JP6286987B2 - Proximity effect correction method, proximity effect correction program, and proximity effect correction device - Google Patents

Description

  The present invention relates to exposure amount correction for reducing the influence of proximity effect generated in a charged particle beam irradiation process in charged particle lithography, and performs correction with higher accuracy than a correction method based on a conventional Gaussian function. The present invention relates to a proximity effect correction method, a proximity effect correction program, and a proximity effect correction apparatus that are enabled.

  Semiconductor photomasks and nanoimprint molds require high-resolution and high-accuracy pattern fabrication, and therefore lithography methods using charged particles are used. In recent years, higher resolution has been demanded.

  In charged particle lithography, it is known that when charged particles are incident on a resist formed on a substrate, reflected particles (backscattering) from the substrate re-enter the resist. Due to this backscattering, for example, when a plurality of adjacent figures are drawn, the apparent exposure amount increases. Further, since the influence of backscattering extends to several tens of μm, even if the exposure amount is the same, the apparent exposure amount differs between a dense pattern and an isolated pattern. As a result, there is a difference between the actual pattern and the design dimension. The above phenomenon is called a proximity effect, and in order to create a highly accurate pattern, it is necessary to draw with an exposure amount that corrects this proximity effect.

ここで、σｆは前方散乱、σｂは後方散乱によるエネルギーの広がりを表す。ηは前方散乱によるエネルギー量と後方散乱によるそれとの比である。式（数１）の右辺第１項は前方散乱を表し、第二項目は後方散乱を表す。 In general, the amount of energy E (x) accumulated in a resist by a particle beam incident on one point on the resist is expressed by a Gaussian function as shown in Equation (Equation 1).

Here, σf represents forward scattering, and σb represents the spread of energy due to backscattering. η is the ratio of the amount of energy due to forward scattering to that due to backscattering. The first term on the right side of the equation (Equation 1) represents forward scattering, and the second item represents backscattering.

周辺のｎ個の図形からのエネルギーＵｉは、式（数３）で表される。

位置Ｘｊ、Ｙｊにおける最適な露光量Ｄｊは、例えば式（数４）もしくは式（数５）で表すことができる。

Ｋは定数である。

η_０は定数である。 The proximity effect correction is calculated by using the backscattering term of the equation (Equation 1) and using the influence of backscattering on the figure obtained from the positional relationship and area of each figure to be drawn. For example, the amount of energy ebi extending from the figure at the center position Xi, Yi, and the dimensions W1, W2 to the position Xj, Yj is expressed by Expression (Equation 2).

The energy Ui from the n surrounding figures is expressed by the formula (Equation 3).

The optimum exposure amount Dj at the positions Xj and Yj can be expressed by, for example, Expression (Expression 4) or Expression (Expression 5).

K is a constant.

η ₀ is a constant.

  As shown in the above equation (Equation 4), there are many methods for expressing the extent of backscattering and the amount of energy by a Gaussian function and correcting the exposure amount based on this.

  There is a method in which the correction of the equation (Equation 4) is performed on each figure, and a correction amount of each figure is obtained by making a subroutine. However, this method takes an enormous amount of time for the correction amount to converge.

  Also, for example, using the integration of the Gaussian function shown in Equation (2), the amount of backscattering by the representative figure is obtained in advance, the figure periphery is blocked, and the influence of the figure on each block is tabulated. There is a method for shortening the time (see Patent Document 1).

  Further, it is assumed that one Gaussian function is insufficient for representing the energy and spread of backscattering, and there is a method of calculating a proximity effect correction amount using a plurality of Gaussian functions. In this method, the scattering width of each Gaussian function, that is, σb in the equation (Equation 1) is different. The drawing area is divided into a large number of micro areas, and the proximity effect correction amount is calculated for each area. However, since the scattering width of each Gaussian function is different, the affected range (number of micro areas to be included in the calculation) is also different. . The proximity effect correction amount in the minute region including the positions Xj and Yj is calculated by performing convolution of the plurality of Gauss functions (see Patent Document 2).

Japanese Patent No. 3011684 Japanese Patent No. 3120051

  The above prior art is a method based on the assumption that a Gaussian function is appropriate as an expression representing the relationship between the amount of energy of backscattering and the affected area. However, if the distribution of energy accumulated in the resist is created using electron beam scattering simulation and the Gaussian function is adapted, a good approximation is not always obtained.

  FIG. 2 is a diagram illustrating an example of a resist film thickness and a substrate structure. In FIG. 2, a resist 1 is formed on a substrate 2 having a metal film. FIG. 3 is a diagram showing the accumulated energy distribution (EID function) in the resist 1 in FIG. FIG. 3 shows the result of matching the accumulated energy distribution and the Gaussian function due to backscattering when an electron beam is incident on one point of the resist 1. As shown in FIG. 3, the Gaussian function represents the phenomenon that the stored energy spreads and the stored energy decreases as the distance from the incident point of the electron beam decreases, but the distance from the center (the incident point of the electron beam). The slope is clearly different between the Gaussian function and the accumulated energy distribution from around 10 μm. The Gaussian function cannot represent a steep slope like the accumulated energy distribution of FIG.

  In the method of Patent Document 2 described above, it is inappropriate to express the amount of backscattering by one Gaussian function, and a plurality of Gaussian functions are used. However, since the influence ranges of each Gaussian function are different, Considering the influence of the backscattering amount between the minute regions, the calculation is complicated.

  As described above, even if the exposure amount is corrected using an approximate function with poor accuracy, it cannot be corrected with sufficient accuracy for an ultra-fine structure, and with a higher accuracy by increasing the number of approximate functions. Even if the amount of backscattering is expressed, there is a problem that enormous calculation is required to actually apply it to the proximity effect correction.

  The present invention solves the above-described problem. By using an approximate function that can represent backscattering more accurately than a Gaussian function that has been used in the prior art, a pattern can be obtained without increasing the amount of calculation. An object of the present invention is to provide a proximity effect correction method, a proximity effect correction program, and a proximity effect correction device that can improve accuracy.

  The present invention is a proximity effect correction with higher accuracy in order to form a pattern with high resolution and high accuracy using charged particle lithography, such as semiconductors, semiconductor photomasks, nanoimprint molds, optical-related elements, biochips, etc. This is for calculating the quantity.

In view of the above problems, the proximity effect correction apparatus according to the present invention relates to charged particle lithography in which a pattern design is drawn, baked, and developed on a resist film formed on a substrate. A proximity effect correction device that obtains a backscatter amount that depends, represents the backscatter amount by an approximate function, and acquires a proximity effect correction amount using the approximate function,
An input unit for inputting information such as drawing pattern design information, a substrate for obtaining a backscattering amount in simulation, a resist film thickness, and charged particle conditions;
A backscattering amount acquisition unit for acquiring an in-resist accumulated energy distribution (EID function) obtained when charged particles are incident on one point on a resist formed on a substrate;
An approximate function acquisition unit that interpolates backscattering amount and spread by fitting an appropriate approximate function to the EID function;
A proximity effect correction amount acquisition unit at positions Xj and Yj that calculates an optimal proximity effect correction amount of the drawing figure at the positions Xj and Yj using the approximation function;
A proximity effect correction amount acquisition unit for all graphics, calculating the proximity effect correction amount for all graphics using the proximity effect correction amount, the drawing pattern design and the approximation function;
A proximity effect correction amount reacquisition unit that recalculates the proximity effect correction amounts of the positions Xj and Yj reflecting the proximity effect correction amounts of all the acquired figures;
The difference between the proximity effect correction amount calculated by the proximity effect correction amount reacquisition unit and the proximity effect correction amount calculated by the proximity effect correction amount acquisition unit at the positions Xj and Yj is taken, and the difference is within an allowable range. If the determination is negative, the proximity effect correction amount calculated by the proximity effect correction amount reacquisition unit is input to the proximity effect correction amount acquisition unit for all the figures, and the determination is affirmative A determination unit that inputs the proximity effect correction amount calculated by the proximity effect correction amount reacquisition unit to the output unit;
An output unit that outputs the proximity effect correction amount input from the determination unit together with information of the drawing pattern design;
It is characterized by providing.

で表される式に従って、後方散乱量や近接効果補正量を算出してもよい。 In the proximity effect correction device, when the accumulated energy value is E and the horizontal direction is X as the approximation function for interpolating the backscattering amount and its spread included in the EID function,

The backscattering amount and the proximity effect correction amount may be calculated according to the formula expressed by:

In view of the above problems, the proximity effect correction method according to the present invention relates to charged particle lithography in which a pattern design is drawn, baked, and developed on a resist film formed on a substrate. Is a proximity effect correction method for obtaining a backscattering amount that depends on, expressing the backscattering amount by an approximate function, and obtaining a proximity effect correction amount using the approximate function,
An input step for inputting information such as drawing pattern design information, substrate and resist film thickness for obtaining backscattering amount in simulation, conditions of charged particles,
A backscattering amount acquisition step of acquiring an accumulated energy distribution (EID function) in the resist obtained when charged particles are incident on one point on the resist formed on the substrate;
An approximate function acquisition step of interpolating backscattering amount and spread by fitting an appropriate approximate function to the EID function;
A proximity effect correction amount acquisition step at positions Xj and Yj for calculating an optimal proximity effect correction amount of the drawing figure at the positions Xj and Yj;
Calculating a proximity effect correction amount for all graphics using the proximity effect correction amount, the drawing pattern design, and the approximation function;
A proximity effect correction amount reacquisition step of calculating again the proximity effect correction amounts of the positions Xj and Yj, reflecting the acquired proximity effect correction amounts of all the figures;
The difference between the correction amount calculated in the proximity effect correction amount reacquisition step and the proximity effect correction amount calculated in the proximity effect correction amount acquisition step at the positions Xj and Yj is calculated, and whether or not the difference is within an allowable range. If the determination is negative, the proximity effect correction amount calculated in the proximity effect correction amount reacquisition step is input to the proximity effect correction amount acquisition step in all the figures, and if the determination is affirmative, A determination step of inputting the proximity effect correction amount calculated in the proximity effect correction amount reacquisition step to the output means;
An output step of outputting the proximity effect correction amount input from the determination step together with information of the drawing pattern design;
It is characterized by providing.

In view of the above problems, the proximity effect correction program according to the present invention relates to charged particle lithography in which a pattern design is drawn, baked, and developed on a resist film formed on a substrate. A proximity effect correction program for obtaining a dependent backscattering amount, expressing the backscattering amount as an approximate function, and causing the computer of the proximity effect correction device to acquire the proximity effect correction amount using the approximate function,
The computer,
Input means for inputting information such as drawing pattern design information, substrate and resist film thickness for obtaining backscattering amount in simulation, conditions of charged particles,
Backscattering amount acquisition means for acquiring an accumulated energy distribution (EID function) in the resist obtained when charged particles are incident on one point on the resist formed on the substrate;
An approximation function acquisition means for interpolating backscattering amount and spread by fitting an appropriate approximation function to the EID function;
A proximity effect correction amount acquisition means at positions Xj and Yj for calculating an optimal proximity effect correction amount of the drawing figure at the positions Xj and Yj;
A proximity effect correction amount acquisition unit for all graphics, calculating the proximity effect correction amount for all graphics using the proximity effect correction amount, the drawing pattern design and the approximation function;
A proximity effect correction amount reacquisition unit that recalculates the proximity effect correction amounts of the positions Xj and Yj reflecting the proximity effect correction amounts of all the acquired figures;
The difference between the proximity effect correction amount calculated by the proximity effect correction amount reacquisition unit and the proximity effect correction amount calculated by the proximity effect correction amount acquisition unit at the positions Xj and Yj is taken, and the difference is within an allowable range. If the determination is negative, the proximity effect correction amount calculated by the proximity effect correction amount reacquisition means is input to the proximity effect correction amount acquisition means for all the figures, and the determination is affirmative The determination means for inputting the proximity effect correction amount calculated by the proximity effect correction amount reacquisition means to the output means,
It is a program that functions as an output unit that outputs the proximity effect correction amount input from the determination unit together with the drawing pattern design information.

  According to the present invention, the proximity effect correction amount is calculated without increasing the amount of calculation by using an approximate function that can represent backscattering more accurately than the Gaussian function that has been used in the prior art, Pattern accuracy can be improved.

The block diagram which shows embodiment of this invention and shows an example of a structure of a proximity effect correction apparatus A figure showing an example of resist film thickness and substrate structure The figure showing the accumulated energy distribution (EID function) in the resist in FIG. The figure which shows an example of the drawing pattern in the Example of this invention The figure which shows the Example of this invention and represents the adaptability to the EID function of a Gaussian function and a Tanh function The figure which shows the Example of this invention and represents the relationship between the distance from Xj and Yj, and the amount of backscattering. The figure which shows the Example of this invention and shows the proximity effect correction amount with respect to the distance with Xj and Yj

Hereinafter, a proximity effect correction system 100 according to an embodiment of the present invention will be described with reference to FIG. FIG. 1 is a schematic block diagram showing a configuration of a proximity effect correction system 100 according to the present embodiment.
As shown in FIG. 1, the proximity effect correction system 100 includes an input unit (input unit) 101, a storage unit (storage unit) 102, a backscattering amount acquisition unit (backscattering amount acquisition unit) 103, and an approximate function acquisition unit ( (Approximation function acquisition means) 104, a proximity effect correction amount acquisition unit (proximity effect correction amount acquisition means) 105 for acquiring the proximity effect correction amounts in the graphics at positions Xj and Yj, and the proximity effect correction amounts of all the figures. A proximity effect correction amount acquisition unit (proximity effect correction amount acquisition unit) 106 and a proximity effect correction amount reacquisition unit (proximity effect correction amount) that recalculates the proximity effect correction amount of the figure at positions Xj and Yj from the corrected exposure amount (Re-acquisition means) 107 and the proximity effect correction amount acquired by the proximity effect correction amount acquisition unit 105 are compared with the proximity effect correction amount acquired by the proximity effect correction amount re-acquisition unit 107, and whether or not the difference is within an allowable range. To judge Comprising a determining unit (determining means) 108, and an output unit (output means) 109.

  The proximity effect correction system 100 has a computer configuration, and is a system related to charged particle lithography that draws and develops a pattern on a resist film formed on a substrate. The proximity effect correction system 100 includes the above-described units in cooperation with a proximity effect correction program for accurately calculating a proximity effect correction amount from a backscatter amount and enabling high-accuracy pattern production. The proximity effect correction system 100 may be configured only by hardware such as a dedicated LSI.

  In the present embodiment, the proximity effect correction apparatus 100 will be described with reference to an example in which the backscattering amount is obtained using simulation, but the apparatus 100 is not limited to this form. For example, the resist pattern may be actually formed by charged particle lithography, the backscattering amount may be obtained from the result, and the proximity effect correction amount may be determined. In the present embodiment, numerical values and parameters used for numerical calculation are examples of the minimum necessary elements, and the backscattering amount and the proximity effect correction amount may be acquired using other elements. .

  The input unit 101 receives input of information used by the proximity effect correction apparatus 100 and stores it in the storage unit 102. Information such as a pattern design to be drawn is input to the input unit 101. The input unit 101 includes a transmission / reception interface for receiving transmission data from the outside of the proximity effect correction apparatus 100, an input interface for inputting data from an external storage device, a man-machine interface using a display, a keyboard, a mouse, a tablet, and the like The input device can be used.

  In addition to the drawing pattern design information, the input unit 101 receives information on the substrate material, resist film thickness, and charged particle conditions (exposure amount) necessary for calculating the backscattering amount. Details of these will be described later.

  The storage unit 102 stores information input from the input unit 101. The storage unit 102 stores drawing pattern design, substrate material, resist film thickness, and charged particle condition information input from the input unit 101. The storage unit 102 can be configured using a storage device such as a RAM, a flash memory storage device, a magnetic disk storage device, and an optical disk storage device.

  Based on the substrate material, resist film thickness, and charged particle conditions stored in the storage unit 102, the backscattering amount acquisition unit 103 assumes that charged particles are incident on one point on the resist and is accumulated in the resist. Energy distribution (EID: Exposure Intensity Distribution). EID includes information on the amount of backscattering. At this time, the calculation range is calculated with a sufficiently wide range in consideration of the spread of charged particles due to elastic scattering. The EID function is expressed by a combination of stored energy by forward scattering and back scattering of charged particles. In the present embodiment, the backscattering amount is obtained by simulation. Actually, charged particle lithography is performed, and the relative backscattering amount with respect to the forward scattering is obtained from the created pattern dimensions and the drawing density and pattern positional relationship. Also good. The acquired backscattering amount is output to the approximate function acquisition unit 104.

ここで、η´はエネルギーの高さ、α、Ｘ´はエネルギーの広がりを表す係数である。取得した近似関数の情報は、位置Ｘｊ、Ｙｊの図形における近接効果補正量取得部１０５に出力される。 The approximate function acquisition unit 104 acquires information on the backscattering amount from the backscattering amount acquisition unit 103, and adapts the approximate function to the backscattering amount. As an approximate function, it is represented by a Tanh function (Tanh: hyperbolic tangent) as shown in Equation (7).

Here, η ′ is the energy height, and α and X ′ are coefficients representing the energy spread. Information about the acquired approximate function is output to the proximity effect correction amount acquisition unit 105 for the figures at the positions Xj and Yj.

Ｋは定数である。

η_０は定数である。 The proximity effect correction amount acquisition unit 105 for the figures at the positions Xj and Yj acquires the information on the approximation function and the information on the drawing pattern design stored in the storage unit 102 from the approximation function acquisition unit 104. The proximity effect correction amount in the figure is calculated.
The proximity effect correction amount acquisition unit 105 calculates the backscattering amount Uj for the positions Xj and Yj, for example, by substituting the positions and areas of the drawing figures around the positions Xj and Yj into the equation (Equation 7). Note that the method of calculating the backscattering amount Uj is not limited to this. For example, the backscattering amount with respect to the drawing density in an arbitrary region is obtained in advance using Expression (Equation 7), and the position Xj, The backscattering amount Uj that affects the positions Xj and Yj may be obtained from the drawing area density around Yj.
By the above method, all the backscattering amounts given to the positions Xj and Yj are obtained from the graphics around the positions Xj and Yj, and the expression (Equation 8) or the expression (Equation 9) so that the backscattering amount does not affect the pattern size accuracy. Use to find the proximity effect correction amount. The obtained proximity effect correction amount (corrected exposure amount Dj) in the figure at the positions Xj and Yj is output to the proximity effect correction amount acquisition unit 106 of all figures. Note that “all figures” here refers to all figures except for figures at positions Xj and Yj.

K is a constant.

η ₀ is a constant.

The proximity effect correction amount acquisition unit 106 for all figures acquires information on the approximation function from the approximation function acquisition unit 104, and the proximity effect at the positions Xj and Yj from the proximity effect correction amount acquisition unit 105 for the graphics at the positions Xj and Yj. The correction amount and the drawing pattern design information stored in the storage unit 102 are acquired.
The proximity effect correction amount acquisition unit 106 for all the figures uses the proximity function information obtained, the proximity effect correction amounts for the positions Xj and Yj, and the drawing pattern design information for the proximity of the figures at the positions Xj and Yj. In the same manner as the effect correction amount acquisition unit 105, the proximity effect correction amount is calculated for all the drawing figures (except for the figures at the positions Xj and Yj). The acquired proximity effect correction amounts of all the figures are output to the proximity effect correction amount reacquisition unit 107 of the figures at the positions Xj and Yj.

  The proximity effect correction amount reacquisition unit 107 stores, in the storage unit 102, information on the proximity effect correction amounts of all the graphics excluding the graphics at the positions Xj and Yj from the proximity effect correction amount acquisition unit 106 of all the graphics. The information of the drawing pattern design being acquired is acquired, and the proximity effect correction amount in the figure at the positions Xj and Yj is acquired again (recalculated). The acquisition method is the same method as the proximity effect correction amount acquisition unit 105 in the figures at the positions Xj and Yj. The re-acquired proximity effect correction amount includes the proximity effect correction amount calculated by the proximity effect correction amount acquisition unit 105 in the figure at the positions Xj and Yj and the proximity effect correction amount calculated by the proximity effect correction amount re-acquisition unit 107. The difference is output to the determination unit 108 that determines whether or not the difference is within an allowable range.

  The determination unit 108 calculates the proximity effect correction amount calculated by the proximity effect correction amount acquisition unit 105 for the graphics at positions Xj and Yj and the proximity effect correction amount calculated by the proximity effect correction amount reacquisition unit 107 for the graphics at positions Xj and Yj. And calculate the difference between them. If the obtained difference is within the allowable range, the proximity effect correction amount information calculated by the proximity effect correction amount reacquisition unit 107 is output to the output unit 109 together with the drawing pattern design information acquired from the storage unit 102. If the difference is outside the allowable range, the proximity effect correction amount calculated by the proximity effect correction amount reacquisition unit 107 is output to the proximity effect correction amount acquisition unit 106 of all figures. Then, the proximity effect correction amount acquisition unit 106 for all the figures performs recalculation of the proximity effect correction amount for all the graphics, and outputs the result of the recalculation to the proximity effect correction amount reacquisition unit 107. Then, the proximity effect correction amount reacquisition unit 107 and the determination unit 108 perform processing similar to the processing described above. The processes of the proximity effect correction amount acquisition unit 106, the proximity effect correction amount reacquisition unit 107, and the determination unit 108 for all figures are repeated until the difference calculated by the determination unit 108 falls within the allowable range.

  The processing in the proximity effect correction amount acquisition unit 106, the proximity effect correction amount reacquisition unit 107, and the determination unit 108 may be calculated as a subroutine. In order to reduce the calculation amount, a proximity effect correction amount depending on the position and the drawing area may be calculated in advance based on the formula (Equation 7) and applied in a table form.

  The output unit 109 acquires and outputs the proximity effect correction amount and drawing pattern design information (drawing pattern position and area information) input from the determination unit 108. The output unit 109 can be configured using an output device such as an output interface connected to an external computer, a memory, or the like.

  By performing charged particle lithography using the proximity effect correction amount output from the output unit 109, a desired resist pattern shape can be created.

  The process of operation of the proximity effect correction apparatus 100 described above is stored in a computer-readable recording medium in the form of a program, and the above processing is performed by the computer system reading and executing this program. The “computer system” herein includes a CPU, various memories, an OS, and hardware such as peripheral devices. Further, the “computer system” includes a homepage providing environment (or display environment) if a WWW (Internet) environment system is used.

Examples are shown below.
In this embodiment, a positive resist is used, but the present invention can also be applied to a negative resist.
As shown in FIG. 1, first, a drawing pattern design is input to the input unit 101. The input pattern design is stored in the storage unit 102. In the present embodiment, a 400 nm Line & Space pattern as shown in FIG. 4 is used. In addition, the substrate condition, resist film thickness, and charged particle condition (exposure amount) are input to the input unit 101. The substrate structure and resist film thickness shown in FIG. 2 are used.

Next, the backscattering amount acquisition unit 103 accumulates when charged particles are incident on one point on the resist 1 based on the substrate conditions, resist film thickness, and charged particle conditions (exposure amount) acquired from the storage unit 102. Get energy distribution. In this embodiment, the energy accumulated in the resist 1 by inelastic scattering is calculated from inner-shell electron excitation, valence electron excitation, free electron excitation, plasmon excitation, etc., but Bethe's stopping power may be used. As a calculation range, a sufficiently wide region is calculated in consideration of scattering due to elastic scattering of charged particles. In this embodiment, the range of radius 25 μm and depth 50 μm is calculated. Further, an electron beam of 50 keV is assumed as the charged particle beam.
FIG. 5 shows a resist accumulation energy distribution (EID function) when an electron beam is incident at 1 C (Coulomb) on one point on the resist 1 with respect to the structure of FIG. It can be seen that the closer to the incident point, the higher the stored energy value, and the farther away, the lower the stored energy.

  Next, the approximate function acquisition unit 104 adapts the approximate function (Tanh function) to the EID function obtained by the backscattering amount acquisition unit 103. FIG. 5 shows a case where a conventional Gaussian function is adapted to an EID function and a result obtained by fitting a Tanh function shown in Expression (Equation 7). Since the proximity effect correction method of the present invention is for reducing the influence of backscattering reflected from the substrate, compatibility with energy due to other factors such as forward scattering is excluded. In the region from the distance of 1 μm to the vicinity of 10 μm from the center, both approximate functions are well adapted to the EID function, but in the region far from the center point by about 10 μm, than the conventional Gaussian function, Tanh It can be seen that the function fits better against a steep slope. Information on the approximate function (Tanh function) obtained by the fitting is output to the proximity effect correction amount acquisition unit 105 in the graphic at the positions Xj and Yj.

The proximity effect correction amount acquisition unit 105 for the figures at the positions Xj and Yj uses the drawing pattern design stored in the storage unit 102 and the information on the approximation function acquired from the approximation function acquisition unit 104 to obtain the figure of the figure at the positions Xj and Yj. The proximity effect correction amount is calculated.
The amount of backscattering can be expressed in combination with various factors related to backscattering, such as the position of the peripheral graphic with respect to the positions Xj and Yj, the drawing area of the peripheral graphic, and the drawing area density including the peripheral graphic. As shown in FIG. 4, the backscattering amount that affects the positions Xj and Yj from other Line & Space patterns is plotted against the distance from the positions Xj and Yj, with the pattern of the positions Xj and Yj and the width of 400 nm as the center.

The amount of backscattering is calculated for the distance pattern from the positions Xj and Yj and the area of the peripheral figure, here a Space pattern with a width of 0.4 nm, using the integration of equation (Equation 7). The result of the backscattering amount obtained from the integration of the Tanh function is shown in FIG. For comparison, FIG. 6 shows the backscattering amount obtained by superimposing the EID function and the backscattering amount obtained from the integration of the Gaussian function of the prior art.
From FIG. 6, it can be seen that the pattern farther from the positions Xj and Yj has a smaller influence of the backscattering effect. As can be seen from the degree of matching between the EID function and the approximate function shown in FIG. 5, in FIG. 6, the Gaussian function and the Tanh function do not have much difference in the region where the distance from the positions Xj and Yj is short, and the EID function It matches well with the overlay. However, as the distance from the positions Xj and Yj increases, it can be seen that the Gaussian function of the prior art starts to deviate from the superposition of the EID functions, and the Tanh function is better suited.

The proximity effect correction amount is calculated using the backscattering amount by the Tanh function shown in FIG. 6 and the equation (Equation 8) or the equation (Equation 9). When the backscattering amount is large, the proximity effect correction amount serves to adjust the exposure amount to be a threshold energy for resolving the resist 1 when the backscattering amount is large. In this embodiment, the case where the line & space pattern having a width of 0.4 μm is in the region of 48 μm (see FIG. 4) is used as a reference, and the proximity effect correction amount at this time is 0 and the exposure amount is 1.
FIG. 7 shows the result of calculating the proximity effect correction amount with respect to the distance between the positions Xj and Yj based on FIG. From FIG. 7, it can be seen that the proximity effect correction amount obtained from the Tanh function is more suitable than the proximity effect correction amount obtained from the superposition of the EID functions.
As the proximity effect correction amount, it is clear that patterning can be performed with higher accuracy if it is calculated using an approximate function (Tanh function) that matches well with the superposition of EID functions.
In the present embodiment, the backscattering amount is calculated using simulation, but the backscattering amount and the affected range may be obtained by actually performing charged particle lithography. In this case, the coefficient of the Tanh function is obtained by adapting the integration of Expression (7) to the backscattering amount obtained in the experiment.
The proximity effect correction amount acquisition unit 105 for the graphics at the positions Xj and Yj outputs the calculated proximity effect correction amount to the proximity effect correction amount acquisition unit 106 for all the graphics.

The proximity effect correction amount acquisition unit 106 for all figures uses the drawing pattern design stored in the storage unit 102 and the information on the approximate function acquired from the proximity effect correction amount acquisition unit 105 for the graphics at positions Xj and Yj. The proximity effect correction amount is calculated for all figures other than the positions Xj and Yj.
The proximity effect correction amount acquisition unit 106 for all the figures outputs the calculated proximity effect correction amount together with the drawing pattern design information to the proximity effect correction amount reacquisition unit 107 for the graphics at positions Xj and Yj.

The proximity effect correction amount reacquisition unit 107 for the graphics at positions Xj and Yj uses the proximity effect correction amounts for all the graphics obtained from the proximity effect correction amount acquisition unit 106 for all graphics, to obtain the graphics at positions Xj and Yj. Recalculate the proximity correction amount at. Also at this time, the integral of equation (Equation 7) is used. Further, the backscatter amount from the graphics around the positions Xj and Yj reflects the proximity effect correction amount acquired from the proximity effect correction amount acquisition unit 106 of all the graphics.
The proximity effect correction amount reacquisition unit 107 outputs the proximity effect correction amount in the figure at the positions Xj and Yj obtained by recalculation to the determination unit 108.

  The determination unit 108 calculates the difference between the calculation result of the proximity effect correction amount acquisition unit 105 and the calculation result of the proximity effect correction amount reacquisition unit 107 in the graphics at the positions Xj and Yj. If the difference is outside the allowable range, the determination unit 108 selects negative (No). When the determination is negative (No), the proximity effect correction amount calculated by the proximity effect correction amount reacquisition unit 107 is output to the proximity effect correction amount acquisition unit 106 of all figures. If the difference is within the allowable range, the determination unit 108 selects affirmative (Yes). If the determination is affirmative (Yes), the determination unit 108 inputs the proximity effect correction amount calculated by the proximity effect correction amount reacquisition unit 107 to the output unit 109 together with the drawing pattern design.

Based on the proximity effect correction amount output from the output unit 109, the exposure amount of the figure is determined, and charged particle lithography is performed. In the present embodiment, an example in which the proximity effect correction amount is calculated for a graphic is shown, but it may be applied by dividing it in an arbitrary area instead of a graphic.
By using the approximate function of Expression (7), it is possible to calculate the proximity effect correction amount with higher accuracy in a wider range where backscattering is performed than in the method using Expression (Expression 1) representing the conventional technique. It was.

  The present invention is preferably applied to proximity effect correction for creating a fine pattern using charged particle lithography, such as a part of a semiconductor or a photomask for a semiconductor, a mold for nanoimprint, an optical-related element, a biochip, etc. Can do.

DESCRIPTION OF SYMBOLS 1 Resist 2 Board | substrate 3 Drawing pattern 100 Proximity effect correction apparatus 101 Input part (input means)
102 Storage unit (storage device)
103 Backscattering amount acquisition unit (backscattering amount acquisition means)
104 Approximate function acquisition unit (approximate function acquisition means)
105 Proximity Effect Correction Amount Acquisition Unit for Figures at Positions Xj and Yj (Proximity Effect Correction Amount Acquisition Unit for Figures at Positions Xj and Yj)
106 Proximity effect correction amount acquisition unit for all figures (proximity effect correction amount acquisition means for all figures)
107 Proximity Effect Correction Amount Reacquisition Unit for Figures at Positions Xj and Yj (Proximity Effect Correction Amount Reacquisition Unit for Figures at Positions Xj and Yj)
108 Judgment part (judgment means)
109 Output unit (output means)
E (x) Accumulated energy value ebi Accumulated energy amount due to backscattering W1 Figure size (x direction)
W2 Figure dimensions (y direction)
Uj Integration of backscatter amount Dj Exposure amount K constant η ₀ constant σf Gaussian function coefficient (spread forward spread)
σb Gaussian function coefficient (spreadback spread)
η Gaussian function coefficient η ′ Tanh function coefficient α Tanh function coefficient X ′ Tanh function coefficient

Claims (4)

With respect to charged particle lithography that draws a pattern design on a resist film formed on a substrate, and bakes and develops it, a backscattering amount that depends on a drawing position and a drawing area is obtained, and the backscattering amount is expressed by an approximate function, A proximity effect correction device that acquires a proximity effect correction amount using the approximate function,
An input unit for inputting information such as drawing pattern design information, a substrate for obtaining a backscattering amount in simulation, a resist film thickness, and charged particle conditions;
A backscattering amount acquisition unit for acquiring an in-resist accumulated energy distribution (EID function) obtained when charged particles are incident on one point on a resist formed on a substrate;
An approximate function acquisition unit that interpolates backscattering amount and spread by fitting an appropriate approximate function to the EID function;
A proximity effect correction amount acquisition unit at positions Xj and Yj that calculates an optimal proximity effect correction amount of the drawing figure at the positions Xj and Yj using the approximation function;
A proximity effect correction amount acquisition unit for all graphics, calculating the proximity effect correction amount for all graphics using the proximity effect correction amount, the drawing pattern design and the approximation function;
A proximity effect correction amount reacquisition unit that recalculates the proximity effect correction amounts of the positions Xj and Yj reflecting the proximity effect correction amounts of all the acquired figures;
The difference between the proximity effect correction amount calculated by the proximity effect correction amount reacquisition unit and the proximity effect correction amount calculated by the proximity effect correction amount acquisition unit at the positions Xj and Yj is taken, and the difference is within an allowable range. If the determination is negative, the proximity effect correction amount calculated by the proximity effect correction amount reacquisition unit is input to the proximity effect correction amount acquisition unit for all the figures, and the determination is affirmative A determination unit that inputs the proximity effect correction amount calculated by the proximity effect correction amount reacquisition unit to the output unit;
An output unit that outputs the proximity effect correction amount input from the determination unit together with information of the drawing pattern design;
A proximity effect correction apparatus comprising: As an approximation function for interpolating the amount of backscattering and its spread, when the stored energy value is E and the horizontal direction is X,

The proximity effect correction apparatus according to claim 1, wherein a backscattering amount and a proximity effect correction amount are calculated according to an expression represented by: With respect to charged particle lithography that draws a pattern design on a resist film formed on a substrate, and bakes and develops it, a backscattering amount that depends on a drawing position and a drawing area is obtained, and the backscattering amount is expressed by an approximate function, In the proximity effect correction method for obtaining the proximity effect correction amount using the approximate function,
An input step for inputting information such as drawing pattern design information, substrate and resist film thickness for obtaining backscattering amount by simulation, and charged particle conditions,
A backscattering amount acquisition step of acquiring an in-resist accumulated energy distribution (EID function) obtained when charged particles are incident on one point on a resist formed on a substrate;
An approximation function obtaining step for obtaining an approximation function for interpolating the backscattering amount and the spread by fitting an appropriate approximation function to the EID function;
A proximity effect correction amount acquisition step at positions Xj and Yj that calculates an optimal proximity effect correction amount of the drawing figure at positions Xj and Yj based on the approximate function;
Calculating a proximity effect correction amount for all graphics using the proximity effect correction amount, the drawing pattern design, and the approximation function;
Proximity effect correction amount calculated in the proximity effect correction amount reacquisition step and the proximity effect correction amount reacquisition step of recalculating the proximity effect correction amounts of the positions Xj and Yj reflecting the proximity effect correction amounts of all the figures The difference between the amount and the proximity effect correction amount calculated in the proximity effect correction amount acquisition step at the position Xj, Yj is determined, and it is determined whether or not the difference is within an allowable range. The proximity effect correction amount calculated in the effect correction amount reacquisition step is input to the proximity effect correction amount acquisition step in all the figures, and if the determination is affirmative, the proximity effect calculated in the proximity effect correction amount reacquisition step A determination step of inputting an effect correction amount to the output step;
An output step of outputting the proximity effect correction amount input from the determination step together with information of the drawing pattern design;
A proximity effect correction method comprising: With respect to charged particle lithography that draws a pattern design on a resist film formed on a substrate, and bakes and develops it, a backscattering amount that depends on a drawing position and a drawing area is obtained, and the backscattering amount is expressed by an approximate function, In the proximity effect correction program that is executed by the computer of the proximity effect correction device that acquires the proximity effect correction amount using the approximate function,
The computer,
Input means for receiving information such as drawing pattern design information, substrate and resist film thickness for obtaining backscattering amount in simulation, conditions of charged particles, etc. using an input device and storing them in a storage device;
Based on charged particle conditions input from the input means and information on the substrate, etc., the accumulated energy distribution (EID function) in the resist obtained when charged particles are incident on one point on the resist formed on the substrate. ) For acquiring the backscattering amount;
An approximation function acquisition means for interpolating backscattering amount and spread by fitting an appropriate approximation function to the EID function;
A proximity effect correction amount acquisition means at positions Xj and Yj for calculating an optimal proximity effect correction amount of the drawing figure at the positions Xj and Yj based on the approximation function;
A proximity effect correction amount acquisition unit for all figures, which calculates a proximity effect correction amount for all figures using the proximity effect correction amount, the drawing pattern design, and the approximation function;
Proximity effect correction amount reacquisition means for recalculating the proximity effect correction amounts at positions Xj and Yj reflecting the proximity effect correction amounts of all the figures,
The difference between the proximity effect correction amount calculated by the proximity effect correction amount reacquisition unit and the proximity effect correction amount calculated by the proximity effect correction amount acquisition unit at the positions Xj and Yj is taken, and the difference is within an allowable range. If the determination is negative, the proximity effect correction amount calculated by the proximity effect correction amount reacquisition means is input to the proximity effect correction amount acquisition means for all the figures, and the determination is affirmative The determination means for inputting the proximity effect correction amount calculated by the proximity effect correction amount reacquisition means to the output means,
A proximity effect correction program for causing a proximity effect correction amount input from the determination means to function as output means for outputting together with the drawing pattern design information.

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