JP2001228597A - Simulation method for fine processing shape - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a simulation method for fine processing shapes for obtaining the information on the resolution, sectional shapes, etc., of a resist of a photomask manufacturing process which execute electron beam exposure. SOLUTION: This method has (a) a region raster conversion step of dividing pixels to plural pixels which are a minimum unit to apply fine processing to assigned region within drawing data, (b) a nearby pixel distribution encoding step of imparting the attributes as to whether the respective pixels overlap on the drawing regions or not to the respective divided pixels, respectively determining the nearby pixel distributions indicating the distribution states of the attributes of the pixels existing within the prescribed nearby distances with the respective pixels as the center and applying the pixel distribution codes for the determined nearby pixel distributions to all of the pixels and (c) a step of executing the prescribed shape simulation relating to all the fixed shape pixel distributions within the fixed shape pixel distribution set and calculating the pixel sectional data of a pixel sectional direction (Z direction) respectively with respect to all of the pixel distribution codes.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for simulating a micro-machined shape, and more particularly to a method for simulating a micro-machined shape in photomask manufacturing by an electron beam drawing method.

[0002]

2. Description of the Related Art In recent years, the density of semiconductor elements (chips) has increased drastically, and mass production of a 64M DRAM having a 0.35 μm design rule has already started.
We are moving into the era of 6MDRAM. Furthermore, recently, chip reduction aimed at cost reduction is remarkable,
The chip size is reduced by miniaturizing the MDRAM to the 0.25 design rule or miniaturizing the 256 MDRAM to the 0.18 design rule. The development of the 0.18 μm design rule is completed, and the development of the 0.15 μm design rule is scheduled to be completed in 2000. For this reason, photomasks, such as reticles for directly reducing and projecting onto a wafer, have been required to have higher precision.

A photomask such as a reticle is usually applied on a metal thin film of a substrate (also called blanks) in which a light-shielding metal thin film is provided on one surface of a transparent substrate such as a quartz glass substrate.
On the photosensitive resist that has been dried, a latent image is formed by irradiating only a predetermined area with ionizing radiation using a drawing apparatus, and a latent image is formed. After obtaining a resist pattern having a shape, the metal thin film is further processed into a resist pattern shape using the resist pattern as an etching resistant resist. As the drawing apparatus, an EB drawing apparatus, an excimer laser drawing apparatus, or the like is used, and corresponding process processing is performed.

In particular, in a photomask manufacturing process for performing electron beam lithography using an EB lithography apparatus, as described above, while high precision of a photomask is required, the processing conditions must be adjusted in advance for the following purposes. It has become necessary to accurately obtain information such as the resolution and cross-sectional shape of the corresponding resist, and electron beam lithography simulation has also been developed. Grasping quality before actual production Establishing process conditions to obtain desired accuracy and yield Development of new resist material Correction of electron beam proximity effect and confirmation of its effect Design and improvement of electron beam lithography system

In the case of electron beam lithography or exposure using an EB lithography system (electron beam exposure system), there is a problem of electron scattering, particularly a problem of back scattering, as described below. To correct the influence of such back scattering (proximity effect), Japanese Patent Application Laid-Open No.
Methods such as changing the irradiation amount of a beam for each figure as in 1658 and performing auxiliary exposure (ghost exposure) with an electron beam blurred in a non-drawing area as in Japanese Patent Application Laid-Open No. 9-260242 have been proposed. It is essential to use an electron beam lithography simulator in order to accurately perform the above, and it can be seen that the inventor of the above-mentioned publication also uses it. Hereinafter, scattering of an electron beam in the case of electron beam drawing or exposure using an EB drawing apparatus (electron beam exposure apparatus) will be briefly described. Electron beams, unlike light, can ignore wave dynamic effects such as diffraction.On the other hand, they have a negative charge, which causes beam broadening due to Coulomb repulsion and scattering due to collisions with sample nuclei and electrons because their mass cannot be ignored compared to light. It needs to be considered. Increasing the accelerating voltage of the irradiated electrons reduces the beam blur due to Coulomb repulsion and the spread due to forward scattering. There is a problem that increases. To make matters worse, this backscattered electron travels a considerable distance to reach the resist layer, and thus has a high degree of freedom.
The width of spread is larger than that of forward scattering.

The theory of electron beam simulation itself is described in reference 1 (SM SZE: “VLSI Technology”).
y ", Second Edition, MacGraw
-Established about 20 years ago as seen in Hill, 1988), but with recent improvements in computer performance, reference 2 (Chris A. Mack: "Electron").
BwamlithographySimulation
ForMasking ", Microelect
tronics Engineering 46, El
severSience, page 283-286,
Commercial versions such as (1999) have finally reached the level of practical use. However, even with the current calculation function, the drawing shape that can be handled by simulation is limited to a simple test pattern due to the limitation of the memory capacity and the calculation time, and is far from the drawing pattern handled by the manufacturing department. There are the following three simulation problems at present. (1) Calculation and load are large (proximity effect calculation of electron beam, etc.) A simulation in which one electron beam is three-dimensionally distributed by the Monte Carlo method is performed, and scanning is performed along given drawing data. The energy storage distribution data of the electron beam is obtained as Dx × Dy × Z voxel data, and the figure to be painted is divided into drawing unit pixels and X × Y
When the number of pixels is reached, the data is X × Y × Dx × D
y × Z calculations are required. (2) The required memory capacity is enormous In the three-dimensional simulation processing, X
× Y × Z voxel data is created. Thereafter, it is necessary to perform development processing and the like on this data. (3) Recalculation load for partial change of simulation conditions Since it is impossible to simulate the entire drawing data of the actual product, a method of processing each small area is used. However, when the drawing data is replaced, the same process is performed. Even under the conditions, all simulations are recalculated, and the calculation load does not change. Even when calculating in two dimensions and wanting to continue in detail in three dimensions, the calculation is completely recalculated.

[0007]

As described above, an electron beam lithography simulation for obtaining information such as the resolution and cross-sectional shape of a resist in a photomask manufacturing process for performing electron beam lithography using an EB lithography apparatus. In (2), there are problems such as (1) a large calculation and load, (2) a large required memory capacity, and (3) a recalculation load is required for a partial change of a simulation condition. I was The present invention provides a method for simulating a micro-processed shape for obtaining information such as resolution and cross-sectional shape of a resist in a photomask manufacturing process for performing electron beam writing using an EB lithography apparatus. Therefore, it is intended to provide a simulation method that can reduce the calculation load, reduce the required memory capacity, and reduce the amount of recalculation for a change in the simulation condition. is there.

[0008]

According to the present invention, there is provided a method for simulating a micro-processed shape, which simulates a processed shape of a medium when performing a micro-process (process) in a cross-sectional direction of a medium having a flat surface. A method for simulating a micromachined shape, comprising the steps of: (a) performing a micromachining process on a designated castle in X and Y two-dimensional drawing data including a plurality of closed figure parts that determine a drawing area; An area raster conversion step of dividing the image into a plurality of pixels as a minimum unit to be applied; and (b) assigning an attribute to each of the divided pixels to determine whether at least each pixel overlaps a drawing area. As a center, a neighboring pixel distribution indicating a distribution state of the attribute of a pixel existing within a predetermined neighboring distance is obtained, and the prepared neighboring pixel distribution is prepared in advance for each obtained neighboring pixel distribution. Extracting a similar fixed pixel distribution from the set of fixed pixel distributions and providing a pixel distribution code corresponding to the fixed pixel distribution to all pixels; and (c) coding all the pixels in the fixed pixel distribution set. A pixel cross section in which a predetermined shape simulation is performed on each of the standard pixel distributions based on predetermined processing conditions, and pixel cross section data in the pixel cross section direction (Z direction) is calculated for all pixel distribution codes. And a data calculation step. Then, in the above, after the pixel cross-section data calculation step, the calculated pixel cross-section data is arranged for all the pixels in the designated area based on the pixel distribution code given to each pixel. And performing a predicted shape constructing step of constructing a predicted shape by obtaining predicted shape data in a micromachining process (process process). In addition, in the above, the pixel cross-section data calculation step performs a predetermined shape simulation in advance on each of the standard pixel distributions in the standard pixel distribution set based on predetermined process conditions, and individually performs all of the standard pixel distributions. The feature is that pixel cross-section data in the pixel cross-section direction (Z direction) for micro-machining processing (process processing) is calculated for all corresponding pixel distribution codes.

In the above, the pixel cross-section data calculation step is to calculate a plurality of pixel cross-section data corresponding to a plurality of micro-machining processing (process processing) times. And a method for constructing a plurality of predicted shapes corresponding to the fine processing (process) time. Further, in the above, the neighboring pixel distribution is a one-dimensional histogram in which the number of neighboring pixels is counted according to the distance from the center pixel, and the fixed pixel distribution set, the fixed pixel distribution, and the pixel distribution code are each a fixed histogram. A set, a fixed histogram, and a histogram code, and the neighborhood pixel coding step includes:
The method is characterized in that the most similar fixed histogram is extracted from a set of fixed histograms prepared in advance, and a histogram code corresponding to the fixed histogram is given to all pixels. Also,
In the above, when weight information is added to the closed figure portion for the fine processing, for a pixel intersecting the closed figure portion having a higher weight, the neighboring pixel distribution is adjusted. is there.

Further, in the above, the pixel cross-section data is a binary value indicating whether the pixel is penetrated or closed, and the predicted shape is two-dimensional shape data. Section data calculation step
(A) Based on the total amount of energy accumulated in the cross-sectional direction (Z direction) of a single pixel by an energy beam applied to the medium, and from a pixel located in the vicinity of the single pixel, based on a given fixed pixel distribution An energy storage amount calculating step of calculating a sum value with the total amount of sneak energy, and (B) determining whether each pixel is lost due to a chemical dissolution process based on the calculated energy storage amount. Or performing a control for accelerating the chemical dissolution process based on a defect state in a pixel adjacent to each pixel, or a shape defect determination step.

Alternatively, in the above, the pixel cross-sectional data is a one-dimensional shape distribution (Z-direction distribution) in a cross-sectional direction, and the predicted shape data is three-dimensional shape data. The calculation step is
(C) The distribution of the amount of energy accumulated in the cross-sectional direction of a single pixel by the energy beam applied to the medium, and the energy sneaking from a pixel located in the vicinity of the single pixel based on a given fixed pixel distribution. An energy storage distribution calculating step of calculating a sum value with the amount distribution,
(D) Based on the calculated energy storage amount, calculate a physical defect distribution formed by a chemical dissolution process that proceeds in a cross-sectional direction (Z direction) of each pixel, or calculate a physical defect distribution in a neighboring pixel of each pixel. A shape defect calculating step of performing control for accelerating the chemical dissolution treatment based on the defect distribution in the cross-sectional direction. In the above, the medium is an electron beam resist, the energy beam is an electron beam, and the Monte Carlo method (Monte Carlo Simulatio) is used.
calculating the energy storage distribution according to n), the chemical dissolution processing is the development processing of the electron beam resist, and the energy storage distribution is converted into the development speed distribution using the Dill equation;
Cell Removal Me
The method is characterized in that a physical defect distribution is calculated based on the method (d.). In the above description, the processing strength of the fine processing is determined by the beam current (d
and the adjustment is performed so as to raise or lower the count value of the obtained histogram according to the magnitude of the beam current set in the closed figure portion.

[0012]

According to the method for simulating a micromachined shape of the present invention, by adopting such a structure, a method for manufacturing a photomask for performing electron beam lithography using an EB lithography system can be used.
A simulation method of the micro-machined shape to obtain information such as the resolution and cross-sectional shape of the resist. The calculation load can be reduced, the required memory capacity can be reduced, and the simulation condition part can be reduced. It is possible to provide a simulation method capable of reducing the amount of recalculation for a change. As a result, quality assurance before actual production, establishment of process conditions to obtain desired accuracy and yield, development of new resist material, correction of electron beam proximity effect and confirmation of its effect, design and improvement of electron beam lithography system , And can be performed efficiently. More specifically, this is a method for simulating a processed shape of a medium when performing a fine processing (process) in a cross-sectional direction of a medium having a flat surface. Area raster conversion, in which a specified castle in X- and Y-two-dimensional drawing data including a plurality of closed figure parts that determine a drawing area is divided into a plurality of pixels that are the minimum units for performing fine processing. And (b) assigning to each divided pixel an attribute indicating whether at least each pixel overlaps the drawing area, and centering on each pixel
A neighboring pixel distribution, which indicates a distribution state of the attribute of a pixel existing within a predetermined neighboring distance, is obtained, respectively, and the obtained neighboring pixel distribution is similar to a determined standard pixel distribution set prepared in advance. (C) extracting a standard pixel distribution and giving a pixel distribution code corresponding to the standard pixel distribution to all pixels;
A predetermined shape simulation is performed on each of the standard pixel distributions in the set of standard pixel distributions based on predetermined processing conditions, and a pixel in the pixel cross-sectional direction (Z direction) is generated for each of the pixel distribution codes. Having a pixel cross-section data calculation step of calculating cross-section data, further after the pixel cross-section data calculation step,
Pixel cross-section data calculated based on the pixel distribution code given to each pixel is arranged for all the pixels in the designated area, and the predicted shape data in the fine processing (process processing) is thereby obtained. This is achieved by performing a predicted shape construction step of constructing a predicted shape. In other words, the energy accumulation distribution data of the electron beam is not directly scanned along with the graphic data, and the proximity relation between the figures is calculated in advance, thereby reducing the number of calculations and the calculation load. In the above, the required memory capacity can be reduced by using a format in which the sectional direction data prepared separately from the two-dimensional data is referred to instead of the voxel data, and even if some conditions are changed. The simulation can be performed by simple recalculation in which the amount of recalculation is reduced as much as possible. In particular, in a method of simulating a micro-machined shape for obtaining information such as resolution of a resist and a cross-sectional shape in a photomask manufacturing process of performing electron beam lithography using an EB lithography apparatus,
By introducing the concept of the standard pattern into the proximity pixel distribution histogram, the creation of the drawing data and the cross-sectional direction data can be made independent. If one side is changed, the other does not need to be recalculated.

The present invention has been developed as a method for simulating a fine processing shape for obtaining information such as resolution and cross-sectional shape of a resist in a photomask manufacturing process for performing electron beam writing using an EB writing apparatus. The present invention can be generally applied to fine processing technology and lithography using a resist as described below. The medium can be applied to other than a photomask. For example, the present invention can be applied to a semiconductor manufacturing process by direct drawing on a silicon wafer using an EB drawing apparatus, and a wafer transfer process by electron beam exposure using an electron beam mask. The present invention also provides a laser beam other than an electron beam,
The present invention can also be applied to a case where an X-ray beam or an ion beam is used as a drawing line source. Further, the present invention can be applied to a photomask manufacturing process for performing electron beam writing using an EB writing apparatus, a process in which baking of a resist (particularly, PEB) is considered, and an etching process.

[0014]

DESCRIPTION OF THE PREFERRED EMBODIMENTS One embodiment of the present invention will be described with reference to the drawings. FIG. 1 is a schematic process drawing of an example of an embodiment of a method for simulating a microfabricated shape according to the present invention, FIG. 2 is a process diagram schematically showing one example shown in FIG. 1, and FIG. FIG. 6 is a diagram for explaining a histogram calculation, FIG. 6 is a schematic diagram for explaining a three-dimensional energy accumulation distribution on a sample by electron beam lithography and a developing process, and FIG. 7 is a diagram for explaining a cell removal method. FIG. 8 is a schematic diagram for explaining a scattering simulation (Monte Carlo method) and inelastic scattering loss energy and the like.
S110 to S230 in FIG. 1 and S505 to S505 in FIG.
S560 and S810 to S890 in FIG. 8 indicate processing steps.

The method for simulating a micro-machined shape according to this embodiment is a method for simulating a developed shape of a positive resist in which a surface portion is selectively subjected to electron beam drawing in a photomask manufacturing process for performing electron beam drawing using an EB drawing apparatus. It is. This will be described with reference to FIGS. First, E
For the X and Y two-dimensional drawing data (S11, FIG. 2A) for the B drawing device, a specified drawing data in the drawing data including a plurality of closed figure parts for determining an electron beam irradiation region (drawing region). An area raster conversion step is performed on the territory, in which the area is divided into a plurality of pixels, which is the minimum unit for performing fine processing. (S
120) Thereby, pixel-divided data is obtained. (S1
30, FIG. 2 (b)) In this example, since the dose amount (irradiation amount) for each pixel to be drawn is constant, if the pixel F (x, y) is a pixel to be drawn, its value is set to 1 In the case of a pixel that is not drawn, the value is set to 0. However, when the dose amount (irradiation amount) for each pixel to be drawn is set to two or more types,
Correspondingly, the value of F (x, y) may be multi-valued and the ON pixels may be weighted. x and y are integer multiples of the minimum pitch in the X and Y directions for performing the development process, respectively.
It is about the minimum step value of the electron beam drawing apparatus.

Next, focusing on each divided pixel,
A neighboring pixel distribution indicating a distribution state of the number of ON pixels where pixels existing within a predetermined neighboring distance and a drawing area overlap is obtained. An example of a method for obtaining the neighboring pixel distribution will be described with reference to FIG. FIG. 3A shows the drawing data and the state of pixel division. In FIG. 3A, reference numeral 310 denotes a drawing area (also a closed figure part), 320 denotes a pixel, and 325 denotes a pixel of interest. , A neighboring pixel distribution for the pixel of interest 325 is determined. FIG. 3B shows the result of counting the number of ON pixels as frequency using the distance between pixel centers as a parameter for the pixel of interest 325. Note that the maximum number indicates the number of pixels at that distance, and the ratio indicates the ratio of the frequency to the maximum at that distance in%. And X
One pixel pitch in the direction or the Y direction is defined as a distance 1.
In addition, in order to make the description easy to understand, here, the distance between pixel centers is set to be close to 5 pixel pitch, data is further compressed, and the distribution of ON pixels is obtained as shown in FIG. This is a neighboring pixel distribution. The range from the practical level to the predetermined pixel center distance is defined as the neighborhood, and the range for obtaining the neighborhood pixel distribution is limited to this range. In this way, a neighborhood pixel distribution is obtained, but for all pixels,
Similarly, the respective neighboring pixel distributions are obtained. (S1
41) For the pixel F (x, y), a histogram pattern H (x, y, z) as shown in FIG. 2C is obtained. Here, H (x, y, z) = Σ _j Σ _i F (x + i, y + j) where r = (i ² + j ² ) ^1/2 . Note that x, y, and z are integer multiples of the pitch in the X, Y, and Z directions of the minimum unit (hereinafter, also referred to as a cell) for performing the development process. Also, electron beam irradiation area (drawing area)
When weight information is added to the closed figure part for fine processing to the closed figure part which determines the value of the closed figure part, the count value of the histogram is increased for pixels overlapping (also referred to as "intersecting") with the closed figure part having a higher weight. , The distribution of neighboring pixels can also be adjusted.

On the other hand, in advance, focusing on the pixel of interest,
When the distance between pixel centers is within a predetermined range, all possible (possible) ON-pixel states for the target pixel are set separately from the drawing data state using the distance between pixel centers as a parameter, Histogram pattern data is obtained (of FIG. 2E), and a histogram ID (id) is assigned to each histogram pattern data, and these are stored as a database. (S210, FIG. 2 (e)) H (x, y, r) = C (r, ID (x, y)) and a histogram pattern H (x, y, z)
Is coded. In this way, a histogram pattern data group (also referred to as a fixed pixel distribution set) and a histogram code group (also referred to as a pixel distribution code group) are stored as a database.

With respect to all the pixels of the drawing data, it is determined which histogram pattern of the database (S210) corresponds to the obtained histogram pattern (FIG. 2C), and the determined histogram pattern is determined. Are determined as histogram IDs corresponding to the pixels. (S14
2, (FIG. 2 (c)) In this manner, the histogram ID is determined for each pixel of the drawing data, and a histogram code group 2 (pixel distribution code 2) corresponding to the drawing data is obtained. (S150)

Next, electron beam scattering calculation (Monte Carlo method)
Based on (S221, FIG. 2 (f)), the stored energy E (z, r) by electron beam irradiation is obtained three-dimensionally.
For all the histogram IDs, the stored energy for each ID (also referred to as an ID pattern) for each sectional direction (Z-axis direction) and for each predetermined pitch (corresponding to the width of the minimum unit (also referred to as a cell) in development processing) Obtain the Z-axis distribution U (z, id). (S222, FIG. 2 (f)) where U (z, id) = Σ _r C (r, id) E (z, r). Next, for each id pattern, the developing speed R (z, id) of each cell only in the Z direction is converted from the energy stored for each cell (S223), and the developing process is executed (S224, FIG. 2 (f)). )), A Z-axis direction development state (also referred to as a development pattern) V (z, id, t) for each id pattern for each development time, that is, cross-sectional data is obtained.
(S230, FIG. 2 (f)) where: R (z, id) = G (U (z, id)) V (z, id, t) = S (R (z, id), t) It is expressed as Thus, the cross-sectional data V (x, y, z, t) corresponding to all the pixels of the drawing data is obtained. Here, V (x, y, z, t) = V (ID (x, y), t).

Next, for all the pixels of the drawing data,
A histogram code group 2 (S150,
FIG. 2D)) and the pixel cross-section data for each ID (S23).
0, FIG. 2 (f))), by arranging pixel cross-section data for each ID in the cross-section direction with respect to each pixel of the drawing data in the cross-section direction, a simulation is executed to obtain a predicted shape. (S160, FIG. 2 (g)) Note that FIG. 2 (g) shows a predicted shape for the entire designated area, and FIG. 2 (g) shows a 10% cross section thereof.

Next, the three-dimensional energy accumulation distribution on the sample by electron beam lithography and the development process will be further described with reference to FIG. First, when the shape of an electron beam (also referred to as an electron beam) to be drawn is set (S505), irradiation is performed according to the shape of the electron beam (also referred to as an electron beam) based on this and the set dose amount of the electron beam. The unit electron beam particle distribution can be obtained by calculation. (S51
0) The beam shape is a projected image of the beam passing through the aperture, and is generally circular or square in a raster EB lithography apparatus or a vector EB lithography apparatus, respectively. Then
Sample (also referred to as medium, but in this example, a photomask)
When the physical specifications are set (S515), electron track calculation is performed by the well-known Monte Carlo method to simulate the scattering of a single electron beam, thereby calculating the energy stored in each part of the sample, Obtain the distribution of electrons accumulated inside the sample. (S521) Incidentally, the electron track calculation (scattering simulation) by the Monte Carlo method and the calculation of the amount of stored energy (inelastic scattering loss energy) three-dimensionally stored in the medium obtained by this are already known, Here, only the flowchart shown in FIG. 8 will be described, and description thereof will be omitted. When a chromium layer is provided as a light-shielding film on a transparent substrate, and the substrate is a photomask substrate further provided with a resist thereon, the resist layer, the chromium layer, the transparent substrate, and the molecular structure, density, and thickness of each, It is a physical specification. Note that the tracking target of the electron track by the Monte Carlo method can be set such as forward scattering of primary electrons, back scattering of primary electrons, secondary electrons, Auger electrons, and phonons (vibration and heat). Then, using the obtained electron beam particle distribution (S511) and unit electron energy accumulation distribution (S521) as data, scanning is performed along a shape based on the drawing data (S53).
0), to obtain a three-dimensional accumulated energy distribution in the sample. (S540) Specifically, a convolution operation is performed for each cell, which is the minimum unit of the development processing, to obtain a three-dimensional accumulated energy distribution in the sample.

In this way, a three-dimensional accumulated energy distribution in the resist can be obtained.
45), using the Dill's equation and the Mack's equation, calculate the developing speed for each cell in the resist, and obtain the entire developing speed distribution. (S550) The development conditions referred to herein include resist specifications, developer concentration,
Temperature.

The formula of Dill is that when the energy stored in the cell f (x, y, z) is U (x, y, z), the developing speed R ( x, y, z)
Is represented as in equation (1). R (x, y, z) = {A + BU (x, y, z) ⁿ } [1-exp (-αz)] + CU (x, y, z) ^k + ε (1) where A, B, n, α, C, and ε are constants, but are experimental values obtained by experiments.

The expression of Mack is that when the energy stored in the cell f (x, y, z) is U (x, y, z), the developing speed R ( x, y, z)
Is expressed as in equation (2). R (x, y, z) = [Rmax {(a + 1) (1-m) ⁿ } / {a + (1-m) ⁿ }] + Rmin (2) where m = e− ^{CU (x, y, z)} (3) where Rmax is the developing speed of the completely exposed resist portion, Rmin is the developing speed of the not completely exposed resist portion, C is a constant, and n is the solubility selectivity. , A are constants represented by equation (4). a = [(n + 1) / (n-1)] (1- _mTH ) ⁿ (4) In the expression (4), _mTH is a threshold value of m. Also in the case of Mack's formula, each constant is an empirical value obtained by experiment.

Next, developing conditions are set, and a resist dissolution image is calculated along the resist surface by the cell removal method. (S560) The development conditions referred to here include a developer fluid condition, a development time, and the like. The cell removal method is based on the Dill equation, Mac
After the development speed of each cell is determined using the formula of k, etc., the time until the set time is divided into fine step times, and development is advanced for each cell at a specified speed by the elapsed time of the step time. A cell volume value is reduced by that amount, and a list (also referred to as a cell list) for registering the outermost layer cells for each progress of the development processing, that is, for each step time, is created, and only the outermost layer cells are created. The subject of development processing. Assuming that the volume value of the undeveloped cell (also referred to as the volume) is 100, the cell in which the volume value of the cell is 0 or a negative value is deleted from the cell list. The inner cell located in the lower layer in the direction is added to the cell list as the outermost layer cell, and this is set as a processing target cell. Hereinafter, an example of calculation of a dissolved image of a resist by the cell removal method will be briefly described with reference to FIG. Before the development process starts, the set of cells to be processed is
As shown in FIG. 7 (a), and as described as the cell ID in the cell list shown in FIG. 7 (d), the outermost layer cells to be processed each have a volume value of 100. The cells have their respective development rates. After the start of the development and a step time T1 later, the volume value (volume) of each cell shown in FIG. 7D is as shown in FIG. 7E.
The volume of each cell is developed at a designated speed for the elapsed time of the step time T1, and the cell volume value is reduced by 100 to that amount.
It has been reduced from. In this case, cell [2,2,
1], cell [3,2,1], cell [2,3,1], and cell [3,3,1] have a volume of 0. Therefore,
Prior to the development of the next step time T1, from the cell list shown in FIG. 7E, the cells [2, 2, 1] and [3,
2,1], cells [2,3,1], and cells [3,3,1] are deleted, and the cells to be deleted are replaced with internal cells located behind these cells ((lower layer in the Z direction). Cell [2,
2,2], cell [3,2,2], cell [2,3,2],
Cell [3,3,2] is added to the cell list as the outermost layer cell, and this is set as the processing target cell. (FIG. 7 (f)) FIG. 7 (f) shows a cell [2, 2, 1] and a cell [3, 2, 2] from a set of cells to be processed before the development process shown in FIG. 1], cell [2,3,1], cell [3,3,
1] is deleted. in this way,
While the cell list is managed at each step time T1, predetermined development is further advanced to obtain a final shape as shown in FIG.

In the case of this example, the database (S210)
The pixel cross-section data (S230) includes the drawing data (S11).
0) is independent and unaffected. For this reason,
The processing steps S210, S220, and S223 are performed in advance.
By performing these and storing them as a database, the processing steps S210, S220,
S223 does not need to be performed, and can be easily handled. That is, when performing the processing steps S110 to S150, the stored database (S210) and pixel cross-section data (S230) may be referred to and used. As a result, the calculation load is reduced as compared with the related art, and the memory capacity required during the processing is reduced. In addition, when partial changes are made, such as when only the drawing graphic data is changed, such as when the simulation area is changed, it is not necessary to recalculate all the data, and quick switching can be performed. In addition, when switching from a state in which simulation is performed in two dimensions to three dimensions as needed, the rate of recalculation is small.

Conventionally, a predicted shape has been constructed by the steps shown in FIG. 4 or FIG. FIG. 5 is a process diagram schematically showing the process of FIG. That is, similarly to the present example, the drawing area raster conversion (S420) is performed, and for each pixel F (x, y) obtained by division, a value 1 is set for a pixel to be drawn, and a value is set for a pixel not drawn. 0, and from the energy distribution E (z, r) accumulated in the medium by a single electron beam obtained from the electron beam track calculation by the Monte Carlo method (S440), Each time, the three-dimensional stored energy U (x, y, z) has been determined. (S450) After the developing speed is determined for each cell in the same manner as in the present embodiment, corresponding to the stored energy U (x, y, z) stored in each cell, which is the minimum unit of the developing process. As in the case of this example, the predicted shape was constructed by the cell removal method.

As a modified example of this embodiment, a resist is used when a medium is replaced with a photomask and a silicon wafer is used and direct drawing is performed by an EB lithography apparatus or when electron beam exposure is performed using an electron beam mask. Development simulation, or laser beam other than electron beam, X-ray beam,
A simulation of a resist when an ion beam is used as a writing line source can be given. Basically, a predicted shape can be obtained in the same manner. Further, in a photomask manufacturing process for performing electron beam writing using an EB lithography apparatus as in this example, a simulation can be performed in consideration of resist baking (especially PEB).

Further, there is a simulation for further simulating the etching of the chromium layer based on the developed shape obtained as in the present embodiment. In this case, an etching condition is set, and a predicted shape by the etching process is obtained by a string model method or the like. The etching conditions include the concentration of the etching gas,
Temperature, etching time, etching fluid conditions and the like can be mentioned. Note that the string model method is well-known, and description thereof is omitted here.

[0030]

As described above, according to the present invention, fine processing such as obtaining information such as resolution and cross-sectional shape of a resist in a photomask manufacturing process of performing electron beam writing using an EB writing apparatus is performed. The simulation method of the shape can reduce the calculation load, reduce the required memory capacity, and provide a simulation method that can reduce the amount of recalculation for changing the simulation conditions. And

[Brief description of the drawings]

FIG. 1 is a schematic process diagram of an example of an embodiment of a method for simulating a micromachined shape according to the present invention.

FIG. 2 is a process diagram schematically showing one example shown in FIG. 1;

FIG. 3 is a diagram for explaining calculation of a histogram of a neighboring pixel distribution;

FIG. 4 is a schematic process diagram of one example of a conventional method of simulating a micromachined shape.

FIG. 5 is a process chart schematically showing one example shown in FIG. 4;

FIG. 6 is a schematic diagram for explaining a three-dimensional energy accumulation distribution on a sample by electron beam lithography and a development process.

FIG. 7 is a diagram for explaining a cell removal method.

FIG. 8 is a schematic diagram for explaining a scattering simulation (Monte Carlo method) and inelastic scattering loss energy and the like.

[Explanation of symbols]

 310 Area to be drawn (also a closed figure part) 320 Pixel 325 Pixel of interest S410 to S460 Processing steps

 ────────────────────────────────────────────────── ─── Continued on the front page (72) Inventor Koji Ishida 1-1-1 Ichigaya-Kaga-cho, Shinjuku-ku, Tokyo F-term (reference) 2N095 BB01 BB10 5F056 AA12 CC12 CC13 DA08

Claims (12)

[Claims] 1. A method for simulating a processed shape of a medium when performing a fine processed process (process process) in a cross-sectional direction of a medium having a flat surface, comprising: Area raster conversion, in which a specified castle in X- and Y-two-dimensional drawing data including a plurality of closed figure parts that determine a drawing area is divided into a plurality of pixels that are the minimum units for performing fine processing. Steps and
(B) Each divided pixel is provided with an attribute indicating whether or not each pixel overlaps the drawing area, and the distribution state of the attribute of pixels existing within a predetermined proximity distance around each pixel A neighboring pixel distribution is obtained, and for each of the found neighboring pixel distributions, a similar fixed pixel distribution is extracted from a previously prepared fixed pixel distribution set, and a pixel distribution corresponding to the fixed pixel distribution is obtained. the code,
A neighboring pixel distribution coding step to be applied to all pixels;
(C) A predetermined shape simulation is performed on each of the standard pixel distributions in the standard pixel distribution set based on predetermined processing conditions, and a pixel cross section direction (Z direction) is determined for all pixel distribution codes. A) calculating a pixel cross-section data in which pixel cross-section data is calculated. 2. The method according to claim 1, wherein after the pixel cross-section data calculation step, all pixels in the designated area are
Predicted shape construction step of arranging the calculated pixel cross-section data based on the pixel distribution code given to each pixel, obtaining predicted shape data in fine processing (process processing) from this, and constructing a predicted shape A method of simulating a micromachined shape. 3. The pixel cross-section data calculating step according to claim 1, wherein a predetermined shape simulation is performed in advance on each of the fixed pixel distributions in the fixed pixel distribution set based on predetermined process conditions. For all pixel distribution codes corresponding to the standard pixel distribution of
Pixel cross-sectional direction (Z
A method for simulating a micromachined shape, which is characterized in that pixel cross-sectional data in the direction (1) is calculated. 4. A pixel cross-section data calculating step according to claim 1, wherein the pixel cross-section data calculating step calculates a plurality of pixel cross-section data corresponding to a plurality of micro-machining processing (process processing) times. The shape construction step is a method of simulating a micromachined shape, wherein a plurality of predicted shapes corresponding to a time of the micromachining processing (process processing) are constructed. 5. The pixel distribution according to claim 1, wherein the neighboring pixel distribution is a one-dimensional histogram in which the number of neighboring pixels is counted according to a distance from the center pixel. The codes are respectively a fixed histogram set, a fixed histogram, and a histogram code, and the neighboring pixel coding step extracts, in the neighboring pixel coding step, the most similar fixed histogram from the prepared fixed histogram set, A method for simulating a micromachined shape, wherein a histogram code corresponding to a standard histogram is given to all pixels. 6. A method according to claim 1, wherein when weight information is added to the closed figure portion for the fine processing, a neighboring pixel distribution is defined for a pixel intersecting the closed figure portion having a higher weight. A method for simulating a micromachined shape characterized by adjusting. 7. The micromachining according to claim 1, wherein the pixel cross-sectional data is a binary value indicating whether the pixel is penetrated or closed, and the predicted shape is two-dimensional shape data. Simulation method of shape. 8. The pixel cross-section data calculating step according to claim 7, wherein: (A) the total amount of energy stored in the cross-section direction (Z direction) of a single pixel by the energy beam applied to the medium; An energy storage amount calculating step of calculating a total value of a total amount of energy sneaking from a pixel located in the vicinity of a single pixel based on the fixed pixel distribution, and (B) an energy storage amount calculated. Determining whether or not each pixel is lost due to chemical dissolution processing, or performing control such as accelerating the chemical dissolution processing based on a defect state in a pixel adjacent to each pixel, a shape defect determination step A simulation method for a micromachined shape, which is expected to consist of: 9. The micro-processed shape according to claim 1, wherein the pixel cross-sectional data is a one-dimensional shape distribution (Z-direction distribution) in a cross-sectional direction, and the predicted shape data is three-dimensional shape data. Simulation method. 10. The pixel cross-section data calculating step according to claim 9, wherein: (C) a distribution of an amount of energy accumulated in a cross-section direction of a single pixel by an energy beam applied to the medium; An energy accumulation distribution calculating step of calculating a sum value of the distribution of the amount of energy sneaking from a pixel located in the vicinity of the single pixel based on the calculated energy accumulation amount; Calculate the physical defect distribution formed by the chemical dissolution processing that proceeds in the cross-sectional direction (Z direction),
Alternatively, there is provided a shape loss calculating step of performing control for accelerating a chemical dissolution process based on a loss distribution in a cross-sectional direction in a pixel in the vicinity of each pixel. 11. The method according to claim 9, wherein the medium is an electron beam resist, the energy beam is an electron beam, and a Monte Carlo method is used.
The energy storage distribution is calculated by the simulation and the chemical dissolution processing is the development processing of the electron beam resist. The energy storage distribution is converted into the development rate distribution using the Dill equation, and the cell removal method (Cell Re) is used.
A method of simulating a micromachined shape, wherein a physical defect distribution is calculated based on a moving method. 12. The method according to claim 9, wherein the processing intensity of the fine processing is a beam current (dose amount) of an electron beam.
And a method for simulating a micro-machined shape, wherein an adjustment is made to increase or decrease the count value of the obtained histogram according to the magnitude of the beam current set in the closed figure part.