TW201820407A - Method and device for obtaining exposure intensity distribution in multibeam electron beam lithography device - Google Patents

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 device for obtaining exposure intensity distribution in multi-beam electron beam drawing device   

The present invention relates to a method and a device for obtaining an exposure intensity distribution in a multi-beam electron beam drawing device, and more particularly, to a computer simulation method for determining the exposure pattern of a shaped layer using a multi-beam electron beam drawing device. Technique of exposure intensity distribution.

In fields such as manufacturing processes of semiconductor devices that require a fine patterning process for a specific material layer, a patterning method using an electron beam drawing device is widely used. If an electron beam drawing device is used, a fine pattern can be exposed on the formed layer based on the given drawing data, so that an extremely fine linear pattern can be formed. For example, Patent Document 1 below discloses a single beam method (VSB method: Variable Shape Beam) of an electron beam drawing device and a drawing method of drawing a desired pattern using the device.

On the other hand, recently, a multi-beam electron beam drawing device capable of simultaneously irradiating a plurality of electron beams has been put into practical use. For example, Patent Document 2 discloses a multi-beam electron beam drawing device that generates a plurality of electron beams by passing an enlarged electron beam through a perforated plate having a plurality of openings, and so on. A specific pattern is drawn on the surface of the sample while the on / off control is performed individually using a shield plate. In addition, Patent Document 3 discloses a method of using a multi-beam electron beam drawing device to perform multiple beam exposures on the same part of the surface of a sample, thereby drawing a gray scale having a gray scale. pattern.

However, it is known that in a patterning method using the electron beam drawing device, the size of a pattern that should actually be formed varies due to a factor called a proximity effect. The proximity effect is a phenomenon (forward scattering) in which a relatively small amount of electrons diffuses in the form of molecules on the inside of the resist when the shaped layer composed of a resist layer or the like is irradiated with an electron beam, or The phenomenon (backscattering) of electrons scattered and scattered in the vicinity of the surface of a metal substrate or the like under the resist layer and bounced back will be described.

Therefore, in order to perform patterning with high accuracy, it is necessary to implement correction that takes into account the proximity effect to the drawing data given to the electron beam drawing device. In order to perform such a correction, it is effective to estimate the exposure intensity distribution which is actually generated when the electron beam is drawn on the formed 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 in a manner that eliminates the error. For example, a method disclosed in Patent Document 4 is to calculate the exposure intensity distribution that would actually be generated by computer simulation in consideration of the proximity effect.

[Prior technical literature]

[Patent Literature]

[Patent Document 1] Japanese Patent Laid-Open No. 2009-253124

[Patent Document 2] Japanese Patent Laid-Open No. 2014-003279

[Patent Document 3] Japanese Patent Laid-Open No. 2010-123966

[Patent Document 4] Japanese Patent No. 5864424

As described above, in order to use the electron beam drawing device for highly accurate patterning, it is necessary to correct the drawing data in consideration of the proximity effect of the electron beam. In addition, in order to perform such a correction, a method of accurately estimating the exposure intensity distribution formed on the formed layer is required. A method for obtaining such an exposure intensity distribution by computer simulation is disclosed in the aforementioned Patent Document 4. In this method, the following simulation is performed: Assuming that the electrons irradiated to the resist layer are distributed according to the intensity distribution expressed by a Gaussian error function, a convolution operation is performed to obtain the exposure intensity distribution of the entire resist layer .

As described above, in recent years, a multi-beam electron beam drawing device has also gradually spread. However, the conventional method disclosed in the above-mentioned Patent Document 4 is basically a method suitable for an electron beam drawing device of a single beam method, and when this method is directly applied to a case of an electron beam drawing device of a multi-beam method, it cannot be accurately performed. Estimated exposure intensity distribution. Also, in the case of the multi-beam method, since the number of beams becomes huge, when the conventional method is directly applied, the calculation load becomes heavy, and simulation requires a large amount of calculation time.

Therefore, an object of the present invention is to provide a simulation method capable of obtaining an exposure intensity distribution of an electron beam irradiation surface with high accuracy in an electron beam drawing device of a multi-beam method, and to provide an exposure intensity distribution capable of implementing the method. Computing device. Furthermore, an object of the present invention is to provide a simulation method capable of performing such calculations for obtaining an exposure intensity distribution in a short time, and to provide an exposure intensity distribution calculation device capable of implementing the method.

(1) The first aspect of the present invention is a simulation method in which the exposure intensity distribution when a specific pattern is exposed and drawn on a formed layer by using a multi-beam electron beam drawing device is defined for the area defined by the electron beam irradiation area. Convolution integrals of a function indicating the intensity of the electron beam irradiation and a point spread function indicating the degree of influence of the reference point on the surroundings at a plurality of reference points, thereby calculating the total exposure intensity at each evaluation point, and using this as a point spread The function uses a function including an opening size parameter determined based on an opening size of a hole of an electron beam drawing device.

(2) The second aspect of the present invention is the simulation method of the first aspect described above, in which the xy plane of the two-dimensional xy orthogonal coordinate system is defined as the irradiation surface of the electron beam, and is located at the coordinates (x ', y') The effect of the reference point T (x ', y') on the evaluation point V (x, y) located at the coordinate (x, y), by expressing the electron beam with respect to the reference point T (x ', y') Convolution in the x-axis and y-axis directions of the function D (x ', y') of the irradiation intensity and the point spread function psf (X, Y) defined as X = x'-x, Y = y'-y This effect is calculated by integration, and as the point spread function psf (X, Y), a function including the opening size parameter B determined based on the opening size of the hole of the electron beam drawing device in addition to the variables X and Y is used.

(3) The third aspect of the present invention is the simulation method of the second aspect described above, in which, as the point spread function psf (X, Y), a function in which the width of the flat portion of the graph is affected by the opening size parameter B is used.

(4) The fourth aspect of the present invention is the simulation method of the third aspect described above, in which, as the point spread function psf (X, Y), in addition to the opening size parameter B, the slope portion including the influence curve is used Function of slope parameter σ.

(5) The fifth aspect of the present invention is the simulation method of the fourth aspect described above, wherein as the point spread function, the following function including the error function erf is used, that is, 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) The sixth aspect of the present invention is the simulation method of the fourth aspect described above, in which as the point spread function, the following function including the inverse trigonometric function arctan is used, that is, 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) The seventh aspect of the present invention is the simulation method of the fourth aspect described above, in which, as the point spread function, an error function erf, a specific constant C, a backscatter parameter β, and a proximity effect correction parameter η are used. The following function, that is, 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 )).

(8) The eighth aspect of the present invention is the simulation method of the first to seventh aspects described above, wherein when the opening portion of the hole of the electron beam drawing device is circular, the diameter of the circle is set as the hole When the opening is a square, the length of one side of the square is the opening size of the hole, and the value obtained by multiplying the opening size by the reduction magnification of the projection lens of the electron beam drawing device is used as the hole-based value. Opening size parameter.

(9) The ninth aspect of the present invention is the simulation method of the first to eighth aspects described above, which is performed: a drawing data input stage, which is a computer input of data representing a pattern drawn by an electron beam drawing device, and Drawing data composed of an array of pixels having pixel values representing the irradiation intensity of each irradiation position of the beam; in the parameter setting stage, the computer sets the opening size parameter determined based on the opening size of the hole of the electron beam drawing device; The calculation matrix production stage is for the computer to prepare two sets of empty calculation matrices composed of a collection of calculation units obtained by dividing each pixel of the drawing data into a plurality of parts. Each unit of the matrix is used to assign a specific unit value based on the pixel value of the pixel including the unit, and an irradiation intensity matrix representing a planar distribution of the irradiation intensity of the electron beam is created. Each unit of the matrix for the second operation is given and included. The element value corresponding to a specific point spread function of the opening size parameter, and a point spread moment representing a planar distribution of the degree of influence represented by the point spread function is produced ; And a convolution operation stage, based computers which use a matrix with the convolution integral irradiation intensity dot matrix of diffusion, and the total exposure intensity is obtained at the respective evaluation points.

(10) The tenth aspect of the present invention is the simulation method of the ninth aspect described above, wherein when the irradiation intensity matrix is created in the calculation matrix creation stage, only the A specific representative unit assigns a specific value determined based on the pixel value of the pixel as a unit value, and assigns a unit value of 0 to other non-representative units.

(11) The eleventh aspect of the present invention is the simulation method of the tenth aspect described above, wherein when the irradiation intensity matrix is created in the calculation matrix production stage, the plurality of calculation units included in the same pixel are located in One or more arithmetic units in the center of the pixel are set as representative units, and other arithmetic units are set as non-representative units.

(12) The twelfth aspect of the present invention is the simulation method of the eleventh aspect described above, wherein when the irradiation intensity matrix is created in the calculation matrix production stage, each pixel of the drawing data is divided vertically and horizontally into odd parts, One arithmetic unit located at the center of each pixel is set as a representative unit, the other arithmetic units are set as non-representative units, and the pixel value of the pixel including the representative unit is assigned to the representative unit as a unit value. A cell value of 0 is assigned to the representative cell.

(13) The thirteenth aspect of the present invention is the simulation method of the eleventh aspect described above, wherein when the irradiation intensity matrix is created in the calculation matrix production stage, each pixel of the drawing data is vertically and horizontally divided into even parts, Set the four arithmetic units located at the center of each pixel as the representative unit, the other arithmetic units as non-representative units, and assign a value of 1/4 of the pixel value of the pixel containing the representative unit to the representative unit. As a unit value, a unit value of 0 is assigned to a non-representative unit.

(14) The fourteenth aspect of the present invention is the simulation method of the tenth aspect described above, wherein when the irradiation intensity matrix is created in the calculation matrix production stage, the existence of the plurality of calculation units included in the same pixel exists. A calculation unit at a position shifted from a center of the pixel in a specific direction by a specific offset is set as a representative unit, and other calculation units are set as non-representative units, and at the stage of making a calculation matrix When making a point spread matrix, a point spread matrix representing a planar distribution of the degree of influence represented by the point spread function is prepared, and the point spread function is obtained by correcting the offset amount in the direction opposite to the specific direction.

(15) The fifteenth aspect of the present invention is the simulation method of the ninth to fourteenth aspects described above, which is performed in the convolution operation stage: the first operation stage is made by performing a Fourier transform on the irradiation intensity matrix Irradiation intensity frequency matrix; in the second operation phase, it is to make a point diffusion frequency matrix by Fourier transforming the point diffusion matrix; in the third operation phase, it is to make an operation that corresponds to the irradiation intensity frequency matrix and the point diffusion frequency matrix. Use the product of the cells as the exposure intensity frequency matrix of the unit values; and the fourth operation stage, which performs an inverse Fourier transform on the exposure intensity frequency matrix to create an exposure that represents the planar distribution of the total exposure intensity at each evaluation point Intensity matrix.

(16) The sixteenth aspect of the present invention is to incorporate a program into a computer and cause the computer to execute the drawing data input stage, parameter setting stage, calculation matrix creation stage in the simulation methods of the ninth to fifteenth aspects, and Convolution operation stage.

(17) The seventeenth aspect of the present invention is an exposure intensity distribution calculation device that calculates an exposure intensity distribution when a specific pattern is exposed and drawn on a formed layer using a multi-beam electron beam drawing device, and is provided with: The data input unit inputs data representing a pattern drawn by the electron beam drawing device and drawing data composed of an array of pixels having pixel values indicating the irradiation intensity of each irradiation position of the beam; a parameter setting unit, which sets The opening size parameter determined based on the opening size of the hole of the electron beam drawing device; the irradiation intensity matrix preparation section is prepared by an assembly of arithmetic units obtained by dividing each pixel of the drawing data into a plurality of parts An empty calculation matrix, and a specific unit value based on the pixel value of a pixel including the unit is assigned to each calculation unit, thereby creating an irradiation intensity matrix representing a planar distribution of the irradiation intensity of the electron beam; a point diffusion matrix creation unit , By assigning a specific point including an opening size parameter to each operation unit of the above-mentioned empty operation matrix And a convolution operation execution unit that performs convolution integration using an irradiation intensity matrix and a point spread matrix to obtain a point spread matrix representing a planar distribution of the degree of influence indicated by the point spread function; The total exposure intensity at each evaluation point is shown.

(18) The eighteenth aspect of the present invention is the exposure intensity distribution calculation device according to the above-mentioned seventeenth aspect, wherein the point spread matrix creation unit uses a function of the width of the flat portion of the graph affected by the opening size parameter B as the point spread function.

(19) The nineteenth aspect of the present invention is the exposure intensity distribution computing device as described in the eighteenth aspect above, in which the point diffusion matrix production unit uses, in addition to the opening size parameter B, the inclination of the inclined portion that affects the graph A function of the parameter σ as a point spread function.

(20) The twentieth aspect of the present invention is the exposure intensity distribution calculation device as described above in the seventeenth to nineteenth aspects, wherein the irradiation intensity matrix creation unit only applies to a specific representative of a plurality of arithmetic units included in the same pixel. A unit assigns a specific value determined based on the pixel value of the pixel as a unit value, and assigns a unit value of 0 to other non-representative units.

(21) The twenty-first aspect of the present invention is the exposure intensity distribution computing device as described in the twentieth aspect above, in which the irradiation intensity matrix creation unit includes one of the plurality of arithmetic units for the same pixel located at the center of the pixel. One or more arithmetic units are referred to as representative units, and other arithmetic units are referred to as non-representative units.

(22) The twenty-second aspect of the present invention is the exposure intensity distribution calculation device as described in the twenty-first aspect, wherein the irradiation intensity matrix creation section divides each pixel of the drawing data into an odd number of sections vertically and horizontally, and is located at the center of each pixel One of the arithmetic units is a representative unit, the other arithmetic units are non-representative units, the pixel value of the pixel including the representative unit is assigned to the representative unit, and the non-representative unit is assigned a unit value of 0. .

(23) The twenty-third aspect of the present invention is the exposure intensity distribution calculation device as described in the twenty-first aspect, wherein the irradiation intensity matrix creation section divides each pixel of the drawing data vertically and horizontally into an even number of parts, and is located at the center of each pixel The four arithmetic units are set as representative units, and the other arithmetic units are set as non-representative units. The representative unit is assigned a value of 1/4 of the pixel value of the pixel including the representative unit as the unit value. A cell value of 0 is assigned to the representative cell.

(24) The twenty-fourth aspect of the present invention is the exposure intensity distribution calculation device according to the twentieth aspect described above, wherein the irradiation intensity matrix creation unit includes a plurality of arithmetic units included in the same pixel at the center of the pixel. The arithmetic unit at a position shifted by a specific offset in a specific direction is set as a representative unit, the other arithmetic units are set as non-representative units, and the point spread matrix creation unit creates a point spread matrix, and the point spread The matrix represents the planar distribution of the degree of influence represented by the point spread function corrected by the offset in the direction opposite to the specific direction.

(25) The twenty-fifth aspect of the present invention is the exposure intensity distribution calculation device as described above in the seventeenth to twenty-fourth aspects, wherein the convolution operation unit includes a first operation unit that performs a Fourier transform on the irradiation intensity matrix, and Production of an irradiation intensity frequency matrix; a second operation unit that generates a point diffusion frequency matrix by performing a Fourier transform on the point diffusion matrix; and a third operation unit that generates an operation that corresponds to the irradiation intensity frequency matrix and the point diffusion frequency matrix The product of the units is the exposure intensity frequency matrix of the unit values; and a fourth arithmetic unit that performs an inverse Fourier transform on the exposure intensity frequency matrix to create an exposure intensity matrix representing a planar distribution of the total exposure intensity at each evaluation point .

(26) The twenty-sixth aspect of the present invention is a person who constructs an exposure intensity distribution calculation device as described above in the seventeenth to twenty-fifth aspects by incorporating a program into a computer.

According to the exposure intensity distribution simulation method and the exposure intensity distribution calculation device of the present invention, by performing a convolution integral of the irradiation intensity distribution function of the electron beam generated based on the drawing data and the point spread function indicating the degree of influence on the surrounding, The exposure intensity distribution generated in the formed layer is obtained. In addition, since a function including an opening size parameter determined based on the opening size of the hole of the electron beam drawing device is used as the point spread function, an optimal simulation of the multi-beam electron beam drawing device can be performed, thereby enabling high accuracy Find the exposure intensity distribution.

In addition, if a calculation is performed using a matrix having unit values other than the representative unit as 0 as the irradiation intensity matrix representing the irradiation intensity distribution of the electron beam, the computational burden of the convolution integral can be greatly reduced, so that it can be performed in a short time. The calculation of the exposure intensity distribution is carried out within.

10‧‧‧ Electron Gun

20‧‧‧ enlarged electron beam

21‧‧‧Each electron beam forming multiple beams

30‧‧‧ condenser lens

40‧‧‧ Orifice

41‧‧‧ opening

50‧‧‧ projection lens

60‧‧‧Sample substrate

61‧‧‧formed layer (resist layer)

70‧‧‧ mobile platform

110‧‧‧Drawing data input department

120‧‧‧ Irradiation Intensity Matrix Production Department

130‧‧‧Parameter Setting Department

140‧‧‧point diffusion matrix production department

150‧‧‧Convolution operation execution unit

151‧‧‧The first operation unit

152‧‧‧Second arithmetic unit

153‧‧‧The third operation unit

154‧‧‧Fourth arithmetic unit

A1, A2 ‧‧‧ rectangular area

a‧‧‧exposure area

B‧‧‧ opening size parameter

b‧‧‧ non-exposed area

C‧‧‧ constant for point spread function

C (m, n) ‧‧‧th m-th row and n-th row arithmetic unit

Da‧‧‧ the width of the pattern in the x-axis direction

Di‧‧‧ Irradiation intensity (dose) of the electron beam during the i-th exposure operation

Din‧‧‧Description

Dout‧‧‧Exposure intensity distribution data

D (x ', y') ‧‧‧Dose / Irradiance Matrix at Reference Point T (x ', y')

D '(f, g) ‧‧‧Irradiance Frequency Matrix

D "(f, y) ‧‧‧Intermediate matrix of irradiation intensity

d‧‧‧pixel spacing

E, E1, E2‧‧‧ electron beam intensity (energy density)

E (5), E (10), E (15) ‧‧‧ Intensity (energy density) of the electron beam

Eth‧‧‧threshold of total exposure intensity

F‧‧‧ Distribution curve of total exposure intensity

f‧‧‧frequency axis

Graph of f (m, n) ‧‧‧point spread function psf

g‧‧‧Distance / frequency axis

H‧‧‧ flat part of the graph

K‧‧‧ Hole opening size

M, M1 ~ M9‧‧‧ exposure intensity distribution curve (Hill)

M (5), M (10), M (15) ‧‧‧ exposure intensity distribution curve (Hill)

Distribution curve of MM‧‧‧total exposure intensity (Dashan)

N‧‧‧Number of exposure operations

P, P1 ~ P5 ‧‧‧ each pixel constituting a two-dimensional pixel arrangement of drawing data

P (i, j) ‧‧‧th pixel in row i and row j

psf‧‧‧Point Spread Function

psf (X, Y) ‧‧‧point spread matrix

psf '(f, g) ‧‧‧point spread frequency matrix

Q, Q1 ~ Q9‧‧‧‧Each irradiation reference point defined on the exposure target surface

Q (0), Q (5), Q (10), Q (15) ‧‧‧ the respective irradiation reference points defined on the exposure target surface

R‧‧‧ Distance between reference point T and evaluation point V

S1 ~ S5‧‧‧‧ Irradiation point of electron beam

Steps in S10 ~ S44‧‧‧‧flow chart

T (x ', y') ‧‧‧reference point at coordinates (x ', y')

U1, U2‧‧‧ sloped part of the graph

V1, V2, V11, V12, V21‧‧‧ evaluation points

V (x, y) ‧‧‧ is the evaluation point at coordinates (x, y)

v (x, y) ‧‧‧‧Evaluation point V (x, y) The amount of accumulated energy (total exposure intensity) / exposure intensity matrix

v '(f, g) ‧‧‧ exposure intensity frequency matrix

w‧‧‧ the width of the flat part H of the graph

X‧‧‧ Horizontal distance between reference point T and evaluation point V

x, x'‧‧‧ the horizontal coordinate axis / horizontal coordinate value defined on the exposure object surface

Y‧‧‧Vertical distance between reference point T and evaluation point V

y, y'‧‧‧ the vertical coordinate axis / vertical coordinate value defined on the exposure object surface

β‧‧‧Backscattering parameters

△ x, △ y‧‧‧‧offset

η‧‧‧ Proximity effect correction parameter

‧‧‧ Beam point diameter

σ‧‧‧ forward scattering parameter

FIG. 1 is a front view (a part is a cross-sectional view) showing a basic structure of a general electron beam drawing device and a drawing principle thereof.

FIG. 2 is a graph showing a distribution of energy density (intensity) of a general electron beam.

FIG. 3 is a plan view (upper section (a)) and a graph (lower section (b)) showing the relationship between the two-dimensional pixel arrangement constituting the drawing data and the intensity distribution of the electron beam irradiated based on the drawing data.

FIG. 4 is a graph showing a principle of controlling stepwise exposure intensity by performing beam irradiation at a number of times corresponding to a pixel value.

FIG. 5 shows the dot diameters of each electron beam according to the pixel pitch d. An example of a state where repeated exposure occurs is a plan view (upper section (a)) and a graph showing the intensity distribution of each electron beam (lower section (b)).

6 is a plan view of a pattern having a width Da in the x-axis direction (upper stage (a)) and a graph showing the principle of exposing the pattern in the form of multiple beams (lower stage (b)).

FIG. 7 is a plan view of a linear pattern having a width Da = 25 nm in the x-axis direction (upper stage (a)) and a diagram showing a pixel arrangement constituting drawing data for exposing the linear pattern (lower stage (b)) .

FIG. 8 is a plan view of a linear pattern having a width Da = 27 nm in the x-axis direction (upper stage (a)) and a diagram showing a pixel arrangement constituting drawing data for exposing the linear pattern (lower stage (b)) .

FIG. 9 is a diagram comparing the order of drawing the same pattern in a single beam (FIG. (A)) and the order of drawing in a multi-beam method (FIG. (B)).

FIG. 10 is a plan view showing a calculation principle of a total exposure intensity at an arbitrary evaluation point V (x, y) when drawing in a single beam method.

FIG. 11 is a diagram showing an example of an arithmetic expression used in the arithmetic principle shown in FIG. 10.

FIG. 12 is a plan view showing a calculation principle of a total exposure intensity at an arbitrary evaluation point V (x, y) when drawing in a multi-beam manner.

FIG. 13 is a diagram showing an example of an arithmetic expression used in the arithmetic principle shown in FIG. 12.

FIG. 14 is a diagram showing an example of an arithmetic expression used in the calculation of the exposure intensity distribution by the simulation method of the present invention when rendering in a multi-beam method.

FIG. 15 is a one-dimensional graph showing an example of the point spread function psf (X, Y) shown in Equation (3) in FIG. 14.

FIG. 16 is a diagram showing an expression of another point spread function psf (X, Y) suitable for the expression (3) of FIG. 14.

FIG. 17 is a diagram showing another expression of the one-point diffusion function psf (X, Y) suitable for the expression (3) of FIG. 14.

FIG. 18 is a flowchart showing a basic sequence of the simulation method of the present invention.

FIG. 19 is a diagram showing a specific production example of the irradiation intensity matrix D (x ′, y ′) in step S30 in FIG. 18.

FIG. 20 is a diagram showing a correspondence relationship between the irradiation intensity matrix D (x ′, y ′) and the point diffusion matrix psf (X, Y) prepared in step S30 in FIG. 18.

FIG. 21 is a diagram showing a concept of a process of performing a convolution operation in step S40 of FIG. 18 based on the drawing data shown in FIG. 19 (a).

FIG. 22 is a diagram showing a modification example of the irradiation intensity matrix D (x ′, y ′) and the point diffusion matrix psf (X, Y) prepared in step S30 of FIG. 18.

FIG. 23 is a diagram showing a concept of a process of performing a convolution operation in step S40 of FIG. 18 on the example shown in FIG. 22.

FIG. 24 is a diagram showing another modified example of the irradiation intensity matrix D (x ′, y ′) prepared in step S30 in FIG. 18.

FIG. 25 is a diagram showing still another modified example of the irradiation intensity matrix D (x ′, y ′) prepared in step S30 in FIG. 18.

FIG. 26 is a diagram showing a principle of performing a convolution operation in step S40 of FIG. 18 using a Fourier transform.

Fig. 27 is a diagram showing a principle of reducing a calculation load by specifying a representative unit and performing a convolution operation using a Fourier transform.

FIG. 28 is a block diagram showing a basic configuration of the exposure intensity distribution calculation device of the present invention.

FIG. 29 is a diagram showing a first example of the exposure intensity distribution obtained by the simulation method of the present invention.

FIG. 30 is a diagram showing a second example of the exposure intensity distribution obtained by the simulation method of the present invention.

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

<<< §1. Drawing principle of multi-beam electron beam drawing device >>>

The present invention is based on the premise of a technique for obtaining an exposure intensity distribution in a multi-beam electron beam drawing device. Therefore, first, for convenience of explanation, the drawing principle of a general multi-beam drawing device is briefly described in advance. FIG. 1 is a front view (a part is a cross-sectional view) showing a basic structure and a drawing principle of a multi-beam electron beam drawing device.

As shown in the figure, the electron beam 20 irradiated from the electron gun 10 is enlarged by a condenser lens 30 that performs an electromagnetic action, and is irradiated to the orifice plate 40 (shown as a sectional view in the figure). A plurality of openings 41 are formed in the orifice plate 40, and only the electron beam 21 passing through the openings 41 is reduced and projected onto the sample substrate 60 below by the projection lens 50 that similarly performs electromagnetic action, and is irradiated onto the sample formed on the sample. The exposure target surface of the formed layer (usually a resist layer) 61 on the upper surface of the substrate 60. The sample substrate 60 is placed on the moving platform 70 and can be moved in the left-right direction of the drawing and the depth direction of the drawing.

Recently, a device having a function has also been put into practical use. This function uses an orifice plate 40 having openings 41 arranged in a two-dimensional matrix shape of 512 × 512, and uses 250,000 or more electron beams 21 to form a layer. The upper surface of 61 is simultaneously exposed to draw a fine pattern. Generally, a shield plate (not shown) is disposed on the lower surface of the orifice plate 40, and a function of individually controlling ON / OFF of each electron beam 21 having passed through the opening portion 41 is provided.

Each of the openings 41 formed in the orifice plate 40 generally has a circular cross section, and each of the electron beams 21 having passed through the openings 41 has a circular cross section. Depending on the situation, an opening with a rectangular cross section may be used. However, the opening 41 has a circular cross section and a circle is formed on the upper surface (exposure target surface) of the formed layer 61 by irradiation with one electron beam 21. The shape of the irradiation point will be described. For example, if the opening portion 41 is a circle with a diameter of 4 μm and the reduction ratio of the projection lens 50 is 1/200, a circular irradiation spot with a diameter of about 20 nm is formed on the surface of the exposure target (strictly speaking, it is slightly larger). point).

It is considered that the energy density of a general electron beam has a distribution corresponding to a Gaussian error function with its central axis as a peak. As described below, in the present invention, a special function is used instead of the Gaussian error function as a function of the energy density of one electron beam 21 passing through the opening 41. Here, it is assumed that the energy density of the electron beam 21 is The distribution corresponding to the Gaussian error function will be described below.

Under this premise, the energy density E (irradiation intensity of the electron beam) of a circular irradiation spot formed on the exposed surface of the formed layer 61 by one electron beam 21 becomes as shown in the graph M of FIG. 2 Shows the distribution corresponding to the Gaussian error function. The horizontal axis of the graph represents a one-dimensional position in units of nm, and the position of the value 0 on the horizontal axis corresponds to the position irradiated by the central axis of one electron beam 21. Actually, a circular irradiation spot having a two-dimensional diffusion is formed on the surface of the exposure target, and the graph showing the energy density E becomes a rotating body obtained by rotating the graph M shown in FIG. 2 around its central axis.

Dimensions on the horizontal axis in the graph of Figure 2 This corresponds to the diameter of a circular irradiation spot formed on the surface of the exposure target in this manner. Therefore, when irradiating an electron beam having an energy density E as shown in FIG. Within a circular exposure, the irradiation intensity of each part decreases from the center toward the periphery with a distribution corresponding to the Gaussian error function. Generally, the size of the beam is expressed in the form of a beam diameter representing the value of the half-value width of the graph in FIG. 2. However, for convenience of explanation, the size shown in FIG. 2 This is called the spot diameter, and it is set as a value corresponding to the beam diameter for processing.

In the case of the single-beam method (VSB method: Variable Shape Beam) electron beam drawing device, only one electron beam is irradiated on the sample substrate 60. Therefore, the cross-sectional shape can be processed into an arbitrary shape such as a rectangle and adjusted. Irradiate at any intensity. However, in the case of a multi-beam electron beam drawing device, there is an advantage that multiple electron beams 21 can be used for extremely high-speed drawing, but it is difficult to individually control the cross-sectional shape of each beam or each beam individually. The intensity. In the case of a device that actually generates up to 250,000 beams, it is not possible to provide a mechanism for individually shaping each electron beam passing through the opening portion 41 of the fine orifice plate or individually adjusting the intensity.

As a result, although the conventional multi-beam electron beam drawing device can be formed on the surface of the exposure target with a diameter There are a plurality of circular irradiation spots, but the irradiation spots cannot be formed into an arbitrary shape, and it is necessary to adopt a method of drawing by on / off control of each electron beam. Therefore, in order to perform drawing control of the multi-beam electron beam drawing device, drawing data (also referred to as a quantization mapping table) composed of a two-dimensional pixel array is used.

Fig. 3 (a) is a plan view (upper section (a)) and a graph (lower section (b)) showing the relationship between the two-dimensional pixel arrangement constituting the drawing data and the intensity distribution of the electron beam irradiated based on the drawing data. At this time, an xy two-dimensional coordinate system is defined on the exposure target surface, and a two-dimensional arrangement of vertical and horizontal square pixels P represented by applying a hatching to the upper right corner of FIG. 3 (a) is defined on the coordinate system. Pixel arrangement. Here, it is assumed that the width in the horizontal direction (x-axis direction) and the vertical direction (y-axis direction) of each pixel P is d. The width d corresponds to the horizontal and vertical distance between 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 an electron beam to be irradiated to the irradiation reference point Q is given as the pixel value of the pixel P. If the drawing data constituted by such a pixel arrangement is given to an electron beam drawing device of a multi-beam method, the drawing device can perform electron beam exposure with a specific intensity distribution on the exposure target surface based on the drawing data. For example, by irradiating an electron beam irradiated to an irradiation reference point Q1 defined as the center of the pixel P1 shown in FIG. 3, an exposure based on a circular irradiation spot S1 is performed on the exposure target surface (xy plane). The electron beam irradiated to the reference point Q2 defined as the center of the pixel P2 is exposed on the exposure target surface (xy plane) based on the circular irradiation point S2.

In this case, the exposure intensity of the irradiation point S1 is determined based on the pixel value E1 of the pixel P1, and the exposure intensity of the irradiation point S2 is determined based on the pixel value E2 of the pixel P2. For example, if it is assumed that each pixel value E1, E2 represents the peak of the distribution corresponding to the Gaussian error function, the exposure intensity distribution of the irradiation points S1 and S2 in the x-axis direction shown in FIG. 3 (a) becomes as shown in FIG. 3 ( b) The graph shown. That is, the exposure intensity distribution of the electron beam irradiated with the irradiation reference point Q1 as a center becomes as wide as the graph M1 Mountain, the exposure intensity distribution of the electron beam irradiated with the irradiation reference point Q2 as the center has a width as shown in the graph M2 Mountain. Here, as described above It is the diameter of the circular irradiation spot.

In addition, in FIG. 3, for convenience of explanation, a state in which irradiation points S1 and S2 are formed for the irradiation reference points Q1 and Q2 of the two pixels P1 and P2 is shown. The positions define the irradiation reference points Q, and the irradiation reference points Q are irradiated with electron beams. Here, the arrangement pitch of the vertical and horizontal directions of the irradiation reference point Q and the arrangement pitch of the vertical and horizontal directions of the pixels P are similarly referred to as a pitch d.

In addition, in the multi-beam electron beam drawing device, the intensity of a plurality of electron beams cannot be individually controlled. Therefore, in the example shown in FIG. 3, both 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 of the same intensity. However, each electron beam can be turned on / off individually by controlling the shielding plate. Therefore, a method is adopted in which, for each of the respective irradiation reference points Q, the on / off control of the separately irradiated electron beams is performed individually, and the exposure intensity is changed by changing the exposure time. In the case of the above example, by setting the irradiation time to the irradiation reference point Q1 to be longer than the irradiation time to the irradiation reference point Q2, an exposure intensity distribution as shown in the graph of FIG. 3 (b) is obtained.

Such exposure time control is actually performed in the form of control of the number of exposures. The reason is that, as shown in FIG. 1, while moving the moving platform 70 two-dimensionally (in the left-right direction and the depth direction of FIG. 1), a plurality of electron beams 21 are two-dimensionally formed on the formed layer 61. Scan and trace.

For example, an exposure time of a few nanoseconds is specified in advance as a unit exposure time during one electron beam irradiation, and each time the one electron beam irradiation is completed, the moving stage 70 is moved by a distance d in the x-axis direction to perform the down One electron beam irradiation, if so, for a specific irradiation reference point Q, exposure is performed per unit exposure time amount by a different electron beam (adjacent electron beam) each time. At this time, if the individual on / off control is performed for each of the respective electron beams each time, although it is staged, a specific exposure intensity can be set for each of the respective irradiation reference points Q.

Specifically, for example, if the exposure intensity distribution like the graph M1 of FIG. 3 (b) is obtained by performing 10 exposures on the irradiation reference point Q1, it is obtained by performing 5 exposures on the irradiation reference point Q2. The exposure intensity distribution as shown in the graph M2 of FIG. 3 (b).

FIG. 4 is a graph showing the principle of performing 16 types of stepwise exposure intensity control by changing the number of exposures for each of the respective irradiation reference points Q. Here, for the convenience of illustration, only examples of the four types of phases 0, 5, 10, and 15 are shown, but in fact, intermediate phases between them are also set, and a total of 16 types of phases 0 to 15 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. A graph of the distribution of the diffusion corresponding to the Gaussian error function.

For example, when 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, define The exposure reference points Q (15), Q (10), Q (5), and Q (0) for the center positions of these pixels are performed near the exposure intensity distribution graph M (15) corresponding to that shown in FIG. 4 , M (10), M (5), M (0). The peak value of each exposure intensity distribution graph becomes a value corresponding to the number of exposures (= pixel value p) at each irradiation reference point position.

That is, for the irradiation reference point Q (0) corresponding to the pixel value p = 0, the electron beam is not irradiated, and the graph M (0) does not actually become a mountain-like graph with substantial content. On the other hand, the irradiation reference point Q (5) corresponding to the pixel value p = 5 is subjected to 5 electron beam irradiations, and the graph M (5) becomes a mountain having a peak intensity E (5). Similarly, for the irradiation reference point Q (10) corresponding to the pixel value p = 10, 10 times of electron beam irradiation is performed, and the graph M (10) becomes a mountain having a peak intensity E (10). For the pixel value p = The irradiation reference point Q (15) corresponding to 15 is subjected to 15 electron beam irradiations, and the graph M (15) becomes a mountain having a peak intensity E (15).

In addition, in FIG. 3, an example in which two pixels P1 and P2 located at positions sufficiently separated from each other are irradiated with different electron beams is described. As in this example The above two electron beams irradiating the reference points Q1 and Q2 will not interfere with each other. However, regarding irradiation The electron beams whose distances are close to a plurality of irradiation reference points will interfere with each other. Generally, the pixel pitch d (the distance between the irradiation reference points Q) is set to be smaller than the spot diameter of the electron beam. Small value. In this case, the exposure target surface is subjected to overlapping exposure by a plurality of electron beams.

Fig. 5 (a) shows the point diameter of each electron beam according to the pixel pitch d Fig. 5 (b) is a graph showing an exposure intensity distribution of each electron beam when such an overexposure occurs when such an overexposure occurs. The example shown here is based on the pixel pitch d (the distance between the irradiation reference points Q) and the spot diameter of the electron beam. Set between = 4d relationship example. In FIG. 5 (a), five pixels P1 to P5 arranged adjacent to each other in the x-axis direction and an electron beam irradiated from five irradiation reference points Q1 to Q5 defined as the center positions of these pixels are shown. The five circular irradiation spots S1 to S5 are formed. As shown in the figure, each of the circular irradiation spots S1 to S5 overlaps with each other, and each part of the exposure target surface receives overlapping exposure through a plurality of irradiation spots.

The exposure intensity distribution graphs M1 to M5 shown in FIG. 5 (b) show the exposure intensity distributions in the x-axis direction with respect to the irradiation points S1 to S5, respectively. Because the irradiation spots S1 to S5 overlap locally, the exposure intensity distribution graphs M1 to M5 also partially overlap. The actual exposure intensity distribution of each part is in the form of the sum of these exposure intensity distribution curves M1 to M5. Given. For example, the irradiation reference point Q3 in the pixel P3 indicated by a thick solid line in the figure is irradiated to generate an electron beam having a circular irradiation point S3. The exposure intensity distribution of the circular irradiation spot S3 becomes a mountain as shown in the graph M3, but as shown in the figure, the adjacent foothills of the other graphs M1, M2, M4, and M5 are also located in the pixel P3. The total exposure intensity in the final pixel P3 refers to the intensity obtained by making all the mountains overlap.

The multi-beam electron beam drawing device can draw a gray pattern with a gray scale on the formed layer based on this principle, and can develop a pattern having a desired shape by developing the exposed formed layer.

Fig. 6 (a) is a top view of a pattern having a width Da in the x-axis direction, and Fig. 6 (b) is a graph showing the principle of exposing the pattern in the form of multiple beams. The x-axis system of the horizontal axis in Fig. 6 (b) corresponds to the x-axis of the horizontal axis in Fig. 6 (a), and the graph in Fig. 6 (b) shows the time when the pattern shown in Fig. 6 (a) is drawn Exposure intensity distribution in the x-axis direction.

Fig. 6 (b) shows nine exposure intensity distribution curves M1 to M9 (hereinafter, referred to as hills) composed of smaller mountains and one exposure intensity distribution curve composed of larger mountains. Graph MM (hereinafter, referred to as Dashan). The hills M1 to M9 represent the exposure intensity distributions based on the individual electron beams irradiated to the irradiation reference points Q1 to Q9, respectively, and overlap with the foothills as in the example shown in FIG. 5 (b). The irradiation reference points Q1 to Q9 are defined as the points of the center points of pixels P1 to P9 (not shown), and are arranged at a specific pitch d. The height (peak intensity) of each hill M1 to M9 is a value corresponding to the pixel value of each pixel P1 to P9.

In the case of the example shown in FIG. 4, the pixel value p is represented by 16 stages of 0-15, that is, 4-bit data. By setting p = 0-15, 16 types of heights that are different from each other can be defined. Hill M (p). Further, in order to form an intensity distribution corresponding to the hill M (p), a total of p exposures are performed. The hills M1 to M9 shown in FIG. 6 (b) are any of the hills in the 16th stage. For example, when the pixel values of the pixels P1 and P9 at both ends are p = 7 and the pixel values of the pixels P2 to P8 in the middle are p = 15, as shown in the figure, the hills M1 and M9 at both ends become medium. The height of the mountain, the middle hills M2 ~ M8 become the mountain with the highest height.

On the other hand, the mountain MM shown in FIG. 6 (b) is a graph showing the distribution of the total exposure intensity obtained when all the hills M1 to M9 are overlapped, and it is a graph equivalent to the sum of the hills M1 to M9 (For the convenience of illustration, the exact sum is not shown). Finally, if exposures are performed on the irradiation reference points Q1 to Q9 for a number of times corresponding to the pixel values of the pixels P1 to P9, the total exposure intensity distribution shown by Dashan MM is obtained in the x-axis direction on the exposure target surface.

When the electron beam irradiation process for performing such exposure on the formed layer 61 is completed, a developing process is then performed on the formed layer 61. The formed layer 61 is composed of a resist layer whose composition is changed by irradiation with an electron beam. In the case of a general resist, it is non-linear. This non-linearity means that if the energy density of the irradiation exceeds a certain threshold Value, the composition hastily changed. Therefore, even in the case where a smooth total exposure intensity distribution is obtained like the mountain MM shown in the figure, if the area where the total exposure intensity in the formed layer 61 is equal to or more than a specific threshold Eth is set as the exposure area a, the total exposure is The area where the intensity does not reach a specific threshold Eth is set as the non-exposed area b, and the composition of the exposed area a changes greatly compared with the composition of the non-exposed area b. Therefore, if the development process is performed on the formed layer 61, pattern formation based on the difference between the exposed area a and the non-exposed area b can be performed.

Specifically, in the case of using a positive-type resist material as the resist layer, only the exposed area a of the forming layer 61 is dissolved in the developing solution by the development process, and the remaining non-exposed area b The formed layer is pattern-formed. When a negative resist material is used as the resist layer, only the non-exposed area b of the formed layer 61 is dissolved in the developing solution by the development process, and the remaining exposed area is used. The formed layer in a is patterned. FIG. 6 shows an example of forming an exposure area a having a width corresponding to the width Da when the mountain MM is divided at a level corresponding to the threshold Eth.

Of course, the calibration of the vertical axis of the graph or the value of the threshold Eth is developed according to the exposure conditions such as the intensity (energy density) of the irradiated electron beam or one exposure time, and the type of resist material or developer used. The conditions change. If these conditions are fixed in advance, the threshold value Eth on the vertical axis of the graph also becomes a fixed value. Therefore, the obtained pattern width Da can be controlled according to the shape of Dashan MM. As described above, the Dashan MM is obtained as the sum of the hills M1 to M9. Therefore, in the end, the pattern width Da can be controlled according to the drawing data defining the pixel values of the respective pixels P1 to P9.

Furthermore, in the above description, for the sake of convenience, the principle of patterning in the x-axis direction of the formed layer is described, but the actual patterning process is the forming of the expanded layer on the xy plane. The layers are patterned, and the same patterning is performed in the y-axis direction. That is, Dashan MM shown in FIG. 6 (b) indicates the exposure intensity distribution in the x-axis direction. However, since the drawing data is given in the form of a two-dimensional pixel arrangement, the same exposure intensity is also obtained in the y-axis direction. distributed. The width in the up-down direction of the pattern shown in FIG. 6 (a) is determined based on the exposure intensity distribution in the y-axis direction.

In the above, the drawing principle of a general multi-beam electron beam drawing device used in the past has been described, but of course, the above description is an example of using a multi-beam electron beam drawing device, and the multi-beam electrons used in implementing the present invention The beam drawing device 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. 7 (a) is a plan view of a linear pattern having a width Da = 25 nm in the x-axis direction, and FIG. 7 (b) is a diagram illustrating a pixel arrangement constituting drawing data for exposing the linear pattern. In the manufacturing process of a semiconductor device, it is necessary to form a plurality of line-shaped patterns having a small line width such as a wiring layer. The linear pattern (hatched portion) shown in FIG. 7 (a) is a slender pattern with a small line width used in this process. Furthermore, the actual linear pattern is that the line length (the length in the y-axis direction of the figure) becomes extremely large compared to the line width (the width in the x-axis direction of the figure) and should be understood as "1" as the literal meaning indicates. "Line" pattern, but in this case, for the sake of illustration, a linear pattern with a greatly reduced line length (a pattern that is understood as a "rectangular" like the hatched part in Figure 7 (a)) is taken as an example. Instructions.

The drawing data shown in FIG. 7 (b) is data given to a multi-beam drawing device in order to form a linear pattern as shown in FIG. 7 (a) on the formed layer, and specific pixels are defined for each pixel. A two-dimensional pixel array obtained by the value p. As explained above in § 1, each pixel P constituting the two-dimensional pixel array has a pixel value p indicating the intensity of an electron beam that should be irradiated to a plurality of irradiation reference points Q, which are The vertical and horizontal sides of the exposure target surface on the forming layer are arranged at a specific pitch d, respectively. Hereinafter, an example in which the vertical and horizontal pixel pitch d of the two-dimensional pixel array is set to d = 5 nm will be described. Therefore, the distance d between the longitudinal and lateral directions of the irradiation reference point Q is also set to d = 5 nm.

The drawing data shown in Fig. 7 (b) is a person who defines such a two-dimensional pixel arrangement on the exposure target surface (xy plane) and assigns a specific pixel value to each pixel. In the case of this example, as each pixel value p, a number ranging from p = 0 to 15 is given. Therefore, the drawing data can be referred to as gray-scale image data having a gray scale value of 4 bits. A pixel functions to designate one of the 16 types of exposure intensity distributions as shown in FIG. 4 by its pixel value p.

Furthermore, in the case of drawing data shown in FIG. 7 (b), the pixel value p of each pixel is taken as any of p = 0 (minimum value) or p = 15 (maximum value), and the intermediate pixel value is taken. The pixels of p = 1 ~ 14 do not exist. This is because the outline of the linear pattern shown in FIG. 7 (a) is consistent with the outline of the pixel, so that a linear pattern can be formed without using intermediate pixel values. That is, in the case of the example shown in the figure, a pixel value p = 15 (maximum value) is assigned to pixels completely included in the linear pattern, and a pixel value p = 0 (minimum value) is assigned to pixels completely including no linear pattern. ) To form descriptive data.

If such drawing data is given to the electron beam drawing device, the irradiation reference point position corresponding to the pixel having the pixel value p = 0 will not be irradiated with the electron beam at all, and the pixel corresponding to the pixel having the pixel value p = 15. The position of the reference point was irradiated with 15 electron beams. As a result, the mountain M (15) shown in FIG. 4 is merged to form a mountain MM, and an exposure area as shown in FIG. 7 (a) is formed on the exposure target surface based on a specific threshold Eth. a (the area where the total exposure intensity becomes equal to or greater than the threshold Eth) and b (the area where the total exposure intensity does not reach the threshold Eth).

If the design of the outline of the linear pattern is consistent with the outline of the pixel as shown in the example shown in FIG. 7 (a), when the linear pattern is arranged on the two-dimensional pixel array, only the line pattern is completely defined. There are two types of pixels: an inner pixel (hereinafter referred to as a complete pixel) and a pixel that does not include a linear pattern at all (hereinafter referred to as an empty pixel). Therefore, if a full pixel is assigned a pixel value of p = 15 (maximum value: indicates the pixel value that irradiates the electron beam at the maximum number of times), a blank pixel is assigned a pixel value p = 0 (minimum: indicates a pixel value that does not irradiate the electron beam at all). ), As shown in Figure 7 (b).

In the case of a patterning process using a general multi-beam electron beam drawing device, generally, when drawing data is provided that shows a line-like pattern in which the contour lines are consistent with the contours of the pixels, it is set to have a non-existent size. Use of standard patterning conditions like accurate pattern of errors. Therefore, in general, when a linear pattern is formed in which the line width Da becomes an integer multiple of the pitch d in the line width direction of the pixel, a position where the contour line of the linear pattern is consistent with the contour of the pixel is performed. The alignment design allows accurate pattern formation without dimensional errors according to standard patterning conditions.

In the case of the example shown in FIG. 7, the pixel pitch d = 5 nm and the line width Da of the linear pattern is 25 nm. Therefore, the line width Da becomes exactly 5 times the pixel pitch d. Therefore, when designing a linear pattern, a design in which the contour lines on the left and right sides are consistent with the contour of the pixel can be performed. If such a design is performed and a pattern forming process (exposure process and development process) is performed under the above-mentioned standard patterning conditions, a physical pattern having a size conforming to the design can be obtained. That is, depending on the formed layer remaining as the exposed area a (when the formed layer is a negative resist) or the formed layer remaining as the non-exposed area b (the formed layer is a positive resist) (Case), a physical pattern having a line width of 25 nm can be formed.

On the other hand, in the case of forming a line-like pattern having a line width of a sub-pixel-level zero-numbered size that does not reach the pixel pitch d, only a pixel corresponding to the zero-sized size on the innermost nearest part of the contour line is given a middle The pixel value is sufficient. Fig. 8 (a) is a plan view of a linear pattern having a width Da = 27 nm in the x-axis direction, and Fig. 8 (b) is a diagram showing a pixel arrangement constituting drawing data for exposing the linear pattern. The line width Da of the linear pattern shown in FIG. 7 is Da = 25 nm. In contrast, the line width Da of the linear pattern shown in FIG. 8 is Da = 27 nm, and the width only becomes 2 nm wider. In the case of the illustrated example, since the pixel pitch d is 5 nm, the width increase of 2 nm is referred to as the sub-pixel-level zero dimension.

Therefore, in the drawing data shown in FIG. 8 (b), the 2nm width increase amount is filled by setting a pixel row having a middle grayscale value of p = 6 as the pixel value p. That is, in the case of the example shown in FIG. 8, a linear pattern having a line width of Da = 27 nm is designed such that the contour line on the left side matches the contour of the pixel. Therefore, regarding the third to seventh lines, The pixel row is given a pixel value p = 15 (maximum value) in the same manner as the example shown in FIG. 7, but the pixel row is given a pixel value p = 6. This is a result of the fact that, since the pixel behavior of the eighth line partially includes pixels of a linear pattern (hereinafter referred to as incomplete pixels), a grayscale value determined according to the content ratio of the linear pattern is given. As the 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 in the third to seventh rows) completely contained in the linear pattern, and no line is included at all. The empty pixels (pixels in rows 1, 2, 9, and 10) of the pattern are assigned a minimum pixel value p = 0. Furthermore, a product 6 obtained by multiplying the content rate of the linear pattern “4/10” by the maximum pixel value p = 15 is given to the incomplete pixels (pixels in the eighth row) that partially include the linear pattern as pixel values.

If the drawing data shown in FIG. 8 (b) is given to the electron beam drawing device, the irradiation reference point position corresponding to the pixel having the pixel value p = 0 is not irradiated with the electron beam at all, and The positions of the irradiation reference points corresponding to the pixels of p = 6 and p = 15, and the irradiation of the electron beam were performed 6 times and 15 times, respectively. Furthermore, the mountain MM obtained by merging the hills of the exposure intensity distribution formed by each of these exposure processes is divided on the basis of a specific threshold Eth, thereby forming a graph as shown in FIG. 8 (a). The exposed area a (the area where the total exposure intensity becomes equal to or higher than the threshold Eth) and the non-exposed area b (the area where the total exposure intensity does not reach the threshold Eth). If actual development is performed, a physical linear pattern having a line width Da = 27 nm is formed. .

<<< §3. Principles of Estimation of Exposure Intensity Distribution in the Present Invention >>>

As described above, in the patterning using the electron beam drawing device, a dimensional change in a pattern that should actually be formed due to the proximity effect. Therefore, in practice, when using specific drawing data to draw an electron beam of a formed layer, it is necessary to estimate the exposure intensity distribution actually obtained by computer simulation, and correct the original drawing data based on the result.

In the aforementioned Patent Document 4, as an example of such an estimation method of the exposure intensity distribution, a method suitable for an electron beam drawing device suitable for a single beam method is disclosed. Therefore, here, the basic principle of the method for estimating the exposure intensity distribution of the present invention will be described while facing the single-beam method and the multi-beam method.

FIG. 9 is a diagram comparing the order of drawing the same pattern in a single beam and the order of drawing in a multi-beam. FIG. 9 (a) shows the order of drawing in a single beam, and FIG. 9 (b) shows The order of drawing in multiple beams. Both indicate the order in which "L-shaped" patterns are drawn on the surface of the exposure target, but there is a large difference between the two.

First, in the order of drawing in a single beam as shown in FIG. 9 (a), only two exposure operations may be performed in total. The single beam method is also called VSB method (Variable Shape Beam), and it is a method that exposes a shaped electron beam to an arbitrary intensity and exposes it to the desired shape (usually one exposure operation). Is an arbitrary rectangular shape). The example shown in FIG. 9 (a) is an example in which the rectangular area A1 is exposed using one electron beam shaped into a square, and the rectangular area A2 is exposed using one electron beam shaped into a rectangle. .

In the case of this example, if the evaluation points V1 and V2 indicated by the x mark in the definition diagram are included, the evaluation point V1 included in the rectangular area A2 refers to the point directly exposed to the electron beam during the second exposure operation. The evaluation point V2 refers to a point that has not been directly irradiated by the electron beam at all. Of course, the exposure intensity of the evaluation point V1 is higher than the exposure intensity of the evaluation point V2. However, due to the influence of the proximity effect, a small amount of energy is also accumulated at the evaluation point V1 during the first exposure operation targeting the rectangular area A1. Similarly, at the evaluation point V2, a small amount of energy is accumulated during two exposure operations in total.

Therefore, the total exposure intensity of the evaluation point V1 becomes the sum of the energy accumulated due to the proximity effect during the first exposure operation and the energy accumulated by direct irradiation during the second exposure operation. Similarly, the total exposure intensity at the evaluation point V2 becomes the sum of the energy accumulated due to the proximity effect during the total of two exposure operations. Due to such a proximity effect, the exposure intensity distribution actually obtained on the exposure target surface does not become a simple “L-shaped” pattern as shown in FIG. 9 (a), but becomes a boundary portion that expands outward.

Therefore, when actually performing two exposure operations, it is necessary to correct the shape or irradiation intensity of the electron beam in consideration of the proximity effect. For example, if there is no proximity effect, the area where the rectangular area A1 and A2 both have the irradiation intensity set to 255 and the exposure operation can be performed as follows. In fact, the first exposure operation for the rectangular area A1 is actually performed. The irradiation intensity was set to 255 at the time, and the irradiation intensity was set to 230 during the second exposure operation for the rectangular area A2.

On the other hand, FIG. 9 (b) shows drawing data provided to the electron beam drawing device when the “L-shaped” pattern shown in FIG. 9 (a) is exposed using the multi-beam electron beam drawing device. . This drawing data is composed of a two-dimensional pixel arrangement similar to the drawing data shown in Fig. 7 (b) or Fig. 8 (b). Each pixel of the drawing data corresponds to each electron beam irradiated by the multi-beam electron beam drawing device, and each pixel value indicates the irradiation intensity of the electron beam.

The outline shown by the dashed line in FIG. 9 (a) corresponds to the outline of the two-dimensional pixel arrangement shown in FIG. 9 (b). If we consider the effect of the descriptive data already described in §2, it can be easily understood that by using the descriptive data shown in Fig. 9 (b), the "L-shaped" shape shown in Fig. 9 (a) can be formed. The same pattern. As described in § 2, 15 electron beam irradiations are performed on the irradiation position corresponding to the pixel having the pixel value p = 15, and 7 electron beam irradiations are performed on the irradiation position corresponding to the pixel having the pixel value p = 7. The irradiation position corresponding to the pixel having the pixel value p = 4 is subjected to 4 electron beam irradiations, and energy corresponding to the number of irradiations is accumulated at each irradiation position.

Of course, one electron beam is not only irradiated to the area corresponding to one pixel, but as shown in FIG. 5, it is also irradiated to adjacent pixels in an overlapping manner. Therefore, one evaluation point defined on the exposure target surface is accumulated. Energy from multiple electron beams. In addition, the electron beam irradiated to a position far away from the evaluation point will also generate an energy supply caused by the proximity effect. Therefore, the final accumulated energy amount (total exposure) is calculated for each evaluation point defined on the exposure target surface. The process of intensity) must become quite complicated.

Here, for convenience of explanation, the basic concept of the exposure intensity distribution estimation method disclosed in the aforementioned Patent Document 4 will be briefly described in advance. This estimation method is suitable for a single-beam electron beam drawing device. It is assumed that the electrons irradiated onto the surface of the exposure target diffuse to the surroundings with an intensity distribution shown by a Gaussian error function, and a resist is calculated by performing a convolution operation. The entire layer's exposure intensity distribution.

FIG. 10 is a plan view showing a calculation principle of a total exposure intensity at an arbitrary evaluation point V (x, y) when drawing in a single beam method. Here, an attempt is made to consider the amount of energy accumulated at an arbitrary evaluation point V (x, y) when the rectangular area A1 shown in FIG. 9 (a) is subjected to the first exposure operation. Now, as shown in the figure, an xy two-dimensional orthogonal coordinate system is defined on the exposure object surface, and it is assumed that the rectangular area A1 is arranged at a regular position on the coordinate system. Specifically, the left side of the rectangular area A1 is arranged at the position of the coordinate value x = l (left), the right side is arranged at the position of the coordinate value x = r (right), and the upper side is arranged at the coordinate value y = t (top Meaning), the lower side is arranged at the coordinate value y = b (bottom meaning).

In the first exposure operation, the rectangular area A1 is irradiated with an electron beam shaped into a rectangular shape, and each part in the rectangular area A1 is irradiated with electrons. However, due to proximity effects such as forward scattering or back scattering, the electrons also reach the position outside the rectangular area A1 like the evaluation point V (x, y) shown in the figure. Therefore, energy accumulation occurs due to the influence. . Therefore, here, the reference point T (x ', y') is defined for the position of the coordinates (x ', y') in the rectangular area A1 which is the irradiation target of the electron beam. The extent to which the amount of accumulated energy of 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 the electrons irradiated to the reference point T (x ', y') on the surroundings becomes a function that depends on the distance from the reference point T (x ', y'), and the evaluation point V (x , Y) The closer to the reference point T (x ', y'), the greater the influence of the electrons radiated to the reference point T (x ', y'). Therefore, in the case of the example shown in FIG. 10, the degree of influence of the evaluation point V (x, y) from the reference point T (x ', y') becomes a function of the distance R between the two points. Of course, the accumulated energy value of the evaluation point V (x, y) is affected not only from the reference point T (x ', y') shown in the figure, but also from the electrons irradiated to all points in the rectangular area A1. Actually, the exposure operation is sequentially performed repeatedly on a plurality of N areas (in the case of the example shown in FIG. 9, N = 2, which is two areas of the rectangular areas A1 and A2).

Therefore, the final amount of accumulated energy (total exposure intensity) at any evaluation point V (x, y) shown in FIG. 10, that is, v (x, y) can be obtained according to the formula (1-I) in FIG. 11 Out (in this case, the evaluation point is represented by an uppercase letter V, and the amount of accumulated energy is represented by a lowercase letter v). Here, the function psf (R) is generally a function called a point spread function, and is a function indicating the degree of influence of a certain reference point T on the surroundings. Generally, the larger the distance R from the reference point T, the more the degree of influence tends to decrease.

The term of the double integral on the right side of formula (1-1) is used to perform the x-coordinate value 1 ~ r () on the point spread function psf (R) with respect to the reference point T (x ', y') shown in FIG. The left end to the right end of the rectangular area A1), and the integral of the y-coordinate value b ~ t (the lower end to the upper end of the rectangular area A1), Di is the irradiation intensity of the electron beam in the exposure operation of the i-th rectangular area Ai ). In addition, σ determines the forward scattering parameter based on the electron acceleration voltage of the electron beam drawing device, the material of the resist, and the like.

The summation Σ at the beginning of the right side of the formula (1-1) is used to add up the results of the exposure operations performed on a plurality of N areas. In the case of the example shown in FIG. 9 (a), it is set to N = 2, and the amount of energy accumulated by the first exposure operation (the exposure operation performed on the rectangular area A1 is set to i = 1) and The sum of the amount of energy accumulated by the second exposure operation (the exposure operation performed on the rectangular area A2 with i = 2) is called the total exposure intensity v (x, y) of the evaluation point V (x, y) ).

As shown in Figure 10, since R = ((x'-x) ² + (y'-y) ² ), so the formula (1-1) in FIG. 11 can be rewritten as formula (1-2). Here, if x'-x = X and y'-y = Y, the point spread function psf (R) can be expressed as psf (X, Y) as a function of X and Y. Therefore, the formula (1 -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 located at a distance X from the specific reference point T in the x-axis direction and a distance Y in the y-axis direction. . Patent Document 4 described above shows an example of using a two-dimensional Gaussian error function as the point spread function psf (X, Y).

Therefore, here, first, an attempt is made to consider applying the calculation method of the exposure intensity distribution based on the premise of the single beam method shown in each formula in FIG. 11 to the multi-beam method. FIG. 12 is a plan view showing a calculation principle of a total exposure intensity at an arbitrary evaluation point V (x, y) when drawing in a multi-beam manner. Compared with the case of the single beam method shown in FIG. 10, the point where the rectangular area A1 is replaced with the pixel P (i, j) is different.

In the calculation of the single beam method shown in FIG. 10, the following processing is performed based on the formula of FIG. 11, that is, for i = 1 to N, the reference point T (x ′, y ') Move and perform a convolution operation to calculate the total exposure intensity v (x, y) at the evaluation point V (x, y). Therefore, in the calculation of the multi-beam method shown in FIG. 12, it is only necessary to perform the following processing, that is, all pixels constituting the drawing data are performed within the range of the pixels P (i, j) in the i-th column and the j-th row. The reference point T (x ', y') is moved to perform a convolution operation, 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 in the arithmetic principle shown in FIG. 12. The final accumulated energy amount (total exposure intensity) at any evaluation point V (x, y) shown in FIG. 12, that is, v (x, y) can be obtained according to the formula (2-1) in FIG. 13. This formula (2-1) corresponds to the formula (1-1) in FIG. 11 and is obtained by replacing the sum Σ of the formula (1-1) with an integral. As described above, recently, using a multi-beam drawing device capable of irradiating 250,000 or more electron beams, the drawing data provided by such an electron beam drawing device has become a pixel array having 250,000 or more pixels. Therefore, in the formula (1-1) of FIG. 11, N becomes a huge value of 250,000 or more.

Therefore, in the formula (2-1) in FIG. 13, the sum Σ is replaced with an integral, and the total exposure intensity v (x, y) is calculated by integrating 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 certain reference point T on the surroundings. On the other hand, D (x ', y') is the irradiation intensity (dose) of the electron beam at the position of the reference point T (x ', y') represented by the coordinates (x ', y'), and becomes pixel-based P (i, j) is determined by the pixel value p. Furthermore, the integral range is in the range of negative infinity to positive infinity in both the x-axis direction and the y-axis direction, because the entire exposure target surface is set as a calculation target.

Finally, the formula (2-1) in FIG. 13 can be called the following formula, that is, a function D () that represents the intensity of electron beam irradiation is performed on a plurality of reference points T (x ', y') defined in the electron beam irradiation area. Convolution integral of x ', y') and a point spread function psf (R) indicating the degree of influence of the reference point T (x ', y') on the surroundings, thereby calculating each evaluation point V (x, y) The total exposure intensity v (x, y).

Here, as shown in Figure 12, since R = ((x'-x) ² + (y'-y) ² ), so the formula (2-1) in Fig. 13 can be modified as in formula (2-2). Here, if x'-x = X and y'-y = Y, the point spread function psf (R) can be expressed as psf (X, Y) as a function of X and Y. Therefore, the formula (2 -2) can be expressed as in formula (2-3). Here, the point spread function psf (X, Y) also indicates the influence of the evaluation point V located at a distance X from the specific reference point T in the x-axis direction and a distance Y in the y-axis direction. Degree of function.

<<< §4. Features of the simulation method of the present invention >>>

The present invention proposes a new simulation method for obtaining an exposure intensity distribution when a specific pattern is exposed and drawn using a multi-beam electron beam drawing device. Here, the characteristics of the new simulation method will be described.

First, the first feature is that the total exposure intensity v () at any evaluation point V (x, y) at the coordinates (x, y) is calculated based on the formula (2-3) shown in FIG. 13. x, y). Furthermore, the second characteristic is that, as the point spread function psf (X, Y) in the formula (2-3), the parameter including the opening size parameter determined based on the opening size of the hole of the electron beam drawing device is used. function.

FIG. 14 is a diagram showing an example of an arithmetic expression used in a calculation for obtaining an exposure intensity distribution by the simulation method of the present invention when rendering in a multi-beam method. Hereinafter, the equations (3), (4), and (5) shown in the drawings will be described.

First, the formula (3) is completely the same as the formula (2-3) shown in FIG. 13 and becomes a basic formula used in the simulation method of the present invention. As mentioned above, the left v (x, y) is the total exposure intensity at any evaluation point V (x, y) at the coordinate (x, y). If the value v (x, y) is calculated for all coordinate positions , The exposure intensity distribution on the surface of the exposure object can be obtained. As described above, the formula (3) represents a function D (x ', y') representing the intensity of the electron beam with respect to a reference point T (x ', y') defined in the electron beam irradiation area, and The expression of the convolution integral of the point spread function psf (X, Y) to the extent that the reference point T (x ', y') affects the surroundings. As mentioned above, X = x'-x and Y = y'-y.

Finally, in the simulation method of the present invention, when the xy plane of the two-dimensional xy orthogonal coordinate system is defined as the irradiation surface of the electron beam, the following processing is performed, that is, for the reference located at the coordinates (x ', y') The effect of the point T (x ', y') on the evaluation point V (x, y) located at the coordinate (x, y). The reference point T (x ', y') indicates the intensity of the electron beam irradiation. Function D (x ', y') and the convolution integral in the x-axis direction and the y-axis direction of the point spread function psf (X, Y) defined as X = x'-x, Y = y'-y The influence. In addition, as the point spread function psf (X, Y), a function including the opening size parameter B determined based on the opening size K of the hole of the electron beam drawing device in addition to the variables X and Y is used.

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

FIG. 15 is a one-dimensional graph showing an example of the point spread function psf (X, Y) shown in the formula (4) in FIG. 14. The horizontal axis represents the X axis, and the vertical axis represents the energy density E. The graph shows the degree of influence of the electron beam irradiated around the position of X = 0 on the surroundings. Figure 2 is also the same kind of graph, but the graph of Figure 2 is a graph of pure Gaussian error function. In contrast, the graph of Figure 15 is a graph of the point spread function including the opening size parameter B. Therefore, the characteristics A trapezoid having a flat portion H having a width w is formed in the central portion.

The opening size parameter B of the formula (4) becomes a parameter that affects the width w of the flat portion H of the graph shown in FIG. 15. The larger the parameter B, the larger the width w. On the other hand, the forward scattering parameter σ before equation (4) becomes a parameter that affects the inclination of the inclined portions U1 and U2 on the left and right of the graph shown in FIG. 15. The larger the parameter σ, the inclination of the inclined portions U1 and U2. The smoother. In addition, FIG. 15 shows a distribution curve in one dimension of the X axis on the horizontal axis. In fact, a distribution curve of the same shape is also obtained in the Y axis direction. Therefore, the curve of the point spread function psf (X, Y) shown in formula (4) actually becomes a three-dimensional table-shaped curve towering on the XY plane, and a flat w-width is formed on the top part. The portion H has an inclined portion formed around the portion H.

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

The simulation method disclosed in the above Patent Document 4 is based on the premise of a single-beam electron beam drawing device, and uses a general Gaussian error function as shown in the graph of FIG. 2 as the equation of FIG. 11 (1-3 ) Is the point spread function psf (X, Y). However, according to various experiments performed by the inventor of the present case, it was determined that, in the case of a single-beam electron beam drawing device, the point spread function psf as shown in the graph of FIG. 2 is used. The simulation is suitable, but in the case of a multi-beam electron beam drawing device, it is preferable to use a point spread function psf having a flat portion H as shown in the graph of FIG. 15.

In addition, it is preferable to set the width w of the flat portion H to a value corresponding to the opening size K of the hole of the electron beam drawing device used. In other words, it is preferable to use a point spread function psf, that is, if the opening portion 41 of the hole is large, the width w of the flat portion H also increases accordingly. The reason is considered to be that, in the case of the multi-beam electron beam drawing device shown in FIG. 1, the energy density distribution of the cross section of the electron beam 20 generated by the electron gun 10 becomes as ordinary as shown in the graph of FIG. 2. The distribution corresponding to the Gaussian error function, but in the case where each electron beam passing through the opening portion 41 of the hole is irradiated to the formed layer 61, the exposure intensity distribution in the formed layer 61 considering the proximity effect becomes a curve as shown in Fig. 15 As shown in the figure, the distribution has flat portions H.

Here, the opening size K of the hole becomes a value that affects the cross-sectional size of each electron beam that has passed through the opening 41 (diameter in the case of a circular cross-section, and length of one side in the case of a square cross-section). As the point spread function psf (X, Y) used in formula (3), it is preferable to use a function represented by a graph having a flat portion H having the respective electron beams that have passed through the opening portion 41. The section size corresponds to the width w.

Therefore, when implementing the present invention, when the opening portion 41 of the hole of the electron beam drawing device is circular, the diameter of the circle is used as the opening size K of the hole, and when the opening portion 41 is square, the The length of one side of the square can be used as the opening size of the hole. Moreover, the value obtained by multiplying the opening size K by the reduction magnification m of the projection lens 50 of the electron beam drawing device may be used as the opening size parameter B determined based on the opening size of the hole.

Specifically, in the case of the electron beam drawing device shown in FIG. 1, as long as the value m‧K based on the opening size K of the hole multiplied by the reduction magnification m of the projection lens 50 is defined by the formula B = m‧K The opening size parameter B is sufficient. For example, in a case where the opening portion 41 of the hole has a circular shape with a diameter of 4 μm and the reduction ratio of the projection lens 50 is 1/200, a value of B = 20 nm may be specified. In this case, the opening size parameter B is equal to the beam diameter or spot diameter of an electron beam formed on the exposure target surface. Corresponding value. Therefore, for example, the term "erf ((B / 2-X) / σ)" in formula (4) is equivalent to the result obtained by dividing the difference between the radius B / 2 of the electron beam and the distance X by the forward scattering parameter σ Value as a Gaussian error function of the variable.

In this way, in Equation (4), in addition to the opening size parameter B, the forward scattering parameter σ is also included. Therefore, 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 according to the electron acceleration voltage of the electron beam drawing device, the material of the resist, and the like. Therefore, in practice, it is only necessary to perform the following operations in advance, that is, the actual measurement is specific to the specific The exposure distribution when a material resist emits electrons at a specific acceleration voltage, and based on the inverse calculation based on the measured result, the forward scattering parameter σ of the combination of the specific material resist and the specific acceleration voltage is determined. value.

Equation (4) in FIG. 14 is an example of the point spread function psf (X, Y) including the opening size parameter B determined based on the opening size K of the hole, and includes 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)). The graph of this function is a mesa-shaped graph having a flat portion H as shown in FIG. 15, and the flat portion H has a point size corresponding to the irradiated electron beam. Corresponding width w. However, the point spread function psf (X, Y) having such characteristics is not limited to the function shown in Equation (4) in FIG. 14.

For example, equation (6) in FIG. 16 is a diagram showing an example of another function suitable for use as the point spread function psf (X, Y) in equation (3) in FIG. 14 and includes 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)) inverse trigonometric function arctan. In the formula (4) of FIG. 14, a Gaussian error function erf is used, but the formula (6) of FIG. 16 uses an inverse trigonometric function arctan instead of the above-mentioned Gaussian error function erf. The following graph can be obtained. Although the graph is slightly different in shape, it essentially has a flat portion H and inclined portions U1 and U2 as shown in FIG. 15. The flat portion H has a width w corresponding to the opening size parameter B. The inclined portions U1 and U2 have a slope corresponding to the forward scattering parameter σ.

In addition, Equation (7) in FIG. 17 is a diagram showing an example of another function suitable for the point spread function psf (X, Y) in Equation (3) in FIG. 14. The function of the constant C, the backscattering parameter β, and the proximity effect correction parameter η, that is, 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 )).

In the equation (7) of FIG. 17, a Gaussian error function erf is used in the same manner as the equation (4) of FIG. 14, but as parameters, in addition to the opening size parameter B and the forward scattering parameter σ, back scattering is used. Parameter β and proximity effect correction parameter η. The backscattering parameter β indicates the backscattered electrons scattered in the vicinity of the surface of the sample substrate 60 below the formed layer (resist layer) 61 and scattered in the resist layer 61 in FIG. 1. The parameter of the degree of scattering, the proximity effect correction parameter η is a parameter representing a ratio based on the photosensitivity of the resist scattered forward by the electron beam and the photosensitivity of the resist based on the backscatter. In addition, C is a specific constant. The parameters β and η are well-known parameters disclosed in, for example, the above-mentioned Patent Document 4, and therefore, detailed descriptions thereof are omitted here.

Equation (7) in FIG. 17 is also an equation representing a graph, which is slightly different in shape, but has a flat portion H as shown in FIG. 15. The flat portion H has a value corresponding to the opening size parameter B. The width w is, therefore, an expression representing an example of a function suitable for use as the point spread function psf (X, Y) in the present invention.

<<< §5. Sequence of the simulation method of the present invention >>>

The simulation method of the present invention is actually executed by a computer processing operation. Here, a specific procedure when the simulation method is executed using a computer will be described.

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

First, in the drawing data input stage of step S10, a process of inputting drawing data is performed. The drawing data is data representing a pattern drawn by the electron beam drawing device. For example, as shown in FIG. 9 (b), the drawing data is composed of an array of pixels having pixel values indicating the irradiation intensity of each irradiation position of the beam. data. The purpose of the simulation performed here is to determine the exposure intensity distribution of the formed layer which is estimated to be obtained in the case where exposure processing is performed on the formed layer on the assumption that such drawing data is given to the electron beam drawing device.

Then, in the parameter setting stage of step S20, setting of the opening size parameter B determined based on the opening size of the hole of the electron beam drawing device is performed. For example, as in the above example, when the opening portion 41 of the hole has a circular shape with a diameter of 4 μm and the reduction ratio of the projection lens 50 is 1/200, a value of B = 20 nm is set. The opening size parameter B is equivalent to the beam diameter or spot diameter of an electron beam formed on the exposure target surface. Or, it is used in the calculation formula in the convolution operation stage of step S40.

In the case of simulation of an electron beam drawing device with a fixed reduction ratio of the opening portion 41 of the hole and the projection lens 50, it is sufficient to set a fixed value in advance as the value of the opening size parameter B, but to perform such a variable electron When simulating the beam drawing device, the value of the opening size parameter B must be input and set each time.

The calculation matrix production stage of step S30 is a preparation stage of the convolution operation stage of step S40. Here, the operation of producing an irradiation intensity matrix and a point diffusion matrix is performed. These matrices are matrix data used by a computer to perform the operation of the formula (3) in FIG. 14. The irradiation intensity matrix is equivalent to D (x ', y') of the formula (3), and becomes a plane representing the intensity of the electron beam irradiation. Matrix data of the distribution. On the other hand, the point spread matrix is equivalent to psf (X, Y) in Equation (3), and is matrix data representing a planar distribution of the degree of influence expressed by a specific point spread function. In the following, for convenience of explanation, the irradiation intensity matrix is expressed using the same symbol "D (x ', y')" as the function D (x ', y') of the formula (3). For the point diffusion matrix, use It is represented by the symbol "psf (X, Y)" which is the same as the function psf (X, Y) in formula (3).

Equation (3) in FIG. 14 is a theoretical equation representing the convolution integral of the function D (x ', y') and the function psf (X, Y). In the convolution operation stage of step S40, an operation based on the theoretical equation is performed. . However, since calculations are performed by a computer, in practice, calculations using continuous variables are not performed, but calculations using discrete values must be performed. The irradiation intensity matrix D (x ', y') is a calculation matrix representing the value of the function D (x ', y') when a specific discrete value is used as the variables x ', y', and the point spread matrix psf ( X, Y) is a calculation matrix representing the value of the function psf (X, Y) when a specific discrete value is used as the variables X and Y. Actual operations are performed using these two sets of operation matrices.

The sampling interval, which is a discrete value of the variable x ', y' or the variable X, Y, may be specified based on the resolution of the exposure intensity distribution obtained by calculation. As explained with reference to FIG. 12, in the present invention, the amount of accumulated energy of a specific evaluation point V (x, y) on the exposure plane is calculated as the degree of influence from a plurality of reference points T (x ', y'). Cumulative value. Further, the spatial distribution of the amount of accumulated energy obtained for the plurality of evaluation points V (x, y) is referred to as the exposure intensity distribution finally obtained. Therefore, for example, when an exposure intensity distribution with a resolution defined by a 1 nm vertical and horizontal interval is to be obtained for the evaluation point V (x, y), it is necessary to set a value obtained by sampling at a 1 nm vertical and horizontal interval as the variable x '. , Y 'or discrete values of variables X, Y. In this case, as the irradiation intensity matrix D (x ', y') and the point diffusion matrix psf (X, Y), it is necessary to prepare a matrix assuming that the vertical and horizontal distances between the cells are 1 nm.

The exposure intensity distribution obtained by the simulation method of the present invention is used to correct the drawing data used in the actual exposure processing. For example, the drawing data shown in FIG. 8 (b) is drawing data prepared to form a linear pattern having a width of Da = 27 nm as shown in FIG. 8 (a). Therefore, when the result of the simulation is to obtain an exposure intensity distribution that forms a linear pattern having a width of Da = 27 nm (in the case of development, it is assumed that a partial residual distribution having a width of Da = 27 nm), No special amendments are required. However, in a case where the width of the formed linear pattern is assumed to be, for example, an exposure intensity distribution of Da = 28 nm, the pixel value "6" of the pixel in the eighth row must be slightly reduced.

In the case of the embodiment shown in FIG. 8, the distance d between pixels constituting the drawing data is d = 5 nm, but the expected value of the line width Da must be obtained with a precision (for example, a unit of 1 nm) smaller than the pixel pitch d. Out. That is, the resolution of the exposure intensity distribution obtained by simulation must be set smaller than the pixel pitch d, and the cell pitch g constituting the arithmetic matrix prepared in step S30 must be set smaller than the pixel pitch d. Therefore, an embodiment in which the distance g between the arithmetic units is set to an integer fraction of the distance d between pixels will be described below.

In the case of the embodiment described here, at the stage of making the calculation matrix in step S30, first, the calculation unit is defined by dividing each pixel of the drawing data into a plurality of parts, and a set of the calculation unit is prepared Two sets of empty operation matrices composed by the body. Next, each unit of the first operation matrix is given a specific unit value based on the pixel value of the pixel including the unit, thereby creating an irradiation intensity matrix D (x ', y') that represents the planar distribution of the irradiation intensity of the electron beam. . On the other hand, each element of the second calculation matrix is assigned a cell value corresponding to a specific point spread function including the opening size parameter B set in step S20, thereby creating a degree of influence indicated by the point spread function. Point spread matrix psf (X, Y).

Here, a specific procedure for making the irradiation intensity matrix D (x ', y') will be described with reference to FIG. 19. Now, consider an example of simulation based on simple drawing data composed of a pixel arrangement of 5 columns and 5 rows as shown in FIG. 19 (a). Each pixel constituting the drawing data is given a specific pixel value p (12 or 15 in the case of the illustrated example), and each pixel value p represents the irradiation intensity of the electron beam irradiated to the position of each pixel. Here, it is assumed that the distance d between pixels constituting the drawing data is d = 5 nm, and the distance g between the arithmetic units constituting each arithmetic matrix is set to g = 1 nm.

If the distance g between the arithmetic units is set as g = 1nm, the vertical and horizontal distances between the evaluation points V (x, y) defined on the exposure target surface are shown in the lower right of FIG. 19 (a). It can also be set to 1 nm. That is, the interval between the evaluation points V11 and V12 arranged adjacently in the horizontal direction (x-axis direction) is 1 nm, and the interval between the evaluation points V11 and V21 arranged adjacently in the vertical direction (y-axis direction) is also 1 nm. Therefore, 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 shape at intervals of 1 nm in length and length, so that an exposure intensity distribution having a resolution of 1 nm can be obtained.

FIG. 19 (b) shows that the pixels P (i, j) in the i-th column and the j-th row of the pixel arrangement constituting the drawing data shown in FIG. 19 (a) are divided into five parts vertically and horizontally to generate a total of 25 calculations. State of cell C (m, n). Since a pixel having a size of 5 × 5 nm is divided into 25 parts to define 25 arithmetic units, the size of each unit becomes 1 × 1 nm. After defining 25 empty arithmetic units in this way, each unit is given a specific unit value based on the pixel value of the pixel including the unit. In the case of the example shown on the left side of FIG. 19 (b), the pixel value "12" of the pixel P (i, j) containing the unit is directly given to all 25 arithmetic units as the unit value, and all 25 operations are performed. The unit value of the used unit becomes "12".

Actually, since all 25 pixels P shown in FIG. 19 (a) are divided into 25 parts, the operation matrix corresponding to the drawing data is composed of 625 operation units, and each operation unit is included. The pixel value of the pixel of the unit (12 or 15 in the case of 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 arithmetic units for 25 columns and 25 rows, and an arithmetic unit C for the mth and nth rows ( m, n) gives a specific unit value based on the pixel value of the pixel containing the unit. Finally, the irradiation intensity matrix D (x ', y') refers to the plane distribution of the irradiation intensity of the electron beam on the surface of the exposure target with the resolution of the distance g between the arithmetic units (in this example, g = 1nm). Matrix data.

Of course, in principle, as shown in the example on the left side of FIG. 19 (b), it is also possible to directly assign the pixel value of the pixel including the unit as the unit value to all units to create the irradiation intensity matrix D (x ', y'). However, in practice, it is preferable to implement a design for reducing the calculation load in step S40. The example shown on the right side of Fig. 19 (b) is an example to which such a design is applied.

Specifically, in the case of the example shown on the right side of FIG. 19 (b), the center of the 25 cells of the matrix shown on the left side of FIG. 19 (b) is indicated by a thick solid line frame in the figure. 24 units other than 1 unit are corrected by setting the unit value to 0. Here, the central unit is called a representative unit, and the other 24 units are called non-representative units. For the representative unit, the pixel value “12” of the pixel P (i, j) including the unit is directly assigned as the unit value, and for the non-representative unit, the unit value “0” is assigned. The reason for reducing the calculation load in step S40 by this design will be described later.

On the other hand, the point spread matrix psf (X, Y) is matrix data representing the plane distribution of the degree of influence represented by the point spread function psf (X, Y) on the exposure target surface with the resolution of the distance g between the arithmetic units. In the case of the embodiment described here, it is assumed that g = 1 nm, and it is composed of a collection of arithmetic units arranged at a pitch of 1 nm in vertical and horizontal directions. The unit value of each calculation unit is determined based on the position of the unit (vertical position X and horizontal position Y) based on the equation (4) in FIG. 14 (Of course, the equation (6) or the graph in FIG. 16 can also be used. Equation 17 of (17)). The distribution of the cell values corresponds to the graph in FIG. 15. Generally, the cells closer to the center of the matrix are assigned larger cell values.

If the irradiation intensity matrix D (x ', y') and the point diffusion matrix psf (X, Y) are produced in the calculation matrix production stage of step S30 in this way, the irradiation is performed in the convolution operation stage of step S40. The convolution integral of the intensity matrix D (x ', y') and the point spread matrix psf (X, Y), to obtain the total exposure intensity (V (x, y)) at each evaluation point V (x, y) of the coordinate (x, y) The amount of accumulated energy) v (x, y).

As described above, in the case of the embodiment described here, as the irradiation intensity matrix D (x ', y') and the point diffusion matrix psf (X, Y), it is prepared to set a matrix with a distance g = 1 nm between the cells. Therefore, an exposure intensity distribution representing the distribution of the total exposure intensity v (x, y) of each evaluation point V (x, y) with a resolution of 1 nm between vertical and horizontal directions can be obtained. In fact, based on the exposure intensity distribution obtained in this way, the size of the pattern that remains when the formed layer 61 (resist layer) is developed is estimated, and the pixel values of the original drawing data are corrected as necessary. Here, description of such a correction method is omitted.

<<< §6. Specific processing of convolution operation >>>

Here, specific processing in the convolution operation phase of step S40 in the flowchart of FIG. 18 will be described. As described above, this process is a process using convolution integration of two sets of arithmetic matrices of the operation intensity matrix D (x ', y') and the point spread matrix psf (X, Y). Theoretically, a process based on FIG. 14 is performed. The convolution operation of the operation formula shown in the formula (3). In addition, the arithmetic matrix is a collection of discretely defined arithmetic units (units arranged with a vertical and horizontal distance of 1 nm in the case of the above example). Therefore, strictly speaking, the operation performed in step S40 is not a "volume "Integral integral" refers to the operation of obtaining "convolution sum". In practice, it becomes an operation using a large number of arithmetic units. Therefore, in this case, for convenience, the "convolution integral" is used. term.

FIG. 20 is a diagram showing a correspondence relationship between the irradiation intensity matrix D (x ′, y ′) and the point diffusion matrix psf (X, Y) prepared in step S30 in FIG. 18. In the upper stage of FIG. 20, the arrangement of the arithmetic unit which constitutes the irradiation intensity matrix D (x ', y') created based on the drawing data shown in FIG. 19 (a) is shown. The area enclosed by a thick solid line frame shown in the figure represents one pixel P (i, j) constituting the drawing data, and the area enclosed by a thin line frame represents one arithmetic unit C (m, n).

As described above, the pixel P (i, j) is composed of a square having a side of 5 nm, and the arithmetic unit C (m, n) is composed of a square having a side of 1 nm. Therefore, one pixel P (i, j) includes 25 arithmetic units C (m, n), and the irradiation intensity matrix D (x ', y') includes a total of 625 arithmetic units. A specific unit value based on the pixel value of the pixel including the unit is assigned to each arithmetic unit (the representation of the unit value of each arithmetic unit is omitted in FIG. 20).

However, in the case of the embodiment described here, as a design to reduce the computational burden, only a specific representative unit included in a plurality of arithmetic units for the same pixel is assigned a pixel value based on the pixel. A specific value is used as a unit value, and a non-representative unit other than the unit value is assigned a unit value of 0.

The example shown in FIG. 20 is an example in which one arithmetic unit located at the center of each pixel is a representative unit and the other arithmetic units are non-representative units. Only the representative unit is shown in black. Therefore, the representative unit shown in black in the figure is assigned the same value as the pixel value (12 or 15) of the pixel at the corresponding position in FIG. 19 (a) as the unit value, and the non-representative unit shown in white in the figure Each cell is assigned a cell value of 0. Finally, the irradiation intensity matrix D (x ', y') prepared in step S30 refers to a cell assigned a value of 12 or 15 to a black-painted cell and a cell assigned a 0 to a white-painted cell as shown in the upper paragraph of FIG. 20. The unit arrangement of values.

On the other hand, the graph psf shown in the lower part of FIG. 20 shows the unit values of the arithmetic units of the point spread matrix psf (X, Y) arranged in a specific column (for example, the column in the vertical center). As shown in FIG. 15, the point spread function psf (X, Y) used in the present invention becomes a function of a trapezoid having a flat portion H and inclined portions U1 and U2. The flat portion H has a width corresponding to the opening size parameter B. w. The inclined portions U1 and U2 have a slope corresponding to the forward scattering parameter σ. Therefore, the graph psf shown in the lower part of FIG. 20 also becomes a graph having a flat portion H and inclined portions U1 and U2. Finally, the point spread matrix psf (X, Y) produced in step S30 refers to a cell arrangement having a cell value distribution corresponding to the graph psf shown in the lower part of FIG. 20 in the X-axis direction and the Y-axis direction.

The convolution operation shown in equation (3) in FIG. 14 can be performed by processing a point diffusion matrix psf (X, Y) having a cell value distribution corresponding to the graph psf in the lower stage of FIG. 20. Relative to the irradiation intensity matrix D (x ', y') shown in the upper part of FIG. 20, two-dimensionally moved at a pitch of 1 nm, and the product of the cell values of the cells located at the corresponding positions of the two matrices is cumulatively added. In the lower part of FIG. 20, a calculation unit C () for calculating the center position of the point spread matrix psf (X, Y) and the irradiation intensity matrix arranged at the center of the pixel P (i, j) in the i-th column and j-th row is depicted The graph psf when the center positions of m, n) coincide.

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

FIG. 21 (b) is a graph showing the unit value of each calculation unit obtained by dividing one pixel into 25 parts. Similarly, the x-axis is taken on the horizontal axis and the unit value D is taken on the vertical axis. There are 25 arithmetic units arranged on the horizontal axis. These units are units obtained by cutting 5 pixels in the third column of the drawing data shown in FIG. 19 (a), which is equivalent to all 25 columns and 25. In the cell arrangement of the row, the cells C (13,1) to C (13,25) in the 13th column and the 1st to 25th row. This example is equivalent to the example shown on the left side of FIG. 19 (b), and all units are assigned the same unit value (i.e., the pixel value D of the pixel containing the unit (the pixel at the corresponding position in FIG. 21 (a))). 12 or 15).

In contrast, FIG. 21 (c) is equivalent to the example shown on the right side of FIG. 19 (b), and only the representative unit located in the center of each pixel among the 25 units arranged in the 13th column is given and the unit containing the unit is assigned. A unit value of the same pixel value D of a pixel is assigned a unit value of 0 to other non-representative units. Specifically, the representative unit C (13,3), C (13,8), C (13,13), C (13,18), C (13,23) of the 13th column is assigned a unit value of 12 or 15. Assign a unit value of 0 to other non-representative units.

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 operation, the graph f is moved two-dimensionally in units of the distance g between calculation units (in this example, g = 1nm), and the two groups of units (corresponding to the irradiation intensity matrix) are located at corresponding positions. The product of the cell values of the cell and the point spread matrix is cumulatively added. A graph f (13, 13) shown in FIG. 21 (d) shows a state where the center of the graph f is aligned with the center position of the representative unit C (13, 13) shown in FIG. 21 (c). . Under this configuration, the unit values (12 or 15) of the five representative units shown in FIG. 21 (c) and each representative unit of the graph f (13, 13) shown in FIG. 21 (d) are obtained. Product of function values f at the same coordinate position.

FIG. 21 (e) shows the distribution of the total exposure intensity obtained by cumulatively adding the product of the unit values at each position by moving the graph f (13, 13) shown in FIG. 21 (d) to the left and right Graph F. Here, a graph f (13, 3) indicated by a dotted line represents a state where 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) shows a state where the graph f is arranged so as to coincide with the center position of the representative unit C (13, 8), and a graph f (13, 13) shown by a solid line represents the graph f A state where the center position of the unit C (13, 13) is aligned, and a graph f (13, 18) indicated by a one-point chain line indicates that the graph f is consistent with the center position of the representative unit C (13, 18) A state where the graph f is arranged in a dotted manner indicates a state where the graph f is arranged so as to coincide with the center position of the representative cell C (13, 23).

The graph F shown in FIG. 21 (e) is a distribution curve of the total exposure intensity obtained by performing such a convolution operation, and is equivalent to the total exposure intensity v (x) shown in the formula (3) of FIG. 14 , Y). Furthermore, as shown in FIG. 21 (b), when the same unit value as the pixel value D is given to all the cells and the irradiation intensity matrix D (x ', y') is created, it is necessary to perform a quadrature operation on all the cells. However, as shown in FIG. 21 (c), when only the representative unit located at the center of each pixel is given the same unit value as the pixel value D to create the irradiation intensity matrix D (x ', y'), the non- The product of the representative units becomes 0, and therefore, operations on the non-representative units can be substantially omitted.

The embodiment shown in FIG. 20 and FIG. 21 is an example in which the arithmetic unit located at the center of each pixel constituting the drawing data is a representative unit. However, the representative unit does not have to be a unit located at the center of each pixel. The unit is set as a representative unit. FIG. 22 is a diagram showing a modification example in which the arithmetic unit located at the lower left of each pixel is a representative unit.

In FIG. 22 (a), the arrangement of the arithmetic units constituting the irradiation intensity matrix D (x ′, y ′) is shown in the same manner as in the upper graph of FIG. 20. The area of the square surrounded by a thick solid line frame with a side of d = 5nm shown in the figure represents one pixel P (i, j) constituting the drawing data, and the area surrounded by a thin line frame with a side of d = 1nm A square area of 1 represents one arithmetic unit C (m, n). Here, the units shown in black in the figure are representative units, and the units shown in white in the figure are non-representative units. In the embodiment shown in the upper part of FIG. 20, a black-colored representative unit is arranged at the center of each pixel, but in the modification shown in FIG. 22 (a), a black-colored unit is arranged at the lower left of each pixel. Representative unit.

FIG. 22 (b) shows a state in which a calculation unit is defined by dividing one pixel P (i, j) shown in FIG. 22 (a) into 25 parts, and a specific unit value is assigned to each calculation unit Illustration. The lower left cell indicated by a thick solid line frame in the figure becomes a representative cell. Therefore, a cell value of "12" (a pixel value of a pixel P (i, j)) is assigned to the representative cell, and other non-representative cells are given. Assign a cell value of "0". If the embodiment shown on the right side of FIG. 19 (b) is compared with the modification shown in FIG. 22 (b), it can be seen that in the latter, the position of the representative unit is downward from the center of the pixel P (i, j). Square position with a specific offset (2 in the case of this example) 2nm).

In other words, the modification shown in FIG. 22 is an example in which, when the irradiation intensity matrix D (x ', y') is created in the calculation matrix creation stage of step S30, a plurality of calculations included in the same pixel are used. The arithmetic unit that exists at a position that is shifted from the center of the pixel to a specific direction by a specific offset is a representative unit, and the other arithmetic units are non-representative units, and can be called This is an example in which a pixel value of a pixel including the unit is directly assigned to each representative unit as a unit value, and a unit value of 0 is assigned to each non-representative unit.

In this way, when a modified example is adopted in which the position of the representative unit is shifted from the center of the pixel to a specific direction by a specific offset when the irradiation intensity matrix D (x ', y') is created, it is preferable to use the production point. The diffusion matrix psf (X, Y) is also corrected by taking this offset into consideration. The reason is that, since each electron beam is irradiated with the center of each pixel as the irradiation target, as shown in the lower graph of FIG. 20, the graph of the point spread function psf is preferably centered on its center and each pixel. Configured in a consistent manner.

Therefore, when the representative unit is set at a position shifted by a specific offset from the center of the pixel in a specific direction as in the modification shown in FIG. 22, the point spread matrix psf (X, Y) is created. In this case, the point spread function psf (X, Y), which is modified by the above-mentioned offset in the direction opposite to the specific direction, is defined, so as to create a point spread matrix representing a planar distribution of the degree of influence represented by the point spread function. can.

Specifically, as long as the point spread function psf (X, Y) shown in the formula (4 ') in FIG. 22 (c) is used instead of the point spread function psf (X, Y) shown in the formula (4) in FIG. 14 and Just make the point spread matrix. The right side of the formula (4 ') is obtained by replacing the variable X on the right side of the formula (4) with the variable "X + △ x" and replacing the variable Y with the variable "Y + △ y". Here, Δx is an offset in the x-axis direction, and Δy is an offset in the y-axis direction. In the case of the example shown in FIG. 22, Δx = 2nm and Δy = 2nm.

FIG. 23 is a diagram showing a concept of a process of performing a convolution operation when the modification shown in FIG. 22 is adopted. Here, FIG. 23 (a) is a diagram exactly the same as FIG. 21 (a), and is a graph showing pixel values D of five pixels constituting the drawing data. 23 (b) is a diagram exactly the same as FIG. 21 (b), and is a graph showing an example in which a pixel value of a pixel including the unit is directly given to all the arithmetic units as a unit value.

In contrast, FIG. 23 (c) shows the lower left unit of each pixel as a representative unit as shown in FIGS. 22 (a) and (b), and assigns only the representative unit to the pixel containing the unit. A unit value having the same pixel value D is assigned a unit value of 0 to other non-representative units. Specifically, the representative cells C (15,1), C (15,6), C (15,11), C (15,16), and C (15,21) of the 15th column are assigned a cell value of 12 or 15. Assign a unit value of 0 to other non-representative units. Comparing FIG. 21 (c) with FIG. 23 (c), it can be seen that in the latter, the position of the bar that represents the unit value of the unit is shifted to the left by an amount equivalent to 2 units (x-axis Offset in direction △ x).

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), as in FIG. 21 (d). A graph f (15, 11) shown in FIG. 23 (d) shows a state where the graph f is arranged at a position corresponding to the center of the graph f 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), and becomes a position shifted to the right by the shift amount Δx in the x-axis direction. Although it is not shown in the figure, it is shifted in the y-axis direction by the shift amount Δy. As a result, the center position of the graph f (15, 11) coincides with the center position of the non-representative unit (13, 13).

Finally, 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) becomes A graph suitable as a graph of a point spread function psf showing the degree of influence of the irradiation spot on the surroundings of the electron beam irradiated with the center of the pixel P (3, 3) as the irradiation target. The correction using the offset amounts Δx and Δy in the formula (4 ′) in FIG. 22 (c) is to perform a convolution operation using a point spread matrix psf (X, Y) arranged at an appropriate position.

Fig. 23 (e) is the same as Fig. 21 (e), and shows the process of adding the cumulative product of the unit values at each position while moving the graph f (15,11) to the left and right, and further shows that The distribution curve F of the total exposure intensity finally obtained through the process. Similarly, only the representative unit located at the lower left of each pixel is given the same unit value as the pixel value D to create the irradiation intensity matrix D (x ', y'). Therefore, the product of non-representative units becomes 0, so it is practically possible Operations on non-representative units are omitted.

If a method of assigning a unit value corresponding to the pixel value of a pixel to a specific representative unit among a plurality of arithmetic units included in each pixel and assigning a unit value of 0 to a non-representative unit other than this is used, Multiple calculation processes can be omitted and the calculation time can be shortened.

Furthermore, in the embodiment described above, only one of the plurality of arithmetic units included in one pixel is set as a representative unit, and the remaining units are set as non-representative units. Each pixel sets a plurality of representative units. Therefore, when the irradiation intensity matrix is created in the calculation matrix production stage, when the basic policy of setting a cell located at the center of each pixel as a representative cell is adopted, it is only necessary to include a plurality of calculation cells included in the same pixel. One or more arithmetic units located at the center of the pixel are set as representative units, and other arithmetic units may be set as non-representative units.

In general, when the irradiation intensity matrix is created in the calculation matrix creation stage, when each pixel of the drawing data is divided into an odd number of parts vertically and horizontally, only one operation unit located at the center of each pixel is set as As the representative unit, the other arithmetic units are set as non-representative units, and the pixel value of the pixel including the representative unit is assigned to the representative unit, and the unit value of 0 is assigned to the non-representative unit. The embodiment shown in FIG. 20 is an example in which each pixel is vertically and horizontally divided into five parts, and one arithmetic unit located at the center of each pixel is set as a representative unit.

In contrast, when each pixel of the drawing data is vertically and horizontally divided into an even number of sections, four arithmetic units are arranged in the center of each pixel. In this case, the four arithmetic units may be set as representative units, and the other arithmetic units may be set as non-representative units. Furthermore, as long as the value of 1/4 of the pixel value of the pixel including the representative unit is assigned to the four representative units, the unit value of 0 may be assigned to the non-representative unit.

FIG. 24 (a) is an example in which each pixel P (i, j) is vertically and horizontally divided for drawing data composed of a pixel arrangement of nine pixels arranged in three columns and three rows with a vertical and horizontal pitch d = 10 nm. By dividing into 10 parts, a computation unit C (m, n) is produced. Since each pixel is vertically and horizontally divided into an even number of sections, four arithmetic units are arranged at the center of each pixel. Therefore, all of the four arithmetic units are set as representative units for the pixel. That is, the cells shown in black in FIG. 24 (a) are representative cells, and the cells shown in white in the figure are non-representative cells. A value of 1/4 of the pixel value of a pixel including the representative unit is assigned to each representative unit, and a unit value of 0 is assigned to a non-representative unit.

FIG. 24 (b) shows a state in which a specific unit value is assigned to each of a total of 100 arithmetic cells C (m, n) included in one pixel P (i, j) shown in FIG. 24 (a). Illustration. A unit value of "3" is given to each of the four groups of representative cells indicated by a thick solid line frame in the figure. This is an example of a case where the pixel value p of the pixel P (i, j) is "12". That is, each representative cell is given a value "3" which is 1/4 of the pixel value "12" of the pixel including the representative cell. In addition, a cell value of 0 is assigned to all non-representative cells.

If a plurality of representative units are set for one pixel in this way, calculations must be performed for each of the plurality of representative units. However, since calculations about non-representative units can also be omitted, the effect of shortening the calculation time can be obtained. Of course, in the case where a plurality of representative units are set for one pixel in this way, the position of each representative unit may be shifted from the center of the pixel toward a specific direction with a specific offset.

However, when dividing into an even number of parts, it is not necessary to set a plurality of representative units, and it is also possible to set only a single representative unit for one pixel. In the case of being divided into an even number of parts, a single representative unit cannot be arranged at the center of the pixel. Therefore, the representative unit is arranged at a position that must be shifted from the center of the pixel toward a specific direction with a specific offset. In this case, as in the example shown in FIG. 22, when creating the point spread matrix psf (X, Y), as long as the function psf (X, Y) corrected by the above-mentioned offset in the opposite direction is defined, can.

In the example shown in FIG. 24 (b), one pixel is evenly divided into 100 units, and four representative units are defined near the center, and each of them is assigned a value of 1/4 of a pixel value "12" of "3" "As the unit value. This is to consider that the representative unit is arranged at the center of the pixel. However, as in the example shown in FIG. 22, if the method of correcting the function psf (X, Y) with a specific offset is used, it can be used at any arbitrary position. A single representative unit is located.

For example, the example shown in FIG. 25 (a) is an example in which one pixel is evenly divided into 100 units in the same way as the example shown in FIG. 24 (a). However, the example shown in FIG. An example in which the lower left corner cell shown in black is set as a single representative unit (for the representative unit of the upper right pixel, the blacking is omitted for the convenience of drawing the arrow indicating the offset). Fig. 25 (b) shows a state in which a specific unit value is assigned to each of a total of 100 arithmetic cells C (m, n) included in one pixel P (i, j) shown in Fig. 25 (a). Illustration. A cell value "12" is assigned to a representative cell in the lower left corner indicated by a thick solid line frame in the figure. This is an example of a case where the pixel value p of the pixel P (i, j) is "12". In addition, a cell value of 0 is assigned to the remaining 99 non-representative cells.

As shown by the arrow on the upper right pixel of FIG. 25 (a), the center of the representative unit in the lower left corner is arranged from the center of the pixel toward the lower left with a specific offset (△ x = 4.5nm in the horizontal direction, and vertical in the vertical direction) △ y = 4.5nm). Therefore, as for the function psf (X, Y), it is only necessary to perform correction with the same offset amount toward the upper right direction. Specifically, as long as the point spread function psf (X, Y) shown in the formula (4 ') in FIG. 22 (c) is used instead of the point spread function psf (X, Y) shown in the formula (4) in FIG. 14 and Just make the point spread matrix. The right side of the formula (4 ') is obtained by replacing the variable X on the right side of the formula (4) with the variable "X + △ x" and replacing the variable Y with the variable "Y + △ y". If the sign is considered, then in the above example, In this case, it is only necessary to set Δx = -4.5nm and Δy = -4.5nm and apply the formula (4 ').

<<< §7. Convolution operation using Fourier transform >>>

In §6, as the specific processing of the convolution operation stage of step S40 in the flowchart of FIG. 18, two groups using the irradiation intensity matrix D (x ', y') and the point spread matrix psf (X, Y) are used. The processing sequence of the convolution integral of the operation matrix is explained. Here, the operation of performing the convolution integration using a Fourier transform will be described.

In general, it is known that if a calculation method using a Fourier transform is applied to the calculation of the convolution integral of the two functions f (A) and f (B), the calculation time can be shortened. In principle, first, by performing the Fourier transform on the functions f (A) and f (B) respectively, the functions f '(A) and f' (B) with the spatial frequency value as a variable are obtained as their products. , Calculate the function f '(C) = f' (A) × f '(B). Finally, if the function f' (C) is inverse Fourier transformed to obtain the function f (C), then the function f (C) ) Is a convolution integral representing two functions f (A) and f (B).

Therefore, when implementing the present invention, in practice, it is preferable to also perform a convolution operation using a Fourier transform. In step S40 of FIG. 18, the processing of the four stages of the first operation stage S41, the second operation stage S42, the third operation stage S43, and the fourth operation stage S44 is described, which is used to perform the description in §7 The process of convolution operation using Fourier transform.

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

First, in the first operation stage S41, as shown in Equation (9), a radiation intensity frequency matrix D '(f, g) is prepared by performing a Fourier transform on the radiation intensity matrix D (x', y '). The irradiation intensity matrix D (x ', y') is a matrix showing the spatial distribution of the irradiation intensity values in the horizontal direction (x'-axis direction) and the vertical direction (y'-axis direction). In contrast, the irradiation intensity frequency matrix D '( f, g) is a matrix that takes the f-axis representing the spatial frequency in the x'-axis direction in the horizontal direction and the g-axis representing the spatial frequency in the y'-axis direction in the vertical direction, and becomes the radiation intensity matrix D (x ' A matrix of complex numbers of spatial frequency components in the x'-axis direction and the y'-axis direction in y ').

Next, in the second operation stage S42, as shown in equation (10), a point spread frequency matrix psf '(f, g) is produced by performing a Fourier transform on the point spread matrix psf (X, Y). The point spread matrix psf (X, Y) is a matrix showing the spatial distribution of the degree of influence in the horizontal direction (X-axis direction) and the vertical direction (Y-axis direction). In contrast, the point spread frequency matrix psf '(f, g) is Take the f-axis representing the spatial frequency in the X-axis direction in the horizontal direction and the g-axis representing the spatial frequency in the Y-axis direction in the vertical direction to become the X-axis direction of the point spread matrix psf (X, Y) and A matrix of complex numbers of spatial frequency components in the Y-axis direction.

Then, in the third operation stage S43, as shown in Equation (11), the corresponding calculation unit is obtained for the irradiation intensity frequency matrix D '(f, g) and the point spread frequency matrix psf' (f, g). The product of the complex number is created as an exposure intensity frequency matrix v '(f, g) having the product as a unit value.

Then, in the final fourth operation stage S44, an exposure intensity matrix v (x, y) is produced by inverse Fourier transform of the exposure intensity frequency matrix v '(f, g) obtained according to formula (11). . The exposure intensity matrix v (x, y) becomes a matrix representing the planar distribution of the total exposure intensity at each evaluation point represented by the coordinates (x, y), that is, the exposure intensity distribution that should be obtained by the simulation of the present invention. matrix.

Furthermore, as described in §6, if the irradiation intensity matrix D (x ', y') is created in the calculation matrix creation stage of step S30, only the unit values corresponding to the pixel values are assigned to the representative units and The method of assigning a unit value of 0 to a non-representative unit can greatly reduce the computational load of the Fourier transform processing shown in Equations (9) and (10), thereby reducing the calculation time.

FIG. 27 is a diagram explaining the principle of reducing the computational burden of the Fourier transform process, and shows a specific order of the Fourier transform process shown in Expression (9). First, FIG. 27 (a) is a diagram showing a unit arrangement of the irradiation intensity matrix D (x ', y'). A unit value corresponding to the pixel value of the original drawing data is contained in each unit.

According to the formula (9), when the irradiation intensity matrix D (x ', y') is Fourier transformed to obtain the irradiation intensity frequency matrix D '(f, g), the following processing is performed first, that is, the horizontal (x The element values arranged in the 'axis direction' are subjected to a Fourier transform to obtain the spatial frequency, and an intermediate matrix D "(f, y) of the irradiation intensity as shown in Fig. 27 (b) is produced. The intermediate matrix D" (f, y of the irradiation intensity) The horizontal axis is the frequency f-axis and the vertical axis is the y'-axis. It is a matrix representing spatial frequency components in the x'-axis direction with respect to each element value of the original irradiation intensity matrix D (x ', y').

For example, in FIG. 27 (a), the cells in the first column, which are surrounded by a thick solid line frame extending in the horizontal direction, respectively contain specific cell values. If a spatial frequency component of a one-dimensional arrangement of the cell values is extracted, The values of the extracted components are arranged on the frequency f axis as unit values, and the cells in the first column shown in FIG. 27 (b) are surrounded by a thick solid line frame extending in the horizontal direction. The cells in the first column are arranged along one dimension of the frequency f axis, and the values of higher components of the spatial frequency f are contained as the cell values from left to right.

Then, for this irradiation intensity intermediate matrix D "(f, y), the Fourier transform is performed on the unit values arranged in the longitudinal direction (y'-axis direction) to obtain the spatial frequency, as shown in Figure 27 (c). The radiation intensity frequency matrix D '(f, g) is shown. The radiation intensity frequency matrix D' (f, g) is a horizontal axis of the frequency f axis and a vertical axis of the frequency g axis, and it is a matrix D indicating the original irradiation intensity. A matrix of spatial frequency components in the x'-axis direction and the y'-axis direction of each unit value of (x ', y').

For example, in FIG. 27 (b), the cells in the second row, which are surrounded by a thick solid line frame extending in the longitudinal direction, respectively contain specific cell values. If a spatial frequency component of a one-dimensional arrangement of the cell values is extracted, When the values of the extracted components are arranged on the frequency g axis as unit values, the unit in the second row shown by a thick solid line frame extending in the longitudinal direction in FIG. 27 (c) is obtained. The cells in the second row are arranged along the one-dimensional axis of the frequency g, and the value of the higher component of the spatial frequency g is contained as the cell value from the top to the bottom.

Methods such as FFT (Fast Fourier Transform) are known for performing a Fourier transform on a one-dimensional array of unit values to extract its spatial frequency components. Therefore, detailed descriptions are omitted here. If the irradiation intensity matrix D (x ', y ') Is a matrix in which only a specific representative unit has a unit value corresponding to a pixel value, and other non-representative units have a unit value of 0, and the calculation load of the Fourier transform process is greatly reduced. The reason is that when the irradiation intensity matrix D (x ', y') shown in Fig. 27 (a) is transformed into the irradiation intensity intermediate matrix D "(f, y) shown in Fig. 27 (b), Omit operations for columns that contain only the cell value 0.

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 unit values of the cells in the first column or the second column are all equal. Becomes 0. In this way, a Fourier transform is performed on a column containing only the value 0 (the column along the x ′ axis), and the result is a column containing only the value 0 (the column along the f axis). Therefore, for such a column, the actual The Fourier transform process can be omitted. For this reason, if only a substantial unit value is given to a representative unit and a unit value of a non-representative unit is set to 0, the calculation load of the Fourier transform process can be greatly reduced, and the overall calculation time can be obtained. Shortened.

<<< §8. Exposure intensity distribution calculation device of the present invention >>>

In the foregoing, the present invention has been explained as a method invention in the form of a simulation method for obtaining an exposure intensity distribution in a multi-beam electron beam drawing device. Here, explanation will be made for explaining the present invention as a device invention in the form of an exposure intensity distribution calculation device for a multi-beam electron beam drawing device.

FIG. 28 is a block diagram showing a basic configuration of the exposure intensity distribution calculation device of the present invention. This exposure intensity distribution calculation device has a function of obtaining an exposure intensity distribution when a specific pattern is exposed and drawn on a formed layer using a multi-beam electron beam drawing device. As shown in the figure, it includes a drawing data input unit 110 and an irradiation intensity matrix. The creation unit 120, the parameter setting unit 130, the point spread matrix creation unit 140, and the convolution operation execution unit 150. In fact, each of these constituent elements is realized by a coordinated action of a computer and a program incorporated into the computer, and the exposure intensity distribution calculation device can be constituted by incorporating a dedicated program into the computer.

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

The parameter setting unit 130 is a component that sets an opening size parameter B that is determined based on the opening size of the hole of the electron beam drawing device. The opening size K of the hole is defined as a value of the opening size formed in the opening portion 41 of the orifice plate 40 as shown in the figure. As described above, when the opening portion 41 is circular, the diameter of the circle is used. When the opening size K of the hole is a square, the length of one side of the square may be used as the opening size of the hole. Further, as the opening size parameter B, a value obtained by multiplying the opening size K by the reduction magnification m of the projection lens 50 of the electron beam drawing device can be used.

In the case of simulation of an electron beam drawing device in which the opening size K of the opening portion 41 of the hole and the reduction magnification m of the projection lens 50 are fixed, as long as a fixed value m‧K is set to the parameter setting portion 130 in advance as the opening size parameter The value of B is sufficient. When performing simulations of such variable electron beam drawing devices, as long as the function of inputting the opening size K and the reduction magnification m each time is set in the parameter setting section 130 in advance, and based on the input value, m · K The value may be set to the value of the opening size parameter B.

The irradiation intensity matrix creation unit 120 is a component that prepares an empty unit composed of a collection of arithmetic units obtained by dividing each pixel of the rendering data input by the rendering data input unit 110 into a plurality of parts. A calculation matrix and a specific unit value based on the pixel value of a pixel including the unit are assigned to each calculation unit, thereby creating an irradiation intensity matrix D (x ', y') representing a planar distribution of the irradiation intensity of the electron beam. The specific manufacturing method of the irradiation intensity matrix D (x ', y') is as described in § 5 with reference to FIG. 19 and the like.

Furthermore, in order to reduce the calculation load, the irradiation intensity matrix creation unit 120 preferably assigns a specific value determined based on the pixel value of the pixel to a specific representative unit included in a plurality of calculation units of the same pixel as a unit value. , Assign a unit value of 0 to the non-representative units. Specifically, as long as one or more arithmetic units located at the center of the pixel among a plurality of arithmetic units of the same pixel are set as representative units, the other arithmetic units are set as non-representative units. Just fine.

When the irradiation intensity matrix creation unit 120 divides each pixel of the drawing data into an odd number of vertical and horizontal portions to define an arithmetic unit, one arithmetic unit located at the center of each pixel may be used as a representative unit. Non-representative units are used as non-representative units. The representative unit is assigned a pixel value of a pixel including the representative unit as a unit value, and a non-representative unit is assigned a unit value of 0. In contrast, when the irradiation intensity matrix creation unit 120 divides each pixel of the drawing data into even-numbered sections to define an arithmetic unit, four arithmetic units located at the center of each pixel may be used as representative units. The other arithmetic units are set as non-representative units, and the representative unit is assigned a value of 1/4 of the pixel value of the pixel including the representative unit as the unit value, and the non-representative unit is assigned a unit value of 0. The details of the above situation are as explained above in §6.

On the other hand, the point spread matrix creation unit 140 is a component that assigns a specific point spread function including the opening size parameter B set by the parameter setting unit 130 to each calculation unit of the empty calculation matrix. A unit value corresponding to psf (X, Y) is used to create a point spread matrix psf (X, Y) representing a planar distribution of the degree of influence represented by the point spread function psf. As the point spread function psf, a function in which the opening size parameter B affects the width w of the flat portion H of the graph and the forward scattering parameter σ affects the inclination of the inclined portions U1 and U2 of the graph as illustrated in FIG. 15 is used. Specific examples of the point spread function psf (X, Y) are exemplified as Equation (4) in FIG. 14, Equation (6) in FIG. 16, and Equation (7) in FIG. 17.

In addition, as in the modified examples shown in FIGS. 22 and 23, the irradiation intensity matrix creation unit 120 can also exist in a plurality of arithmetic units included in the same pixel in a specific direction from the center of the pixel to a specific direction. The calculation unit for the position after the displacement is set as a representative unit, and the other calculation units are set as non-representative units, and an irradiation intensity matrix D (x ', y') is created. In this case, the point spread matrix creation unit 140 only needs to create a point spread matrix psf (X, which represents the plane distribution of the degree of influence represented by the point spread function corrected by the offset in the direction opposite to the specific direction. Y) (see Fig. 22 (c)).

The convolution operation execution unit 150 is a constituent element that performs calculations using the irradiation intensity matrix D (x ', y') produced by the irradiation intensity matrix creation unit 120 and the point intensity matrix creation unit 140 The convolution integral of the point spread matrix psf (X, Y) is used to obtain the total exposure intensity at each evaluation point.

In the case of the illustrated embodiment, the convolution operation execution unit 150 has a function of performing a convolution integral using a Fourier transform. Therefore, the convolution operation execution unit 150 includes a first operation unit 151 (means for executing the processing of Expression (9) in FIG. 26), which performs a Fourier transform on the irradiation intensity matrix D (x ', y'), and Create an irradiation intensity frequency matrix D '(f, g); a second operation unit 152 (means for executing the processing of formula (10) in FIG. 26), which performs a Fourier transform on the point diffusion matrix psf (X, Y), The point spread frequency matrix psf '(f, g) is made; the third arithmetic unit 153 (means for executing the processing of the formula (11) in FIG. 26) is used to create the irradiation intensity frequency matrix D' (f, g) and the points The diffusion intensity matrix psf '(f, g) corresponds to the product of the corresponding arithmetic units as the unit value of the exposure intensity frequency matrix v' (f, g); and a fourth arithmetic unit 154, which v '(f, g) is subjected to an inverse Fourier transform, and an exposure intensity matrix v (x, y) representing a planar distribution of the total exposure intensity at each evaluation point is produced.

The specific processing sequence of such a convolution integral using the Fourier transform is as described in §7. In this way, the exposure intensity matrix v (x, y) produced by the fourth arithmetic unit 154 is output as the exposure intensity distribution data Dout.

<<< §9. Examples of exposure intensity distributions obtained using the present invention >>>

Finally, an example of the exposure intensity distribution obtained by the present invention is shown. FIG. 29 is a diagram showing a first example of the exposure intensity distribution obtained by the inventive simulation method. FIG. 29 (a) is a diagram in which the drawing data prepared for drawing a linear pattern having a width of 50 nm is an image in gray tones. On the left side of the figure, pixel values corresponding to each density of gray tones are shown as examples. As shown in the figure, a pixel value of 15 is assigned to pixels inside the linear pattern, and a pixel value of 0 is assigned to pixels outside. The pixel distance d is set to d = 5nm, and 10 pixels with a pixel value of 15 are arranged in the widthwise direction of the linear pattern.

FIG. 29 (b) is a diagram showing an irradiation intensity matrix D (x ', y') created based on the drawing data shown in FIG. 29 (a) as an image in gray tones. The irradiation intensity matrix is composed of a collection of arithmetic units arranged at a pitch g. This example is an example in which an arithmetic unit is defined by dividing one pixel vertically and horizontally into five parts as shown in FIG. 20, and the distance g between the units is set to g = 1 nm. The smaller black dots in the figure represent the representative unit located in the center of each pixel, and 15 which is the same as the pixel value is assigned as the unit value.

Fig. 29 (c) is a convolution integration operation performed on the irradiation intensity matrix D (x ', y') shown in Fig. 29 (b) and a specific point spread matrix psf (X, Y) (not shown). The obtained exposure intensity matrix v (x, y), that is, the image of the exposure intensity distribution represented as a gray tone. On the left side of the figure, unit values (calculated values of v (x, y)) corresponding to respective densities of gray tones are shown as examples. The closer to black, the greater the exposure intensity (the amount of accumulated energy). The two white lines in the figure represent the outline of the linear pattern shown in FIG. 29 (a). Thus, the result shown in FIG. 29 (c) shows an appropriate exposure intensity distribution obtained when exposure processing is performed based on the drawing data shown in FIG. 29 (a).

On the other hand, FIG. 30 (a) is a diagram in which another drawing material prepared for drawing a linear pattern having a width of 50 nm is also shown as a gray tone image. On the left side of the figure, as an example, it is shown in gray and gray. Adjust the pixel value corresponding to each density. In the case of this example, the pixel distance d is set to d = 10 nm, and a total of 6 pixels are arranged in the width and width direction of the linear pattern. A pixel value of 15 is assigned to four pixels arranged near the center of the linear pattern along the horizontal direction, and a pixel value of 7 is assigned to one pixel arranged on the left and one pixel arranged on the right.

FIG. 30 (b) is a diagram showing an irradiation intensity matrix D (x ', y') created based on the drawing data shown in FIG. 30 (a) as an image in gray tones. The irradiation intensity matrix is composed of a collection of arithmetic units arranged at a pitch g. This example is an example in which one pixel is vertically and horizontally divided into 10 parts as shown in FIG. 24 to define an arithmetic unit. The distance g between units is set to g = 1 nm. The smaller gray dots in the figure indicate the four representative units located in the center of each pixel, and a value corresponding to 1/4 of the pixel value is assigned as the unit value.

Fig. 30 (c) is a convolution integration operation performed on the irradiation intensity matrix D (x ', y') shown in Fig. 30 (b) and a specific point spread matrix psf (X, Y) (not shown). The obtained exposure intensity matrix v (x, y), that is, the image of the exposure intensity distribution represented as a gray tone. On the left side of the figure, unit values (calculated values of v (x, y)) corresponding to respective densities of gray tones are shown as examples. Similarly, the closer to black, the greater the exposure intensity (the amount of accumulated energy). The two white lines in the figure represent the contour lines of the linear pattern shown in FIG. 30 (a). As such, the results shown in FIG. 30 (c) also represent an appropriate exposure intensity distribution obtained when the exposure processing is performed based on the drawing data shown in FIG. 30 (a).

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 operation time until the result is greatly reduced.

Claims (26)

    A simulation method for obtaining exposure intensity distribution in a multi-beam electron beam drawing device is a simulation method for obtaining an exposure intensity distribution when a multi-beam electron beam drawing device is used to expose and draw a specific pattern on a formed layer, which is characterized by: It includes a process of performing convolutional integration of a function indicating the intensity of electron beam irradiation and a point spread function indicating the degree of influence of the reference point on the surroundings to a plurality of reference points defined in the electron beam irradiation area, whereby The total exposure intensity at each evaluation point is calculated, and as the above-mentioned point spread function, a function including an opening size parameter determined based on the opening size of the hole of the electron beam drawing device is used.         For example, the simulation method of the first scope of the patent application, in which the xy plane of the two-dimensional xy orthogonal coordinate system is defined as the irradiation surface of the electron beam, and the reference point T (x ', y') at the coordinate (x ', y') is defined. ) Affects the evaluation point V (x, y) located at the coordinate (x, y), by referring to the function D (x ', y) of the electron beam irradiation intensity with respect to the reference point T (x', y ') ') And the convolution integral in the x-axis direction and the y-axis direction of the point spread function psf (X, Y) defined as X = x'-x, Y = y'-y, and calculated as the point spread The function psf (X, Y) uses, in addition to the variables X and Y, a function including an opening size parameter B determined based on the opening size of the hole of the electron beam drawing device.         For example, the simulation method of item 2 of the patent application range, wherein as the point spread function psf (X, Y), a function that affects the width of the flat portion of the graph by the opening size parameter B is used.         For example, the simulation method of item 3 of the patent application range, wherein as the point spread function psf (X, Y), a function including a parameter σ that affects the inclination of the inclined portion of the graph in addition to the opening size parameter B is used.         For example, the simulation method of item 4 of the scope of patent application, wherein as the point spread function, the following function including the error function erf is used, that is, 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)).         For example, the simulation method of the fourth item of the patent application, wherein as the point spread function, the following function including the inverse trigonometric function arctan is used, that is, 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)).     For example, the simulation method of item 4 of the scope of patent application, wherein as the point spread function, the following functions including the error function erf, a specific constant C, the backscatter parameter β, and the proximity effect correction parameter η are used, that is, 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 )).     For example, if the simulation method of any of items 1 to 7 of the scope of patent application is applied, when the opening portion of the hole of the electron beam drawing device is circular, the diameter of the circle is set as the opening size of the hole. In the case of a square, the length of one side of the square is the opening size of the hole, and the value obtained by multiplying the opening size by the reduction magnification of the projection lens of the electron beam drawing device is used as the opening determined based on the opening size of the hole. Size parameters.         For example, the simulation method according to any one of claims 1 to 7 includes: a drawing data input stage, which is a computer input of data representing a pattern drawn by an electron beam drawing device, and is irradiated with each of the beams. The drawing data composed of the arrangement of pixels of the pixel value of the irradiation intensity at the position; the parameter setting stage is a computer setting of the opening size parameter determined based on the opening size of the hole of the electron beam drawing device; the matrix making stage for the calculation is The computer prepares two sets of empty operation matrices composed of a collection of operation units obtained by dividing each pixel of the drawing data into a plurality of parts, and assigns a basis to each unit of the first operation matrix. A specific unit value including the pixel value of the pixel of the unit is used to create an irradiation intensity matrix representing the planar distribution of the irradiation intensity of the electron beam. Each unit of the second calculation matrix is given a specific value including the above-mentioned opening size parameter. The point value corresponding to the point spread function is used to make a point spread that represents the planar distribution of the degree of influence represented by the above point spread function Matrix; and convolution stage, for which the computer system using the irradiation intensity of the dot matrix with the convolution integral of the diffusion matrix, and obtains the total exposure intensity at the respective evaluation points.         For example, in the simulation method of the 9th patent application range, when the irradiation intensity matrix is created in the calculation matrix production stage, only a specific representative unit among a plurality of calculation units included in the same pixel is assigned a pixel based on the pixel. A specific value determined by the value is used as a unit value, and a unit value of 0 is assigned to a non-representative unit other than the unit value.         For example, the simulation method of the tenth item of the patent application scope, wherein when the irradiation intensity matrix is created in the calculation matrix production stage, one or more of the calculation units included in the same pixel are located at the center of the pixel. The arithmetic unit is a representative unit, and the other arithmetic units are non-representative units.         For example, the simulation method of the 11th scope of the patent application, wherein when the irradiation intensity matrix is created in the calculation matrix production stage, each pixel of the drawing data is divided into an odd number of sections vertically and horizontally, and an operation located at the center of each pixel is calculated. A unit is used as a representative unit, and other arithmetic units are used as non-representative units. A pixel value of a pixel including the representative unit is assigned to the representative unit, and a unit value of 0 is assigned to the non-representative unit.         For example, the simulation method for the scope of patent application No. 11, in which when the irradiation intensity matrix is created in the calculation matrix production stage, each pixel of the drawing data is divided vertically and horizontally into even parts, and the four operations located at the center of each pixel are calculated. Use the unit as a representative unit, set the other arithmetic units as non-representative units, and assign a value of 1/4 of the pixel value of the pixel including the representative unit to the above-mentioned representative unit as the unit value. Assign a cell value of 0.         For example, in the simulation method of the scope of application for patent item 10, when the irradiation intensity matrix is created in the calculation matrix production stage, a plurality of calculation units included in the same pixel exist in a specific direction from the center of the pixel to a specific direction. A calculation unit for a position after a specific offset is set as a representative unit, and other calculation units are set as non-representative units. When a point spread matrix is created in the calculation matrix creation stage, the representation is made by The point-spreading matrix of the planar distribution of the degree of influence indicated by the point-spreading function is obtained by correcting the point-spreading function in the direction opposite to the specific direction by the above-mentioned offset.         For example, the simulation method of the ninth scope of the patent application, which is performed in the convolution operation stage: the first operation stage is to make a radiation intensity frequency matrix by performing a Fourier transform on the irradiation intensity matrix; the second operation stage, which is A point diffusion frequency matrix is produced by performing a Fourier transform on the point diffusion matrix. In the third operation stage, an exposure is set in which a product of a calculation unit corresponding to the irradiation intensity frequency matrix and the point diffusion frequency matrix is set as a unit value. Intensity frequency matrix; and a fourth operation stage, which performs an inverse Fourier transform on the above-mentioned exposure intensity frequency matrix to produce an exposure intensity matrix representing a planar distribution of the total exposure intensity at each evaluation point.         A program that causes a computer to execute a drawing data input stage, a parameter setting stage, a calculation matrix creation stage, and a convolution operation stage in the simulation method of any one of claims 9 to 15.         An exposure intensity distribution calculation device used in a multi-beam electron beam drawing device is an operator for obtaining an exposure intensity distribution when a multi-beam electron beam drawing device is used to expose and draw a specific pattern on a formed layer. : Drawing data input section, which inputs drawing data representing the pattern drawn by the electron beam drawing device, and drawing data composed of an array of pixels having pixel values indicating the irradiation intensity of each irradiation position of the beam; the parameter setting section, It sets the opening size parameter determined based on the opening size of the hole of the electron beam drawing device; the irradiation intensity matrix production section prepares a collection of arithmetic units obtained by dividing each pixel of the drawing data into a plurality of parts An empty calculation matrix composed of a volume and a specific unit value based on a pixel value of a pixel including the unit is assigned to each calculation unit, thereby creating an irradiation intensity matrix representing a planar distribution of the irradiation intensity of the electron beam; point spread The matrix creation unit is configured to add and include each of the operation units of the empty operation matrix. A unit point value corresponding to a specific point spread function of the opening size parameter, and a point spread matrix representing a planar distribution of the degree of influence represented by the point spread function is prepared; and a convolution operation execution unit that performs the use of the above-mentioned irradiation intensity matrix and The convolution integral of the above point spread matrix is used to obtain the total exposure intensity at each evaluation point.         For example, the exposure intensity distribution calculation device for item 17 of the scope of patent application, wherein the point spread matrix creation section uses a function of the width of the flat portion of the graph affected by the opening size parameter B as the point spread function.         For example, the exposure intensity distribution calculation device of the 18th scope of the application for a patent, wherein the point spread matrix creation unit uses a function including a parameter σ that affects the inclination of the slope portion of the graph in addition to the opening size parameter B as the point spread function.         For example, the exposure intensity distribution calculation device according to any one of claims 17 to 19, wherein the irradiation intensity matrix creation unit assigns a pixel based on the pixel to a specific representative unit among a plurality of calculation units included in the same pixel. A specific value determined by the value is used as a unit value, and a unit value of 0 is assigned to a non-representative unit other than the unit value.         For example, the exposure intensity distribution calculation device of the patent application No. 20, wherein the irradiation intensity matrix creation unit sets one or more calculation units located at the center of the pixel among a plurality of calculation units of the same pixel as a representative The unit is a non-representative unit.         For example, the exposure intensity distribution calculation device of the 21st patent application range, wherein the irradiation intensity matrix creation section divides each pixel of the drawing data into an odd number of sections vertically and horizontally, and sets a calculation unit located at the center of each pixel as a representative unit. , The other arithmetic unit is set as a non-representative unit, the pixel value of the pixel including the representative unit is assigned to the above-mentioned representative unit as a unit value, and the unit value 0 is assigned to the above-mentioned non-representative unit.         For example, the exposure intensity distribution calculation device for the scope of application for patent No. 21, wherein the irradiation intensity matrix creation section divides each pixel of the drawing data into even parts, vertically and horizontally, and sets the four arithmetic units located at the center of each pixel as the representative units. The other arithmetic units are set as non-representative units, and the above-mentioned representative units are assigned a value of 1/4 of the pixel value of the pixel including the representative units as unit values, and the non-representative units are assigned unit values of 0.         For example, the exposure intensity distribution calculation device of the patent application No. 20, wherein the irradiation intensity matrix creation unit shifts a plurality of calculation units included in the same pixel from a center of the pixel toward a specific direction by a specific offset. The arithmetic unit at the subsequent position is set as a representative unit, the other arithmetic units are set as non-representative units, and the point diffusion matrix creation unit creates a point diffusion matrix. The point diffusion matrix indicates that the The plane distribution of the degree of influence indicated by the point spread function after the direction is corrected by the above-mentioned offset.         For example, the exposure intensity distribution calculation device for item 17 of the scope of patent application, wherein the convolution operation section includes: a first operation section that generates a radiation intensity frequency matrix by Fourier transforming the irradiation intensity matrix; a second operation section that borrows A point diffusion frequency matrix is produced by performing a Fourier transform on the point diffusion matrix; a third operation unit creates an exposure intensity frequency in which a product of a calculation unit corresponding to the irradiation intensity frequency matrix and the point diffusion frequency matrix is used as a unit value A matrix; and a fourth arithmetic unit that generates an exposure intensity matrix representing a planar distribution of the total exposure intensity at each evaluation point by performing an inverse Fourier transform on the exposure intensity frequency matrix.         A program that enables a computer to function as an exposure intensity distribution computing device as in any one of claims 17 to 25 of the scope of patent application.