation matrix creation stage (S30), each pixel (P (i, j)) of the drawing data is divided into even numbers in the vertical and horizontal directions. The four calculation cells located at the center of the pixel are designated as representative cells, the other calculation cells are designated as non-representative cells, and the representative cell has a value of ¼ of the pixel value of the pixel including the representative cell. A simulation method for obtaining an exposure intensity distribution in a multi-beam electron beam imaging apparatus, characterized in that a non-representative cell is given as a value and a cell value of 0 is given.
The simulation method according to claim 10, wherein
Among the plurality of calculation cells included in the same pixel (P (i, j)) when the irradiation intensity matrix (D (x ′, y ′)) is generated in the calculation matrix generation stage (S30), The calculation cell existing at a position displaced by a predetermined offset amount (Δx, Δy) in the predetermined direction from the center of the pixel is a representative cell, and the other calculation cells are non-representative cells.
When the point spread matrix (psf (X, Y)) is created in the calculation matrix creation stage (S30), the point spread function is corrected by the offset amount (Δx, Δy) in the opposite direction to the predetermined direction. A simulation method for obtaining an exposure intensity distribution in a multi-beam electron beam imaging apparatus, wherein a point spread matrix (psf (X, Y)) indicating a planar distribution of the degree of influence is generated.
The simulation method according to any one of claims 9 to 14,
In the convolution operation stage (S40),
A first calculation step (S41) for creating an irradiation intensity frequency matrix (D ′ (f, g)) by Fourier transforming the irradiation intensity matrix (D (x ′, y ′));
A second calculation step (S42) for creating a point spread frequency matrix (psf ′ (f, g)) by performing a Fourier transform on the point spread matrix (psf (X, Y));
An exposure intensity frequency matrix (v ′) having a cell value as the product of the corresponding calculation cells of the irradiation intensity frequency matrix (D ′ (f, g)) and the point spread frequency matrix (psf ′ (f, g)). A third computation stage (S43) for creating (f, g));
An exposure intensity matrix (v (x) indicating a planar distribution of the total exposure intensity at each evaluation point (V (x, y)) by performing an inverse Fourier transform on the exposure intensity frequency matrix (v ′ (f, g)). , Y)) to create a fourth computation stage (S44);
A simulation method for obtaining an exposure intensity distribution in a multi-beam electron beam imaging apparatus.
A drawing data input step (S10), a parameter setting step (S20), a calculation matrix creation step (S30), and a convolution calculation step (S40) in the simulation method according to any one of claims 9 to 15. A program to be executed by a computer.
An exposure intensity distribution calculation apparatus that performs an operation for obtaining an exposure intensity distribution (MM) when a predetermined pattern is exposed and drawn on a molding layer (61) using a multi-beam electron beam drawing apparatus,
A drawing data input unit (110) for inputting drawing data (Din) including data indicating a pattern drawn by the electron beam drawing apparatus and having a pixel value indicating the irradiation intensity at each irradiation position of the beam; ,
A parameter setting unit (130) for setting an aperture size parameter (B) determined based on the aperture size of the aperture (40) of the electron beam lithography apparatus;
An empty calculation matrix comprising a set of calculation cells (C (m, n)) obtained by dividing each pixel (P (i, j)) of the drawing data into a plurality is prepared. Irradiation intensity for creating an irradiation intensity matrix (D (x ′, y ′)) showing a planar distribution of electron beam irradiation intensity by giving a predetermined cell value based on the pixel value of the pixel including the cell to the cell for use A matrix creation unit (120);
The degree of influence indicated by the point spread function by giving a cell value according to a predetermined point spread function (psf) including the opening size parameter (B) to each calculation cell of the empty calculation matrix A point spread matrix creating unit (140) for creating a point spread matrix (psf (X, Y)) indicating a plane distribution of
A convolution calculation execution unit (150) that performs convolution integration using the irradiation intensity matrix and the point spread matrix to obtain a total exposure intensity (v (x, y)) at each evaluation point (V (x, y)). )When,
An exposure intensity distribution calculation apparatus used for a multi-beam electron beam drawing apparatus.
In the exposure intensity distribution calculation apparatus according to claim 17,
The point spread matrix creating unit (140) uses a function in which the width of the flat portion of the graph is influenced by the aperture size parameter B as the point spread function (psf), and is used for the multi-beam electron beam drawing apparatus. Intensity distribution calculation device.
In the exposure intensity distribution calculating apparatus according to claim 18,
The point spread matrix creation unit (140) uses, as the point spread function (psf), in addition to the aperture size parameter B, a function including a parameter σ that affects the inclination of the inclined portion of the graph. An exposure intensity distribution calculation device used in a line drawing apparatus.
The exposure intensity distribution calculation apparatus according to any one of claims 17 to 19,
The irradiation intensity matrix creation unit (120) has the pixel value of the pixel only for a specific representative cell among the plurality of calculation cells (C (m, n)) included in the same pixel (P (i, j)). An exposure intensity distribution calculation device used for a multi-beam electron beam lithography apparatus, wherein a predetermined value determined based on the above is given as a cell value, and a cell value of 0 is given to other non-representative cells.
In the exposure intensity distribution calculation apparatus according to claim 20,
The irradiation intensity matrix creation unit (120) includes one or more of the plurality of calculation cells (C (m, n)) included in the same pixel (P (i, j)) positioned at the center of the pixel. An exposure intensity distribution calculation apparatus used for a multi-beam electron beam lithography apparatus, wherein the calculation cell is a representative cell and the other calculation cells are non-representative cells.
In the exposure intensity distribution calculating apparatus according to claim 21,
The irradiation intensity matrix creation unit (120) divides each pixel (P (i, j)) of the drawing data (Din) into odd and vertical numbers, and sets one calculation cell located at the center of each pixel as a representative cell. The other calculation cells are non-representative cells, pixel values of pixels including the representative cells are given to the representative cells as cell values, and a cell value of 0 is given to the non-representative cells. An exposure intensity distribution calculation device used for a beam electron beam drawing apparatus.
In the exposure intensity distribution calculating apparatus according to claim 21,
The irradiation intensity matrix creation unit (120) divides each pixel (P (i, j)) of the drawing data (Din) into an even number in each of the vertical and horizontal directions, and uses four calculation cells located at the center of each pixel as representative cells. The other calculation cells are set as non-representative cells, and the representative cell is given a cell value that is 1/4 of the pixel value of the pixel including the representative cell, and the non-representative cell is given a cell value of 0. An exposure intensity distribution calculation device used for a multi-beam electron beam lithography apparatus.
In the exposure intensity distribution calculation apparatus according to claim 20,
The irradiation intensity matrix creation unit (120) has a predetermined offset in a predetermined direction from the center of the pixel among a plurality of calculation cells (C (m, n)) included in the same pixel (P (i, j)). A calculation cell existing at a position displaced by an amount (Δx, Δy) is a representative cell, and the other calculation cells are non-representative cells.
A point spread matrix (140) indicating a plane distribution of the degree of influence indicated by the point spread function (psf) corrected by the offset amount (Δx, Δy) in a direction opposite to the predetermined direction by the point spread matrix creation unit (140). psf (X, Y)). An exposure intensity distribution calculation device used for a multi-beam electron beam drawing apparatus.
The exposure intensity distribution calculation apparatus according to any one of claims 17 to 24,
The convolution unit (150)
A first calculation unit (151) for creating an irradiation intensity frequency matrix (D ′ (f, g)) by performing Fourier transform on the irradiation intensity matrix (D (x ′, y ′));
A second calculation unit (152) that creates a point spread frequency matrix (psf ′ (f, g)) by performing Fourier transform on the point spread matrix (psf (X, Y));
An exposure intensity frequency matrix (v ′) having a cell value as the product of the corresponding calculation cells of the irradiation intensity frequency matrix (D ′ (f, g)) and the point spread frequency matrix (psf ′ (f, g)). A third calculation unit (153) for creating (f, g));
An exposure intensity matrix (v (x) indicating a planar distribution of the total exposure intensity at each evaluation point (V (x, y)) by performing an inverse Fourier transform on the exposure intensity frequency matrix (v ′ (f, g)). , Y)) creating a fourth computing unit (154);
An exposure intensity distribution calculation device used for a multi-beam electron beam lithography apparatus.
A program that causes a computer to function as the exposure intensity distribution calculation device according to any one of claims 17 to 25.