Method of forming photomask using calibration pattern, and photomask having calibration pattern

A method of forming a photomask using a calibration pattern that may exactly transfer a desired pattern to a substrate. The method includes providing one-dimensional calibration design patterns each having first design measures and providing two-dimensional calibration design patterns each having second design measures; obtaining one-dimensional calibration measured patterns using the one-dimensional calibration design patterns and obtaining two-dimensional calibration measured patterns using the two-dimensional calibration design patterns; obtaining first measured measures of the one-dimensional calibration measured patterns and obtaining second measured measures of the two-dimensional calibration measured patterns; establishing a correlation between the first measured measures and the second measured measures; and converting a main measured measure of a main pattern into a corresponding one of the first measured measures using the correlation.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of Korean Patent Application No. 10-2010-0129997, filed on Dec. 17, 2010, in the Korean Intellectual Property Office, and entitled: “Method of Forming Photomask Using Calibration Pattern, and Photomask Having Calibration Pattern,” which is incorporated by reference herein in its entirety.

BACKGROUND

Embodiments relate to a method of forming a photomask, and more particularly, to a method of forming a photomask using a calibration pattern that may exactly transfer a desired pattern to a substrate.

2. Description of the Related Art

As semiconductor devices become more highly integrated, widths and intervals between patterns formed on a semiconductor substrate are decreasing, and patterns having an intricate two-dimensional shape are increasing. Thus, a technology for calculating a mean-to-target (MTT) of a pattern having a two-dimensional shape is required.

SUMMARY

One or more embodiments provide a method of forming a photomask using a calibration pattern that may exactly transfer a desired pattern to a substrate.

One or more embodiments provide a method of forming a photomask, the method comprising providing one-dimensional calibration design patterns each having first design measures and providing two-dimensional calibration design patterns each having second design measures, obtaining one-dimensional calibration measured patterns using the one-dimensional calibration design patterns and obtaining two-dimensional calibration measured patterns using the two-dimensional calibration design patterns, obtaining first measured measures of the one-dimensional calibration measured patterns and obtaining second measured measures of the two-dimensional calibration measured patterns, establishing a correlation between the first measured measures and the second measured measures, and converting a main measured measure of a main pattern into a corresponding one of the first measured measures using the correlation.

After converting the main measured measure of the main pattern into the corresponding one of the first measure measures, the method may include obtaining a mean-to-target (MTT) of the main pattern, and correcting the main pattern using the MTT of the main pattern.

Obtaining the MTT of the main pattern may include selecting the one-dimensional calibration measured pattern and the one-dimensional calibration design pattern based on the first measured measure into which the main measured measure of the main pattern is converted, calculating a difference between the first design measures of the one-dimensional calibration design pattern and the first measured measures of the one-dimensional calibration measured pattern, and establishing the difference as the MTT of the main pattern.

The first design measures and the second design measures may vary corresponding to each other.

Calculating the correlation may include calculating a correlation between square roots of the first measured measures and the second measured measures. The method as claimed in claim1, wherein converting the main measured measure of the main pattern into the corresponding one of the first measured measures using the correlation includes measuring the main measured measure of the main pattern, substituting the main measured measure of the main pattern to the correlation as the second measured measures, and calculating the first measured measure corresponding to the main measured measure using the correlation.

Converting the main measured measure of the main pattern into the corresponding one of the first measured measures using the correlation may include measuring the main measured measure of the main pattern, selecting the two-dimensional calibration measured pattern having the second measured measure corresponding to the main measured measure of the main pattern, selecting the one-dimensional calibration measured pattern corresponding to the selected two-dimensional calibration measured pattern using the correlation, and converting the main measured measure into the first measured measure of the selected one-dimensional calibration measured pattern.

Selecting the two-dimensional calibration measured pattern having the second measured measure corresponding to the main measured measure of the main pattern may include selecting the two-dimensional calibration measured pattern having the second measured measure that is the same as the main measured measure.

Selecting the two-dimensional calibration measured pattern having the second measured measure corresponding to the main measured measure of the main pattern may include selecting the two-dimensional calibration measured pattern having the second measured measures that is proximal to the main measured measure.

The correlation may be a continuous function or a discontinuous relationship between the first measured measures and the second measured measures.

The first design measures may change by a constant amount.

The second design measures may change by a constant amount.

Converting the main measured measure into the first measured measure may include converting a square root of the main measured measure into the first measured measure.

Providing the one-dimensional calibration design patterns may include providing first one-dimensional calibration design patterns extending in a first direction and second one-dimensional calibration design patterns extending in a second direction, the first direction being at a predetermined angle with respect to the first direction.

One or more embodiments provide a method of forming a photomask, the method including calculating a correlation between a one-dimensional pattern and a two-dimensional pattern, and correcting the two-dimensional pattern using a mean-to-target (MTT) of the one-dimensional pattern obtained by the correlation.

One or more embodiments provide a method of forming a photomask, the method including obtaining first measurements of a one-dimensional calibration pattern including a plurality of one-dimensional designs, the plurality of one-dimensional designs being step-wise different from each other by a predetermined amount, obtaining second measurements of a two-dimensional calibration pattern including a plurality of two-dimensional designs, the plurality of two-dimensional designs being step-wise different from each other by the predetermined amount, determining a correlation between the first measurements and the second measurements, and converting a main measurement of a main pattern into a corresponding one of the first measurements based on the determined correlation.

Corresponding ones of the one-dimensional designs and the two-dimensional designs have a same length.

The one-dimensional designs may include at least one line and/or space pattern, and the two-dimensional designs include square patterns.

The predetermined amount may be a constant amount.

The plurality of one-dimensional designs may include first one-dimensional designs extending in a first direction, and second one-dimensional designs extending in a second direction, and the plurality of two-dimensional designs include portions extending in the first direction and portions extending in the second direction, the first direction being at a predetermined angle relative to the second direction.

One or more embodiments provide a photomask including a main pattern region in which a main pattern is formed, and a calibration pattern region disposed outside of the main pattern region, wherein the calibration pattern region area includes two-dimensional calibration patterns each having an area increasing with a constant variation, and being sequentially arranged according to the area, and one-dimensional calibration patterns each having a length increasing with a constant variation to correspond to the corresponding two-dimensional calibration pattern.

Each of the one-dimensional calibration patterns may include a first one-dimensional calibration design pattern and a second one-dimensional calibration design pattern, wherein the first one-dimensional calibration design patterns extend in a first direction and the second one-dimensional calibration design patterns extend in a second direction having a predetermined angle with respect to the first direction.

DETAILED DESCRIPTION

It will be understood that when an element, such as a layer, a region, or a substrate, is referred to as being “on,” “connected to” or “coupled to” another element, it may be directly on, connected or coupled to the other element or intervening elements may be present. In contrast, when an element is referred to as being “directly on,” “directly connected to” or “directly coupled to” another element or layer, there are no intervening elements or layers present. Like reference numerals refer to like elements throughout. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items.

Exemplary embodiments are described herein with reference to cross-sectional illustrations that are schematic illustrations of exemplary embodiments (and intermediate structures). As such, variations from the shapes of the illustrations as a result, for example, of manufacturing techniques and/or tolerances, are to be expected. Thus, exemplary embodiments should not be construed as limited to the particular shapes of regions illustrated herein but may be to include deviations in shapes that result, for example, from manufacturing. For example, an implanted region illustrated as a rectangle may, typically, have rounded or curved features and/or a gradient of implant concentration at its edges rather than a binary change from implanted to non-implanted region. Likewise, a buried region formed by implantation may result in some implantation in the region between the buried region and the surface through which the implantation takes place. Thus, the regions illustrated in the figures are schematic in nature and their shapes may be not intended to illustrate the actual shape of a region of a device and are not intended to limit the scope of exemplary embodiments.

FIG. 1illustrates a top plane view of an exemplary embodiment of a photomask1. Referring toFIG. 1, the photomask1may include a main pattern area2, and a calibration pattern area3.

Patterns for forming microelectronic devices, e.g., a transistor, may be formed in the main pattern area2. In the description of exemplary embodiments herein, pattern refers to a main pattern10. The main pattern10may be included in a photomask layout, and may have any shape, e.g., a polygonal shape, a curved shape, a combination thereof, etc. More particularly, e.g., the main pattern10may have a shape such as a triangular shape, a rectangular shape, a square shape, a parallelogram shape, a diamond shape, a trapezoid shape, a semicircular shape, a circular shape, an oval shape, a combination thereof, etc.

The calibration pattern area3may be disposed outside of the main pattern area2. The calibration pattern area3may include a plurality of two-dimensional calibration design patterns20, and a plurality of one-dimensional calibration design patterns30. In the exemplary embodiment ofFIG. 1, the one-dimensional calibration design patterns30are arranged in a column of an array and the two-dimensional calibration design patterns20are arranged in another column of the array.

Herein, a one-dimensional pattern may refer to a pattern that extends substantially along a one direction, e.g., a pattern that has a significantly longer length than width such as a line, a line-space-line-space pattern, etc. Herein, a two-dimensional pattern may refer to a pattern that extends along two-directions, e.g., a square, rectangle, etc. More particularly, e.g., a two-dimensional pattern may refer to a pattern having a length and width of a same and/or substantially same size, e.g., a square general contact hole pattern.

Referring toFIG. 1, areas of the two-dimensional calibration design patterns20may respectively increase by, e.g., a constant amount. The two-dimensional calibration design patterns20may be sequentially arranged according to area size, e.g., smallest to largest area. A plurality, e.g., five, twenty-five, etc., of the two-dimensional calibration design patterns20may be disposed in an array, e.g., along a first direction (e.g., y-direction). More particularly, e.g., referring to the exemplary embodiment ofFIG. 1, the calibration pattern area3may include a plurality of two dimensional calibration design patterns, e.g.,20a,20b,20c,20d,20e,20f,20g. In the exemplary embodiment ofFIG. 1, each of the two dimensional calibration design patterns20athrough20ghas a general square shape such that a width, e.g., along y-direction, is equal to and/or substantially equal to a length, e.g., along a second direction (e.g., x-direction) thereof, but respective areas of the two dimensional calibration design patterns20athrough20gmay be different. For example, the two-dimensional calibration design pattern20amay be disposed in the middle of the array and a size of each side thereof may be 100 nm in length (i.e., width=100 nm and length=100 nm) such that an area of the two-dimensional calibration design pattern20amay be 10,000 nm2. Respective lengths and/or widths of the two-dimensional calibration design patterns20b,20c,20ddisposed above the two-dimensional calibration design pattern20aalong the y-direction may gradually vary, e.g., may gradually decrease by a constant amount. More particularly, e.g., lengths and widths of the two-dimensional calibration design patterns20b,20c,20dmay be 95 nm, 90 nm, 85 nm, respectively, and thus, areas of the two-dimensional calibration design patterns20b,20c,20dmay be 9,025 nm2, 8,100 nm2, 7,225 nm2, respectively. Further, respective lengths and/or widths of the two-dimensional calibration design patterns20e,20f,20gdisposed below the two-dimensional calibration design pattern20arelative to the y-direction may gradually vary, e.g., may gradually increase by the constant amount. More particularly, e.g., lengths and widths of the two-dimensional calibration design patterns20d,20f,20gmay be 105 nm, 110 nm, 115 nm, respectively, and thus, areas of the two-dimensional calibration design patterns20e,20f,20gmay be 11,025 nm2, 12,100 nm2, 13,225 nm2, respectively.

Further, e.g., each of the one-dimensional calibration design patterns30may include a plurality of design patterns. More particularly, e.g., each of the one-dimensional calibration design patterns30may include a first one-dimensional calibration design pattern40and a second one-dimensional calibration design pattern50. Further, in the exemplary embodiment ofFIG. 1, respective ones of the first one-dimensional calibration design patterns40and the second one-dimensional calibration design patterns50are adjacent to each other. Also, in the exemplary embodiment ofFIG. 1, respective ones of the first one-dimensional calibration design patterns40, the second one-dimensional calibration design patterns50, and the two-dimensional calibration design patterns are aligned along the x-direction so as to form rows of the array.

Referring toFIG. 1, each of the first one-dimensional calibration design patterns40and each of the second one-dimensional calibration design patterns50may correspond to a general square shape as defined, e.g., by one or more lines and spaces. More particularly, e.g., each of the first one-dimensional calibration design patterns40may include one or more lines extending in the second direction, e.g., x-direction, and the second one-dimensional calibration design patterns50may include one or more lines extending in the first direction, e.g., y-direction. The first direction may be at a predetermined angle relative to the second direction, e.g., the first direction may be perpendicular to the second direction. In one or more embodiments, the first one-dimensional calibration design patterns40may substantially and/or completely correspond to the second one-dimensional calibration design patterns50, but rotated relative to each other, so as to extend along different directions (e.g., x-direction, y-direction, respectively).

Referring toFIG. 1, respective lengths and/or widths of each of the one-dimensional calibration design patterns30may vary, e.g., increase, along to the y-direction. More particularly, respective lengths (x-direction) and/or widths (y-direction) of the one-dimensional calibration design patterns30may increase by a constant amount relative to the y-direction. Further, a dimension, e.g., respective lengths (x-direction) of lines and/or spaces in the one-dimensional calibration design patterns30may vary, e.g., relative to a direction, e.g., the y-direction. In the exemplary embodiment ofFIG. 1, lengths and widths of the one-dimensional calibration design patterns30decrease upward along the y-direction. More particularly, in the exemplary embodiment ofFIG. 1, lengths and/or widths of the first one-dimensional calibration design patterns40and the second one-dimensional calibration design patterns50decrease by a constant amount upward along the y-direction so as to correspond to the lengths and/or widths of corresponding ones of the two-dimensional calibration design patterns20aligned therewith along the x-direction. Further, in the exemplary embodiment ofFIG. 1, areas of the one-dimensional calibration design patterns30, e.g., the first one-dimensional calibration design patterns40and/or the second one-dimensional calibration design patterns50, may vary, e.g., respectively increase by a constant amount, relative to the y-direction. The one-dimensional calibration design patterns30may be sequentially arranged according to area size, e.g., smallest to largest area. Referring toFIG. 1, respective widths (y-direction) of each of the one-dimensional calibration patterns30may be different from respective lengths (x-direction) thereof.

FIG. 2illustrates a schematic diagram patterns formed on a corresponding surface1′ using the photomask1ofFIG. 1.

Referring toFIG. 2, actual patterns are formed on a corresponding surface1′ in accordance with the main pattern10, the two-dimensional calibration design patterns20, and the one-dimensional calibration design patterns30of the photomask1. The actual patterns may be photoresist patterns, hard mask patterns, aerial image emulating patterns, etc. The photoresist patterns may be patterns formed by using a photoresist material that is generally used in the art. The hard mask patterns may include various materials, e.g., silicon oxide, silicon nitride, etc. The aerial image emulating patterns generally refer to an image formed on a photoresist. The aerial image emulating patterns are formed by an aerial image emulator without undergoing an exposure process. The aerial image emulator may be an aerial image measurement system (AIMS) made by Carl Zeiss AG or a mask inspection tool.

Herein, the actual pattern refers to a measured pattern. Referring toFIG. 2, a main measured pattern10′, a plurality of two-dimensional calibration measured patterns20′, and a plurality of one-dimensional calibration measured patterns30′ may be formed corresponding to the main pattern10, the two-dimensional calibration design patterns20, and the one-dimensional calibration design patterns30, respectively. Each of the one-dimensional calibration measured patterns30′ may include a first one-dimensional calibration measured pattern40′ corresponding to the first one-dimensional calibration design pattern40and a second one-dimensional calibration measured pattern50′ corresponding to the second one-dimensional calibration design pattern50′.

FIGS. 3 through 6illustrate diagrams of exemplary relationships between exemplary embodiments of the two-dimensional calibration design pattern20and the one-dimensional calibration design pattern30ofFIG. 1.

Referring toFIG. 3, in one or more embodiments, a one-dimensional calibration design pattern30aand a two-dimensional calibration design pattern20ahave a relationship in which a length a1of one side of the two-dimensional calibration design pattern20ais equal to a length b1of the one-dimensional calibration design pattern30a. The length b1of the one-dimensional calibration design pattern30amay be a length of a line32aor a length of a space34a.

Referring toFIG. 4, in one or more embodiments, a one-dimensional calibration design pattern30band a two-dimensional calibration design pattern20bhave a relationship in which a length (or width) a2of one side of the two-dimensional calibration design pattern20bis equal to a sum of widths of all lines and spaces of the one-dimensional calibration design pattern30b. More particularly, e.g., in the exemplary embodiment ofFIG. 4, the length (or width) a2of the two-dimensional calibration design pattern20bmay equal the sum b1of widths w of each of the lines32band a width c of a space34bbetween the lines32bof the one-dimensional calibration design pattern30b, that is, b1=2w+c. The sum b1may include various numbers of lines32and spaces34within the one-dimensional calibration design pattern30b.

Referring toFIG. 5, in one or more embodiments, a one-dimensional calibration design pattern30cand a two-dimensional calibration design pattern20chave a relationship in which a length (or width) a3of one side of the two-dimensional calibration design pattern20cis equal to a width c of a space34cof the one-dimensional calibration design pattern30c.

Referring toFIG. 6, in one or more embodiments, a one-dimensional calibration design pattern30dand a two-dimensional calibration design pattern20dhave a relationship in which a length (or width) a4of one side of a two-dimensional calibration design pattern20dis equal to a width w of a line32dof the one-dimensional calibration design pattern30d.

Respective areas of the two-dimensional calibration design patterns20described with reference toFIGS. 3 through 6may change with a constant variation as described above with regard toFIG. 1, and respective sizes, e.g., widths and/or lengths, of the one-dimensional calibration design pattern30may change in correspondence thereto.

FIG. 7illustrates a flowchart of an exemplary embodiment of a method of forming a photomask.

Referring toFIG. 7, the method of forming the photomask may include calculating a correlation between a one-dimensional pattern and a two-dimensional pattern (S1) and correcting the two-dimensional pattern using a mean-to-target (MTT) of the one-dimensional pattern based on the correlation (S2).

FIG. 8illustrates a flowchart of an exemplary embodiment of a method of forming a photomask.

Referring toFIG. 8, one-dimensional calibration design patterns each having first design measures and two-dimensional calibration design patterns each having second design measures are provided (S10).

The one-dimensional calibration design patterns may be linear patterns, for example, line-and-space patterns. In one or more embodiments, the first design measures may have a dimension, e.g., length dimension, that may change by a constant variable. In addition, as illustrated inFIG. 1, the one-dimensional calibration design patterns may provide the first one-dimensional calibration design patterns40extending in the second direction, e.g., x-direction, and the second one-dimensional calibration design patterns50extending in the first direction, e.g., y-direction, at a predetermined angle, e.g., 90 degrees, with respect to the first direction.

Each of the two-dimensional calibration design patterns may have a triangular shape, a rectangular shape, a square shape, a parallelogram shape, a diamond shape, a trapezoid shape, a semicircular shape, a circular shape, an oval shape, a combination thereof, etc. Also, the second design measures may have an area dimension that may change with a constant variation.

The first design measures and the second design measures may correspond as described with reference toFIGS. 3 through 6. The first design measures may be, for example, the length b1of the one-dimensional calibration design pattern30aillustrated inFIG. 3, the sum b2of the widths w of the lines32bof the one-dimensional calibration design pattern30band the width c of the space34billustrated inFIG. 4, the width c of the space34cof the one-dimensional calibration design pattern30cillustrated inFIG. 5, or the width d of the line32dof the one-dimensional calibration design pattern30dillustrated inFIG. 6. Also, the second design measures may be, for example, an area “a1×a1” of the two-dimensional calibration design pattern20aillustrated inFIG. 3, an area “a2×a2” of the two-dimensional calibration design pattern20billustrated inFIG. 4, an area “a3×a3” of the two-dimensional calibration design pattern20cillustrated inFIG. 5, or an area “a4×a4” of the two-dimensional calibration design pattern20dillustrated inFIG. 6.

Referring toFIG. 8, one-dimensional calibration measured patterns may be obtained using the one-dimensional calibration design patterns, and two-dimensional calibration measured patterns may be obtained by using the two-dimensional calibration design patterns (S20).

Referring toFIG. 8, first measured measures of the one-dimensional calibration measured patterns are obtained, and second measured measures of the two-dimensional calibration measured patterns may then be obtained (S30). The first measured measures may correspond to the first design measures, and the second measured measures may correspond to the second design measures. In general, the first measured measures and the second measured measures may change relative to values of the first design measures and the second design measures, and the respective values of the first measured measures and the second measured measures may decrease or increase.

In this regard, the first measured measure may have a length dimension. For example, the first measured measure may be a measure of the one-dimensional calibration measured pattern corresponding to the length b1of the one-dimensional calibration design pattern30aillustrated inFIG. 3. Alternatively, the first measured measure may be a measure of the one-dimensional calibration measured pattern corresponding to the sum b2of the widths w of the line32band the width c of the space34bof the one-dimensional calibration design pattern30billustrated inFIG. 4. Alternatively, the first measured measure may be a measure of the one-dimensional calibration measured pattern corresponding to the width c of the space34cof the one-dimensional calibration design pattern30cillustrated inFIG. 5. Alternatively, the first measured measure may be a measure of the one-dimensional calibration measured pattern corresponding to the width c of the line32dof the one-dimensional calibration design pattern30dillustrated inFIG. 6. The above-described methods of measuring the first measured measure are well known to one of ordinary skill in the art. For example, a method of dividing the one-dimensional calibration measured pattern into a plurality of pixels and counting the number of pixels corresponding to the first measured measure is used.

In one or more embodiments, the second measured measure may have an area dimension. For example, the second measured measure may be a measure of the two-dimensional calibration measured pattern corresponding to the area “a1×a1” of the two-dimensional calibration design pattern20aillustrated inFIG. 3. Alternatively, the second measured measure may be a measure of the two-dimensional calibration measured pattern corresponding to the area “a2×a2” of the two-dimensional calibration design pattern20billustrated inFIG. 4. Alternatively, the second measured measure may be a measure of the two-dimensional calibration measured pattern corresponding to the area “a3×a3” of the two-dimensional calibration design pattern20cillustrated inFIG. 5. Alternatively, the second measured measure may be a measure of the two-dimensional calibration measured pattern corresponding to the area “a4×a4” of the two-dimensional calibration design pattern20dillustrated inFIG. 6. The above-described methods of measuring the second measured measure are well known to one of ordinary skill in the art. For example, a method of dividing the two-dimensional calibration measured pattern into a plurality of pixels and counting the number of pixels corresponding to the second measured measure may be used.

Referring toFIG. 8, a correlation between the first measured measures and the second measured measures may then be established (S40). The correlation may be a correlation between square roots of the first measured measures and the second measured measures represented by an area. The second measured measures may be a continuous function of the first measured measure or there may be a discontinuous relationship between the first measured measures and the second measured measures.

Referring toFIG. 8, a main measured measure of a main pattern may be converted into the first measured measure by using the correlation (S50). The main pattern may include a main design pattern and a main measured pattern corresponding to the main design pattern as illustrated inFIGS. 1 and 2. The main pattern may be, e.g., a one-dimensional pattern, a two-dimensional pattern. One or more embodiments may provide a method of forming a photomask including a main pattern that is a two-dimensional pattern. The converting operation will be described with reference toFIGS. 9 and 10.

Referring toFIG. 8, a mean-to-target (MTT) of the main pattern may then be obtained (S60), and the main pattern may be corrected using the MTT of the main pattern (S70). An exemplary method of obtaining of the MTT will be described with reference toFIG. 11.

Referring toFIG. 9, in one or more embodiments, converting the main measured measure of the main pattern into the first measured measure using the correlation (S50a) may include the following operations.

Referring toFIG. 9, the main measured measure of the main pattern, that is, the main measured pattern, may be obtained (S510). The main pattern may be a two-dimensional pattern, and the main measured measure may have an area dimension. Methods of measuring the main measured measure are well known to one of ordinary skill in the art. For example, a method of dividing the main pattern into a plurality of pixels and counting the number of pixels corresponding to the second measured measures may be used. The main measured measure of the main pattern may then be substituted in the correlation with the second measured measures (S520). In this regard, a square root of the main measured measure may be substituted in the correlation calculation. The first measured measure corresponding to the main measured measure may then be calculated using the correlation (S530). Thus, the main measured measure may be converted into the calculated first measured measure (S540). This method may be used when the correlation is a continuous function between the first measured measures and the second measured measures.

Referring toFIG. 10, in one or more other embodiments, converting the main measured measure of the main pattern into the first measured measure using the correlation (S50b) may include the following operations.

The main measured measure of the main pattern is measured (S511). The two-dimensional calibration measured pattern having the second measured measures corresponding to the main measured measure of the main pattern may be selected (S521). In this regard, the two-dimensional calibration measured pattern having the second measured measure that is the same as the main measured measure of the main pattern may be selected. Alternatively, the two-dimensional calibration measured pattern having the second measured measure that is proximal to the main measured measure of the main pattern may be selected. The one-dimensional calibration measured pattern corresponding to the selected two-dimensional calibration measured pattern may be selected using the correlation (S531), and thus, the main measured measure may be converted into the first measured measure of the selected one-dimensional calibration measured pattern (S541). This method may be used when the correlation is a discontinuous relationship between the first measured measures and the second measured measures.

FIG. 11illustrates a flowchart of an exemplary embodiment of obtaining the MTT of the main pattern.

Referring toFIG. 11, obtaining the MTT of the main pattern may include the following operations.

The one-dimensional calibration measured pattern and the one-dimensional calibration design pattern may be selected based on the first measured measure according to which the main measured measure of the main pattern is converted (S610). Then, a difference between the first design measures of the one-dimensional calibration design pattern and the first measured measure of the one-dimensional calibration measured pattern may be calculated, and a difference may be established as the MTT of the main pattern (S620).

FIG. 12illustrates a graph of a correlation between the first measured measures and the second measured measures, according to an exemplary embodiment.

FIG. 12illustrates a correlation between square roots of the second measured measures and the first measured measures. Circles illustrated inFIG. 12show values obtained by setting square roots of the areas of the two-dimensional calibration measured patterns formed by setting the two-dimensional calibration design patterns ofFIG. 1as x-axis values and by setting measured measures of the one-dimensional calibration measured patterns formed by the one-dimensional calibration design patterns corresponding to the two-dimensional calibration design patterns as y-axis values. In the exemplary embodiment ofFIG. 12, each of the circles corresponds to one of the two-dimensional calibration design patterns, e.g., fifteen circles corresponding to fifteen two-dimensional calibration design patterns are illustrated. When the correlation is a discontinuous relationship, only values corresponding to the circles may be used. However, when the correlation is a continuous function, all values corresponding to a proximal line of a least square method with respect to the circles may be used.

FIG. 13illustrates a schematic diagram of an exemplary embodiment of an imaging system1000for executing a method of forming a photomask, according to an embodiment of the inventive concept.

Referring toFIG. 13, a computer system1300for executing a method of forming a photomask may be a general-use workstation. The computer system1300may be a stand-alone type, a network type computer system, etc. The computer system1300may include a single processor or a multiprocessor for measurements. Also, the computer system1300may be a parallel-processing computer system.

The computer system1300may execute a series of executable commands, which are stored in a program storage medium1100, for example, a compact disk (CD) or a digital video disk (DVD), or received via wired/wireless communication networks, such as the Internet. The computer system1300may receive a file including information regarding design patterns or photomask layouts from a database regarding the above-described design patterns or a photomask layout file storage1200, for example, a database or any other storage medium, and may execute a command to read the file. The computer system1300may perform a process of calculating an MTT or a process of correcting a photomask using the measured MTT according to one or more embodiments on a design pattern or a photomask layout and may generate a file including information regarding the performed process. Then, the computer system1300may perform a comparison/inspection process to check if a desired photomask layout is formed, and may transmit the photomask layout to a mask recording apparatus1400to enable the manufacture of a photomask.

The imaging system1000may include a provision mechanism for providing one-dimensional calibration design patterns each having first design measures and two-dimensional calibration design patterns each having second design measures, a measured pattern obtainment mechanism for obtaining one-dimensional calibration measured patterns by using the one-dimensional calibration design patterns and obtaining two-dimensional calibration measured patterns by using the two-dimensional calibration design patterns, a measured measure obtainment mechanism for obtaining first measured measures of the one-dimensional calibration measured patterns and obtaining second measured measures of the two-dimensional calibration measured patterns, a correlation establishment mechanism for establishing a correlation between the first measured measures and the second measured measures, a conversion mechanism for converting a main measured measure of a main pattern into the first measured measure using the correlation, an MTT obtainment mechanism for obtaining an MTT of the main pattern, and a correction mechanism for correcting the main pattern using the MTT of the main pattern.

Features may be embodied as non-transitory computer-readable codes on a computer readable recording medium. A computer-readable recording medium may be any data storage device that can store programs or data that may be thereafter read by a computer system. Examples of the computer-readable recording medium include read-only memory (ROM), random-access memory (RAM), CD-ROMs, magnetic tapes, hard disks, floppy disks, flash memory, optical data storage devices, etc. Here, a program stored in a recording medium may be expressed in a series of instructions used directly or indirectly within a device with a data processing capability, such as, computers. Thus, a term “computer” involves all devices with data processing capability in which a particular function is performed according to a program using a memory, input/output devices, and arithmetic logics.

A method of forming a photomask may include providing one-dimensional calibration design patterns each having first design measures and two-dimensional calibration design patterns each having second design measures, obtaining one-dimensional calibration measured patterns by using the one-dimensional calibration design patterns, obtaining two-dimensional calibration measured patterns by using the two-dimensional calibration design patterns, obtaining first measured measures of the one-dimensional calibration measured patterns, obtaining second measured measures of the two-dimensional calibration measured patterns, establishing a correlation between the first measured measures and the second measured measures, converting a main measured measure of a main pattern into the first measured measure by using the correlation, obtaining an MTT of the main pattern, and correcting the main pattern by using the MTT of the main pattern. The recording medium may store programmed commands enabling each the above-described operations to be performed when the method of forming a photomask is executed in a computer.

The foregoing is illustrative of exemplary embodiments and is not to be construed as limiting thereof. Although exemplary embodiments have been described, those of ordinary skill in the art will readily appreciate that many modifications are possible in the exemplary embodiments without materially departing from the novel teachings and advantages of the exemplary embodiments. Accordingly, all such modifications are intended to be included within the scope of the claims. Exemplary embodiments are defined by the following claims, with equivalents of the claims to be included therein.