JP5786152B2 - Design method of mold for nanoimprint - Google Patents

Description

  The present invention relates to a method for designing a nanoimprint mold used for manufacturing semiconductor elements, optical elements and the like.

  In the manufacture of highly integrated LSIs and fine optical elements, techniques for realizing fine pattern processing at a low cost are becoming increasingly important. One such technique is nanoimprint lithography (see, for example, Patent Document 1).

  Nanoimprint lithography uses a mold (mold) with a desired concavo-convex pattern formed on the surface in advance, and presses the mold pattern directly onto the resin film formed on the substrate, thereby forming the concavo-convex pattern on the surface of the resin film. The technology to do.

  Nanoimprint lithography can form uneven patterns by a simple method, and in recent years, it has been found that ultrafine patterns of several tens to several nanometers can be formed, so the next generation that requires patterning of 50 nm or less It is expected as a candidate for lithography technology.

  With reference to FIG. 9, the manufacturing process of the uneven | corrugated pattern in nanoimprint lithography is demonstrated easily. FIG. 9 is a cross-sectional view showing the main steps of nanoimprint lithography.

  First, as shown in FIG. 9A, a resist film 2 formed of a resin on a substrate 1 which is a fine structure is heated to a predetermined temperature, and a piston rod (not shown) is provided above the resist film 2. The mold 3 fixed to () is disposed. Next, as shown in FIG. 9B, the piston rod is operated to lower the mold 3 and press the resist film 2 with a predetermined pressure. Finally, as shown in FIG. 9C, the mold 3 is raised and separated from the resist film 2. In this way, the fine uneven pattern of the mold 3 is transferred to the resist film 2 on the substrate 1.

  A method for producing the mold 3 used in the above-described nanoimprint lithography will be briefly described. The mold for nanoimprinting is produced by the same method as that for the photomask. Specifically, after forming a metal mask layer on the surface of a substrate made of silicon carbide or the like, a resist is applied thereon. A fine pattern is drawn on the resist film using an electron beam or ultraviolet rays, and developed using an ortho-xylene solution or the like. Next, dry etching is performed using a reactive gas.

  In the dry etching process, the metal mask layer is first etched and then the substrate is etched. If dry etching is continued to such an extent that the metal mask layer disappears, a mold having a concavo-convex pattern is completed.

  As described above, in nanoimprint lithography, a resist film formed of a resin material is cured using heat or ultraviolet rays, but a dimensional error (Critical Dimension Error, hereinafter referred to as “CD error”) occurs due to shrinkage during curing. .

  For this reason, in application to a semiconductor element or the like that requires high dimensional accuracy, it is necessary to predict shrinkage including three-dimensional shape change and compensate for the shrinkage when designing a mold.

  In the field of resin injection molding using a mold, a method for designing a mold in consideration of shrinkage of the resin accompanying cooling has been proposed and spread (for example, see Patent Document 2).

  However, in the field of nanoimprint lithography, no specific proposal has yet been made for a method of designing a mold by compensating for resin shrinkage.

JP 2007-50663 A Japanese Patent Laid-Open No. 9-277260

  The present invention has been made in view of the above-described problems, and an object of the present invention is to provide a nanoimprint mold design method capable of compensating for resin shrinkage and realizing a pattern having a dimension substantially equal to a design value.

In order to achieve the above object, a method for designing a mold for nanoimprinting according to the present invention has a plurality of uneven patterns arranged at equal intervals, and the pattern is transferred to a film made of a flexible material by pressing. A method for designing a mold for nanoimprinting,
When the pattern of the convex portions formed on the surface of the film is a rectangular parallelepiped having a line width w ₁ , a height h ₁ , and a length L ₁ , the line width of the concave portion of the nanoimprint mold corresponding to the convex portion is set. The line width w ₃ is calculated using the following formula (1).

式（１）において、ｐ（ｗ ₁ ）は一般的な空間周波数の遮断関数の形式で表現した予測関数であり、下記式（２）で与えられる。

In the formula (1), p (w ₁₎ is predicted function der expressed in the form of a cut-off function of a general spatial frequency is, given by the following equation (2).

ここで、αは線収縮係数、ｗ₀はカットオフ長、ｋは補正係数、ｎは補正次数である。

Here, α is a linear contraction coefficient, w ₀ is a cutoff length, k is a correction coefficient, and n is a correction order.

Method of designing a mold for nanoimprinting of the above, the aforementioned correction coefficient k when the length L ₁ with respect to the line width w ₁ is less than 2 times 1.0, the length L ₁ with respect to the line width w ₁ is 2 The correction coefficient k is 1.0 to 1.6 when it is more than twice and less than 20 times, and the correction coefficient k is 1.6 when the length L ₁ is 20 times or more with respect to the line width w ₁ . Is preferred. The correction order n is preferably 2.

The nanoimprint mold design method according to the present invention is a nanoimprint mold design method having a plurality of uneven patterns arranged at equal intervals and transferring the pattern to a film made of a flexible material by pressing. There,
When the convex pattern formed on the surface of the film is a rectangular parallelepiped having a line width w ₁ , a height h ₁ , and a length L ₁ , the height of the concave portion of the nanoimprint mold corresponding to the convex portion is set. The height h ₃ is calculated using the following formula (3).

式（３）において、ｑ（ｈ ₁ ）は一般的な空間周波数の遮断関数の形式で表現した予測関数であり、下記式（４）で与えられる。

In the formula (3), q (h ₁₎ is prediction function der expressed in the form of a cut-off function of a general spatial frequency is, given by the following equation (4).

ここで、αは線収縮係数、ｗ₀はカットオフ長、ｋは補正係数、ｎは補正次数である。

Here, α is a linear contraction coefficient, w ₀ is a cutoff length, k is a correction coefficient, and n is a correction order.

In the nanoimprint mold design method described above, it is preferable that the correction coefficient k is 1.65 and the correction order n is 2.

  By employing the nanoimprint mold design method of the present invention, it is possible to compensate for resin shrinkage and realize a concavo-convex pattern having dimensions approximately equal to the design value.

It is a perspective view which shows the external appearance of the microstructure manufactured using the mold for nanoimprint. It is sectional drawing explaining the design method of the mold for nanoimprint concerning this invention. It is a graph which shows the predicted value of the line width after shrinkage | contraction with respect to the line width of a mold computed using Formula (2) and Formula (5). It is a graph which shows the line | wire width of the mold which performed correction | amendment using Formula (1) and Formula (2). It is a graph which compares and shows the simulation result of the shrinkage | contraction rate with respect to line | wire width, and a measured value. It is a graph which shows the relationship between a residual film thickness and the shrinkage amount of the resist of a line width direction. The predicted height of the mold after shrinkage relative to the mold height, calculated using Equation (4) and Equation (6), and the height of the mold subjected to correction using Equation (3) and Equation (4) It is a graph which shows. It is a graph which shows the relationship between a residual film thickness and the shrinkage amount of the resist of a height direction. It is sectional drawing which shows the main processes of nanoimprint lithography.

  A method for designing a nanoimprint mold (hereinafter abbreviated as “mold”) according to an embodiment of the present invention will be described below with reference to the drawings.

(Embodiment 1)
FIG. 1 shows an overview of a microstructure manufactured using a mold. In the present invention, it is assumed that a fine structure generally called a “Line & Space” pattern in which convex portions and concave portions are repeatedly arranged at a predetermined interval is manufactured. In the figure, members having the same functions as those shown in FIG.

  As shown in FIG. 1, a microstructure 20 is obtained by pressing a resist film 2 using a mold 3 to be described later. A rectangular parallelepiped having a line width w, a height h, and a length L is formed on a remaining film layer 21. Shaped convex portions 22 are repeatedly formed at predetermined intervals.

  The resin material used for the resist film 2 differs depending on the curing method. When the thermosetting method is adopted, for example, polymethacrylic acid (PMMA) which is a kind of acrylic resin is used. On the other hand, when the photocuring method is employed, for example, “PAK-01” (trade name of Toyo Gosei Co., Ltd.), which is a kind of photocuring resin, is used.

<Design method in the line width direction of the mold>
Hereinafter, of the mold designing methods according to the present invention, the designing method in the line width direction of the mold will be specifically described with reference to FIG.

FIGS. 2A to 2C show a cross section of the region indicated by the arrow A in FIG. 1, and the resist film 2 formed on the substrate 1 is pressed with the mold 3 in the manufacturing process of the microstructure 20. Indicates the state of FIG. 2A shows a state before the pressed resist film 2 is cured. In the figure, the line width w ₁ and the height h ₁ are the design values of the convex portion 22, in other words, the line width and height (depth) of the concave portion 31 formed in the mold 3 in a form corresponding to the convex portion 22. Show.

When shrinkage does not occur in the resist film 2 at the time of curing, a convex portion 22 having a cross-sectional shape with a line width w ₁ and a height h ₁ is formed, but actually, as shown in FIG. In addition, the resist film 2 shrinks during curing, and the line width becomes w ₂ and the height becomes h ₂ .

Therefore, as shown in FIG. 2C, if the line width w ₃ of the mold 3 is designed to be large so that the line width w ₂ of the resist film 2 after shrinkage is equal to the design value w ₁ , the shrinkage is reduced. The fine structure 20 having a line width substantially equal to the design value w ₁ can be manufactured by compensating for the influence.

Although the thickness t of the remaining film layer 21 also slightly shrinks, as will be described later, the shrinkage of the thickness t does not affect the line width w ₂ and height h ₂ of the convex portion 22. Will be described as not changing.

The inventors derived a prediction function p (w) expressed in the form of a general spatial frequency cutoff function based on the result of simulation for compensation of shrinkage due to curing of the resin containing the resist material. Then, it was found that when the prediction function p (w) was used to correct the mold 3 in the line width direction, an uneven pattern having a line width substantially equal to the design value w ₁ was obtained.

Specifically, if the line width w ₃ determined by the following formula (1) including the prediction function p (w) is used as the correction value of the line width of the mold 3, “Line” having a line width substantially equal to the design value w ₁ is used. & Space ”pattern.

  The following formula (2) lists the optimal formula as the prediction function p (w). The shrinkage rate Δw / w of the resist film line width is expressed as a general spatial frequency cutoff function (filter characteristic) format. It is a thing fitted to.

In the above equation (2), w ₀ is a cutoff length, α is a linear contraction coefficient, k is a correction coefficient, and n is a correction order. Of these parameters, the cut-off length w ₀ indicates the boundary value of the repetition interval of the convex portions of the resist film . Usually, the cut-off length w ₀ is 10 times the design value height h ₁ .

  The linear shrinkage coefficient α indicates the degree of shrinkage of the material constituting the fine structure 20, and has different values depending on the material and the curing method (thermal curing or photocuring).

The correction coefficient k is a coefficient for performing correction for bringing the value calculated using the prediction function close to the result of the simulation (fitting). Correction coefficient k, when time length L ₁ with respect to the line width w ₁ is less than 2 times 1.0, the length L ₁ is less than 20 times 2 times the line width w ₁ is It is 1.6 when the length L ₁ is 20 times or more with respect to 1.0 to 1.6 and the line width w ₁ . In the “Line & Space” pattern, the length L in the longitudinal direction of the convex portion 22 is much larger than the line width w, so k is set to 1.6 unless otherwise specified.

  The correction order n is an order for performing correction for fitting the value calculated using the prediction function and the simulation result, and is normally 2.0.

The calculation of the line width w ₃ using the equations (1) and (2) can be performed using a commercially available personal computer (hereinafter referred to as “PC”). Specifically, the design value w _{1 of the} line width and the value of each parameter (w ₀ , α, k, n) are inputted from the keyboard, and the calculation is installed in the ROM (Read Only Memory) or hard disk of the PC. The software is read and calculation is performed.

<Explanation of simulation results>
Next, the line width value calculated by the design method of the present invention and the simulation result will be described with reference to FIGS.

The solid line in FIG. 3 shows the result of calculating the predicted value of the line width w ₂ after shrinkage with respect to the line width w ₁ of the mold using the above-described equation (2) and the following equation (5). The broken line is the mold line width w ₁ shown as a reference.

In the calculation, the cutoff length w ₀ = 500 nm of equation (1), the linear shrinkage coefficient α = 0.1, the correction coefficient k = 1.6, and the correction order n = 2. A value indicated by Δ in the figure is a value (line width w ₂ ) in which a CD error is predicted by simulation. In the simulation, “MARC” (product of MSC Software), which is a commercially available software for structural analysis, was used.

FIG. 3 shows that the line width w ₂ of the transfer pattern is smaller than the line width w ₁ of the mold 3, and the amount of shrinkage depends on the line width and height of the mold. Further, it can be seen that the line width w ₂ calculated using the equations (2) and (5) matches the predicted value of the CD error by the simulation indicated by Δ.

The solid line in FIG. 4 shows the line width w ₃ of the mold 3 calculated (ie, corrected) using the above-described equations (1) and (2). Also it shows the result of simulating the line width w ₂ after shrinkage by using the line width w ₃ of the mold 3 after correction by △. The broken line is a value of the line width w ₂ after shrinkage when the line width of the mold 3 is w ₃ , calculated using the above formulas (2) and (5).

As shown in FIG. 4, when the line width w ₃ of the mold 3 calculated using the prediction function p (w) of Expression (2) is used, the line width w ₂ after shrinkage matches the design value w ₁ . That is, the line width w _{3 of the} mold in which the CD error is corrected is obtained by using the prediction function of Expression (2).

  Incidentally, the line width indicated by Δ in FIGS. 3 and 4 is a value obtained as a result of simulation using commercially available software for structural analysis, and is an actual measurement value of a fine structure manufactured using a resist. Absent. However, the simulation results using this software agree well with the measured values. FIG. 5 shows a simulation result (● in the figure) and an actual measurement value (□ in the figure) of the shrinkage rate Δw / w with respect to the line width w. Here, the linear shrinkage coefficient α was set to 0.073.

  As shown in FIG. 5, the simulation result and the actual measurement value almost coincide with each other in a region with a small line width (that is, a region where the aspect ratio of the convex portion 22 is small), and the software used for the simulation is reliable. Recognize.

  Next, it will be described with reference to FIG. 6 that there is no dependency of the remaining film thickness t on the shrinkage of the resist in the line width direction. Δw in FIG. 6 indicates a simulation result of the contraction amount in the line width direction. 3 and 4 show the simulation results when the remaining film thickness t is 25 nm. As shown in FIG. 6, the shrinkage amount Δw in the line width direction is independent of the remaining film thickness t. Since it is almost constant, it can be seen that Equation (2) can be applied to other remaining film thicknesses.

In the present embodiment, the correction method (that is, the design method) in the mold line width direction against resist shrinkage has been described, but this method can also be applied to shrinkage in the longitudinal direction of the mold. In that case, the line width w in the equations (1) and (2) is replaced with the length L, and the cut-off length w ₀ is replaced with the cut-off length L ₀ .
In this case, the longitudinal cutoff length L ₀ = 10 × h. Regarding the correction coefficient k, in the “Line & Space” pattern, the line width w is very small compared to the length L, so k = 1.0. Further, the correction order n = 2.0.

(Embodiment 2)
In the first embodiment, the design method in the line width direction of the mold has been described. In the present embodiment, the design method in the height direction of the mold will be described.

<Design method in the mold height direction>
As shown in FIG. 2A, when the resist film 2 does not shrink during curing, a convex portion 22 having a cross-sectional shape having a line width w ₁ and a height h ₁ is formed. Actually, as shown in FIG. 2 (b), the resist film 2 contracts during curing, and the line width becomes w ₂ and the height becomes h ₂ .

Therefore, as shown in FIG. 2C, if the mold height h ₃ is designed to be large so that the height h ₂ after shrinkage is equal to the design value h ₁ , the effect of shrinkage can be compensated. A fine structure 20 having a line width substantially equal to the design value h ₁ can be manufactured.

The inventors have made a prediction function q expressed in the form of a general spatial frequency cutoff function on the basis of simulation by a method similar to the above-described prediction function p (w) for compensation of shrinkage due to resin curing. (H) was derived. It has been found that when the height direction of the mold 3 is corrected using this prediction function q (h), an uneven pattern having a height substantially equal to the design value h ₁ can be obtained.

Specifically, if the height h ₃ determined by the following equation (3) including the prediction function q (h) is used as a correction value for the height of the mold 3, “Line” having a height substantially equal to the design value h ₁ is used. & Space ”pattern.

  The following formula (4) lists an optimal formula as the prediction function q (h).

In Expression (4), w ₀ is a cutoff length, α is a linear contraction coefficient, k is a correction coefficient, and n is a correction order. The definitions of the cut-off length w ₀ , the linear contraction coefficient α, the correction coefficient k, and the correction order n are the same as the definitions described in the first embodiment. Further, the calculation of the height h ₃ using the equations (3) and (4) can be performed using a commercially available PC as in the first embodiment.

<Explanation of simulation results>
Next, the mold height calculated by the design method of the present invention and the simulation results will be described with reference to FIG.

The thin solid line in FIG. 7 shows the result of calculating the predicted value of the height h ₂ after shrinkage with respect to the mold height h ₁ using the above formula (4) and the following formula (6). Also, the thick solid line in FIG. 7 shows the mold height h ₃ calculated (that is, corrected) using the above-described equations (3) and (4).

In the calculation, the cutoff length w ₀ = 200 nm, the linear contraction coefficient α = 0.01, the correction coefficient k = 1.65, and the correction order n = 2 in Expression (4). Further, the value indicated by ◯ in the figure is the result of simulating the height h ₂ after shrinkage using the height h ₁ of the mold 3 (that is, the predicted value of the CD error). As in the first embodiment, “MARC” (product of MSC Software), which is commercially available structural analysis software, was used for the simulation. The broken line in FIG. 7 is a design value h ₁ of the heights indicated by reference.

As is apparent from FIG. 7, the transfer pattern height h ₂ (shown by a thin solid line) is smaller than the mold height h ₁ (shown by a broken line), and the amount of shrinkage depends on the mold line width and height. Depends on the size. Further, when the height h ₃ of the mold 3 calculated using the equations (3) and (4) (shown by a thick solid line) is used, the height h ₂ after shrinkage matches the design value h ₁ . That is, by using the prediction function of Expression (4), the mold height h ₃ in which the CD error is corrected can be obtained.

  Next, it will be described with reference to FIG. 8 that there is no dependency of the remaining film thickness t on the resist shrinkage in the height direction. Δh in FIG. 8 indicates the simulation result of the contraction amount in the height direction. FIG. 7 described above shows the simulation result when the remaining film thickness t is 25 nm. As shown in FIG. 8, the amount of contraction Δh in the height direction is constant regardless of the remaining film thickness t. Therefore, it can be seen that Equation (4) can be applied to other remaining film thicknesses.

  In each of the above embodiments, the case where a fine structure is manufactured by pressing a resist film has been described. However, a mold manufactured by the design method of the present invention is a resin other than a resist or a glass having a low viscosity. The present invention can also be applied to the case where a microstructure is manufactured using a flexible material such as a material.

DESCRIPTION OF SYMBOLS 1 Substrate 2 Resist film 3 Mold 20 Fine structure 21 Residual film layer 22 Projection

Claims (5)

A method for designing a mold for nanoimprinting having a plurality of uneven patterns arranged at equal intervals and transferring the pattern to a film made of a flexible material by pressing,
When the pattern of the convex portions formed on the surface of the film is a rectangular parallelepiped having a line width w ₁ , a height h ₁ , and a length L ₁ , the line width of the concave portion of the nanoimprint mold corresponding to the convex portion is set. A method for designing a mold for nanoimprinting, wherein the line width w ₃ is calculated using the following formula (1).

In the formula (1), p (w ₁₎ is predicted function der expressed in the form of a cut-off function of a general spatial frequency is, given by the following equation (2).

Here, α is a linear contraction coefficient, w ₀ is a cutoff length, k is a correction coefficient, and n is a correction order. When the length L ₁ is less than twice the line width w ₁ , the correction coefficient k is 1.0,
When the length L ₁ is 2 times or more and less than 20 times the line width w ₁ , the correction coefficient k is 1.0 to 1.6,
When the length L ₁ is 20 times or more with respect to the line width w ₁ , the correction coefficient k is 1.6.
The nanoimprint mold design method according to claim 1 , wherein the mold is a nanoimprint mold. The nanoimprint mold design method according to claim 1 , wherein the correction order n is two. A method for designing a mold for nanoimprinting having a plurality of uneven patterns arranged at equal intervals and transferring the pattern to a film made of a flexible material by pressing,
When the convex pattern formed on the surface of the film is a rectangular parallelepiped having a line width w ₁ , a height h ₁ , and a length L ₁ , the height of the concave portion of the nanoimprint mold corresponding to the convex portion is set. The method for designing a mold for nanoimprinting, wherein the height h ₃ is calculated using the following formula (3).

In the formula (3), q (h ₁₎ is prediction function der expressed in the form of a cut-off function of a general spatial frequency is, given by the following equation (4).

Here, α is a linear contraction coefficient, w ₀ is a cutoff length, k is a correction coefficient, and n is a correction order. The nanoimprint mold design method according to claim 4 , wherein the correction coefficient k is 1.65 and the correction order n is 2.

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