JP2014029888A - Drawing method, drawing device and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a drawing method capable of obtaining stored energy from each rectangle after being divided into patterns with fast processing, or calculation, speed and with high accuracy.SOLUTION: Regarding a method for calculating stored energy from each rectangle derived by dividing a pattern drawn on a sample, the method being used to obtain the optimum irradiation amount of an electron beam having its proximity effects corrected, the prevent invention is adapted to obtain a discrete function map composed of energy distribution of each of a plurality of elements in advance and then obtain stored energy from each rectangle according to the function map. Since only a simple calculation needs to be made according to a previously obtained map, or the energy distribution of each element, this method makes it possible to obtain stored energy from each rectangle at a discretionary point quickly without taking much time. Also, even when grid intervals of each individual element are narrowly set, stored energy can be highly accurately obtained from rectangles in a short time.

Description

  In order to draw a desired circuit pattern on a sample such as a mask substrate using an electron beam, the present invention relates to a drawing method for obtaining an electron beam irradiation amount optimal for reducing the dimensional change of the circuit pattern due to the proximity effect. And a drawing apparatus and a program. In particular, the present invention relates to the calculation of the stored energy from each rectangle obtained by dividing the pattern that needs to be taken into consideration in order to obtain the optimum dose, and to the technique for obtaining the stored energy from each rectangle at high speed and with high accuracy.

  In recent years, along with further higher integration of semiconductor integrated circuits such as LSIs, circuit dimensions and circuit line widths required for semiconductor devices have been reduced year by year. In order to form circuit patterns having desired dimensions and line widths on these semiconductor devices, high-precision original patterns (also called reticles or masks) are required. For example, a resist film is used to generate such original patterns. 2. Description of the Related Art Conventionally, a drawing apparatus using a so-called lithography technique that draws an original pattern by irradiating an electron beam (electron beam) or the like on a metal substrate (mask substrate, etc.) coated with a coating is known.

  By the way, when an electron beam is irradiated onto a sample such as a mask substrate, an effect called a proximity effect that changes the dimension of a resist pattern formed on the sample appears. This is because the beam is irradiated to unintended locations on the sample due to the forward scattered electrons and back scattered electrons generated when the irradiated electrons collide with the resist, metal substrate, etc. As a result, the circuit is mainly used. This is a phenomenon that causes the line width of the resist pattern to change according to the density of the pattern, and the effect of the proximity effect becomes more pronounced with the further miniaturization of the circuit in the conventional drawing apparatus. There was an inconvenience.

  Therefore, as one of the effective methods for correcting the proximity effect, the electron beam dose optimal for reducing the change in the line width of the resist pattern due to the proximity effect (referred to as the optimum dose or optimum dose). There is known a dose correction method for determining the above according to the density of the circuit pattern. Specifically, the effective electron beam dose exceeds the area where the circuit pattern is dense, so control is performed to reduce the irradiation time, while the effective electron beam dose is applied where the circuit pattern is sparse. Control is performed to increase the irradiation time. By doing so, the change in the line width of the resist pattern due to the proximity effect is reduced. As an example of a method for determining such an optimum irradiation amount of an electron beam, for example, there is a technique described in Non-Patent Document 1 shown below.

M.Parikh, J.Appl.Phys50 (1979), p4371-4383

ただし、数１はｎ個の評価点、ｍ個の矩形があるときの方程式を例に示したものである。Ｄ_iは矩形ｉのドーズ量であり、Ｅ_threasholdは各評価点での蓄積エネルギーの目標値（共通の値：定数）である。 The method described in Non-Patent Document 1 shows the relationship between the irradiation amount (dose amount) of an electron beam and the photosensitive amount at a predetermined position (called an evaluation point) of a circuit pattern formed on a sample. This is a method in which the optimum irradiation amount of the electron beam at each position is obtained by obtaining an inverse matrix of the matrix expressed by the determinant shown in Equation 1 (a method called a self-alignment method or a matrix method) Is). The determinant (FD = E) shown in Equation 1 shows the influence from each of a plurality of rectangles (dividing various figures constituting the circuit pattern formed on the sample into beam irradiation units) for setting the irradiation amount. Taking into account, the objective condition that “the accumulated energy at all the evaluation points is equal” is expressed by an equation using the energy scattering formula F _ij as shown in the equations (2) and (3).

However, Formula 1 shows an example when there are n evaluation points and m rectangles. D _i is the dose amount of the rectangle i, and E _threshold is the target value (common value: constant) of the stored energy at each evaluation point.

上記相関関数行列の要素Ｆ_ijは、矩形ｉからの評価点ｊでのエネルギーの散乱の作用の大きさ（蓄積エネルギー）を示す。 The elements F _ij (≡ = 1,..., M = 1,..., N) of the correlation function matrix are calculated according to the following formula 2, for example.

The element F _ij of the correlation function matrix indicates the magnitude of energy scattering (accumulated energy) at the evaluation point j from the rectangle i.

Here, for example, as shown in the left diagram of FIG. 9, around the rectangle (specifically, the rectangle after pattern division to be drawn) whose four sides are at the respective coordinates (l, b, r, t). The stored energy e (x, y) at an arbitrary point (x, y) can be obtained by integrating a PSF function indicating a final energy distribution when a certain point on the sample is irradiated with an electron beam. Yes (see Equation 3). Further, if the PSF function shown in Equation 3 can be approximated by a Gaussian distribution, Equation 3 can be expressed by a product of an erf function (error function) as a product of the Gaussian distribution shown in Equation 4. it can.

  The approximate expression expressed by the combination of the Gaussian distribution shown in the above equation 4 has an advantage that it can be calculated quickly because it is easy to integrate. However, with the further progress of miniaturization of circuit dimensions and circuit line widths required for recent semiconductor devices, the approximation by the Gaussian distribution as described above has become insufficient in accuracy (ie, PSF function). Cannot be approximated with a Gaussian distribution).

ここで、ｓは隣接する点と点との間隔（グリッド間隔）、ｗは長方形（描画対象の矩形）の幅、ｈは長方形（描画対象の矩形）の高さである（図９右図参照）。 By the way, when the PSF function cannot be approximated by a Gaussian distribution, the approximate expression shown in Equation 4 cannot be used (however, this is not limited to the case of using the self-alignment method). Therefore, when the PSF function cannot be approximated by a Gaussian distribution, as shown in the right diagram of FIG. 9, one side of a rectangle (rectangle to be drawn) having four sides located at coordinates (l, b, r, t) Considering it as a set of points (coordinates (X _i , Y _j )), the stored energy e (x, y) at an arbitrary point (x, y) around the rectangle may be calculated according to Equation 5.

Here, s is an interval between adjacent points (grid interval), w is a width of a rectangle (rectangle to be drawn), and h is a height of a rectangle (rectangle to be drawn) (see the right figure in FIG. 9). ).

  The advantage of the method of calculating the stored energy e (x, y) at an arbitrary point (x, y) according to the above equation 5 is that the calculation accuracy increases if the grid interval s of each point is set to be narrow (fine). It is in that point. Therefore, in the current situation where it is necessary to draw a miniaturized circuit pattern on a sample, the grid interval s should be set narrow in order to obtain an optimum irradiation amount of an electron beam with good correction accuracy as the miniaturization progresses. I understand it.

  However, the disadvantage of the method of calculating the stored energy e (x, y) at an arbitrary point (x, y) according to the above formula 5 is that the calculation time increases if the grid interval s is set narrow. Therefore, when it is necessary to set the grid interval s narrow in order to obtain the optimum irradiation amount of the electron beam having sufficient correction accuracy according to the recent miniaturization of the circuit pattern, the optimum irradiation of the electron beam. The calculation of the stored energy used to calculate the quantity takes an enormous amount of time, and it is difficult to use it for highly integrated semiconductor devices such as LSI patterns because of time constraints. was there.

  The present invention has been made in view of the above points, and the stored energy from each rectangle after pattern division used for obtaining the optimum electron beam dose for reducing the dimensional change of the circuit pattern due to the proximity effect. An object of the present invention is to provide a drawing method, a drawing apparatus, and a program capable of obtaining stored energy from each of the rectangles with high processing speed, that is, calculation speed and with high accuracy.

  The drawing method according to the present invention obtains an electron beam irradiation dose optimal for reducing the dimensional change of the pattern due to the proximity effect for each arbitrary rectangle that divides a circuit pattern to be drawn on a sample. For each of the second rectangles, stored energy, which is a substantial electron beam irradiation amount from a second rectangle other than the first rectangle within a predetermined range based on the first rectangle targeted for irradiation of the second rectangle A method of obtaining a discrete function map comprising energy distributions for each of a plurality of elements when an electron beam is irradiated to a predetermined position; and the second method according to the obtained discrete function map. Obtaining stored energy from the rectangle.

（ただし、ｓ；各要素間のグリッド間隔、Ｎ；Ｒ／ｓ（ＲはＰＳＦ定義域））
により求めることを特徴とする。 As a preferred embodiment of the present invention, the step of obtaining the discrete function map comprises:

(Where s: grid spacing between elements, N: R / s (R is PSF domain))
It is calculated | required by.

（ただし、x；第１矩形上の任意の点のＸ座標位置、y；第１矩形上の任意の点のＹ座標位置、x_i；関数マップ上の各要素のｘ座標位置、y_j；関数マップ上の各要素のｙ座標位置、ｓ；各要素間のグリッド間隔、Ｎ；Ｒ／ｓ（ＲはＰＳＦ定義域））
に基づいて求めることを特徴とする。 Further, the step of obtaining the stored energy from the second rectangle includes the stored energy from the second rectangle,

(Where x: X coordinate position of an arbitrary point on the first rectangle, y; Y coordinate position of an arbitrary point on the first rectangle, x _i ; x coordinate position of each element on the function map, y _j ; Y coordinate position of each element on the function map, s; grid spacing between each element, N; R / s (R is PSF domain)
It calculates | requires based on.

  Further, the step of obtaining stored energy from the second rectangle includes a step of specifying a combination of a plurality of third rectangles having arbitrary sizes according to the second rectangle, and the specification according to a discrete function map. A step of obtaining stored energy for each of the plurality of third rectangles, and a step of adding and subtracting the obtained stored energy from the third rectangle in accordance with the combination mode.

  By doing this, since it is only necessary to perform simple calculations according to the function map obtained in advance, that is, the energy distribution of each element, the accumulated energy from each rectangle after pattern division is increased at high speed, that is, time is reduced. You will be able to ask without spending. Further, according to this, even when the grid interval of each element is set to be narrow, the stored energy from each rectangle with high accuracy can be obtained in a short time.

  The invention can be constructed and implemented not only as a method invention but also as an apparatus invention. Further, the present invention can be implemented in the form of a program of a processor such as a computer or a DSP, or can be implemented in the form of a storage medium storing such a program.

  According to the present invention, a discrete function map consisting of energy distributions for each of a plurality of elements is obtained in advance, and the accumulated energy from each rectangle is obtained according to this function map. There is an effect that the accumulated energy from each rectangle after pattern division can be obtained with high speed, that is, calculation speed and accuracy.

It is a conceptual diagram which shows one Example of the whole structure of the drawing apparatus to which the drawing method which concerns on this invention is applied. It is a flowchart which shows one Example of the optimal irradiation amount calculation process of the electron beam for every rectangle in the optimal irradiation amount calculation part. It is a flowchart which shows one Example of the stored energy calculation process in each evaluation score in a stored energy calculation part. It is a conceptual diagram which shows an example of the chip | tip range which calculates optimal irradiation amount by proximity effect correction | amendment. It is a conceptual diagram which shows an example of a discrete "function map". It is a conceptual diagram which shows an example of the simulation result which determines a PSF domain. It is a conceptual diagram for demonstrating the procedure which calculates | requires the stored energy from the rectangle in arbitrary points using a discrete function map. It is a conceptual diagram which shows an example of the type | formula of the stored energy used when it is necessary to refer the energy distribution outside a PSF definition area. It is a conceptual diagram which shows the prior art example which calculates the stored energy by discretization.

  Embodiments of the present invention will be described below in detail with reference to the accompanying drawings.

  FIG. 1 is a conceptual diagram showing an embodiment of the overall configuration of a drawing apparatus to which a drawing method according to the present invention is applied. The drawing apparatus shown here is an electron beam drawing apparatus as an example, where 10 is a sample chamber, 11 is a target (sample), 12 is a sample stage, 20 is an electron optical column, and 21 is an electron gun. , 22a to 22e are various lens systems, 23 to 26 are various deflection systems, 27a is a blanking plate, and 27b and 27c are aperture masks for beam shaping. Further, 31 is a sample stage drive circuit unit, 32 is a laser side long system, 33 is a deflection control circuit unit, 34 is a blanking control circuit unit, 35 is a variable shaped beam size control circuit unit, 36 is a buffer memory and control circuit unit , 37 is a control calculation unit, 38 is an optimum dose calculation unit, and 40 is a CAD system.

  The operation of the electron beam drawing apparatus shown in FIG. 1 will be briefly described. The electron beam irradiated from the electron gun 21 is turned on / off by the blanking deflector 23. By adjusting the length of the electron beam irradiation time at this time, the present apparatus can change the amount of electron beam irradiation according to the irradiation position of the target 11 placed on the sample stage 12. Yes. The electron beam that has passed through the blanking plate 27a is shaped into a rectangular beam by the beam shaping deflector 24 and the beam shaping aperture masks 27b and 27c, and the size of the rectangle is variable. The electron beam shaped into the rectangular shape is deflected and scanned on the target 11 by the scanning deflectors 25 and 26, and a desired pattern is drawn on the target 11 by this beam scanning. That is, a desired pattern drawn on the target 11 is divided into a combination of a plurality of rectangles (first rectangles), and an electron beam is irradiated to each rectangle (first rectangle).

  The optimum irradiation amount of the electron beam for each rectangle (that is, the length of the electron beam irradiation time) is calculated by the optimum irradiation amount calculation unit 38 based on the original data for electron beam exposure created by the CAD system 40. The optimum irradiation amount calculation unit 38 is a computer including a CPU, a ROM, a RAM, and the like, for example, and corrects the proximity effect to calculate the optimum irradiation amount of the electron beam for each rectangle. Here, by using a conjugate gradient method and solving a determinant that can be expressed by the above equation 1 (for the sake of convenience, described as Ax = b), the optimum irradiation for calculating the optimum irradiation amount of the electron beam for each rectangle is calculated. The quantity calculation unit 38 is shown as an example.

When the conjugate gradient method is used to calculate the optimum dose, the determinant Ax = b can be solved by repeating the multiplication of the correlation function matrix (A) and the vector (x). Therefore, a processing procedure for solving the determinant (Ax = b) by the conjugate gradient method will be described below. First, it is assumed that r _k = b−Ax _k and p _k = r _k (k = 0) as initial values. P _k and r _k are intermediate variable vectors, and k indicates the number of repeated calculations. Next, the determinant Ax = b is solved to obtain x by repeatedly performing the following equations 8 to 13 until a predetermined repetition condition is satisfied. In addition, the parenthesis notation (*) with a dot in each numerical formula shown below represents an inner product.

By the way, “A” of Ap _k that appears in the process of the above calculation procedure is a matrix of size m × n, and “p _k ” is a vector of size m (see Equation 1). Therefore, in order to calculate Ap _k by a normal method, m × m multiplication is required, and since such calculation is performed for each repeated calculation, reducing the calculation amount of the processing speeds up the processing time. It can be understood that it is important to In view of the fact that the number of elements of “A” is the square of the number of rectangles, using the above calculation procedure as it is requires a great amount of calculation time and is inconvenient.

Therefore, in order to solve the determinant (Ax = b) at high speed, the optimum dose calculation unit 38 according to the present embodiment includes a stored energy calculation unit 39. In the accumulated energy calculation unit 39, and note that Ap _k appearing in the course of the calculation procedure is equal to the stored energy at each evaluation point when the dose of each rectangle is "p _k", the Ap _k The value is managed with one stored energy for each rectangular element (having one evaluation point as described below). That is, since the previous matrix [A] represents the behavior of the system, the determinant Ax = b means that the accumulated energy at each evaluation point when the dose amount of each rectangle is [x] is [b]. It means that it has become. Therefore, it is sufficient computing the stored energy at each evaluation point in the accumulated energy calculator 39, the Ap _k to manage a huge matrix A comprising a number of elements increases and decreases in proportion to the number and the number of rectangles of the evaluation points There is no need to perform calculations.

  Here, the stored energy calculation unit 39 obtains energy distributions from a plurality of quarter planes (corresponding to a third rectangle) using a discrete function map (see FIG. 5 described later) calculated in advance. The accumulated energy at any point (specifically, the evaluation point in the first rectangle) according to the energy distribution from the arbitrary rectangle (second rectangle) can be obtained by combining them (described later). (See FIG. 7). By doing so, calculation of the optimum irradiation amount of the electron beam for each rectangle (second rectangle) can be processed at higher speed. A specific calculation procedure will be described later.

  Hereinafter, a procedure for calculating the electron beam optimum irradiation amount (optimum dose amount) for each rectangle (second rectangle) will be described with reference to FIGS. 4 to 7 separately shown. FIG. 2 is a flowchart showing an embodiment of the process for calculating the optimum electron beam dose (optimum dose) for each rectangle in the optimum dose calculator 38 shown in FIG.

  Step S1 appropriately divides each of a plurality of figures Z1 to Z7 (figure constituting a circuit pattern; see FIG. 4) specified based on the original electron beam exposure data acquired from the CAD system 40 into a plurality of rectangles. To do. For example, as shown in FIG. 4, each figure Z1-Z7 is divided into a plurality of rectangles having a size of about 1/10 of the backscattering diameter. At this time, when the original shape is a figure other than a square, such as the figures Z1, Z3, Z4, and Z5 shown in FIG. 4, the figure is formed by combining a plurality of rectangles of the size. Split. In the example shown here, the figure Z1 is divided into three rectangles, the figure Z3 is divided into two rectangles, the figure Z4 is divided into four rectangles, and the figure Z5 is divided into two rectangles. In this way, each of the figures Z1 to Z7 is divided into one or more rectangles having different sizes. Since any known method for dividing the figures Z1 to Z7 into one or more rectangles may be used, a detailed description thereof is omitted here.

  In step S2, one energy evaluation point is determined for each of the divided rectangles. As shown in FIG. 4, in the normal PEC, the center position of the longest outer peripheral part forming each rectangle is determined as an energy evaluation point (indicated by a black circle in the figure). This is different from the conventionally known self-alignment method in which the center positions of all the pieces forming each rectangle are determined as energy evaluation points (that is, there are four evaluation points). In the case of Gray Scale PEC, the center position of each rectangle may be determined as the energy evaluation point.

In step S3, as an initialization process for solving the determinant Ax = b as shown in Equation ₁ , the initial value “0” is set to the (initial) dose amount x ₀ of each rectangle, and p ₀ and r ₀ (= b-Ax ₀ ) is set to an appropriate energy target value. Here, b is an m-ary column vector. Further, p _k and r _k as described above is an intermediate variable vector, k shows a number of iterations. As the energy target value, in the case of a normal PEC, the energy target value of the outer periphery of the figures Z1 to Z7 to which each rectangle belongs, and in the case of Gray Scale PEC, the layers including the figures Z1 to Z7 to which each rectangle belongs ( ) Is set for each stored energy target value.

  In step S4, the discretization grid interval s and the PSF domain are determined in order to perform a discrete calculation by regarding the surface as a set of many points as shown in FIG. The discretization grid interval s is determined to be a sufficiently small value with respect to the change of the PSF function. On the other hand, the PSF domain is used to define the domain of a “function map” (see FIG. 5) to be described later. For example, according to a simulation result using a PSF function (approximate expression) as shown in FIG. It is determined. Specifically, a range in which the energy value is equal to or greater than a predetermined value (distance from the electron beam incident point) is determined as the PSF domain. Alternatively, the user may determine an arbitrary range as the PSF domain according to the simulation result.

As a PSF function (approximate expression) used for performing the above simulation, for example, there is a double Gaussian approximate expression as shown in Expression 14. Here, since the PSF domain is simply determined, the PSF function may be approximated by a double Gaussian approximation formula or the like.

  The PSF function shown in Equation 14 indicates the final energy distribution when an electron beam is irradiated to a certain point on the sample, r is the distance from the electron beam incident point, C is a constant, and η is the electron beam. Ratio of resist exposure due to forward scattering and resist exposure due to backscattering (proximity effect correction factor), α and β are forward scattering spreads (forward scattering diameter) or backscattering, which are determined according to the acceleration voltage, respectively. Is a predetermined value representing the spread (backscattering diameter). The values of α and β are, for example, when the acceleration voltage is 20 KeV (27 nm, 2 um), when it is 50 KeV (30 nm, 10 um), and when it is 100 KeV (10 nm, 32 um).

  Needless to say, the PSF function (approximate expression) used for performing the simulation for determining the PSF domain is not limited to the double Gaussian approximate expression described above, and other known approximate expressions may be used. Further, for example, the PSF function (approximate expression) used for the simulation may be determined mainly according to the acceleration voltage of the electron beam and the material of the substrate.

上記Ｎは、Ｎ＝Ｒ（ＰＳＦ定義域）／ｓ（離散化グリッド間隔）により求められる。なお、この数１５で用いるＰＳＦ関数は、ＰＳＦ定義域を決定する際に用いたのと同じ近似式（例えば数１４に示したダブルガウシアン近似式など）を用いればよい。また、上記エネルギー分布（Ｅ_ij）を初期化する際には、個々の点のスポット配置や密度等を考慮してエネルギー計算を行うようにしてよい。 In step S5, initialization of the discrete “function map E” is executed. Here, a matrix [E] having a size of 2N × 2N is secured in advance, and the energy distribution (E _ij ) when an arbitrary point (coordinates (I, J)) on the function map is irradiated with the electron beam. Is calculated according to Equation 15 for each element of the matrix.

N is obtained by N = R (PSF domain) / s (discretization grid interval). Note that the PSF function used in Expression 15 may use the same approximate expression (for example, the double Gaussian approximate expression shown in Expression 14) used when determining the PSF domain. Further, when the energy distribution (E _ij ) is initialized, the energy calculation may be performed in consideration of the spot arrangement and density of each point.

FIG. 5 shows an example of a discrete “function map E”. In FIG. 5, elements for D _IJ = 1 are indicated by black circles, and elements for D _IJ = 0 are indicated by white circles. In this discrete “function map E”, a surface having a size of 2R × 2R (R is a PSF domain) is regarded as a set of points (elements), and D _{IJ is} obtained when each element is irradiated with an electron beam. The energy distribution E _ij from the quarter plane (only the range in the upper right of the coordinate axis xy in the figure) including only elements where = 1 is represented for each element.

In step S6, Ap _k (see Equation 8) that appears in the processing procedure for solving the determinant (Ax = b) by the conjugate gradient method is calculated by the stored energy calculation unit 39. As described above, in order to calculate the Ap _k by the stored energy calculating unit 39, the stored energy q _k at the determined energy evaluation point may be calculated. The stored energy q _k is energy (distribution) obtained by the resist by electron collision.

Here, the calculation procedure of the stored energy q _k at each evaluation point in the stored energy calculation unit 39 will be described with reference to FIG. FIG. 3 is a flowchart showing an embodiment of a stored energy calculation process at each evaluation point in the stored energy calculation unit A.

  Step S21 specifies one energy evaluation point (divided rectangle assumed to be an electron beam irradiation target; corresponding to the first rectangle). In step S22, one rectangle (corresponding to the second rectangle) among the rectangles obtained by dividing the figures Z1 to Z7, which is included in a predetermined range (influence range) that can affect the specified one energy evaluation point, is obtained. Determine to be processed. Here, as the “influence range”, which is a range that can affect the one specified energy evaluation point, for example, the outer periphery of a rectangle (first rectangle) is widened by about four times the forward scattering diameter. It may be determined to an arbitrary range such as a range of about 500 nm. In that case, it is preferable to determine the “influence range” according to how much the influence of forward scattering and the influence of back scattering are taken into account.

  In FIG. 4, as an example, in the case where it is assumed that the energy evaluation point H <b> 2 of the figure Z <b> 2 (first rectangle) is specified, the “influence range” that can affect the energy evaluation point H <b> 2 is indicated by a square frame indicated by a dotted line. It is shown for convenience. Then, one of the rectangle Z1a and the rectangle Z1b obtained by dividing the figure Z1 included in the “influence range” is sequentially determined as a processing target rectangle (second rectangle).

  A step S23 specifies a combination of quarter planes (third rectangles) having a plurality of arbitrary sizes forming the determined rectangle (second rectangle). In step S24, stored energy from each of the specified plurality of quarter planes is obtained using a discrete function map E (see FIG. 5). In step S25, the accumulated energy from the determined rectangle at the one specified energy evaluation point is obtained based on the obtained accumulated energy from each of the plurality of quarter planes.

  Here, the procedure for obtaining stored energy from a rectangle at one energy evaluation point according to the above-described steps S23 to S25 will be specifically described. For example, the case where the stored energy e (x, y) from the rectangle Z1a at the energy evaluation point H2 shown in FIG. 4 is obtained will be described as an example with reference to FIG. Here, it is assumed that the four sides of the rectangle Z1a are located at the coordinates (l, b, r, t), respectively. FIG. 7 is a conceptual diagram for explaining a procedure for obtaining stored energy from a rectangle at an arbitrary point using a discrete function map.

Here, an equation for obtaining the stored energy F (x, y) at an arbitrary point (x, y) using the above-described discrete function map E (see FIG. 5) is shown in Expression 16.

x _i represents the x coordinate position of each element on the function map E, and y _j represents the y coordinate position of each element on the function map E. As can be understood from Equation 16, the stored energy F (x, y) at an arbitrary point (x, y) is the four surrounding points surrounding the arbitrary point (x, y) in the discrete function map E. It is obtained by bilinear interpolation based on each energy distribution (E _ij ) of (element).

First, when the stored energy F (x, y) of the energy evaluation point H2 at the coordinate position (x, y) indicated by the x mark in the figure according to the above equation 16 is obtained, it can be expressed as F (xl, yb). This is based on the energy distribution of each element included in the quarter plane B1. That is, the stored energy F (x, y) at an arbitrary point (x, y) obtained by the above equation 16 is obtained according to the energy distribution (E _ij ) of all the elements included in a certain quarter plane. However, since the quarter plane B1 is a rectangle having a wider range including the rectangle Z1a (the range indicated by hatching in the figure), in order to obtain the stored energy from the rectangle Z1a at an arbitrary point (x, y), 16 cannot be used as it is, and it is necessary not to consider the energy distribution (E _ij ) of each element within the range not included in the rectangle Z1a.

  Therefore, in the present embodiment, a combination of a plurality of quarter planes (four quarter planes B1, B2, B3, and B4 in the example of FIG. 7) having a plurality of arbitrary sizes forming the rectangle Z1a is specified. (See step S23), the stored energy at an arbitrary point (x, y) in each of the specified plurality of quadrants is obtained according to equation 16 (see step S24), and the respective calculation results are added and subtracted from the rectangle Z1a. The stored energy e (x, y) is obtained (see step S25). Here, the quadrature plane B2 in the range where the y coordinate is larger than t in the quarter plane B1 and the quadrature plane B3 in the range where the x coordinate is larger than r in the quarter plane B1 are specified, and an arbitrary point ( Find the stored energy F (x, y) at x, y). A plurality of quarter planes B1, B2, and B3 forming these rectangles Z1a have a relationship as shown in FIG.

When the stored energy from the quarter planes B2 and B3 is obtained according to Equation 16, they can be expressed as F (xl, yt) and F (xr, yb), respectively. Therefore, in order not to consider the energy distribution (E _ij ) of each element included in the range not included in the rectangle Z1a as shown in FIG. 7, the stored energy F (xl, yb) based on the quarter plane B1 ), The stored energy F (xl, yt) and F (xr, yb) based on the quarter planes B2 and B3 are subtracted. However, this subtraction is not convenient because the overlapping partial range (the range surrounded by the dotted line in the figure) of each range shown in FIG. 7 is subtracted twice. Therefore, the accumulated energy F (xr, yt) based on the quarter plane B4 that is the partial range is added as an adjustment amount to the subtraction result. In this way, for example, the stored energy e (x, y) from the rectangle Z1a at the energy evaluation point H2 of the rectangle Z2 is obtained.

An example of the final equation for obtaining the stored energy e (x, y) from the rectangle Z1a at the energy evaluation point H2 of the rectangle Z2 can be expressed as in Expression 17.

Each term shown in Equation 17 is obtained by each energy distribution (E _ij ) of the four elements as shown in Equation 16, and the energy distribution (E _ij ) of each of these elements is previously determined by initialization according to _Equation 15. The value being calculated. According to Equation 17, the stored energy F (x, y) at an arbitrary point (x, y) can be obtained by simple calculation. If so, even if it is a case where the grid interval s between individual points needs to be set narrow in order to obtain an optimum irradiation amount of the electron beam with good correction accuracy, any point with high accuracy ( The stored energy F (x, y) at x, y) can be obtained at high speed, that is, without taking time.

By the way, there is a case where an arbitrary point for obtaining the stored energy from the rectangle is at a position outside the PSF definition area (that is, outside the function map). When an arbitrary point is located outside the PSF domain and it is necessary to refer to the energy distribution (E _ij ) outside the PSF domain, x and y are rounded up (or rounded down) to the boundary of the PSF domain. What is necessary is just to use the formula of the accumulated energy of time. An example is shown in FIG.

  FIG. 8 is a conceptual diagram showing an example of an equation of stored energy used when it is necessary to refer to an energy distribution outside the PSF domain. In FIG. 8, the outside of the square frame indicated by the bold line corresponds to the outside of the PSF definition area, and the stored energy expression when x and y are rounded up (or rounded down) to the boundary of the PSF definition area around the square frame. Shown for convenience. According to each stored energy formula F (x, y) shown in FIG. 8, it is understood that the value of the boundary of the PSF domain may be used when it is necessary to refer to a value outside the PSF domain. .

  Returning to the description of FIG. 3, step S26 accumulates the accumulated energy obtained for each rectangle included in the “influence range” calculated in the process. In step S27, it is determined whether or not the accumulated energy calculation has been performed for all rectangles included in the “influence range”. If it is determined that the accumulated energy calculation has not been performed for all rectangles having a positional relationship overlapping with the “influence range” (NO in step S27), the process returns to step S22 and is included in the “influence range”. The accumulated energy is calculated in the same manner for other rectangles. On the other hand, if it is determined that the accumulated energy calculation has been performed for all rectangles having a positional relationship overlapping with the “influence range” (YES in step S27), it is determined whether or not the above processing has been performed for all energy evaluation points. (Step S28).

  If it is determined that the above process has not been performed for all energy evaluation points (NO in step S28), the process returns to step S21. When it is determined that the above process has been performed for all energy evaluation points (YES in step S28), this process ends. In this way, the accumulated energy is obtained for each evaluation point determined for each rectangle after the figure division. That is, in the present embodiment, based on the energy distribution (discrete function map E) obtained in advance, the energy distribution is calculated individually for each of the quarter planes constituting the rectangle by the combination, and then accumulated. The accumulated energy of the energy evaluation points can be obtained at a high calculation speed.

Returning to the description of FIG. 2, in step S7, (p _k · q _k ) and (r _k · r _k ) of all the figures Z1 to Z7 are summed. In other words, find a Σp _k q _k and Σr _k r _k. In step S8, α _k = Σr _k r _k / Σp _k q _k (corresponding to the processing of Expression 8 in the processing procedure of the conjugate gradient method). In step S9, x and r of all the figures are set to x _{k + 1} = x _k + α _k p _k (corresponding to the processing of Formula 9 in the processing procedure of the conjugate gradient method)
r _{k + 1} = r _k −α _k p _k (corresponding to the processing of Formula 10 in the processing procedure of the conjugate gradient method)
And

In step S10, (r _{k + 1} · r _{k + 1} ) of all the figures are summed (hereinafter, this is described as ΣrrNext). Step S11 determines whether or not ΣrrNext is sufficiently small, that is, whether or not the calculation error is smaller than a preset allowable value. If it is determined that ΣrrNext is sufficiently small (YES in step S11), the iterative calculation is terminated and the column vector x is output as the optimum correction amount for each figure (step S15).

On the other hand, if it is determined that ΣrrNext is not sufficiently small (NO in step S11), the process returns to the process in step S6 after performing the processes in step S12, step S13, and step S14. Run repeatedly. In step S12, β _k = ΣrrNext / Σr _k r _k (corresponding to the processing of Formula 11 in the processing procedure of the conjugate gradient method). In step S13, p of all figures is updated to p _{k + 1} = r _{k + 1} + β _k p _k (corresponding to the process of Formula 12 in the processing procedure of the conjugate gradient method). In step S14, “1” is added to the number of repetitions k (corresponding to the processing of Equation 13 in the processing procedure of the conjugate gradient method).

  Note that the repetition condition for determining whether or not to repeat the above-described calculation process is not limited to the above-described condition on the magnitude of ΣrrNext (see step S11). For example, there is a method of setting the number of iterations after investigating the number of iterations that converges in advance by simulation or the like, and a method of confirming that the error no longer fluctuates even after repeated calculations. Theoretically, the maximum upper limit number of repetitions is m.

  As described above, in this embodiment, a calculation method of accumulated energy from each rectangle obtained by dividing a pattern to be drawn on a sample, which needs to be calculated prior to obtaining the optimum irradiation amount of the electron beam with the proximity effect corrected. In relation to the above, a discrete function map composed of energy distributions for each of a plurality of elements is obtained in advance, and stored energy from each rectangle is obtained according to this function map. According to this, since it is only necessary to perform a simple calculation according to the function map obtained in advance, that is, the energy distribution of each element, the accumulated energy from each rectangle at an arbitrary point is speeded up, that is, it takes time. It will be able to ask without. Moreover, even when the grid interval of each element is set to be narrow, there is an advantage that the accumulated energy from a rectangle with high accuracy can be obtained in a short time.

  As mentioned above, although an example of embodiment was demonstrated based on drawing, this invention is not limited to this, It cannot be overemphasized that various embodiment is possible. For example, in the above-described embodiments, the drawing method according to the present invention is applied to a variable shaped beam type electron beam drawing apparatus. However, the drawing method can be applied to other types of drawing apparatuses. Further, the present invention can be applied to an ion beam drawing apparatus using an ion beam instead of an electron beam. Further, the present invention is not limited to the intended use of the electron beam drawing apparatus. For example, in addition to the purpose of directly forming a resist pattern on a wafer, the present invention can also be used when creating an X-ray mask, an optical stepper mask, a reticle, and the like. In addition, various modifications can be made without departing from the scope of the present invention.

The drawing method according to the present invention can be applied to the case where the accumulated energy from each rectangle used for obtaining the optimum electron beam dose with the proximity effect corrected as described above is obtained according to the above processing. As well as, for example, when it is assumed that the electron beam was irradiated according to the dose for each arbitrarily input rectangle so that the user can determine the optimum dose of the electron beam based on the drawing prediction It goes without saying that the present invention can also be applied to the case of calculating the stored energy from each rectangle used when performing the simulation process for displaying the circuit pattern formed on the substrate. That is, you may use when simulating energy distribution.
In the above-described embodiments, the method of calculating the optimum electron beam dose using the conjugate gradient method is shown. However, the present invention is not limited to this, and the accumulated energy described later in the process of deriving the optimum electron beam dose is described. Any other conventionally known method such as a self-alignment method may be adopted as long as it includes a calculation process. However, as described above, the use of the conjugate gradient method is more advantageous than the use of other conventionally known methods such as the self-alignment method because the calculation time can be further shortened.

10 ... Sample chamber 11 ... Target (sample)
DESCRIPTION OF SYMBOLS 12 ... Sample stage 20 ... Electro-optic lens barrel 21 ... Electron gun 31 ... Sample stage drive circuit unit 32 ... Laser length measurement system 33 ... Deflection control circuit unit 34 ... Blanking control circuit unit 35 ... Variable shaping beam size control circuit unit 36 ... buffer memory and control circuit part 37 ... control calculation part 38 ... common benefit gradient method calculation part 39 ... stored energy calculation part 40 ... CAD system H2 ... energy evaluation points Z1 to Z7 ... figure (circuit pattern)

Claims (6)

In order to obtain the optimum electron beam irradiation amount for reducing the dimensional change of the pattern due to the proximity effect for each arbitrary rectangle that divides the circuit pattern to be drawn on the sample, the first electron beam irradiation target is obtained. A drawing method for obtaining, for each of the second rectangles, stored energy that is a substantial electron beam irradiation amount from a second rectangle other than the first rectangle within a predetermined range with respect to the rectangle;
Obtaining a discrete function map comprising energy distributions for each of a plurality of elements when an electron beam is irradiated at a predetermined position;
And a step of obtaining stored energy from the second rectangle according to the obtained discrete function map. The step of obtaining the discrete function map includes a discrete function map,

(Where s: grid spacing between elements, N: R / s (R is PSF domain))
The drawing method according to claim 1, wherein the drawing method is obtained by: The step of determining the stored energy from the second rectangle includes the stored energy from the second rectangle,

(Where x: X coordinate position of an arbitrary point on the first rectangle, y; Y coordinate position of an arbitrary point on the first rectangle, x _i ; x coordinate position of each element on the function map, y _j ; Y coordinate position of each element on the function map, s; grid spacing between each element, N; R / s (R is PSF domain)
The drawing method according to claim 2, wherein the drawing method is obtained based on the above.   The step of obtaining stored energy from the second rectangle includes a step of specifying a combination of a plurality of third rectangles having an arbitrary size according to the second rectangle, and a plurality of the specified plurality according to a discrete function map. The drawing according to claim 3, further comprising: obtaining stored energy for each of the third rectangles; and adding / subtracting the obtained stored energy from the third rectangle in accordance with the combination mode. Method. In order to obtain the optimum electron beam irradiation amount for reducing the dimensional change of the pattern due to the proximity effect for each arbitrary rectangle that divides the circuit pattern to be drawn on the sample, the first electron beam irradiation target is obtained. A drawing apparatus for obtaining, for each of the second rectangles, stored energy that is a substantial electron beam irradiation amount from a second rectangle other than the first rectangle within a predetermined range with respect to the rectangle of
Means for obtaining a discrete function map comprising energy distributions for each of a plurality of elements when an electron beam is irradiated at a predetermined position;
A drawing apparatus comprising: calculating means for obtaining stored energy from the second rectangle according to the obtained discrete function map.   The program for making a computer perform each step in the drawing method in any one of Claims 1 thru | or 4.

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