Complementary division mask, method of producing mask, and program

A complementary division method able to suppress a pattern deformation by wet washing, having the steps of determining a definite division length able to suppress the pattern deformation when wet washing to a width and distance of a pattern that is assumed the pattern deformation over an elasticity limit is easiest given by wet washing in advance, dividing the entire line-and-space patterns at the determined division length in the longitudinal direction to divide suitably the line-and-space pattern by a simple algorithm, and further providing a method of producing a mask and program.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a complementary division method, a method of producing a mask, and a program, in particular a complementary division method utilized to a pattern formation of a stencil mask used for a lithography process of a semiconductor device, a method of producing a mask, and a program.

2. Description of the Related Art

As a next generation exposure technology instead of photolithography, a projection exposure technology using electron beam has been developed. The projection exposure technology has an electron projection lithography (EPL) technology using accumulated electron beam of around 100 kV to form a mask pattern enlarged with a device pattern at the constant times on a mask similarly to photolithography and use, and a low energy beam proximity projection lithography (LEEPL) technology using low energy electron beam of around 2 kV to form a mask pattern having same time as a device pattern on a mask and use.

H. C. Pfeiffer,Jpn. J. Appl. Phys.34, 6658 (1995) discloses masks used in the above exposure technology that mask differs from a photomask, is formed on it with a thin film region (membrane) of around 0.1 to 10 μm, and formed on that with a mask pattern as apertures. And these membrane materials have been proposed with silicon, silicon carbonate, and silicon nitride.

In the stencil mask, a pattern having unaperture portions in the middle portion like the doughnut shaped pattern will come out and cannot be formed. Therefore, the pattern has to be divided into a plurality of complementary patterns, formed with the respective pattern at the other portion on the mask or at the another mask, and exposed at several times so as to connect the respective complementary patterns at a wafer.

However, as shown inFIG. 1A, when a thin film3ais formed with apertures5aof line-and-space (L/S) patterns and then wet washed, the thin film (struts) between the apertures5ais loaded such that the struts contact the adjoining struts (beams) when washing. As a result, it suffers from the disadvantage in that the respective adjusting struts deform and do not return to their original formations, as shown inFIG. 1B.

Japanese Unexamined Patent Application No.2001-274072 discloses a technology considering a pattern deformation by washing that the pattern is divided into grid portions having defined dimension. However, it has been a disadvantage that a complimentary division algorithm is complicated. And Japanese Unexamined Patent Application No. 2001-274072 discloses an example of the line-and-space pattern, however a division rules thereof is not disclosed.

SUMMARY OF THE INVENTION

An object of the present invention is to provide a complementary division method able to form a division pattern able to suppress a pattern deformation by wet washing, a method of producing a mask, and a program.

To achieve the above object, according to a first aspect of the present invention, there is provided a complementary division method for dividing a pattern comprising apertures formed at a mask, having a step of dividing the pattern to be divided at a division length able to suppress a pattern deformation when wet washing, in the longitudinal direction of the pattern.

According to a second aspect of the invention, there is provided a method of producing a mask having the steps of sampling a pattern to be divided from a designed pattern and dividing the sampled pattern to be divided by a division length able to suppress a pattern deformation in the longitudinal direction of the pattern when wet washing, distributing the divided patterns to difference regions to determine an arrangement of the divided patterns, forming apertures of the divided patterns based on the determined arrangement of the divided patterns at the different regions of a mask blanks, and wet-washing a mask formed with the apertures.

According to a third aspect of the invention, there is provided a program processed in a computer for making a complementary division process for dividing a pattern comprising apertures formed at a mask, wherein a division length of the pattern is determined according to a width and distance of the pattern, the division length being defined as that the maximum stress loaded to a film between the pattern is not over an elasticity limit of the film when wet washing, the program comprising the following steps processed by the computer sampling a pattern to be divided from a designed pattern, determining the division length according to the width and distance of the pattern, and dividing the sampled pattern to be divided by the determined division length in the longitudinal direction of the pattern.

According to a fourth-aspect of the invention, there is provided a program processed in a computer making a complementary division process dividing a pattern comprising apertures formed at a mask, wherein a division length of a pattern having the smallest width and distance in the pattern to be divided is determined, the division length being defined as that the maximum stress loaded to a film between the patterns is not over an elasticity limit of the film when wet washing, the program comprising the following steps processed by the computer of sampling the pattern to be divided from a designed pattern, and dividing the sampled pattern to be divided by the division length in the longitudinal direction.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Next, preferred embodiment of the present invention will be explained with reference to the drawings.

First Embodiment

FIG. 2Ais a plane view of a stencil mask produced by a method of producing a mask according to the present embodiment, whileFIG. 2Bis a perspective view enlarged with an exposure region.

As shown inFIG. 2A, the stencil mask is arranged with an exposure region2irradiated with X-ray, ion beam, or electron beam at a middle portion of a substrate in disk shape for example. As shown inFIG. 2B, a thin film having a thickness of around 100 nm to 10 μm (hereinafter called as a “membrane”) is formed with a not shown aperture pattern. The exposure region2is formed with a reinforcement portion4having a large thickness for reinforcing strength of the thin membrane3. A region divided by the reinforcement portion4becomes a region enabling pattern formation. The above stencil mask is made by an SOI wafer for example, and the thickness of the reinforcement portion4is a similarly to the thickness of an 8-inch silicon wafer substrate, for example, about 725 μm.

FIG. 3is a perspective view enlarged with a region enabling pattern formation. The apertures5corresponding to the pattern are not formed at the reinforcement portion4, but are formed at the membrane3of the region enabling pattern formation. In the stencil mask, the pattern is constituted by the apertures5, so the pattern such as a doughnuts pattern unable to support its middle portion cannot be formed in this shape.

FIG. 4is a plane view of a line-and-space pattern. If the apertures5of the line-and-space pattern are formed at the membrane3, the strength of the membrane3drops and the washing destruction may be occurring. Due to this, the pattern like this is not applied to form in this shape. Therefore, not only the above doughnut pattern but also line-and-space pattern are carried out with a suitable division process, and have to be distributed and arranged on a mask.

The present embodiment will be explained with a complementary division method of a pattern to be divided, in particular, the line-and-space pattern.FIG. 5is a flow chart for determining a complementary division standard of the line-and-space pattern.

A relative equation for determining the complementary division standard is calculated. In the step of wet washing, due to a water pressure variation causing by a convection current of liquid in a washing bath, a difference of pressures at liquid-vapor interface causing by the surface tension of liquid, and other various factors, the unaperture portions of the mask are considered to load. The load is assumed mainly surface tension of liquid;

FIG. 6is a view showing a step loaded to the struts by the surface tension of liquid in the step immersing a mask in liquid or drying.

FIG. 6is corresponding to the hatched portions of the line-and-space pattern inFIG. 4. The line-and-space pattern can be assumed corresponding to which the struts (beams) made by membrane having its width WL(the membrane region) are arranged at the distance WS. The side portions21of the struts shown by the hatched portions are fixed by the surrounding membrane. The struts constituted with the line-and-space pattern are struts structure fixed both sides, so the other side portions22are fixed similarly to the hatched portion side.

The struts structure are loaded to the struts serving as the unaperture portions in wet washing of the mask and drying in maximum, when the region23between two struts is filled with liquid and the region outside thereof hardly ever filled with liquid. And then, the struts are acted with a pressure P in the arrow direction. This is because that if the both regions between the struts23are filled with liquid, the pressure is cancelled. The above pressure is indicated by the following equation (1).

Note that, “γ” indicates the surface tension of liquid filled between the struts, “θ” indicates a contact angle between the struts surface contacting liquid and liquid, and “WS” indicates the distance between the struts shown inFIG. 6.

The maximum bending moment M occurring at the struts if considering the above pressure P as an uniform load is indicated by the following equation (2) if being the thickness H and the length L of the struts each other.

The maximum stress σmaxloaded to the struts is indicated by the following equation (3) based on the following equation (2) if the width of the struts is indicated by “WL”.

If the maximum stress σmaxis larger than same threshold σC, that is, σmax>σC, the struts may be deformed over an elastic deformation. As a result, the relation between the length L and width WLof the struts not deformed and the distance WSadjoining the struts is indicated by the following equation (4).

In the above equation, the coefficient k1is indicated by the following equation (5).

If the length L of the struts is indicated by “LC” when the maximum stress σmaxis equal to the threshold σC, the conditional equation of the pattern length in that the maximum stress loaded to a film between the patterns, when wet washing, is equal to the elastic limit of the film in the width WLand the distance WSof the predetermined struts is indicated by the following equation (6).

“LUL” is multiplied with the suitably coefficient (safety coefficient) smaller than 1 by LC, and is indicated by the following equation (7).

The complementary division of the stencil mask is performed by making the above LULas the maximum volume of L, as a result the stencil mask in that washing is difficulty caused with the deformation of the struts can be provided. The above equations are referred to the document (Namatsu et al.Appl. Phys. Lett. Vol66, p2656, 1995) explained with the load to the struts structure fixed one side, applied with the theory of the load to the struts structure fixed one side to the struts structure fixed both side, and calculated.

As above mentioned, the relative equation for the complementary division standard is calculated, then the coefficient k1of the above equation (5) is prepared by experiment in the struts structure fixed both side of the stencil mask. Because, the above coefficient k1is changed due to the Young's modulus of the membrane materials for using or a method of wet washing.

Therefore, the line-and-space pattern is formed on the membrane to produce a washing test sample so as to be able to prepare the limit length LCof the struts not deforming when washing. The structure of the washing test sample does not have to be equal to the membrane thickness or the membrane size of the structure of the stencil mask used for projection in practical. That is, the test sample may have the membrane materials same as the stencil mask used for projection and have a structure considered equally to the Young's modulus.

FIG. 7Ais a view showing the structure of the washing test sample. The washing test sample is arranged with the line-and-space pattern LSnm(n=1, 2, . . . , m=1, 2, . . . ) having various widths WL, distances WS, and lengths L in a matrix. The respective line-and-space patterns LSnmhave four struts having the length Lnm, the width WLn, and the distance WSn, shown inFIG. 7B.

As shown inFIG. 7A, the washing test sample is formed with the line-and-space pattern having a plurality of pattern lengths Lnm(m=1, 2, . . . , Lnm<Lnm+1) in the respective n corresponding to the plurality pairs of the width and distances ({WL, WS}, n=1, 2, . . . ).

In the present embodiment, the pattern of the struts structure fixed both sides arranged with four struts shown inFIG. 7Bis fixed with WL/WSby 2, and is changed with WSwithin the limit of 70 to 200 nm and L/WSwithin the limit of 5 to 200 to form the sample on a silicon membrane of about 500 nm thickness and use.

Next, the test sample produced in the step ST2is washed, and the boundary portions Lnm=Lnm′ between the pattern length Lnm=Lnm+1′ deformed with the pattern after washing and the pattern length Lnm=Lnm′ not deformed in the above respective pairs of {WLn, WSn} are prepared. The Lnm′ prepared by this is used and made LC=Lnm′, then the coefficient k1is calculated by using the above equation (6).

In the present embodiment, the washing is performed at the following condition or possibly close to the condition when washing the stencil mask used for projection.

The washing apparatus is used with FL820L made by Dai Nippon Screen MFG. Co., Ltd. or UW8000 made by Tokyo Electron Limited. These two apparatus are performed with the steps from washing by the plurality of washes by water or rinse chemicals to drying in single bath, that is, one bath type apparatus in that the method of replacing from pure water to chemical or replacing from chemicals to pure water is not draining at once and pouring water, but can be replacing from the previously chemicals to others gradually by the over flow. The dry systems thereof are common in the point of using isopropyl alcohol (hereinafter, called as an “IPA”), but the former is utilizing the Marangoni effect by the difference of the surface tensions of IPA and water and drying by low pressure and the later is using IPA vapor drying by an atmospheric pressure, so these are different points.

The one bath type washing apparatus can be kept with sufficiently wettability and be exchanged with chemicals. So the number of times passing through liquid-vapor interface when washing sample, that is, caused with the stress at the struts due to the surface tension, are only two when immersing a sample first in liquid and drying. Due to this, comparing with the case of using numerous bath type wet washing apparatus or a spin type washing apparatus for general use (the number of times passing though the liquid-vapor interface are increasing), the pattern deformation can be considered to small. And the spin type washing apparatus is used with a spin drying method in general. If the spin drying method is applied to the stencil mask, the centrifugal force occurs adding to the surface tension, as a result, the factors deformed with a mask pattern are increasing, and so the stress loaded to the struts is considered to increasing.

The pulling rate and dipping rate of the sample when immersing the sample at the washing apparatus are set at the minimum rate able to self-convey in the respective apparatus. The flow rates for supplying liquid are set at two kinds of that one (1) is the minimum flow rate within the limit able to process automatically and the other (2) is the flow rate similarly to the real chemicals process. The washing process time is similaly to real chemical process. And the temperature of liquid is room tempreture, and chemicals is not used but only pure water is used.

FIG. 8shows an experimental result in the case of washing the test sample at the above washing condition. The following conditions 1 to 4 are plotted with the distance WSat y-axis and (LC/WL)2at x-axis. The difference of the conditions 1 to 4 and the coefficient k1calculated by parameter fitting will be mentioned hereinafter.

The condition 1 is case of using UW8000 as the washing apparatus and employing the above (1) as the flow rate for providing liquid, so the coefficient k1becomes 0.22. The condition 2 is a case of using UW8000 as the washing apparatus and employing the above (2) as the flow rate for providing liquid, so the coefficient k1becomes 0.24. The condition 3 is a case of using FL820L as the washing apparatus and employing the above (1) as the flow rate for providing liquid, so the coefficient k1becomes 0.23. The condition 4 is a case of using FL820L as the washing apparatus and employing the above (2) as the flow rate for providing liquid, so the coefficient k1becomes 0.23.

As mentioned above, the experiment used the washing apparatus using in particularly after the pattern formation at the stencil mask is satisfied with the strait-line relation shown in the above equation (6) in the respective conditions 1 to 4, therefore is shown that the assumption considered in the present embodiment is adequate.

Next, the complementary division standard, that is, the coefficient A and LULin the above equation (7), is determined. LULshown in the above equation (7) is a function of variables WSand WL. And the method dividing the line-and-space pattern by a division length of LULis determined whether the entire {WS, WL} are applied to the same A (1) or applied to same LUL(2).

In the case of (1), for example, the value of the coefficient A such as A=0.6 is directly determined in advance. The pattern portions for complementary dividing are specified with the distances WSand the widths WLin the entire regions, then LULare determined by the equation (7) in the respective {WS, WL}.

In the case of (2), {WS, WL} considered the most critical condition to the pattern deformation by washing are sampled to determine LULin that case, and applied with the same division length to the entire {WS, WL} uniformity. Here, the critical condition is defined a condition of the width and the distance of the pattern that is assumed the pattern deformation over an elasticity limit is easiest given by wet washing, and corresponding to a condition the smallest width and distance in the pattern to be divided. For example, in the case of determining {WS, WL}={70 nm, 70 nm} and A=0.55, if the coefficient k1=0.24 prepared in the step ST3is substituted, LULbecomes about 2 μm. In particular, in the washing experiment of the step ST3, the pattern of {WS, WL}={70 nm, 70 nm} and L=2 μm is confirmed to not deform after washing.

The program according to the present embodiment is processed by computer with the complementary division process for dividing the line-and-space pattern at the complementary division condition determined like above.

FIG. 9is a block diagram showing an embodiment of hardware of a data processing apparatus (computer) determining the complementary division condition by reading the program according to the present embodiment.

The data processing apparatus has an input portion11, an output portion12, an interface (I/F)13, a random access memory (RAM)14, a memory portion15, and a central processing unit (CPU)16. And the input portion11, the output portion12, the I/F13, the RAM14, the memory portion15, and the CPU16are connected by a bus BS.

The input portion11outputs a desired input data to the CPU16. For example, the input portion11is a keyboard, a mouse, a compact disc type read-only memory (CDROM) (recordable (R) or rewritable (RW)) drive, a floppy (a registered trademark) disk (FD) drive, or other input apparatus.

The output portion12supplies data corresponding to a desired output data outputted from the CPU16. For example, the output portion12is a display device and displays an image corresponding to output data outputted from the CPU16. The I/F13transmits and receives a desired data to the other data processing apparatus according to control of the CPU16.

The RAM14is used as a workspace when the CPU16performs the predetermined process. The memory portion15writes and reads the desired data by the CPU16.

The memory portion15is housed with a program150according to the present embodiment for example. The program150includes the processing step of the complementary division process according to the present invention for example, and is performed at the RAM14as a workspace by the CPU16.

FIG. 10is a flow chart of the complementary division process performed by the above program. Here, the complementary division standard will be explained in the case of employing the above (1) method.

First, a pattern is sampled from a designed pattern data, and estimated whether the sampled pattern is a pattern to be divided or not (step ST11). The pattern to be divided includes not only the line-and-space pattern, but also the above doughnut pattern and a leaf pattern, so if being these patterns, the respective suitable complementary division processes are performed. If not being the pattern to be divided, the division processes are not performed and portions to be distributed are determined (step ST14).

When the sampled pattern is the line-and-space pattern shown inFIG. 11A, the WLand WSof the line-and-space pattern are specified, then the division length LULis calculated by the equation (7) and the vale of A (step ST12). That is, the WLand WSare substituted to the equation (7) to calculate the LUL, or a compensation table is prepared in advance and the WLand WSare specified to determine the LULsatisfied with the equation (7).

The line-and-space pattern is divided at the division length determined like above (step ST13), and the divided pattern is determined with the portion to be distributed (step ST14). In basically, in the region enabling pattern formation shown inFIG. 3, the divided pattern is distributed so as to have uniformity density. Therefore, the line-and-space pattern shown inFIG. 11Ais distributed into the division pattern shown inFIG. 11Band the division pattern shown inFIG. 11Cas a pair at the any portions enabling pattern formation.

The processes from the above step ST11to the step ST14are performed to the entire patterns including the pattern data (step ST15). After finishing the complementary division processes for the entire patterns, an electron beam directly describing apparatus describes a complementary division pattern at a mask blanks formed with a resist on the membrane3using complementary divided data. Then, the resist is developed, and the membrane is etched using the resist pattern as an etching mask to form apertures of the complementary division pattern at the mask blanks (step ST16).

After that, the resist is removed, and the stencil mask is washed by wet washing similarly to the above washing experiment to finish a process of producing the stencil mask. The wafer formed with the resist is exposed with shifting the stencil mask at several times, so the wafer is jointly transferred with the division pattern divided complementary to form the pattern before dividing (step ST18).

The complementary division process shown inFIG. 10shows an example dividing according to the complementary division standard shown in case (1), but the complementary division standard shown in case (2) may be used. In this case, the step ST12is not performed and the sampled line-and-space pattern is applied with uniformity division length. For example, the entire line-and-space pattern is divided in the longitudinal direction at the division length of 2 μm. The subsequent steps are similarly to the mention above.

In the complementary division method according to the present embodiment, the line-and-space pattern is determined with a rule for determining the division length able to suppress the pattern deformation when wet washing in advance, determined with the suitable division length in each time according to the width and distance of the pattern of the respective line-and-space pattern, and divided in the longitudinal direction. Therefore, the line-and-space can be suitably divided by simple algorithm.

On the other hand, in the designed pattern, the width and distance of the pattern that is assumed the pattern deformation over the elasticity limit is easiest given by wet washing are determined with the definite division length able to suppress the pattern deformation when wet washing, then the entire line-and-space patterns are divided at the determined division length in the longitudinal direction. As a result, the line-and-space patterns can be suitably divided by simpler algorithm.

The result obtained by the test sample is applied to a theory of the load to the struts structure fixed both sides, so the rule for determining the above division length or the suitable division length is calculated. As a result, the washing destruction of the stencil mask in practical can be suppressed certainly.

Therefore, the method of producing the stencil mask applied with the above complementary division method can suppress a washing destruction of the stencil mask, so can produce the stencil mask having reliability with no pattern deformation.

Summarizing the effects of the invention, the pattern deformation by wet washing of the stencil mask can be suppressed.

Note that, in the present embodiment, the coefficient k1is prepared by the experiment, but may be prepared by using the values of γ, θ, and σcprepared from documents or by experiment each other.