JP5495540B2 - Drawing method and drawing apparatus - Google Patents

Description

  The present invention relates to a drawing method and a drawing apparatus, and for example, relates to an electron beam drawing apparatus that obtains an irradiation amount that has been subjected to proximity effect correction and a drawing method thereof.

  Lithography technology, which is responsible for the progress of miniaturization of semiconductor devices, is an extremely important process for generating a pattern among semiconductor manufacturing processes. In recent years, with the high integration of LSI, circuit line widths required for semiconductor devices have been reduced year by year. In order to form a desired circuit pattern on these semiconductor devices, a highly accurate original pattern (also referred to as a reticle or a mask) is required. Here, the electron beam (electron beam) drawing technique has an essentially excellent resolution, and is used for producing a high-precision original pattern.

FIG. 22 is a conceptual diagram for explaining the operation of a conventional variable shaping type electron beam drawing apparatus.
The variable shaped electron beam (EB) drawing apparatus operates as follows. In the first aperture 410, a rectangular opening for forming the electron beam 330, for example, a rectangular opening 411 is formed. Further, the second aperture 420 is formed with a variable shaping opening 421 for shaping the electron beam 330 having passed through the opening 411 of the first aperture 410 into a desired rectangular shape. The electron beam 330 irradiated from the charged particle source 430 and passed through the opening 411 of the first aperture 410 is deflected by the deflector, passes through a part of the variable shaping opening 421 of the second aperture 420, and passes through a predetermined range. The sample 340 mounted on a stage that continuously moves in one direction (for example, the X direction) is irradiated. That is, the drawing area of the sample 340 mounted on the stage in which the rectangular shape that can pass through both the opening 411 of the first aperture 410 and the variable shaping opening 421 of the second aperture 420 is continuously moved in the X direction. Drawn on. A method of creating an arbitrary shape by passing through both the opening 411 and the variable forming opening 421 is referred to as a variable shaped beam (VSB) method.

  Here, when a sample such as a mask coated with a resist film is irradiated with an electron beam, there is a factor that fluctuates the dimension of the resist pattern, such as a proximity effect. The proximity effect is a phenomenon in which irradiated electrons are reflected by the mask and re-irradiate the resist, and the affected range is about a dozen μm. The proximity effect is a phenomenon in which the resist is re-irradiated. Conventionally, the irradiation dose is determined by predicting the dimension after irradiation using a threshold model using accumulated energy due to forward scattering and accumulated energy due to back scattering.

  FIG. 23 is a diagram showing a relationship between a conventional threshold model and pattern dimensions. When the accumulated energy distribution of the resist shown in FIG. 23B is given, the width between two points where the predetermined threshold and the energy distribution intersect is defined as the dimension of the resist pattern as shown in FIG. It was. Therefore, a threshold value with a desired dimension is determined, and an irradiation amount corresponding to the energy of the threshold value is determined. However, there is no guarantee that this threshold model is correct.

FIG. 24 is a diagram illustrating an example of a difference between the case where the irradiation dose is determined using a conventional threshold model and the optimum irradiation dose based on experiments. Here, the Pavcovic formula was used to determine the dose for correcting the proximity effect. Here, this formula is expressed by D (x) = const / (1 + ηU (x)). Here, D (x) is the optimum irradiation amount, η is a parameter indicating the magnitude of the proximity effect, and ηU (x) is the backscattering amount at the location x when all patterns are drawn with the irradiation amount of intensity 1. is there. As shown in FIG. 24, there is a slight difference between the case where the dose is determined by the conventional threshold model and the optimum dose from the experiment. In particular, with the recent miniaturization of patterns, such a shift becomes a big problem. In addition, research has been conducted on a technique for obtaining the dose for proximity effect correction. For example, a document has been proposed that proposes the idea that the shape of a resist pattern after development that determines the pattern dimensions is determined by the maximum value of accumulated energy due to forward scattering of charged particle beams and the value of accumulated energy due to backscattering. (For example, refer to Patent Document 1). This document describes a method for obtaining an optimum dose by a perturbation method starting from the Pavcovic formula. However, this method is not always satisfactory in terms of correction accuracy and calculation speed.
Japanese Patent No. 3455048

  As described above, in charged particle beam lithography represented by electron beam lithography, there are factors that cause the resist pattern dimensions to fluctuate, such as proximity effects, when a sample such as a mask coated with a resist film is irradiated with an electron beam. To do. Therefore, for example, when drawing a pattern that requires accuracy on the order of nanometers (nm), there arises a problem that an uneven distribution occurs in the finished dimension of the drawing pattern due to the influence of the “proximity effect”. . When correcting the proximity effect, even if the irradiation amount is determined by the conventional threshold model, a deviation exceeding the allowable limit occurs with the recent miniaturization of the pattern.

  Therefore, an object of the present invention is to provide a drawing method and a drawing apparatus capable of overcoming such problems and obtaining a dose with a proximity effect corrected with higher accuracy.

The drawing method of one embodiment of the present invention includes:
A step of solving the equation of accumulated energy due to backscattering of a charged particle beam , which is defined by a polynomial having a second-order or higher-order term of the irradiation amount, the irradiation amount being an unknown, and determining the irradiation amount ,
Irradiating a charged particle beam with the obtained irradiation amount and drawing a pattern on the sample;
It is provided with.

  As described in Patent Document 1, the shape of a resist pattern after development for determining a pattern dimension is determined by the maximum value of accumulated energy due to forward scattering of a charged particle beam and the value of accumulated energy due to backscattering. In the present invention, using this concept, the stored energy by backscattering defined by a polynomial having a second-order or higher-order term of irradiation dose using the stored energy function by forward scattering and the stored energy function by backscattering. The equation of By solving the equation of accumulated energy due to such backscattering, it is possible to obtain the irradiation dose with more optimal proximity effect correction.

In addition, a correlation between the pattern density and the dose is obtained in advance by experiments,
It is preferable that the parameters of each term are defined so that the above-described equation is in accordance with the above-described correlation.

  In addition, it is preferable that the irradiation amount at which a desired design dimension is obtained when the evaluation pattern in which figures are repeatedly arranged at a predetermined pattern density is drawn with variable irradiation amounts is correlated with the predetermined pattern density. is there.

A drawing method according to another aspect of the present invention includes:
A step of solving the nonlinear equation related to the dose, and determining the dose by setting the dose as an unknown,
Irradiating the charged particle beam with the determined irradiation amount and drawing a pattern on the sample;
It is characterized by having

The drawing device of one embodiment of the present invention includes:
An equation in which the parameters of each term are defined so as to follow the correlation between the pattern density and the dose determined in advance by experiments, and is a polynomial having a second-order or higher-order term of the dose with the dose as an unknown. is defined, a calculation unit for determining the amount of irradiation by solving the equation of stored energy by nonlinear, backscattered charged particle beam with respect to dose,
A drawing unit that irradiates a charged particle beam with the obtained irradiation amount and draws a pattern on the sample;
Characterized by comprising a.

A drawing method according to another aspect of the present invention includes:
A correlation equation between the pattern density and the dose is obtained in advance, and the pattern density in the correlation formula is replaced with the amount obtained by dividing the accumulated energy due to the standardized backscattering of the charged particle beam by the dose. Solving the nonlinear equation for determining the dose,
Irradiating a charged particle beam with the obtained irradiation amount and drawing a pattern on the sample;
It is provided with.

  In addition, it is preferable that the parameters of each term be defined so that the nonlinear equation follows the correlation indicated by the correlation equation.

  In addition, when an evaluation pattern in which figures are repeatedly arranged at a predetermined pattern density is drawn with variable doses, the dose at which a desired design dimension is obtained is correlated with a predetermined pattern density. The relationship is preferred.

A drawing apparatus according to another aspect of the present invention includes:
A correlation equation between the pattern density and the dose is obtained in advance, and the pattern density in the correlation formula is replaced with the amount obtained by dividing the accumulated energy due to the standardized backscattering of the charged particle beam by the dose. An arithmetic unit that solves the nonlinear equation relating to the amount of irradiation, and
A drawing unit that irradiates a charged particle beam with the obtained irradiation amount and draws a pattern on the sample;
It is provided with.

  According to the present invention, it is possible to perform drawing with a dose with a proximity effect corrected with higher accuracy. As a result, a highly accurate pattern dimension can be obtained.

  Hereinafter, in each embodiment, a configuration using an electron beam will be described as an example of a charged particle beam. However, the charged particle beam is not limited to an electron beam, and may be a beam using other charged particles such as an ion beam.

Embodiment 1 FIG.
FIG. 1 is a diagram illustrating a main part of a flowchart of a drawing method according to the first embodiment.
In FIG. 1, the drawing apparatus 100 includes a drawing unit 150 and a control unit 160. The drawing apparatus 100 is an example of a charged particle beam drawing apparatus and an example of an electron beam drawing apparatus. The drawing unit 150 includes an electron column 102 and a drawing chamber 103. In the electron column 102, an electron gun 201, a blanking (BLK) deflector 212, a blanking (BLK) aperture 214, an illumination lens 202, a first aperture 203, a projection lens 204, a deflector 205, a second An aperture 206, an objective lens 207, and a deflector 208 are disposed. An XY stage 105 is disposed in the drawing chamber 103. On the XY stage 105, a sample 101 to be drawn is arranged. The sample 101 includes a mask substrate. For example, mask blanks in which a pattern is not yet formed are included. The sample 101 has a surface coated with a resist that is exposed to an electron beam. The control unit 160 includes a control computer unit 110, a deflection control circuit 120, and magnetic disk devices 140 and 142. The control computer unit 110, the deflection control circuit 120, and the magnetic disk devices 140 and 142 are connected to each other via a bus (not shown). In the control computer unit 110, an irradiation amount calculation unit 112, a transfer unit 114, a drawing data processing unit 116, buffer memories 118 and 119, and a memory 111 are arranged. The processing contents of the irradiation amount calculation unit 112, the transfer unit 114, and the drawing data processing unit 116 may be executed by a computer by software. Or you may carry out by the hardware by an electric circuit. Or you may make it implement by the combination of the hardware and software by an electrical circuit. Alternatively, a combination of such hardware and firmware may be used. Information input into the control computer unit 110 or information during and after the arithmetic processing is stored in the memory 111 each time. In FIG. 1, constituent parts necessary for explaining the first embodiment are shown. Needless to say, the drawing apparatus 100 may normally include other necessary configurations.

First, the idea proposed in Patent Document 1 described above will be described. The idea is that the shape of the resist pattern after development that determines the pattern dimension is determined by the maximum value of accumulated energy due to forward scattering of the charged particle beam and the value of accumulated energy due to back scattering. This will be described below.
FIG. 2 is a diagram showing an example of the distribution of forward scattered energy and backward scattered energy by the electron beam accumulated in the resist in the first embodiment. In FIG. 2, the vertical axis indicates the energy E accumulated in the resist, and the horizontal axis indicates the position x. Here, x means a vector and indicates the coordinates (x, y) of the position x (the same applies hereinafter). In addition, when D (x) is an irradiation amount, in FIG. 2, the maximum value 10 (top position portion) of the forward scattered energy distribution 12 is indicated by a function kD (x). In addition, the maximum value 20 (top position portion) of the backscattering energy distribution 22 that changes substantially horizontally is indicated by a function kB (x). k is a coefficient for converting the irradiation amount into energy. FIG. 2 shows an energy distribution in a 1: 1 line and space pattern as an example.

  FIG. 3 is a cross-sectional view showing an example of how the development of the resist on the sample 101 in the first embodiment proceeds. In FIG. 3, the resist on the substrate is shown. Therefore, the bottom surface becomes the substrate surface. FIG. 3A shows a state where development has not progressed yet. Development of the resist proceeds from the state shown in FIG. 3A in the order of FIG. 3B, FIG. 3C, and FIG. And the dimension between resists in the position of the bottom face shown in FIG.3 (d) used as the contact surface of a resist and a board | substrate becomes a pattern dimension.

  FIG. 4 is a diagram showing another example of the distribution of the forward scattered energy and the back scattered energy by the electron beam accumulated in the resist in the first embodiment. FIG. 4A shows the energy distribution when there is no other pattern around the single pattern. The forward scattered energy distribution 12 is the same as in FIG. Further, with respect to the backscattering energy distribution 22, it is assumed that the maximum value 20 becomes constant by additionally irradiating the periphery. FIG. 4B shows the energy distribution when there is no other pattern around the wide single pattern. The forward scattered energy distribution 12 is the same as in FIG. Further, with respect to the backscattering energy distribution 22, it is assumed that the maximum value 20 becomes constant by additionally irradiating the periphery. 4A and 4B, the resist development proceeds in the same manner as in FIG. 3, as in FIG.

Here, in FIG. 2 to FIG. 4, the condition that the forward scattering energy distribution 12 and the spread of the electron beam 200 do not reach other patterns with the same film thickness and the same electron beam 200 using the same resist material. Below, the contact position between the resist and the substrate and the shape of the resist after development are determined by the maximum value 10 and the maximum value 20. In other words, if the maximum value 10 and the maximum value 20 are determined, the inclination of the resist after development is determined from the beam profile and the resist thickness. As a result, the resist shape is determined. As a result, the dimension of the resist pattern is determined.
The above is the idea proposed in Patent Document 1. The method of this embodiment that realizes this concept will be described below.
In the first embodiment, irradiation with the proximity effect corrected using a function kD (x) indicating the maximum value 10 of the forward scattering energy distribution 12 and a function kB (x) indicating the maximum value 20 of the backscattering energy distribution 22. Create an equation for the quantity D (x).

The accumulated amount of forward scattered energy can be represented by the function kD (x) described above. Further, the function kB (x) described above is defined by the following equation (1) using the proximity effect correction coefficient η and the function g (x) for the accumulated amount of backscattered energy. For example, a Gaussian function is preferably used as the function g (x).
(1) kB (x) = kη∫D (x ′) g (xx ′) dx ′
Here, the integration is performed on the figure of the LSI pattern. The same applies hereinafter unless otherwise specified.

In such a case, the pattern dimension G (or G ′) is a function G (kD (x) + kB (x), kB (x)) or GB with the function kD (x) and the function kB (x) as arguments. '(KD (x), kB (x)). Therefore, the equation of the dose D (x) with the proximity effect corrected is defined by the following formula (2-1) or formula (2-2) using the constant C.
(2-1) G (kD (x) + kB (x) = C
(2-2) G ′ (kD (x), kB (x)) = C

Since the expression (2-1) and the expression (2-2) differ only in the way of expression, they will be described below using the expression (2-2). By converting the equation (2-2), it can be defined as the equation (3).
(3) B (x) = G ′ (C, kD (x))

Further, the threshold model described above, a constant value the following equation (4) using the E ₀ is satisfied.
(4) (1/2) D (x) + η∫D (x ′) g (xx ′) dx ′ = E ₀

In Equation (4), the first term represents the forward scattering energy, and the second term represents the backscattering energy. Using the relationship between the coefficient m and the expression (3), the expression (4) in the threshold model can be expressed by the following expression (5-1). Further, when equation (5-1) is modified, it can be expressed by equation (5-2).
(5-1) mkB (x) = − kD (x) + C
(5-2) mB (x) = − D (x) + C ′

Such a threshold model is not necessarily accurate as described above, but is close to a correct value although there is an error. Therefore, the following equation (6) can be derived by assuming that the more accurate relationship is slightly different from equation (5-2). Here, C ′ is newly set as C. The absolute value | δ | of δ is set to a value sufficiently smaller than 1 (| δ | << 1).
(6) mB (x) = {− D (x) + C} ^{(1 + δ)}

Equation (6) can be expanded to the first order with respect to δ and transformed into the following equation (7).
(7) mB (x) = {− D (x) + C} ^{(1 + δ)}
= {-D (x) + C} {-D (x) + C} ^δ
= {-D (x) + C} [1 + δ {-D (x) + C}]
= {− D (x) + C} + δ {−D (x) + C} ²
= ΔD (x) ² − {2Cδ + 1} D (x) + {C + C ² δ}

When equation (7) is modified using equation (1) described above, it can be expressed by equation (8-1) below.
(8-1) mη∫D (x ′) g (xx ′) dx ′
= ΔD (x) ² − {2Cδ + 1} D (x) + {C + C ² δ}
Alternatively, by generalizing equation (8-1), equation (7) can be expressed as equation (8-2).
(8-2) η∫D (x ′) g (xx ′) dx ′
= ΑD (x) ² −βD (x) + γ
Alternatively, in the case of a pattern configuration in which the figure dimension l (for example, 200 nm) is sufficiently smaller (l << σ) than the backscattering spread σ (for example, 10 μm) and a uniform pattern is repeated, the pattern density Using ρ, the accumulated amount of backscattered energy B (x) = ηρD (x) can be defined. In such a case, the irradiation amount becomes a constant value D because the pattern repeats uniformly. For example, this is true in a 1: 1 line and space pattern. Therefore, in such a case, equation (8-2) can be modified and equation (7) can be expressed as equation (8-3).
(8-3) ηρD = αD ² −βD + γ

  As described above, it is defined by a polynomial having a second or higher order term of the dose D (x) as shown in the equation (8-1), the equation (8-2), or the equation (8-3). Thus, an equation of stored energy due to backscattering of the electron beam 200 can be obtained. In other words, as shown in the equation (8-1), the equation (8-2), or the equation (8-3), a nonlinear equation related to the dose D (x) can be obtained.

FIG. 5 is a diagram showing an example of a difference between the case where the dose is determined by the equation in Embodiment 1, the case where the dose is determined by the conventional threshold model, and the optimum dose by experiment. In FIG. 5, the vertical axis represents the dose D, and the horizontal axis represents the pattern density ρ. In FIG. 5, a desired design dimension was obtained when an evaluation pattern (for example, a 1: 1 line and space pattern) in which figures were repeatedly arranged at a predetermined pattern density ρ was drawn with variable dose D. The dose D is correlated with the predetermined pattern density ρ. In this way, a correlation between the pattern density ρ and the dose D at which a desired design dimension is obtained is obtained in advance by experiments. FIG. 5 shows the result of fitting to the experimental result by the Pavcovic formula (D = 1 / (1 + ηρ)), which is a conventional threshold model. Here, in the first embodiment, the equation (8-3) is first defined as the following equation (9-1) so that it can be easily compared with the conventional model. Moreover, a solution (9-3) can be obtained by transforming the equation (9-1) into the equation (9-2).
(9-1) ηρD = aD ² −D / 2 + 1
(9-2) aD ² − (1/2 + ηρ) D + 1 = 0
(9-3) D = [1/2 + ηρ−√ {(1/2 + ηρ) ² −4a}] / (2a)

  In the equation (9-1), for easy comparison with the conventional model, by setting the coefficient a to 0, the Pavcovic formula (D = 1 / (1 + ηρ)) used in the conventional threshold model and The coefficient of each term was set so that it might correspond. Then, the equation (9-3) is fitted to the experimental result shown in FIG. 5 to obtain the parameters η and a. Thus, the correlation between the pattern density ρ and the dose D is obtained in advance by experiment, and the equation shown in the equation (9-1), the equation (9-2), or the equation (9-3) is the correlation. The parameters of each term are defined along As a result, it has been difficult to match the experimental result with the conventional threshold model, but as shown in FIG. For example, in FIG. 5, by setting η = 0.8 and a = 0.02, the experimental result can be substantially matched.

This is because, as shown in Equation (9-1), the accumulated energy due to the backscattering amount is approximated by a polynomial having a second-order or higher term of the irradiation amount D (nonlinear polynomial of the irradiation amount D) and an equation that connects. is there. Conventionally, as indicated by Pubkovich's formula, it has been defined by a polynomial with a first-order term of the dose D without a second-order or higher term of the dose D. For this reason, it has been difficult to match the experimental results. However, in the first embodiment, as shown in the equation (9-1), the equation (9-2), or the equation (9-3), it is approximated by a polynomial having a quadratic term of the dose D. It can be adjusted to the experimental results with high accuracy.
Going back further, the reason for this success is that the original equation (in the present embodiment, considering that B (x) = ∫D (x ′) g (xx ′) dx ′) This is because (6) was a nonlinear equation with respect to the dose D (x). That is, for D (x), the second order term is included in addition to the 0th order and the first order. On the other hand, the conventional method is a linear equation with respect to D (x) as shown in Equation (4). That is, for D (x), there are only 0th order and 1st order, and there is no second order or higher.

  Here, for ease of comparison with the conventional model, an equation using two parameters η and a is used as an example. However, the equation is not limited to this, and the equations (8-1) and (8-2) are used. Needless to say, the parameters of each term shown in the equation (8-3) may be defined so as to follow the above-described correlation.

  FIG. 6 is a graph showing the relationship among the pattern size, the proximity effect correction coefficient, and the pattern density in the first embodiment. In FIG. 6, the vertical axis represents the pattern dimension L, and the horizontal axis represents the proximity effect correction coefficient η. FIG. 6 shows how the pattern dimensions change at each pattern density ρ while changing the proximity effect correction coefficient η. In FIG. 6, the pattern density ρ = 0 (0%), 0.5 (50%), and 1 (100%). In the conventional threshold model, it is difficult to cross three pattern density ρ lines at one point. For example, in order to match the line A with the pattern density ρ = 0 and the line B with the pattern density ρ = 0.5, it is necessary that A = B. In order to match the line B with the pattern density ρ = 0.5 and the line C with the pattern density ρ = 1, it is necessary that B = C. Therefore, two parameters (η and a) are obtained from these two equations. Therefore, in most cases, a ≠ 0 should be the case. However, in the conventional method, since one parameter η is obtained with a = 0, only one of A = B or B = C is established. For this reason, the optimum proximity effect correction coefficient η is not uniquely determined, and as a result, a deviation from the experimental result occurs as shown in FIG. On the other hand, in the first embodiment, since there are two parameters η and a, it is possible to intersect three lines of pattern density ρ at one point. Therefore, the optimum proximity effect correction coefficient η can be uniquely determined, and as a result, it can be substantially matched with the experimental result as shown in FIG.

As described above, first, the parameter of each term is in accordance with the above-described correlation, using the equation of accumulated energy due to the backscattering of the electron beam 200 shown in Equation (8-3), from the correlation, The parameters η, α, β, γ are obtained. Here, as described above, the equation (8-3) is such that the figure dimension l (for example, 200 nm) is sufficiently smaller than the backscattering spread σ (for example, 10 μm) (l << σ). This is also the case with a pattern configuration that repeats a uniform pattern. However, the actual drawing pattern is not limited to this case. Therefore, first, a solution of Expression (8-2), which is a general expression not limited to this case, is obtained. The solution of equation (8-2) can be obtained by performing iteration using the following equations (10-1) and (10-2).
(10-1) D (x) = lim D _n (x) (where n → ∞)
(10-2) D _{n + 1} (x) = D _n (x) + dn _{+ 1} (x)

First, the first term D ₀ (x) is obtained. n indicates the number of repetitions (n ≧ 0). Expression (8-2) is transformed into Expression (11) below.
^{_{(11) αD 0 (x)}} 2 -βD 0 (x)
−ηD ₀ (x ′) ∫g (xx ′) dx ′ + γ = 0

Here, a is the following formula (12-1), b is the following formula (12-2), and c is the following formula (12-3).
(12-1) a = α
(12-2) b = β + ηU (x)
(12-3) c = γ
Here, the function U (x) is represented by the following expression (13).
(13) U (x) = ∫g (xx ′) dx ′
Equation 11 can be solved for D ₀ (x) because it is a quadratic equation with a, b, and c as coefficients. Although there are two solutions, a solution that becomes infinite at the limit where a is zero is physically meaningless, so a solution that does not become zero at that limit is taken. Then, the first term D ₀ (x) is obtained by the following equation (14-1) when b ≧ 0 and by the following equation (14-2) when b <0.
(14-1) D ₀ (x) = {b−√ (b ² −4ac)} / (2a)
(14-2) D ₀ (x) = {b + √ (b ² -4ac)} / (2a)

Then, consider the second and subsequent times. It is assumed that the correction calculation amount D _n (x) is known up to the n-th time. As described above, D _{n + 1} (x) is expressed as equation (10-2), and when this is substituted into D (x) in equation (8-2), the following equation is obtained as an equation for the unknown quantity d _n (x): (15) is obtained.
_{(15) 0 = αD n (} x) 2 -βD n (x)
−η∫D _n (x ′) g (xx ′) dx ′
+ Αd _{n + 1} (x) ² + 2αD _n (x) d _{n + 1} (x) −βd _n (x)
−η {∫g (xx ′) dx ′} d _{n + 1} (x) + γ

Here, a is the following formula (16-1), b is the following formula (16-2), and c is the following formula (16-3).
(16-1) a = α
(16-2) b = -2αD _n (x) + β + ηU (x)
_{(16-3) c = αD n (} x) 2 -βD n (x) -ηU (x) + γ
Here, the function U (x) is defined by the above equation (13), and V _n (x) is defined by the following equation (17).
(17) V _n (x) = ∫D _n (x ′) g (xx ′) dx ′
Equation (15) can be solved for d _{n + 1} (x) because it is a quadratic equation with coefficients a, b, and c. Although there are two solutions, since a solution that becomes infinite at the limit where a is zero is physically meaningless, a solution that does not become zero at that limit is taken. Then, d _{n + 1} (x) is obtained by the following equation (18-1) when b ≧ 0, and by the following equation (18-2) when b <0.
(18-1) d _{n + 1} (x) = {b−√ (b ² −4ac)} / (2a)
(18-2) d _{n + 1} (x) = {b + √ (b ² -4ac)} / (2a)

There was thus _determined, determine the _D 1 (x) with _D 0 (x) and _d 1 (x). _Then, a _D 2 (x) with _D 1 (x) and _d 2 (x). In this way, D _{n + 1} (x) may be obtained sequentially using D _n (x) and d _{n + 1} (x). In obtaining the irradiation amount D _{n + 1} (x), it is preferable that the repetition number n is large, but D ₂ (x) can ensure sufficient accuracy. The number of repetitions may be adjusted according to the target accuracy.

The drawing apparatus 100 obtains the dose D _{n + 1} (x) with the proximity effect corrected by solving the general formula (8-2). Then, the electron beam 200 is irradiated with the irradiation amount D _{n + 1} (x) to draw a pattern on the sample 101. First, the drawing apparatus 100 inputs drawing data including pattern data from the outside of the apparatus and stores it in the magnetic disk device 140.

FIG. 7 is a diagram illustrating a main part of a flowchart of the drawing method according to the first embodiment.
In FIG. 7, the electron beam drawing method includes a dose calculation step (S100) for obtaining an optimum dose corrected for the proximity effect, a data transfer step (S116), a drawing data processing step (S120), and a drawing step. A series of steps (S122) is performed. The dose calculation step (S100) includes, as its internal steps, a pattern density ρ (x) calculation step (S102), a function U (x) calculation step (S103), and a dose D ₀ (x) calculation step (S104). ), A function V _{n + 1} (x) calculation step (S106), a function d _{n + 1} (x) calculation step (S108), a dose D _{n + 1} (x) calculation step (S110), a determination step (S112), A series of steps called a feedback step (S114) is performed.

  FIG. 8 is a conceptual diagram for explaining the parallel processing method according to the first embodiment. The drawing area of the sample 101 is virtually divided into strips with a width that can be deflected in the y direction, for example. Then, drawing is performed in order for each virtually divided stripe region 30. Therefore, each stripe region 30 becomes a drawing unit region. For example, in the example of FIG. 8, the (l-2) th stripe region 30 is drawn, and then the (l-1) th stripe region 30 is drawn. Next, the (l) th stripe region 30 is drawn, and then the (l + 1) th stripe region 30 is drawn. In this way, each stripe region 30 is drawn in order.

Here, in order to perform the drawing step (S122), as the premise, in the drawing data processing step (S120), the dose D _{n + 1} (x) is input and set to the dose D _{n + 1} (x). Shot data must be generated. In order to perform the drawing data processing step (S120), it is necessary to obtain an optimum dose D _{n + 1} (x) in which the proximity effect is corrected in the dose calculation step (S100). . Therefore, the drawing operation stops if another process is waiting for the process until one of the processes is completed. In the first embodiment, these processes are performed in parallel. Specifically, pipeline processing is performed. That is, when performing a drawing process (S122) on a certain stripe area 30, simultaneously, a data transfer process (S116) and a drawing data processing process (S120) are performed on one previous stripe area 30, and at the same time, Further, an irradiation amount calculation step (S100) is performed on the one stripe region 30 ahead. By performing the pipeline processing in this way, it is possible to prevent the drawing operation from stopping in order to wait for the processing of another process. As a result, the drawing time can be shortened and the throughput can be improved.

FIG. 9 is a conceptual diagram showing a range of a region for calculating proximity effect correction in the first embodiment. In FIG. 9, for example, in calculating the irradiation amount D _{n + 1} (x) for the (l) -th stripe region 30, the proximity effect can be influenced by other stripe regions 30, so Some are taken into account when calculating. Assuming that the influence range of the proximity effect is σ, for example, it may be included in the calculation region 60 by 6σ on one side. In calculating the correction amount, the optimum irradiation amount is calculated for the regions of both sides 6σ, and then the optimum irradiation amount for the target stripe region is used as a solution. That is, the dose obtained for each 6σ region on both sides is not used.

FIG. 10 is a diagram showing mesh regions in the first embodiment. In correcting the proximity effect, first, the drawing area of the sample 101 is virtually divided into a mesh shape with a predetermined mesh size Δ. FIG. 10 shows a part of the stripe region 32 divided into meshes. Then, for each mesh region 34, a dose D _{n + 1} (x) with the proximity effect corrected is obtained. The size of the mesh region 34 (small region) is preferably set sufficiently smaller than the backscattering spread σb. For example, about 1/10 of the backscattering spread σb is preferable. For example, when σb = 10 μm, it is preferable to set Δ = 1 μm.

In S (step) 100, as the dose calculation step, the dose calculation unit 112 reads the pattern data from the magnetic disk device 140, solves the equation shown in the equation (8-2) for each mesh region 34, and outputs each pattern data. The dose D _{n + 1} (x) in the mesh region 34 is obtained. The equation shown in Expression (8-2) is an equation of accumulated energy due to backscattering of the electron beam 200, which is defined by a polynomial having a second-order or higher-order term of the irradiation amount as described above. In obtaining the dose D _{n + 1} (x), the following internal processes are performed.

  In S <b> 102, as a pattern density ρ (x) calculation step, the dose calculation unit 112 calculates the area of the internal figure for each mesh region 34 and calculates the pattern density ρ (x) of each mesh region 34.

In S <b> 103, as a function U (x) calculation process, the dose calculation unit 112 calculates a function U (x) for each mesh region 34. The function U (x) is defined by the following equation (19-1). And the calculation of Formula (19-1) is specifically calculated using the following Formula (19-2).
(19-1) U (x) = ∫g (xx ′) dx ′
(19-2) U (x _i ) = ΣΣg (x _i -x _j ) ρ (x _j ) Δ ²

In S104, as the dose D ₀ (x) calculation step, the dose calculation unit 112 uses the function U (x) obtained by the equation (19-2) for each mesh region 34 to set the dose D ₀ ( x) is calculated. The dose D ₀ (x) can be obtained from the above-described formula (14-1) or formula (14-2).

In S106, as the function V _{n + 1} (x) calculation step, the dose calculation unit 112 calculates the function V _{n + 1} (x) using the dose D _n (x) obtained so far for each mesh region 34. To do. The function V _{n + 1} (x) is defined by the following equation (20-1). And the calculation of Formula (20-1) is specifically calculated using the following Formula (20-2). Here, first, the function V ₁ (x) is calculated.
(20-1) V _{n + 1} (x) = ∫g (xx ′) D _n (x) dx ′
(20-2) V _{n + 1} (x _i ) = ΣΣg (x _i −x _j ) D _n (x _i ) ρ (x _j ) Δ ²

In the above-described formula (19-2) and the formula (20-2), _{x i} denotes the central coordinates of the i-th small region. For example, ρ (x _i ) indicates the pattern density in the i-th small region.

In S108, as the function d _{n + 1} (x) calculation step, the irradiation amount calculation unit 112 performs the function U (x) and (ii) irradiation amount obtained by Expression (19-2) for each mesh region 34. The function d _{n + 1} (x) is calculated using D _n (x) and the function V _{n + 1} (x) obtained by the equation (20-2). The function d _{n + 1} (x) can be obtained from the above equation (18-1) or equation (18-2). Here, first, the function d ₁ (x) is calculated.

In S110, as the dose D _{n + 1} (x) calculation step, the dose calculation unit 112 uses the obtained dose D _n (x) and the function d _{n + 1} (x) for each mesh region 34 to calculate the dose. D _{n + 1} (x) is calculated. The dose D _{n + 1} (x) can be obtained from the above-described equation (10-2). Here, first, the dose D ₁ (x) is calculated.

In S112, as a determination step, the dose calculation unit 112 determines whether n is a predetermined number k for each mesh region 34. If n = k is not satisfied, the process proceeds to the feedback step (S114). If n = k, the dose D _{n + 1} (x) is output to the buffer memory 118 or the buffer memory 119.

  In S <b> 114, as a feedback process, the dose calculation unit 112 adds 1 to n for each mesh region 34. Then, the feedback is made to S106.

As described above, the function V _{n + 1} (x) calculation step (S106) to the feedback step (S116) are repeated until n = k. Then, the dose calculation unit 112 outputs the dose D _{n + 1} (x) in which n has reached the predetermined number k for each mesh region 34 to the buffer memory 118 or the buffer memory 119. Such output is alternately output to the buffer memory 118 or the buffer memory 119 for each stripe region 30. That is, when the dose D _{n + 1} (x) for the (l) th stripe region 30 is temporarily stored in the buffer memory 118, the dose D _{n + 1} (x for the (l + 1) th stripe region 30 is stored. ) Is temporarily stored in the buffer memory 119.

In S <b _> 116, as a data transfer process, the transfer unit 114 reads information on the irradiation amount D _{n + 1} (x) for one stripe region 30 stored from the buffer memory 118 or the buffer memory 119, and sends it to the drawing data processing unit 116. Forward. That is, information on the irradiation amount D _{n + 1} (x) for one previous stripe region 30 that has already been calculated by the irradiation amount calculation unit 112 is read and transferred.

In S120, as a drawing data processing step, the drawing data processing unit 116 reads pattern data from the magnetic disk device 140, performs a plurality of stages of data conversion processing, and generates shot data that can be used for the drawing operation. The drawing data processing unit 116 reads from the magnetic disk device 140 the pattern data for the previous stripe region 30 that has already been calculated by the dose calculation unit 112, and generates shot data for the stripe region 30. The shot data also includes information on the dose D _{n + 1} (x) for each mesh region 34. Shot data is stored in the magnetic disk device 142. The deflection control circuit 120 reads shot data for one stripe region 30 from the magnetic disk device 142 and outputs a deflection voltage to each deflector along the shot data.

In S122, as a drawing process, the drawing unit 150 draws a pattern on the sample 101 by irradiating the corresponding position of the sample 101 with the obtained irradiation amount D _{n + 1} (x). The operation of the drawing unit 150 will be described below.

  An electron beam 200 is emitted (irradiated) from the electron gun 201. The electron beam 200 emitted from the electron gun 201 illuminates the entire first aperture 203 having a rectangular hole, for example, a rectangular hole, by the illumination lens 202. Here, the electron beam 200 is first formed into a rectangle, for example, a rectangle. Then, the electron beam 200 of the first aperture image that has passed through the first aperture 203 is projected onto the second aperture 206 by the projection lens 204. The position of the first aperture image on the second aperture 206 is deflection-controlled by the deflector 205, and the beam shape and size can be changed. As a result, the electron beam 200 is shaped. Then, the electron beam 200 of the second aperture image that has passed through the second aperture 206 is focused by the objective lens 207 and deflected by the deflector 208. As a result, the desired position of the sample 101 on the continuously moving XY stage 105 is irradiated.

  Here, when the electron beam 200 on the sample 101 reaches the irradiation time t in which a desired irradiation amount is incident on the sample 101, blanking is performed as follows. That is, in order to prevent the sample 101 from being irradiated with the electron beam 200 more than necessary, for example, the electron beam 200 is deflected by the electrostatic BLK deflector 212 and the electron beam 200 is cut by the BLK aperture 214. This prevents the electron beam 200 from reaching the surface of the sample 101. The deflection voltage of the BLK deflector 212 is controlled by the deflection control circuit 120.

  When the beam is ON (blanking OFF), the electron beam 200 emitted from the electron gun 201 follows the trajectory indicated by the solid line in FIG. On the other hand, in the case of beam OFF (blanking ON), the electron beam 200 emitted from the electron gun 201 travels on the trajectory indicated by the dotted line in FIG. 1 before the BLK aperture 214. In addition, the inside of the electron column 102 and the drawing chamber 103 are evacuated by a vacuum pump (not shown) to form a vacuum atmosphere in which the pressure is lower than the atmospheric pressure. From the start of passing through the BLK aperture 214 due to blanking ON until the blocking by blanking OFF, the electron beam 200 for one shot is obtained.

FIG. 11 is a conceptual diagram for explaining a method of interpolation of dose in the first embodiment. When the center of the shot is at the center 42 of the mesh region 34, the internal figure 40 may be drawn by irradiating the electron beam 200 with the obtained dose D _{n + 1} (x) for the mesh region 34. However, as shown in FIG. 11, when the center of the shot is at a position 52 deviated from the center of the mesh region 34, it is preferable to perform linear interpolation using the irradiation amount D _{n + 1} (x) for the surrounding mesh region 34. is there. For example, when it is on the boundary between the two mesh regions 8 and 9, D _{n + 1} (x) at such a position is ½ of the sum of the doses D _{n + 1} (x) for both mesh regions 8 and 9 This is preferable. The figure 50 may be drawn using the linearly interpolated dose D _{n + 1} (x).

Embodiment 2. FIG.
In the first embodiment, the optimum irradiation amount is obtained by solving the equation of the backscattering energy B (x). However, the present invention is not limited to this. In the second embodiment, a correlation equation between the dose and the pattern density is obtained in advance, and a nonlinear equation that can be obtained by replacing the pattern density of the correlation formula with an amount obtained by dividing the backscattering energy B (x) by the dose. A method for obtaining the optimum dose by solving will be described. The configuration of the drawing apparatus in the second embodiment is the same as that in FIG. The contents other than those described below are the same as those in the first embodiment.

When the figure size is sufficiently smaller than the backscattering spread σ and the pattern density ρ is constant, the optimum dose D is obtained from the experiment, and the dose D and the pattern density ρ shown in the following equation (21) are obtained. It is assumed that the correlation function p ^* is obtained from an experiment.
(21) D = p ^* (ρ, Δl)

Here, Δl is a difference between the design dimension and the developed resist dimension (actually obtained dimension including an error due to the proximity effect). When the pattern density ρ is constant, the pattern density ρ can be expressed by the following equation (22).
(22) ρ = B ^* (x) / D

Here, D is an irradiation amount, and B ^* (x) is a standardized accumulated energy of backscattering and is expressed by the following equation (23).
(23) B ^* (x) = ∫D (x ′) g (xx ′) dx ′
Here, the integration is performed on the figure of the LSI pattern. The same applies hereinafter unless otherwise specified.
In the following discussion, it is assumed that the function g (x) satisfies the following condition (formula (24)).
(24) ∫g (x) dx = 1
Here, the integration region is the entire drawing region, and x and y are set to −∞ to + ∞, respectively.

Here, when the figure size as described above is sufficiently smaller than the backscattering spread σ and the pattern density ρ is constant, the standardized accumulated backscattering energy B ^* (x) and the dose D Is a constant value and does not depend on location. In this case, when the pattern density ρ is replaced by the amount obtained by dividing the normalized backscattering accumulated energy B ^* (x) by the irradiation amount D using the equation (22), the equation (21) is expressed by the following equation: It can be modified as shown in (25).
(25) D = p ^* (B ^* (x) / D, Δl)

Expression (25) is established when the pattern density ρ is constant. However, it is unnatural that Formula (23) is considered to hold only when the pattern density ρ is constant, and it is natural that it is considered to hold even in other cases. Therefore, it is assumed that Equation (25) holds even in a general case where the pattern density ρ is not constant. Thereby, the proximity effect correction equation shown in the following equation (24) is obtained.
(26) D (x) = p ^* (B ^* (x) / D (x), Δl)

Next, a nonlinear equation related to the dose D (x) is obtained using a model that is an example of the equation (26). A simple model of the resist process is introduced. This model is performed by introducing a specific term of the function p ^{* in} the equation (24). Here, even if the conventional threshold model is not accurate, the difference has not been so great since it has been used for manufacturing masks. Therefore, when the pattern density ρ is constant, the optimum dose D is expressed as the following equation (27).
(27) D = 1 / {p (Δl) + q (Δl) · ρ + r (Δl) · ρ ² }

Here, p (Δl), q (Δl), and r (Δl) are coefficients. These coefficients represent the characteristics of the resist process. That is, the coefficient depends on Δl, resist, development conditions, and the like. Here, if r (Δl) is zero, Expression (27) becomes Expression (28) shown below.
(28) D = 1 / {p (Δl) + q (Δl) · ρ}

The solution of Equation (28) is a solution of the pattern density method based on the conventional threshold model. However, as described in the first embodiment, there is an error in the conventional threshold model. In other words, it [rho ² term is not zero becomes important. Here, as described above, the pattern density ρ in Expression (27) is replaced with an amount obtained by dividing the accumulated backscattering energy B ^* (x) normalized as shown in Expression (22) by the irradiation amount D. And equation (27) can be transformed into equation (29) below.
(29) D = 1 / [p (Δl) + q (Δl) · B ^* (x) / D
+ R (Δl) · {B ^* (x) / D} ² ]

Further, as described above, assuming that the pattern density ρ is established even in a general case where the pattern density ρ is not constant, the proximity effect correction equation shown in the following equation (28) is obtained from the equation (29).
(30) D (x) = 1 / [p (Δl) + q (Δl) · B ^* (x) / D (x)
+ R (Δl) · {B ^* (x) / D (x)} ² ]

When the equation (30) is transformed, an equation represented by the following equation (31) is obtained.
(31) p (Δl) D (x) ² + q (Δl) · D (x) · B ^* (x) −D (x)
+ R (Δl) · B ^* (x) ² = 0

Equation (31) can be obtained using Equation (23) as a nonlinear equation related to the dose D (x) shown in Equation (32) below.
(32) p (Δl) D (x) ²
+ Q (Δl) · D (x) · ∫D (x ′) g (xx ′) dx ′
−D (x) + r (Δl) · {∫D (x ′) g (xx ′) dx ′} ² = 0

  By solving the nonlinear equation relating to the dose D (x) shown in the equation (32), the optimum dose D (x) with the proximity effect corrected can be obtained.

Here, if the dose D (x) is not accurate, a correction error ε (x) occurs. As for the equation (31), when the correction error ε (x) is small and the Taylor error is expanded to the first order and deformed, the correction error ε (x) can be expressed by the following equation (33). .
(33) ε (x) = − {p (Δl) D (x) ² + q (Δl) · D (x) · B ^* (x)
−D (x) + r (Δl) · B ^* (x) ² }
/ {P ′ (Δl) D (x) ² + q ′ (Δl) · D (x) · B ^* (x)
+ R ′ (Δl) · B ^* (x) ² }

However, the constants p ′ (Δl), q ′ (Δl), and r ′ (Δl) are represented by the following formulas (34-1) to (34-3).
(34-1) p ′ (Δl) = dp (Δl) / dΔl
(34-2) q ′ (Δl) = dq (Δl) / dΔl
(34-3) r ′ (Δl) = dr (Δl) / dΔl

The correction equation (31) is non-linear with respect to the unknown function D (x), but the solution of the correction equation (31) is an iteration of the above-described formulas (10-1) to (10-2). It can be obtained by doing. The first approximate dose D ₀ (x) is expressed by the following equation (35).
(35) D ₀ (x) = 1 / {p (Δl) + q (Δl) U (x)
+ R (Δl) · U (x) ² }

Here, the function U (x) is the above-described equation (13). An unknown function d _{n + 1} (x) is _expressed by the following equation (36-1) when a _{n + 1} (x) ≠ 0 and b _{n + 1} (x) ≧ 0, and a _{n + 1} (x) ≠ 0. When b _{n + 1} (x) <0, the following equation (36-2) is obtained. When a _{n + 1} (x) = 0, the following equation (36-3) is obtained.
(36-1) d _{n + 1} (x) = [− b _{n + 1} (x) + √ {b _{n + 1} (x) ²
-4a _{n + 1} (x) c _{n + 1} (x)}] / {2a _{n + 1} (x)}
(36-2) d _{n + 1} (x) = [− b _{n + 1} (x) −√ {b _{n + 1} (x) ²
-4a _{n + 1} (x) c _{n + 1} (x)}] / {2a _{n + 1} (x)}
(36-3) d _{n + 1} (x) = − c _{n + 1} (x) / b _{n + 1} (x)

Further, a _{n + 1} (x), b _{n + 1} (x), and c _{n + 1} (x) are defined by the following equations (37-1) to (37-3).
(37-1) a _{n + 1} (x) = p (Δl) ² + q (Δl) U (x)
+ R (Δl) · U (x) ²
(37-2) b _{n + 1} (x) = 2p (Δl) D _n (x) −1
+ Q (Δl) U (x) D _n (x)
+ {Q (Δl) + 2r (Δl) · U (x)} ∫D _n (x ′) g (xx ′) dx ′
(37-3) cn _{+ 1} (x) = p (Δl) D _n (x) ² −D _n (x)
+ Q (Δl) D _n (x) ∫D _n (x ′) g (xx ′) dx ′
+ R (Δl) {∫D _n (x ′) g (xx ′) dx ′} ²

There was thus _determined, determine the _D 1 (x) with _D 0 (x) and _d 1 (x). _Then, a _D 2 (x) with _D 1 (x) and _d 2 (x). In this way, D _{n + 1} (x) may be obtained sequentially using D _n (x) and d _{n + 1} (x). In determining the irradiation amount D _{n + 1} (x), it is preferable that the repetition number n is large. However, for example, in the example described later, a sufficient accuracy can be ensured at about D ₅ (x). The number of repetitions may be adjusted according to the target accuracy.

Here, also in the second embodiment, the dose D _{n + 1} (x) may be obtained by executing each step described in S100 of FIG. 7 described above. The subsequent steps are the same as in the first embodiment.

As described above, the dose calculation unit 112 of the drawing apparatus 100 solves the nonlinear equation related to the dose D (x) shown in Expression (32), thereby correcting the dose D _{n + 1} (x) with the proximity effect corrected. Ask for. Then, the drawing unit 150 draws a desired pattern on the sample 101 by irradiating the sample 101 with the electron beam 200 with the irradiation amount D _{n + 1} (x).

Next, the correction accuracy of the dose D _{n + 1} (x) with the proximity effect corrected, which is obtained by the nonlinear equation in Embodiment 2, will be described.

For comparison, the following equation (38) based on the threshold model is introduced.
(38) D (x) / 2 + η∫D (x ′) g (xx ′) dx ′ = D ₀

Here, 2D ₀ corresponds to the irradiation amount of the isolated pattern. In addition, the following conditions are imposed.
(39-1) D ₀ = 1 / {2p (Δl)}
(39-2) η = {q (Δl) + r (Δl)} / {2p (Δl)}

  In the above description, in the second embodiment, it is assumed that the threshold model is not established and Equation (27) is established, and therefore Equation (38) is merely an approximate equation.

The conditions for finding the correction accuracy are as follows. A spread function g (x) related to backscattering is assumed as in the following equation (40).
(40) g (x) = {1 / (πσ _b ² )} exp {− (x−x ′) / σ _b ² }

The right side of Expression (40) corresponds to double Gaussian approximation. The value of the backscattering spread σ _b is 10 μm. The value of p (Δl), q (Δl ), r (Δl) , respectively, and ^{0.08cm 2 /μC,0.096cm 2 /μC,0.032cm 2 / μC} . The values of p ′ (Δl), q ′ (Δl), and r ′ (Δl) are −0.001 cm ² / (nm · μC), 0.0001 cm ² / (nm · μC), 0.0 cm ² / (Nm · μC). Generally speaking, the unit of p ′ (Δl), q ′ (Δl), r ′ (Δl) should be written as cm / μC. However, in order to easily understand that these amounts have a dimension of 1 / (irradiation amount × dimension error), the unit is expressed as cm ² / (nm · μC). If the values of p (Δl), q (Δl), and r (Δl) are used, the parameters of the approximate correction equation are determined by the equations (39-1) and (39-2), and D ₀ = 6.25 μC. / Cm ² and η = 0.8.
These quantities can be expressed in the general unit system as follows. The value of p (Δl), q (Δl ), r (Δl) , ^{respectively,} will be set to ^{8.0m 2 /C,9.6m 2 /C,3.2m 2 / C} . The values of p ′ (Δl), q ′ (Δl), and r ′ (Δl) are set to −1.0 × 10 ⁸ m / C, −1.0 × 10 ⁷ m / C, and 0.0 m / C. Become. D ₀ has a _value of D ₀ = 6.25 × 10 ⁻² C / m ² .

First, a case where the pattern density is uniform will be described. In the second embodiment, it is assumed that the threshold model is not established, but the optimum dose is expressed by Expression (27). In the method of the second embodiment, since the equation (27) is used as it is, no error occurs. Therefore, in the following, only the error generated by the method assuming the threshold model is obtained. Further, as the solution of equation (38) assuming a threshold model, the Pubkovich solution shown in the following equation (41) is used.
(41) D = D ₀ / (1/2 + ηρ)

  If the threshold model is established, since the pattern density is uniform, this equation (41) is accurate. However, as described above, the threshold model is not established here, and the equation (27) is established, so the equation (41) is merely an approximate solution.

  FIG. 12 is a graph comparing the corrected dose in Embodiment 2 with the corrected dose based on the Pavkovic solution. In FIG. 12, the graph indicated by “T” indicates the corrected dose based on the Pubkovic solution obtained by Expression (41). Further, the graph indicated by “R” indicates the corrected dose and the actually measured value in the second embodiment obtained by the equation (25).

  FIG. 13 is a graph showing the dimensional error of the corrected dose based on the Pavkovic solution. FIG. 13 shows the dimensional error of the corrected dose obtained by the equation (41). Equation (32) was used to calculate the error. In the example of FIG. 13, it can be seen that the maximum error in the conventional threshold model reaches 8 nm.

Next, a case where the pattern density changes suddenly will be described.
FIG. 14 is a diagram illustrating an example of an evaluation pattern for estimating the correction accuracy by the method according to the second embodiment. In FIG. 14, an evaluation pattern 61 having a width of 2 W is used. Here, the dimension W is sufficiently larger than the spread sigma _b backscatter. In FIG. 14, the pattern density is 100% for the right half width W region of the evaluation pattern 61, and the pattern density is 0% for the left half width W region of the evaluation pattern 61. Therefore, the pattern density is 100% in the region 62 that is entirely located in the region of the right half width W. The region 64 is a region from −5σ to 5σ including the boundary, and the pattern density suddenly changes from 100% to 0% at the center.

  Here, along the dose calculation step (S100) described with reference to FIG. 7, the correction accuracy is estimated at every location of the pattern for each mesh region. This is equivalent to estimating an error even for a region without a figure. When a correction dimensional error ε (x) occurs at a location x in the inner area of the pattern, this error means that if a very small figure is placed at the location x, the correction error of that figure is ε (x). It means to become.

  FIG. 15 is a graph comparing the corrected dose in the second embodiment and the corrected dose based on the approximate expression of the threshold model using the evaluation pattern of FIG. FIG. 15 shows the result obtained for the region 64. In FIG. 15, the vertical axis represents the corrected dose, and the horizontal axis represents the relative position (x / σ) normalized by the influence range σ. In FIG. 15, the graph indicated by “Q” indicates the corrected dose determined by the approximate expression (37) of the threshold model. In addition, the graph indicated by “S” represents the nonlinear equations shown in Expression (31) expressed by Expression (10-1), Expression (10-2), and Expression (35) to Expression (37-3). The corrected dose in Embodiment 2 calculated | required by the iteration using the type | formula is shown.

  FIG. 16 is a diagram showing a correction error result when an approximate expression of a conventional threshold model is used using the evaluation pattern of FIG. FIG. 16 shows the result obtained for the region 64. In FIG. 16, the vertical axis represents the correction error, and the horizontal axis represents the relative position (x / σ) normalized by the influence range σ. In FIG. 16, the numerical values shown in each graph indicate the number of iterations. As shown in FIG. 16, it can be seen that an error of 8 nm remains even when nine iterations of iteration are performed when the corrected dose is obtained by the approximate expression (38) of the threshold model. This error is caused by the fact that the correction equation itself is approximate, that is, by assuming a threshold model. Therefore, it is an error that cannot be avoided in principle in a situation where the threshold model does not hold.

FIGS. 17 and 18 are diagrams showing correction error results when the nonlinear equation in the second embodiment is used using the evaluation pattern of FIG.
17 and 18 show the results obtained for the region 64. FIG. 17 and 18, the vertical axis represents the correction error, and the horizontal axis represents the relative position (x / σ) normalized by the influence range σ. The numerical values shown in each graph in FIGS. 17 and 18 indicate the number of iterations. In FIG. 17, the result of 1 to 6 times is shown. FIG. 18 shows the results up to 5 to 10 times. As shown in FIGS. 17 and 18, in the method of the second embodiment, the errors are suppressed to 1 nm or less and 0.3 nm or less by 5 and 8 iterations, respectively. As described above, high correction accuracy can be obtained by using the method of the second embodiment.

Embodiment 3 FIG.
In the first and second embodiments, the method for obtaining the corrected dose by correcting the proximity effect has been described. However, as a cause of the dimensional error, there is a CD variation (for example, a loading effect) due to fogging or a process in addition to the proximity effect. . Therefore, in the third embodiment, a case will be described in which correction of the CD variation due to the fogging and the process is performed together with the correction of the proximity effect described above. The configuration of the drawing apparatus in the third embodiment is the same as that in FIG. The contents other than those described below are the same as those in the second embodiment.

  First, a case where the present invention is applied to fog correction will be described. A phenomenon called fogging deteriorates the dimensional accuracy, which is caused by unnecessary exposure as well as the proximity effect. Therefore, similar to the proximity effect correction, the fog correction has been performed by changing the irradiation amount for each location. Conventionally, for the fog correction, the optimum dose has been calculated based on a threshold model. In order to apply the technique described in the second embodiment to this fogging phenomenon, the following may be performed.

The difference between proximity effect correction and fog correction in addition to proximity effect correction is that the background of energy loss in the resist is due to backscattered electrons in the former, and in the latter In addition, it is only the sum of re-reflected electrons due to fogging. Therefore, the backscattering energy B (x) and the normalized backscattering energy B ^* (x) may be expressed by the following formulas (42-1) and (42-2).
(42-1) B (x) = kη∫D (x ′) g (xx ′) dx ′
+ Kθ∫D (x ′) g _F (xx ′) dx ′
(42-2) B ^* (x) = ∫D (x ′) g (xx ′) dx ′
+ (Θ / η) ∫D (x ′) g _F (xx ′) dx ′

Here, the integration is performed on the figure of the LSI pattern. The same applies hereinafter unless otherwise specified. Θ is a fogging parameter. k is a coefficient. Further, in the equations (42-1) and (42-2), equations obtained by deleting the second term are equations for correcting only the proximity effect. Further, g _F (x) is a spread function in the case of fogging, and satisfies the following condition (Equation 43)).
(43) ∫g _F (x ′) dx ′ = 1
Here, the integration is the entire drawing area, and x and y are set to −∞ to + ∞, respectively.
A function system of the above-described equation (31) is obtained by experiment for proximity effect correction. For example, the parameters may be determined by obtaining the equation (31). And using Formula (42-2) for B ^* (x) in Formula (31), for example, Formula (10-1), Formula (10-2), Formula (35)-Formula (37-3) Utilizing this, the correction equation is solved by iteration to find the optimum dose (corrected dose). Then, if drawing is performed while controlling the irradiation amount in accordance with the determined correction irradiation amount, the influence of fogging can be corrected with high accuracy by the method of Embodiment 3 simultaneously with the proximity effect correction.

  Next, a case where the present invention is applied to correction of CD fluctuation (for example, loading effect) by a process will be described. There are many phenomena that cause dimensional errors in mask manufacturing and wafer processes. These include long-range loading effects and microloading effects that occur during etching, and flares that occur in the lithography apparatus. It is difficult to suppress these errors only by improving the apparatus. For this reason, the dimensions of the graphic in the design pattern are corrected and changed in advance, and the desired dimensions are obtained by performing a factoring process (manufacturing method).

This correction is performed as follows. The range affected by the figure is called the interaction distance and is represented by σ _L. For example, in the case of the loading effect, the value of σ _L is about 1 cm, which is much larger than the proximity effect spread of 10 μm. The LSI pattern is divided into small areas (mesh areas) sufficiently smaller than σ _L (for example, σ _L / 10), and an optimal dimensional correction amount is calculated for each small area using an appropriate method. In addition, the dimension of the figure existing inside is corrected by the correction amount. If a figure corrected in this way is formed on a mask or a resist is formed in such a corrected pattern, a desired dimension can be obtained by passing through a subsequent process (for example, etching).

  Here, for each region, there are two methods for correcting the dimension of the figure existing inside by the correction amount. One is a method of using a CAD system to change the design pattern itself at the data level. The other is a method of drawing by changing the irradiation amount depending on the place when drawing with the EB drawing apparatus.

  In performing the latter method, the method in the second embodiment can be used. That is, the function system of the above-described equation (24) is obtained by experiments for proximity effect correction. For example, the parameters may be determined by obtaining the equation (29). Here, it is important to obtain the dependency of the parameter dimensional change Δl.

FIG. 19 is a graph illustrating an example of a change of the coefficient p (Δl) of the nonlinear equation in the second embodiment with respect to Δl.
FIG. 20 is a graph showing an example of a change of the coefficient q (Δl) of the nonlinear equation in the second embodiment with respect to Δl.
FIG. 21 is a graph illustrating an example of a change of the coefficient r (Δl) of the nonlinear equation in the second embodiment with respect to Δl.
A dimension correction amount Δl caused by CD variation (for example, loading effect) due to the process is determined by an appropriate method for each region. Next, referring to the graphs of FIGS. 19 to 21, the values of the parameters p (Δl), q (Δl), and r (Δl) for proximity effect correction corresponding to the dimension correction amount Δl are also determined. As a result, since the nonlinear equation (31) of the proximity effect is obtained for each small region, for example, Equation (10-1), Equation (10-2), Equation (35) to Equation (37-) for each small region. Using 3), the nonlinear dose (32) is solved by iteration to find the optimum dose (corrected dose). Then, if drawing is performed while controlling the irradiation amount in accordance with the calculated corrected irradiation amount, a pattern whose dimension is corrected with respect to the CD variation (for example, loading effect) due to the process as well as the proximity effect is formed. Then, the formed pattern is matched with the design dimension through the process. In this way, by setting the coefficients p (Δl), q (Δl), and r (Δl) of the nonlinear equation (31) corresponding to the dimensional correction amount Δl for the CD variation (for example, loading effect) due to the process, it depends on the process. The influence of CD fluctuation (for example, loading effect) can be corrected with high accuracy by the method of Embodiment 3 simultaneously with the proximity effect correction.

Embodiment 4 FIG.
In the fourth embodiment, another simpler solution than the solution of the nonlinear equation (32) described in the second embodiment will be described. The configuration of the drawing apparatus in the fourth embodiment is the same as that in FIG. The contents other than those described below are the same as those in the second embodiment.

In this embodiment, the case where r (Dl) is small is considered, and the solution of equation (42) is obtained by the perturbation method with r (Dl) as a minute amount. As a simple example, let us consider up to the first order for r (Dl), and assume that the solution is expressed as the following equation (44).
(44) D (x) = D ₀ (x) + r (Dl) D ₁ (x)
That is, for r (Dl), terms higher than the second order, for example, r (Dl) ² and r (Dl) ³ are regarded as sufficiently small amounts and approximated to be zero.
By substituting equation (44) into equation (32) and setting the second-order or higher term for r (Dl) to zero, equations (45-1) and r (Dl) are obtained as zero-order equations for r (Dl). Equation (45-2) is obtained as a linear equation relating to).
(45-1) p (Δl) D ₀ (x)
+ Q (Δl) ∫D ₀ (x ′) g (xx ′) dx′−1 = 0
(45-2) {1-2p (Δl) D ₀ (x)
−q (Δl) ｌD ₀ (x ′) g (xx ′) dx ′} D ₁ (x)
−q (Δl) · D ₀ (x) · ∫D ₁ (x ′) g (xx ′) dx ′
= {∫D ₀ (x ′) g (xx ′) dx ′} ²
A solution of D ₀ (x) can be obtained by solving the equation (45-1) by a method described later. Thus, since D ₀ (x) is a known function, the only unknown function included in equation (45-2) is D ₁ (x), and the equation is a linear equation with respect to D ₁ (x). It is. This equation can also be solved by the method described below.

Next, a method for obtaining numerical solutions of equations (45-1) and (45-2) will be described.
Both Equation (45-1) and Equation (45-2) are special cases of Equation (46) below.
(46) s (x) f (x) + t (x) ∫f (x ′) g (xx ′) dx ′
= U (x)
Here, the unknown is f (x). If s (x) is replaced by p (Δl), t (x) is replaced by q (Δl), u (x) is replaced by 1, and f (x) is replaced by D ₀ (x), equation (46) is transformed into the equation (45-1). Therefore, if such replacement is performed with the solution shown below, the solution of Equation (45-1) is obtained, and if numerical calculation is performed using this, a highly accurate numerical solution of Equation (45-1) can be obtained. Can be sought.
Also, s (x) is the following equation (47), t (x) is -q (Δl) · D ₀ (x), u (x) is {∫D ₀ (x ′) g (x− If x ′) dx ′} ² and f (x) is replaced with D ₁ (x), then equation (46) becomes equation (45-2).
(47) s (x) = 1−2p (Δl) D ₀ (x)
−q (Δl) ∫D ₀ (x ′) g (xx ′) dx ′
Therefore, if such a replacement is performed with the solution shown below, the solution of Equation (45-2) is obtained, and if numerical calculation is performed using this, a highly accurate numerical solution of Equation (45-2) can be obtained. Can be sought.
The solution of the integral equation (46) and the function f (x) can be obtained by iterating according to the following equations (48-1) and (48-2).
(48-1) f (x) = lim f _n (x) (where n → ∞)
(48-2) f _{n + 1} (x) = f _n (x) + t _{n + 1} (x)

First, the first term f ₀ (x) is obtained by the following equation (49).
(49) f ₀ (x) = u (x) / {s (x) + t (x) ∫g (xx ′) dx ′}
After being determined to f _n (x), as shown in Equation (48-2) _to obtain the _{f n +} 1 (x) and by adding the seeking _{t n +} 1 (x) to _f n (x) However, this t _{n + 1} (x) is obtained by the following equation (50).
(50) t _{n + 1} (x) = − e _{n + 1} (x) / {s (x)
+ T (x) ∫g (xx ′) dx ′}
However, e _{n + 1} (x) is expressed by the following equation (51).
(51) e _{n + 1} (x) = f _n (x) s (x)
+ T (x) ∫f _n (x ′) g (xx ′) dx′−u (x)

As described above, the functions D ₀ (x) and D ₁ (x) are obtained, and the solution D (x) of the equation (32) can be obtained from the two by the equation (44). According to the fourth embodiment, the corrected dose can be obtained with a simpler solution than the solution shown in the second embodiment.

  In the above description, the processing content or operation content described as “˜part” or “˜process” can be configured by a program operable by a computer. Or you may make it implement by not only the program used as software but the combination of hardware and software. Alternatively, a combination with firmware may be used. When configured by a program, the program is recorded on a recording medium such as a magnetic disk device, a magnetic tape device, an FD, or a ROM (Read Only Memory). For example, it is recorded on the magnetic disk device 146.

  In FIG. 1, the control computer unit 110 further includes an example of a storage device such as a RAM (random access memory), a ROM, a magnetic disk (HD) device, and an input unit via a bus (not shown). Connected to a keyboard (K / B), mouse, monitor as an example of output means, printer, or external interface (I / F) as an example of input output means, FD, DVD, CD, etc. Absent.

  The embodiments have been described above with reference to specific examples. However, the present invention is not limited to these specific examples. For example, such a proximity effect correction method can be applied to correction in optical lithography.

  In addition, although descriptions are omitted for parts and the like that are not directly required for the description of the present invention, such as a device configuration and a control method, a required device configuration and a control method can be appropriately selected and used. For example, although the description of the control unit configuration for controlling the drawing apparatus 100 is omitted, it goes without saying that the required control unit configuration is appropriately selected and used.

  In addition, all charged particle beam writing apparatuses and charged particle beam writing methods that include elements of the present invention and that can be appropriately modified by those skilled in the art are included in the scope of the present invention.

FIG. 3 is a diagram illustrating a main part of a flowchart of a drawing method according to Embodiment 1. 6 is a diagram illustrating an example of a distribution of forward scattering energy and back scattering energy by an electron beam accumulated in a resist in Embodiment 1. FIG. 3 is a cross-sectional view showing an example of how to proceed with development of a resist on a sample 101 in Embodiment 1. FIG. FIG. 10 is a diagram showing another example of the distribution of forward scattered energy and back scattered energy by the electron beam accumulated in the resist in the first embodiment. It is a figure which shows an example of the shift | offset | difference with the case where the irradiation amount is determined with the equation in Embodiment 1, the case where the irradiation amount is determined with the conventional threshold model, and the optimum irradiation amount by experiment. 4 is a graph showing the relationship among pattern dimensions, proximity effect correction coefficients, and pattern density in the first embodiment. FIG. 3 is a diagram illustrating a main part of a flowchart of a drawing method according to Embodiment 1. 3 is a conceptual diagram for explaining a parallel processing method in Embodiment 1. FIG. 6 is a conceptual diagram illustrating a range of a region for calculating proximity effect correction according to Embodiment 1. FIG. 3 is a diagram showing a mesh area in the first embodiment. FIG. FIG. 3 is a conceptual diagram for explaining a method of dose interpolation in the first embodiment. It is the graph which compared the corrected irradiation amount in Embodiment 2, and the correction irradiation amount based on the solution of Pubkovic. It is a graph which shows the dimensional error of the correction | amendment dose based on the solution of Pubcovic. FIG. 10 is a diagram showing an example of an evaluation pattern for estimating the correction accuracy by the method in the second embodiment. It is the graph which compared the corrected irradiation amount in Embodiment 2 and the correction irradiation amount based on the approximate expression of a threshold value model using the evaluation pattern of FIG. It is a figure which shows the result of the correction | amendment error at the time of utilizing the approximate expression of the conventional threshold value model using the evaluation pattern of FIG. It is a figure which shows the result of the correction | amendment error at the time of utilizing the nonlinear equation in Embodiment 2 using the evaluation pattern of FIG. It is a figure which shows the result of the correction | amendment error at the time of utilizing the nonlinear equation in Embodiment 2 using the evaluation pattern of FIG. 10 is a graph showing an example of a change of a coefficient p (Δl) of a nonlinear equation in Embodiment 3 with respect to Δl. 10 is a graph showing an example of a change of a coefficient q (Δl) of a nonlinear equation in Embodiment 3 with respect to Δl. 10 is a graph illustrating an example of a change of a coefficient r (Δl) of a nonlinear equation in Embodiment 3 with respect to Δl. It is a conceptual diagram for demonstrating operation | movement of the conventional variable shaping type | mold electron beam drawing apparatus. It is a figure which shows the relationship between the conventional threshold value model and pattern dimension. It is a figure which shows an example of the shift | offset | difference with the case where the irradiation amount is determined with the conventional threshold value model, and the optimal irradiation amount by experiment.

Explanation of symbols

10, 20 Maximum value 12 Forward scattering energy distribution 22 Back scattering energy distribution 30, 32 Stripe area 34 Mesh area 40, 50 Figure 42 Center 52 Position 61 Evaluation pattern 62, 64 Small area 100 Drawing apparatus 101, 340 Sample 102 Electron tube 103 Drawing room 105 XY stage 110 Control computer unit 111 Memory 112 Irradiation amount calculation unit 114 Transfer unit 116 Drawing data processing unit 118, 119 Buffer memory 120 Deflection control circuit 140, 142 Magnetic disk device 150 Drawing unit 160 Control unit 200 Electron beam 201 Electron gun 202 Illumination lens 203, 410 First aperture 204 Projection lens 205, 208 Deflector 206, 420 Second aperture 207 Objective lens 212 BLK deflector 214 BLK aperture 330 Electron beam 11 opening 421 shaped opening 430 a charged particle source

Claims (3)

The dose is determined by solving an equation of accumulated energy due to backscattering of the charged particle beam, which is defined by a polynomial having a second-order or higher-order term of the dose, with the dose being unknown. Process,
Irradiating the charged particle beam with the determined irradiation amount and drawing a pattern on the sample;
With
The correlation between the pattern density and the dose is obtained in advance by experiments,
In the drawing method, a parameter of each term is defined so that the equation follows the correlation.   When the evaluation pattern in which figures are repeatedly arranged at a predetermined pattern density is drawn with variable irradiation doses, the irradiation dose at which a desired design dimension is obtained is set as the correlation with the predetermined pattern density. The drawing method according to claim 1, wherein: An equation in which the parameters of each term are defined so as to follow the correlation between the pattern density and the dose obtained in advance by experiments, and the polynomial having a second or higher order term of the dose with the dose as an unknown and in defined, non-linear with respect to the dose, by solving the equation of accumulated energy due to backscattering of charged particle beam determine the dose calculation unit,
A drawing unit that irradiates the charged particle beam with the obtained irradiation amount and draws a pattern on the sample;
Drawing apparatus comprising the.

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