DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0064] Referring now to the figures of the drawing in detail and first, particularly, to FIGS. 1 A- 2 D thereof, there is shown the use of one and the same dark-field mask structure to illustrate the differences between known methods for determining phase conflicts (FIGS. 2 A- 2 D) and the method according to the invention (FIGS. 1 A- 1 C).

[0065] A dark-field mask 10 has transparent regions 1 , which are to be imaged into electrical circuit elements such as interconnects or the like.

[0066] The transparent regions 1 are illustrated as a hatched polygon progression in FIG. 2B . Situated between the individual sections of the polygon progression are critical regions 2 , in which the distance between individual sections of the polygon progression falls below a predetermined minimum value. The task is to allocate to the individual sections of the polygon progression the phases which have a phase difference Δφ=180°.

[0067] The method proceeds from FIG. 2B in accordance with U.S. Pat. No. 5,923,566 in order to determine free spaces F ₁ , F ₂ and F ₃ , as is illustrated in FIG. 2C . In this case, the free spaces F ₁ and F ₃ indicate the same elementary phase conflict determined by F ₁ . F ₃ is composed of F ₁ and F ₂ , F ₂ not representing a phase conflict on account of its even number of interactions (4). Consequently, one and the same phase conflict is unneccessarily indicated twice.

[0068] The method described in the reference by Moniwa et al. mentioned in the introduction is illustrated in FIG. 2 D and yields the three cycles (1251), (123451) and (23452). Among these cycles, only the first two cycles mentioned have an odd number of nodes and accordingly represent two phase conflicts. The second-mentioned cycle is composed of the other two elementary cycles. Since the third cycle has an even number of nodes, only one phase conflict exists in reality, which phase conflict is determined by the first elementary cycle and is unnecessarily indicated doubly by the second cycle.

[0069] By contrast, in the method according to the invention, after the critical regions 2 have been determined, contiguous regions 3 lying outside the transparent and the critical regions 1 and 2 are determined, which are designated as areas L ₁ and L ₂ in FIG. 1B . These areas are also referred to as lands below. Afterward, outer boundaries 4 of the lands L ₁ and L ₂ are determined and their interactions or stretches of contact with the critical regions 2 are determined. As can be seen in FIG. 1 C, the outer boundary of the land L ₁ unambiguously produces the sole expected phase conflict in an efficient manner. The localized phase conflict is visualized by the outer boundary 4 illustrated as a polygon progression in FIG. 1C . By contrast, the outer boundary around the land L ₂ does not indicate a phase conflict since the number of stretches of contact with critical regions 2 is even (4).

[0070] FIGS. 3 A- 3 C illustrate a more complex dark-field mask 100 , which illustrates the inadequacy of the method described in U.S. Pat. No. 5,923,566 in comparison with the present invention. First, in accordance with FIG. 3 B, the transparent regions 1 are represented in the form of polygon progressions and critical regions 2 between them are determined. The lands L ₁ to L ₄ are then defined as illustrated. In accordance with FIG. 3 C, the outer contours 4 a , 4 b and 4 c of the lands that have an odd number of stretches of contact with the critical regions 2 indicate the localized phase conflicts. In the present case, the phase conflict that is localized by the outer boundaries of L ₃ is not detected by the method taught in U.S. Pat. No. 5,923,566. The reason for this is that the interleaved phase conflict is localized by two free spaces, namely the lands L ₃ and L ₄ with even numbers of interactions 8 and 6 , respectively. Thus, this example shows the reliability of the method according to the invention compared with the method of taught in U.S. Pat. No. 5,923,566 with regard to dark-field masks.

[0071] The dark-field masks described above are shaped in such a way that the critical regions are rectangular or, more generally, trapezoidal sections of different length which extend along one direction. However, the case may also arise where two or more trapezoidal straight sections of this type, which extend in different directions, abut one another. In this case, the determination of overlap regions between the trapezoidal straight sections is added to the determination of lands.

[0072] An example of a phase mask of this type is illustrated in FIGS. 4 A- 4 C. Three transparent regions 1 are disposed relative to one another on the phase mask 10 such that critical regions 2 are produced, within which the transparent regions 1 fall below a predetermined minimum distance from one another. The critical regions 2 form a T-shaped structure, that is to say a structure in which two rectangular straight sections run toward one another and form an overlap region 13 . The overlap region 13 is determined by drawing the mutually crossing straight sections beyond the points at which they abut one another, the region jointly enclosed by the continuation lines drawn or the intersection of the continuation lines drawn defining the overlap region 13 . In order to determine a degenerate critical region, the overlap region 13 is subtracted from the critical region 2 . An outer boundary 14 around the overlap region 13 thus has three stretches of contact with the three degenerate critical regions 2 a and thus signals a phase conflict on account of the odd number of stretches of contact.

[0073] A further dark-field mask structure is illustrated in FIG. 5 A, which structure exhibits a double T structure (2T structure) in comparison with the single T structure shown in FIG. 4A . In accordance with FIG. 5 B, two overlap regions 13 are determined and these are subtracted from the critical, nontransparent regions 2 , thereby producing the degenerate critical regions 2 a . The outer boundaries 14 around the overlap regions 13 in each case have three stretches of contact with end sections of straight, degenerate critical regions 2 a , so that two phase conflicts are thereby indicated. This two-fold phase conflict cannot be detected by the method taught in U.S. Pat. No. 5,923,566 already cited.

[0074] Overlap regions 13 of this type do not exist in the case of the dark-field masks of FIGS. 1A to 3 C. Consequently, the critical regions are identical to the degenerate critical regions in these cases.

[0075] FIGS. 6A, 6B illustrate a further dark-field mask, which contains a further type of region containing a phase conflict.

[0076] FIG. 6A illustrates the dark-field mask structure, which has a contiguous transparent region 1 , which, by way of example, represents an interconnect structure to be imaged by the phase mask and is surrounded by a nontransparent region. The transparent region 1 is shaped in such a way that it encloses, between two path sections, a critical, nontransparent region 2 that falls below a predetermined structure size. The critical region 2 thus ends in the midst of a region containing the transparent region 1 . A so-called end region 13 a is to be produced in this case. The end region 13 a is generated by a line overlying the short side edge of the end section of the critical region 2 being expanded outward by an infinitesimally small amount (sizing operation). The outer boundary 14 is then made around the end region 13 a.

[0077] Afterward, the degenerate critical regions 2 a are generated again, in the manner mentioned, by subtracting overlap regions 13 that are possibly present from the critical regions 2 .

[0078] Since the critical region 2 does not contain an overlap region 13 in the present case, a degenerate critical region 2 a (hatched) is generated from it without any alteration. The outer boundary 14 thus has a stretch of contact with the degenerate critical region 2 a , so that a phase conflict is indicated by it owing to the odd number of stretches of contact.

[0079] The text below illustrates exemplary embodiments in accordance with a second aspect of the method according to the invention with regard to the application to bright-field masks.

[0080] FIG. 7A illustrates a simple exemplary embodiment of a bright-field mask structure 20 , which contains nontransparent regions 21 against a transparent background. In accordance with FIG. 7 B, phase-shifting elements 22 (shown hatched) are defined on both sides of the nontransparent, critical regions 21 . The critical regions 21 are held to be those regions that fall below a specific, predetermined minimum width or minimum structure size. The phase-shifting elements can be defined, by way of example, as in U.S. Pat. No. 5,537,648 ( FIG. 6 and associated description text). With regard to this procedure, U.S. Pat. No. 5,537,648 is incorporated by reference into the disclosure content of the present application.

[0081] Afterward, in accordance with FIG. 7 C, overlap regions 23 between straight sections of the critical regions 21 are determined in precisely the same way as already described in connection with the dark-field mask of FIGS. 5 A- 5 B. The overlap regions are determined as follows.

[0082] The case may arise where two or more trapezoidal, straight sections that extend in different directions abut one another. The determination of overlap regions between the trapezoidal straight sections is of importance in this case. One example of this is the T-shaped structure shown enlarged in FIG. 7E . The nontransparent regions 21 form a T-shaped branching structure, that is to say a structure in which two—in this example—rectangular, straight sections run toward one another and form the overlap region 23 . The overlap region 23 can be defined for example by drawing the mutually crossing straight sections beyond the points at which they abut one another, the region jointly enclosed by the continuation lines or the intersection of the continuation lines drawn defining the overlap region 23 . In order to determine the degenerate critical region, the overlap region 23 is subtracted from the nontransparent critical regions 21 . An outer boundary 24 around the overlap region 23 thus has three stretches of contact with three degenerate critical regions 21 a and thus signals a phase conflict on account of the odd number of stretches of contact.

[0083] The degenerate critical regions 21 a are generated by subtracting the overlap regions 23 from the critical regions 21 . The outer boundaries 24 with respect to the overlap regions 23 and lands are then generated, as can be seen in the circular detail of FIG. 7E . A phase conflict is present precisely when the outer boundary 24 has an odd number of interactions or stretches of contact with degenerate critical regions 21 a . In accordance with FIG. 7 E, the outer boundary 24 around the overlap region 23 is in contact with the three degenerate critical regions 21 a and thus unambiguously signals a T phase conflict.

[0084] The phase conflict is not detected by the method in accordance with the reference by Moniwa et al. because no cycle is produced upon application of the non-directional conflict graph, specifically since only two phase-shifting elements and one contiguous critical structure are present.

[0085] FIGS. 8 to 11 illustrate the action of the method according to the invention in accordance with its second aspect on the basis of a more complex bright-field mask structure.

[0086] First, FIG. 8 illustrates a bright-field mask 200 with the nontransparent regions 21 , which are to be imaged into circuit elements such as interconnects or the like. In accordance with FIG. 9 , in the manner already explained, the phase-shifting elements 22 (hatched polygons) are determined on both sides of the straight sections of the nontransparent regions 21 , since the nontransparent regions 21 are classified as critical thereby defining critical regions 21 .

[0087] The bright-field mask 200 exhibits two further types of regions in addition to the lands and the overlap regions 23 ( FIG. 10A ). Whenever straight sections of the nontransparent regions 21 end in the midst of a phase-shifting element 22 , a so-called end region 23 a is to be generated. The latter is generated simply by, as shown in the circularly enlarged detail of FIG. 10B, a line overlying the short side edge of the end section of the nontransparent region 21 being expanded outward by an infinitesimally small amount, “sizing operation”. The outer boundary 24 is then made around the end region 23 a and makes contact with the short side edge of the end section of the nontransparent region 21 . Furthermore, as can be seen in the circularly enlarged detail of FIG. 10 C, an end region 23 b is to be generated where a critical region 21 ends at a critical interaction region. Critical interaction regions are regions between phase-shifting elements 22 in which a predetermined distance between the phase-shifting elements 22 is undershot. The end region 23 b is likewise generated by a “sizing operation” by, as shown in the circularly enlarged detail of FIG. 10C, a line overlying the short side edge of the end section of the nontransparent region 21 being expanded outward by an infinitesimally small amount. The outer boundary 24 made around the end region 23 b thus makes contact with the short side edge of the end section of the nontransparent region 21 .

[0088] The overlap regions 23 between straight sections of the nontransparent regions 21 and end regions 23 a , 23 b of straight sections which end in the midst of the phase-shifting element 22 or an interaction region are thus determined in accordance with FIGS. 10 A- 10 C. Degenerate critical regions are then defined by subtracting the overlap regions 23 from the nontransparent regions 21 . In accordance with FIG. 11 , phase conflicts are indicated by the outer boundaries 24 of lands, overlap regions 23 or end regions 23 a , 23 b which make contact with an odd number of end sections of the degenerate critical regions derived from the nontransparent mask fields 21 . The end regions 23 a , 23 b thus always signal a phase conflict since they make contact with precisely one end section of the nontransparent region 21 . Consequently, FIG. 11 reveals the eight unambiguously localized phase conflicts 24 with respect to the bright-field mask structure of FIG. 8 using the eight dark outer boundaries 24 . The second phase conflict that is interleaved on the left-hand side of the FIG. 11 cannot be detected by the method of U.S. Pat. No. 5,923,566 since the two free spaces adjoining it are assigned even numbers of interactions 6 and 4 . Consequently, there are two types of so-called end region conflicts K 1 and K 2 . An end region conflict is present precisely when the corresponding line ends in the midst of the phase-shifting element 22 (K 1 ) or a critical interaction region between two phase-shifting elements 22 (K 2 ). These two types of end region conflicts are depicted in FIG. 11 .

[0089] FIG. 12 illustrates a detail from a gate plane that is intended to be produced using a bright-field phase mask. The interconnects of minimal width which are represented therein are critical structures and must therefore be realized by phase elements disposed on both sides, while the widened portions (contact pads or landing pads) do not have critical widths.

[0090] Generated phase-shifting elements are represented on both sides of the interconnects, the elements having the two different phases 0° and 180° and, accordingly, being identified by two different hatchings. What are marked in a chessboard-like manner are the parts of interconnects (gates in this case) which cannot be correctly imaged in the case of the phase allocation presented, since both sides of the gate are exposed with the same phase. In FIG. 12 , they are designated as phase conflicts 34 and 35 lying within the boundary 30 . A further phase conflict 36 lies outside the boundary 30 .

[0091] The cause of the left-hand phase conflict of the two non-localized phase conflicts can be seen in the fact that the affected gate adjoins the same phase shifter at both sides. The cause of the right-hand phase conflict cannot be seen as easily. The question arises as to why a phase allocation that avoids the phase conflict cannot be found. The cause lies in the cycle exhibited by the boundary 30 . Five critical gates and continuously five phase shifters are lined up along this path. The phase shifters encountered by this path cannot alternately be allocated to the two phases. This fact can easily be demonstrated with the aid of the boundary 30 . It is only by virtue of the method according to the invention that clear indication is given, however, that actually only one phase conflict, rather than two, is present in the discussed part of the detail.

[0092] In a practical application of the method according to the invention, the phase conflicts determined are visualized on a display device such as a screen by highlighting the polygons or large outer boundaries that correspond to the phase conflicts.