JP2002353087A - Method for simulating charged particle lithography, computer program for executing charged particle lithographic simulation and apparatus thereof - Google Patents

Abstract

PROBLEM TO BE SOLVED: To simulate a charged particle lithography with high accuracy and at a high speed. SOLUTION: A method for simulating charged particle lithography comprises the step of calculating a storage energy stored in a resist film, when charged particles are incident via a resist film provided on a substrate, a step of providing a region in which the particles are scattered as a calculating region for calculating scattering, a step of dividing the calculating region into a plurality of first regions, a step of calculating the storage energy stored in each region when a predetermined number of the charged particles are sequentially incident from a predetermined incident point, a step of dividing the calculating region into a plurality of second regions as re-observed from the plurality of the first regions, based on a distribution of the energy, and a step of further calculating the energy stored in each of the plurality of the regions, when a predetermined number of the particles are sequentially incident from the predetermined incident point.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

[0001] The present invention relates to charged particle lithography simulation. More specifically, the present invention relates to charged particle lithography simulation having both high speed and high accuracy.

[0002]

2. Description of the Related Art In recent years, with the integration of semiconductor devices, there is an increasing need to form fine patterns with strict requirements on dimensional accuracy. One of the techniques for forming a fine pattern is a charged particle lithography technique using an electron beam, ions, or the like. However, this charged particle lithography technique generally involves a proximity effect phenomenon. The proximity effect phenomenon refers to a phenomenon in which irradiated charged particles are scattered in the resist film, or re-enter the resist film after being scattered in the substrate. Due to the influence of the proximity effect, it is difficult to form a resist pattern faithful to the design data. Therefore, a process simulation for examining the influence of the proximity effect under various conditions becomes effective. The manufacturing process based on the simulation result is an optimal process that minimizes the proximity effect or considers a way to avoid the proximity effect.

FIG. 6 shows a typical charged particle lithography system.
It is a flowchart which shows three steps of a simulation. The charged particle lithography simulation is roughly divided into an energy distribution f accumulated in a resist film on a substrate by a charged particle beam incident from one point.
A step of calculating (z, r) (step S61), and a step of calculating a pattern drawing of the accumulated energy E (x, y, z) based on the energy distribution f (z, r) (step S62). And a step (step S63) of calculating the development process using the stored energy E (x, y, z).

[0004] Step S61 will be described below. FIG.
FIG. 3 is a diagram showing a trajectory of a single-point incident charged particle beam calculated by the Monte Carlo method. The charged particles interact with the resist film and the substrate, and are scattered in various directions while losing energy. When calculating the scattering process, FIG.
(A) and (b), a calculation region of a certain size centered on the incident point (radius r = 0 to Rmax, film thickness z =
0 to Zmax). Then, in the radial direction and the film thickness (depth) direction, it is divided into donut-shaped minute elements having division sizes dr and dz, respectively. Division size dr and d
z has a constant size. Then, the energy lost in each element when the charged particles having the predetermined energy are made incident (that is, the energy stored in the resist film) is calculated. This calculation is usually performed for all the predetermined numbers of charged particles (for example, 10,000 to 1000).
00) calculation for each particle when incident. The result of the calculation is a data table of the stored energy in the radial direction and the depth direction.

FIG. 9 is a diagram showing a calculation result of a stored energy distribution in a radial direction at a certain depth. This is 1
An electron beam of 00 kV is made incident on one point on the semiconductor substrate, and a distribution of stored energy in a radial direction centering on the incident point at a certain depth is obtained. On the other hand, FIG. 10 is a diagram showing a distribution of stored energy in a depth direction at a certain position (Eiichi Nomura, Ph.D.
1)). As the resist film becomes thicker, a stored energy distribution also occurs in the depth direction. Depending on the energy of the electron beam,
It is understood that not only the magnitude and range of the stored energy change, but also the energy differences E1 and E2 occur between the upper surface and the lower surface of the resist film.

Subsequently, step S62 (FIG. 6) will be described. In this step, the stored energy distribution when the design circuit pattern is drawn is calculated at each depth using the data table of the stored energy in the radial direction and the depth direction obtained in step S61 (FIG. 6). FIG. 11A shows a design circuit pattern. Chang (J. Vac. Sci. Te
chnol. Vol. 12, pp1271, Nov./Dec. 1975) and the ring method of Moniwa et al. (J. Vac. Sci. Techn)
ol. Vol. B10, pp2771, 1992)
Using the technique described in Japanese Patent No. 0540, the stored energy distribution is calculated at each depth. The calculation area (FIG. 8C) of the stored energy distribution used at this time is the same as FIGS. 8A and 8B. (B) of FIG.
3 shows a stored energy distribution at a certain depth. FIG. 11B also shows an enlarged view of a part of the pattern in which the stored energy distribution is expressed by contour lines.

Step S63 (FIG. 6) The stored energy distribution E at each of the x, y, and z positions thus obtained.
The developing process is calculated based on (x, y, z), and the resist pattern shape is predicted.

[0008]

In the conventional charged particle lithography simulation as described above, if the calculation area is large, the time required for the calculation including steps S61, S62 and S63 becomes long. This corresponds to the radial division width d of the calculation area in step S61 (FIG. 6).
r, since the division width dz in the depth direction is constant, if the calculation area is increased, the number of divisions of the calculation area increases in proportion thereto. As in the above example, when the number of incident charged particles used in the calculation is set to a very large number of 10,000 to 100,000, and the scattering process is continuously calculated until the energy of these particles becomes a certain value or less. The range of a particle increases as the energy of the particle increases, and the number of calculation elements in which the energy is stored increases. For example, when high acceleration is performed at 100 kV, the range affected by scattering is as wide as about 60 μm (FIG. 9). If this is calculated in a calculation area divided at equal intervals in the radial direction by rings having equal intervals of 0.01 μm, 6000 elements are required per depth. Since it is necessary to calculate this for all incident charged particles, it takes an enormous amount of calculation time.

In some cases, the amount of change between elements in a certain depth direction and elements in another depth may differ greatly, but if they are divided at equal intervals in the depth direction, the calculation accuracy deteriorates.

It is an object of the present invention to perform high-speed and high-accuracy charged particle lithography simulation.

[0011]

According to the charged particle lithography / simulation method of the present invention, the energy stored in the resist film when the charged particles are incident through the resist film provided on the substrate is obtained. A charged particle lithography simulation method for calculating, wherein an area where the charged particles are scattered is provided as a calculation area for calculating the scattering, and the calculation area is divided into a first plurality of areas, Calculating a stored energy stored in each of the first plurality of regions when a predetermined number of the charged particles are sequentially incident from a predetermined incident point; based on the distribution of the stored energy,
The calculation area is changed to a second area by reviewing the first plurality of areas.
Step of dividing into a plurality of regions, when a predetermined number of the charged particles are further sequentially incident from a predetermined incident point,
Calculating the stored energy stored in each of the second plurality of regions, thereby achieving the above object.

The step of dividing into the second plurality of regions includes the step of dividing the calculation region based on the distribution of the stored energy such that the contribution ratio of the energy stored in each region to the incident point is constant. The step may be a dividing step.

The first and second plurality of regions are a plurality of ring regions defined between concentric circles centered on the incident point, and the width of the ring region in the first plurality of regions is Equally, the width of the ring region may be different in the second plurality of regions.

The first and second plurality of regions are plate-like regions divided into layers in the depth direction from the incident point, and the width of the plate-like regions is equal in the first plurality of regions. In the second plurality of regions, the width of the plate-like region may be different.

A computer-executable program executed by a computer according to the present invention includes a charged particle lithography method for calculating the energy stored in a resist film when the charged particles are incident through a resist film provided on a substrate. A program executed by a computer for performing a simulation, wherein a step of providing a region where the charged particles are scattered as a calculation region for calculating the scattering; and a step of dividing the calculation region into a first plurality of regions. Calculating a stored energy stored in each of the first plurality of regions when a predetermined number of the charged particles are sequentially incident from a predetermined incident point; based on the distribution of the stored energy, Dividing the calculation region into a second plurality of regions by reviewing the first plurality of regions; and further dividing the calculation region from a predetermined incident point. When sequentially enter the charged particles having a predetermined number, composed of a step of calculating the second storage energy stored in each of the plurality of regions, thereby the objective described above being achieved.

The step of dividing into the second plurality of regions includes the step of dividing the calculation region based on the distribution of the stored energy such that the contribution ratio of the energy stored in each region to the incident point is constant. The step may be a dividing step.

The first and second plurality of regions are a plurality of ring regions defined between concentric circles centered on the incident point, and the width of the ring region in the first plurality of regions is Equally, the width of the ring region may be different in the second plurality of regions.

The first and second plurality of regions are plate-like regions divided into layers in the depth direction from the incident point, and the width of the plate-like regions is equal in the first plurality of regions. In the second plurality of regions, the width of the plate-like region may be different.

A charged particle lithography / simulation apparatus according to the present invention is a charged particle lithography / simulation apparatus for calculating the energy stored in a resist film when the charged particles are incident through a resist film provided on a substrate. A simulation apparatus according to the above method,
A storage unit for storing an area provided by the step of providing an area according to the program, and a storage unit for storing an area provided by the method according to any one of claims 1 to 4 or any one of claims 5 to 8 The program includes the step of dividing into a first plurality of regions, the step of calculating stored energy stored in each of the first plurality of regions, the step of calculating, and the second plurality of regions. An operation unit that performs the step of dividing and the step of calculating the accumulated energy stored in each of the second plurality of regions, thereby achieving the above object.

[0020]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The configuration of a charged particle lithography simulation system will be described below with reference to the accompanying drawings. Then, Embodiments 1 to 1 using the charged particle lithography / simulation system
3 will be described.

FIG. 12 is a diagram showing a charged particle lithography simulation system (hereinafter, simulation system) 10. Simulation system 1
Reference numeral 0 denotes a computer or the like that performs processing of the present invention, which will be described later with reference to FIGS. That is, the simulation system 10 performs a process simulation for examining the influence of the proximity effect under various conditions.
The manufacturing process based on the simulation result is an optimal process in which the proximity effect is minimized or a method for avoiding the proximity effect is considered. The proximity effect means that the irradiated charged particles are scattered in the resist film or re-enter the resist film after being scattered in the substrate, as described in the related art. The difference from the conventional simulation is that the simulation system 10 can perform a high-speed and high-accuracy simulation.

FIG. 12A is a block diagram showing the appearance of the simulation system 10, and FIG. As shown in FIG. 12A, the simulation system 10 inputs data (eg, a keyboard (and / or a mouse)) for inputting information (an instruction from a user and data for the simulation) necessary for performing a simulation. The system includes a unit 11, a display unit 15 that is a monitor for displaying simulation results, and a computer main body 16 that performs main processing of the simulation. More specifically, it is as shown in FIG. That is, the simulation system 10 includes a bus 1, a central processing unit (hereinafter, CPU) 2, a random access memory (hereinafter, RAM) 3, a read-only memory (hereinafter, ROM) 4, an arithmetic unit 5, an external Storage device 6
And a data input unit 11 and a display unit 15.

Hereinafter, each component of the simulation system 10 will be described. The bus 1 is a signal line that electrically connects each component. The CPU 2 is a processing device that performs overall processing of the simulation system 10. For example, the CPU 2 executes a computer program for performing the processing of the present invention, and controls each component to operate properly. The RAM 3 is a volatile memory used when the CPU 2 performs processing such as execution of a computer program (software). The processing operation of the simulation system 10 is performed based on execution steps of a computer program (software) stored in the main memory 23. The computer program is, for example, as part of an operating system or a predetermined OS.
It may be defined as an application program that operates on the above. The ROM 4 stores the simulation system 1
0 is a non-volatile memory that stores a program for performing basic input / output operations such as at the time of startup.

The operation unit 5 is a processing device that performs the most important processing in the present invention. Detailed processing of the arithmetic unit 5 will be described later. Although the arithmetic unit 5 and the CPU 2 are described as separate components, the function of the arithmetic unit 5 may be realized by the CPU 2.

The external storage device 6 stores an operating system (OS) program that controls the operation of the simulation system 10, an application program that runs on the OS (for example, a computer program that performs the processing of the present invention), and the like. Further, the external storage device 6 may store an initial setting or the like when the calculation unit 5 performs the calculation. For example, the division width in the radial direction and the division width in the depth direction of the calculation area (FIGS. 3, 4, and 5) at the start of the calculation. The external storage device 6 is, for example, a hard disk,
It is a well-known storage device such as a CD drive, a DVD-ROM drive, and a tape streamer. The computer program recorded in the external storage device 6 is read out and stored in the RAM
3 is executed by the CPU 2 or the arithmetic unit 5.

As described above, the data input unit 11
Keyboard, mouse, etc. The data for simulation input to the data input unit 11 is, for example, the energy of the charged particles and the thickness of the resist film.

The configuration of the simulation system 10 has been described above. Hereinafter, Embodiments 1 to 3 of the present invention will be described. In the following first to third embodiments, the terms “ring” and “calculation area” will be referred to. As shown in FIG. 3A, for example, as shown in FIG. 3A, when a charged particle is incident on a resist film via a z-axis path, the ring is defined by a circle centered on the incident point and an interval dr. A donut-shaped area defined between the circle adjacent to the circle is shown (FIG. 3 (a) is a view in which a part of the donut-shaped area is cut for explanation). The “calculation region” is a region in which the charged particles are scattered, and is a region in which the calculation of the scattering process is performed. In FIG. 3A, the radius r = 0 to Rma
The region of x and the thickness z = 0 to Zmax is defined as a calculation region.

(Embodiment 1) With reference to FIG. 1, a calculation process performed by the arithmetic unit 5 (FIG. 12) will be described. FIG.
9 is a flowchart showing a flow of calculation processing of charged particle beam lithography simulation. The flow of this calculation processing includes the calculation of the stored energy distribution at the time of point incidence (step S11) and the calculation of the pattern drawing process (step S1).
2) and a development process calculation (step S13). The feature of the first embodiment and the later-described second and third embodiments is that, during the calculation of the stored energy distribution at the time of the point incidence in step S11, the number of divisions of the calculation region is sequentially reviewed and the number is optimized. It is in. By reducing the divided elements of the unnecessary calculation area, the area determination during calculation and the calculation amount of the stored energy amount are reduced, and the total calculation time is shortened.

Step S11 is a calculation of the stored energy distribution at the time of point incidence. That is, a process in which an electron beam incident on one point on the resist film surface is scattered by the resist film or the underlying substrate and energy is lost is calculated by the Monte Carlo method. From this, the energy loss per unit volume at each position (z, r) is calculated. z is a parameter of a distance in the depth direction from the incident surface, and r is a parameter of a distance in a radial direction of a circle centering on the incident position. The energy loss corresponds to the stored energy when viewed from the resist film or the substrate side. Hereinafter, the stored energy distribution at the position (z, r) is represented by f (z, r).

FIG. 2 is a flowchart showing step S11 (FIG. 1) in more detail. The features of the first embodiment are shown in FIG. First, the charged particles are made incident on one point, and the stored energy distribution f (z, r) per unit volume is calculated for a plurality of rings in the calculation region by the Monte Carlo method (step S21). The position (z, r) covers all positions in the calculation area. As will be described later with reference to FIG. 3, the calculation region is divided into a plurality of rings in the radial direction and is divided into a plurality of plate-like layers also in the depth direction. Therefore, the position (z, r) is defined for each ring and for each layer in the depth direction of each ring. At the start of the calculation, the width dr of each of the plurality of rings, and
The thickness dz of each layer is constant.

Next, it is determined whether or not the stored energy distribution of a predetermined number of charged particles has been obtained (step S22). The number of charged particles during the simulation is usually 10
000 to 100,000. In step S22, for example, it is determined whether or not the accumulated energy distribution of 1000 charged particles has been obtained. If not, the process returns to step S21. If so, then all stored energy distributions f for each charged particle calculated so far
Using (z, r), a ring width at which the contribution rate of the stored energy to the incident point is constant is obtained (step S2).
3). Specifically, at a given depth z, any two rings _{r i} and, for the ring _{r j,} stored energy _dE ri by contributions from each ring (P), _{and, dE} rk (P) is less The radius _ri , _outer , _{ri , inner} , r
_{j, outer} and r _{j, inner} may be determined.

[0032]

(Equation 1)

If the amount of calculation is significantly increased by strictly performing numerical calculations, it is possible to perform approximate calculation as appropriate and perform high-speed processing. In this case, "constant contribution ratio" does not necessarily mean that the contribution ratio is strictly constant, but it is sufficient that the contribution ratio is close to constant. Since the stored energy tends to decrease as the distance from the incident point increases (for example, FIG. 9), the obtained ring width increases as the distance from the center increases. That is, at the start of the calculation, the equally divided ring width is changed. Strictly, even when the distance is far from the incident point, the stored energy may locally increase due to various factors. In this case, it is understood that the obtained ring width becomes smaller.

Thereafter, it is determined whether or not the stored energy distribution of all charged particles has been obtained (step S24).
If so, the process ends. The calculation result of the stored energy distribution of all the charged particles becomes a data table of the stored energy in the radial direction and the depth direction. On the other hand, if the stored energy distributions of all the charged particles have not been obtained, the process returns to step S21. It should be noted that after returning to step S21, the stored energy distribution is calculated again with the obtained ring width and ring number. By reducing the number of ring divisions in the calculation region in this way, the need to determine which ring the charged particle scattered and traversing which ring in Monte Carlo calculation is greatly reduced, and the calculation time can be significantly reduced. Also, the calculation time for allocating the lost energy to each ring can be shortened.

FIG. 3 is a diagram showing a calculation step of the stored energy distribution of the charged particle incident at one point by the processing of the first embodiment. FIG. 3A shows a calculation area at the start of the calculation. As is clear from the figure, the width dr of the ring is constant. Not all rings are shown for convenience of description, but the number of rings is approximately 6000. (B) shows a calculation area under calculation. Compared with (a), the width dr of the ring tends to be narrower as it is closer to the z-axis and wider as it is further away. In this way, unnecessary radial elements are reduced by sequentially reviewing and optimizing the ring width so that the influence of each ring on the incident point contributes equally during the calculation. Accordingly, the time required for the calculation unit 5 (FIG. 12) to determine an area during calculation and to allocate stored energy is reduced, and the total calculation time is also reduced. (C)
Indicates a calculation area at the end of the calculation. Compared with (b), the width dr of the ring is further modified. At the end of the calculation, the number of rings can be reduced to about 20. This result is stored in the RAM 3 (FIG. 12) or the external storage device 6 (FIG. 12) as a table having the minimum number of elements, that is, an optimum stored energy data table. By calculating, changing, and gradually optimizing the ring width of each ring during the Monte Carlo calculation, the calculation load of the arithmetic unit 5 (FIG. 12) during the calculation can be greatly reduced. The ring width obtained in this manner is used in a pattern drawing process described later, and the amount of calculation can be further reduced in the pattern drawing process.

Referring again to FIG. 1, when the calculation in step S11 is completed, in step S12, a pattern drawing process calculation is performed. That is, the calculated energy distribution f (z, r) (where r = (x, y)) constitutes a stored energy data table, and using this stored energy data table, the drawing area A
The cumulative accumulated energy E (x, y, z) affecting a certain position P (x, y, z) is calculated for all layers. For this calculation, the so-called reciprocity theorem can be used. The “reciprocity theorem” is a theorem that the energy E stored at a certain point P by drawing the area A is equal to the energy E ′ stored in the area A by drawing the point P. Thus, the stored energy E (x, y, z) at the point P
Is, in each of a plurality of rings around the point P, an area dARj of an overlapping portion of the drawing area A, each ring (radius Rj, width dRj), and stored energy per unit volume at the radius Rj. By multiplying and integrating over all rings with overlap. Specifically, E (x, y, z) = Σ f (z, R
j) · dARj.

This calculation is repeated for each pattern and each point P (x, y) at a certain z = zi position.
The calculation of the pattern drawing process at the zi position is performed. As a result, the accumulated energy distribution E at the depth z = zi is obtained.
(X, y, zi) is obtained. After that, the above-described pattern drawing process is performed on all layers in the thickness direction of the resist film,
Cumulative accumulated energy distribution E (x, y,
z).

In the following step S13, after completion of each of the above-described steps, the developing process is calculated using the accumulated energy distribution E (x, y, z) to predict the resist pattern shape.

The first embodiment has been described. In the charged particle lithography simulation according to the first embodiment, when calculating a distribution of stored energy in a resist film due to a single-point incident charged particle beam in a calculation region divided into a ring shape in a radial direction, each ring has a ring shape. By reviewing the width in the middle of the Monte Carlo calculation, the calculation can be performed with a smaller number of elements than in the past, so that the calculation becomes faster. As a result of the calculation, the number of elements in the data table is minimized, and an optimal stored energy data table can be created.

(Embodiment 2) In Embodiment 1, during the calculation of the stored energy distribution at the time of point incidence in step S11 (FIG. 1), the ring width of the calculation area (radial division width)
Were sequentially reviewed to optimize the number of divisions. In the second embodiment, the division width in the depth direction of the calculation area is sequentially reviewed to optimize the number of divisions. The depth direction refers to a direction perpendicular to the resist film on which the charged particles are incident and the incident direction of the charged particles. In the flow of the calculation processing according to the second embodiment, the words “ring” and “ring width” in the flowcharts of FIGS. 1 and 2 are referred to as “division region in the depth direction” and “division width in the depth direction”. Just read it. Since the flowcharts of FIGS. 1 and 2 have been described in the first embodiment,
The description is omitted.

FIG. 4 is a diagram showing a process of calculating the stored energy distribution of the charged particle incident at one point by the process of the second embodiment. FIG. 4A shows a calculation area at the start of the calculation. As is clear from the figure, the division width dz in the depth direction is constant. (B) shows a calculation area under calculation. (A)
As compared with, the division width dz in the depth direction tends to be narrower as it is closer to Zmax and wider as it is farther from Zmax. This means that the number of divisions is smaller as it is closer to the resist film and the upper surface of the substrate, and is larger as it is closer to the lower surface of the substrate.
As described above, during the Monte Carlo calculation, the division width in the depth direction is sequentially reviewed and optimized so that the influence of each of the divided elements in the depth direction on the incident point has an equal contribution. Unnecessary depth factors are reduced. Therefore, the time required for the calculation unit 5 (FIG. 12) to determine the area during calculation and the allocation of the stored energy is reduced, and the total calculation time is also reduced. (C) shows the calculation area at the end of the calculation. Compared with (b), the division width dz in the depth direction is further corrected. As a result, the RAM 3 (FIG. 12) or the external storage device 6 (FIG.
Stored in 2).

From the above, by calculating and changing the ring width of each ring during Monte Carlo calculation and gradually optimizing,
The calculation load of the operation unit 5 (FIG. 12) during the calculation can be greatly reduced. The division width dz in the depth direction obtained in this manner is used in a pattern drawing process described later, as shown in FIG. 4D, and the amount of calculation can be further reduced in the pattern drawing process. Since the amount of energy per element in the depth direction becomes equal and there is no element having a large change, the accuracy of calculation in the pattern drawing step and the development step is improved.

(Embodiment 3) Embodiment 3 is a combination of Embodiments 1 and 2. That is,
During the calculation of the stored energy distribution at the time of the point incidence in step S11 (FIG. 1), the ring width (division width in the radial direction) and the division width in the depth direction of the calculation region are sequentially reviewed to optimize each division number. I do. The flow of the calculation processing according to the third embodiment is as shown in the flowcharts of FIGS. 1 and 2 regarding the division in the radial direction. The division width in the depth direction is as described in the second embodiment. Since the flowcharts of FIGS. 1 and 2 have already been described, description thereof will be omitted.

FIG. 5 is a diagram showing a calculation process of a stored energy distribution of charged particles incident at one point according to the processing of the third embodiment. FIG. 5A shows a calculation area at the start of the calculation. As can be seen, the width of the radial ring dr
Is constant, and the division width dz in the depth direction is also constant. (B) shows a calculation area under calculation. Compared with (a), the width dr of the ring in the radial direction tends to be narrower as it is closer to the z-axis and wider as it is farther from the z-axis. Further, the division width dz in the depth direction tends to be narrower as it is closer to Zmax and wider as it is farther from Zmax. Thus, in the middle of the calculation, the influence of each ring on the incident point has an equal contribution, and the influence of each divided element in the depth direction on the incident point has an equal contribution. By sequentially reviewing and optimizing the division width dr in the radial direction and the division width dz in the depth direction,
Unnecessary radial and depth factors are simultaneously reduced. Therefore, the time required for the calculation unit 5 (FIG. 12) to determine the area during calculation and to allocate the stored energy is reduced.
The total calculation time will also be reduced. (C) shows the calculation area at the end of the calculation. Compared with (b), the division width dr in the radial direction and the division width dz in the depth direction are further modified. This result is stored in the RAM 3 (FIG. 12) or the external storage device 6 (FIG. 12) as a table having the minimum number of elements, that is, the optimum stored energy data table.

As described above, by changing the number of each element in the calculation area during Monte Carlo calculation and gradually optimizing the calculation area, the calculation load of the arithmetic unit 5 (FIG. 12) during calculation can be greatly reduced. . The division width dr in the radial direction and the division width dz in the depth direction obtained in this manner are used in a pattern drawing process described later, as shown in FIG. Calculation amount can be reduced. Since the amounts of energy per element in the radial direction and in the depth direction become equal, and there is no element having a large change, the accuracy of calculation in the pattern drawing step and the developing step is improved.

In the above embodiment, the case where the number of divisions of the area is gradually reduced has been described. As another example,
The number of divisions may be given in advance, and the calculation may be performed to optimize the division width. For example, the number of divisions may be set to 20, and the division width may be determined based on Equation 1 above.

As is clear from the above description of the first to third embodiments, according to the present invention, in the simulation of the charged particle lithography process, calculation under various conditions is performed in order to achieve both high prediction accuracy and high-speed calculation. It can be executed with high accuracy and greatly helps process optimization.

The flowcharts shown in FIGS. 1 and 2 are realized as a computer program for performing the processes represented by the flowcharts. Such a computer program is a simulation system 10
It is read and executed by the simulation system shown in FIG. Such a computer program is recorded on a magnetic recording medium such as an optical disk such as a CD or DVD, a floppy (registered trademark) disk, a semiconductor recording medium such as a flash memory, or transmitted via a network such as the Internet. .

[0049]

According to the method, the computer-executable program, and the apparatus of the present invention, the stored energy is obtained by using the first plurality of regions, and the first energy is obtained based on the distribution of the stored energy. The plurality of areas are divided into a second plurality of reviewed areas. Each of the more appropriately reviewed numbers of the second plurality of regions is used to calculate the stored energy stored, so that unnecessary divided regions of the calculation region are reduced, and the region under calculation is reduced. The amount of determination and the calculation of the amount of stored energy can be reduced. Therefore, the total calculation time is reduced.

More specifically, since the second plurality of regions are divided so that the contribution ratio of the energy stored in each region to the incident point is constant, the second plurality of regions is smaller than the number of the first plurality of regions. At least the second plurality of regions can be divided.

Assuming that the first and second plurality of regions are a plurality of ring regions defined between concentric circles centered on the incident point, the widths of the ring regions are different in the second plurality of regions. The widths of the first plurality of regions are uniformly divided equally, and the second plurality of regions can be divided into a smaller number than the number of the first plurality of regions.

If the first and second plurality of regions are plate-like regions divided into layers in the depth direction from the incident point, the second region
The width of the plate-like region is different in the plurality of regions. Since the width in the depth direction of the first plurality of regions is uniformly divided uniformly,
The second plurality of regions can be divided into a smaller number than the first plurality of regions. Thus, even when the amount of change is significantly different between elements in a certain depth direction and elements at another depth, calculation can be performed without deteriorating accuracy.

[Brief description of the drawings]

FIG. 1 is a flowchart showing a flow of calculation processing of charged particle beam lithography simulation.

FIG. 2 is a flowchart showing in more detail a calculation of a stored energy distribution at a point incidence.

FIG. 3 is a diagram illustrating a calculation process of a stored energy distribution of charged particles incident at one point according to the processing of the first embodiment.

FIG. 4 is a diagram showing a calculation process of a stored energy distribution of charged particles incident at one point according to the processing of the second embodiment.

FIG. 5 is a diagram showing a calculation process of a stored energy distribution of charged particles incident at one point according to the processing of the third embodiment.

FIG. 6 is a flowchart showing three steps of a typical charged particle lithography simulation.

FIG. 7 is a diagram showing the trajectory of a single-point incident charged particle beam calculated by the Monte Carlo method.

FIG. 8 is a diagram showing a calculation process of a stored energy distribution of charged particles incident at one point according to a conventional example.

FIG. 9 is a diagram showing a calculation result of a stored energy distribution in a radial direction at a certain depth.

FIG. 10 is a diagram showing a stored energy distribution in a depth direction at a certain position.

FIG. 11 is a diagram showing a design circuit pattern and a stored energy distribution at a certain depth.

FIG. 12 illustrates a charged particle lithography simulation system.

[Description of Signs] 1 bus, 2 CPU, 3 RAM, 4 RO
M, 5 arithmetic unit, 6 external storage device, 10 simulation system, 11 data input unit, 15 display unit, 16 computer body

Claims (9)

[Claims] 1. A charged particle lithography system for calculating the energy stored in a resist film when the charged particles are incident through a resist film provided on a substrate.
A simulation method, comprising: providing a region in which the charged particles scatter as a calculation region for calculating the scattering; dividing the calculation region into a first plurality of regions; Calculating the stored energy stored in each of the first plurality of regions when the number of the charged particles is sequentially incident; and calculating the calculated region based on the distribution of the stored energy. Reviewing one of the plurality of regions and dividing the plurality of regions into a second plurality of regions; and further sequentially applying a predetermined number of the charged particles from a predetermined incident point to each of the second plurality of regions. Calculating the stored stored energy. 2. The method according to claim 1, wherein the step of dividing into the second plurality of regions is performed based on the distribution of the stored energy such that a contribution ratio of energy stored in each region to the incident point is constant. The charged particle lithography simulation method according to claim 1, which is a step of dividing a region. 3. The first and second plurality of regions are a plurality of ring regions defined between concentric circles centered on the incident point. In the first plurality of regions, the first and second plurality of regions are defined as ring regions. 3. The charged particle lithography simulation method according to claim 2, wherein the width of the ring region is different in the second plurality of regions, and the width of the ring region is different in the second plurality of regions. 4. The first and second plurality of regions are plate-like regions divided into layers in a depth direction from the incident point, and the first plurality of regions have a width of the plate-like region. 4. The charged particle lithography apparatus according to claim 2, wherein the widths of the plate-like regions are different in the second plurality of regions.
Simulation method. 5. A charged particle lithography system for calculating the energy stored in a resist film when the charged particles are incident through a resist film provided on a substrate.
A program executed by a computer that performs a simulation, wherein a step of providing a region where the charged particles are scattered as a calculation region for calculating the scattering, and a step of dividing the calculation region into a first plurality of regions are provided. Calculating a stored energy in each of the first plurality of regions when a predetermined number of the charged particles are sequentially incident from a predetermined incident point; based on the distribution of the stored energy, Dividing the calculation region into a second plurality of regions by reviewing the first plurality of regions; and a step of sequentially inputting a predetermined number of the charged particles from a predetermined incident point. Calculating the stored energy stored in each of the plurality of regions by the computer that performs the charged particle lithography simulation. Program to be line. 6. The step of dividing into a second plurality of regions, the calculating based on the distribution of the stored energy such that a contribution ratio of energy stored in each region to the incident point is constant. The computer-executed program for performing a charged particle lithography simulation according to claim 5, which is a step of dividing a region. 7. The first and second plurality of regions are a plurality of ring regions defined between concentric circles centered on the incident point. In the first plurality of regions, the first and second plurality of regions are the ring regions. The computer-implemented program for performing a charged particle lithography simulation according to claim 6, wherein the width of the ring region is different in the second plurality of regions, and the width of the ring region is different in the second plurality of regions. 8. The first and second plurality of regions are plate-like regions divided into layers in the depth direction from the incident point, and the width of the plate-like region in the first plurality of regions is set. The charged particle lithography method according to claim 6 or 7, wherein widths of the plate-like regions are different in the second plurality of regions.
A program executed by a computer that performs a simulation. 9. A charged particle lithography system for calculating the energy stored in a resist film when the charged particles are incident through a resist film provided on a substrate.
A storage device for storing an area provided by the step of providing an area according to any one of claims 1 to 4, or a program according to any one of claims 5 to 8. And a first program according to any one of claims 1 to 4 or a program according to any one of claims 5 to 8.
The step of dividing into a plurality of regions, the step of calculating the stored energy stored in each of the first plurality of regions, the step of calculating, the step of dividing into a plurality of regions, and A charged particle lithography simulation apparatus comprising: a calculation unit that performs the step of calculating the stored energy stored in each of the second plurality of regions.