CN105022872B - The three pattern photomask layout decomposition methods for minimizing and legalizing based on disaggregated cost - Google Patents

The three pattern photomask layout decomposition methods for minimizing and legalizing based on disaggregated cost Download PDF

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CN105022872B
CN105022872B CN201510394778.XA CN201510394778A CN105022872B CN 105022872 B CN105022872 B CN 105022872B CN 201510394778 A CN201510394778 A CN 201510394778A CN 105022872 B CN105022872 B CN 105022872B
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pattern
point
conflict
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dyeing
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朱文兴
李兴权
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Fuzhou University
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Abstract

The present invention relates to a kind of three pattern photomask layout decomposition methods for being minimized and being legalized based on disaggregated cost, three pattern photomask layout resolution problems are divided into two stages solutions by this method, initial pattern layout is converted into non-directed graph first, problem scale is then reduced using figure reduction method；First stage is dyed using a loose Optimized model to pattern, and second stage considers that introduce suture is divided into the modes of multiple sub-patterns to eliminate conflict as much as possible by a pattern, realizes final dyeing.It is reasonable that the three pattern photomask layout decomposition method methods of the present invention are decomposed, and efficiently quick, decomposition result is good.

Description

The three pattern photomask layout decomposition methods for minimizing and legalizing based on disaggregated cost
Technical field
Technical field of lithography in being manufactured the invention belongs to VLSI techniques, it is particularly a kind of minimized based on disaggregated cost and The three pattern photomask layout decomposition methods to legalize.
Background technology
In current VLSI photolithographic fabrications, the continuous increase of footprint and the continuous reduction of unit size.It is right In the unit of below 22nm specifications, traditional photoetching technique has been unable to meet demand；And for advanced extreme ultraviolet photolithographic EUV, due to reasons such as light source and materials, can't industrially it be promoted.Therefore, multiple pattern photoetching decomposition technique carries Go out, the good plan in undoubtedly whole photoetching development transition period, triple pattern photoetching techniques are just a process that, it is studied It can be very good the technique manufacture bottleneck for solving large scale integrated circuit.
Two major classes can be divided into by being currently used in the algorithm for solving the triple pattern photomask layout resolution problems of VLSI：Based on analysis Decomposition method and based on didactic decomposition algorithm.The general thinking of method based on analysis is that constitution optimization model is relaxed Solution, then by relaxation solution similar to feasible solution.This method can obtain relatively good decomposition result, but shortcoming is its search Solution space is big, solves time length.And the thinking based on didactic method is with various figure reduction technologies, and problem scale is contracted It is small, then preferably dyeing solution is found using heuristic dyeing.Heuristic can quickly find solution, but the popularization of its method Property it is poor, possibly can not be applicable simultaneously for different minimum dyeing gaps.
Following one or more problems be present in existing triple pattern photoetching decomposition methods：(1) when calculating conflict projection Projected only with line projection rather than face, actual projection above is only the real reflection of conflict projection；(2) local punching can not be found Prominent (native conflict), the discovery of local conflicts is a critically important step for problem, and it is empty that it can greatly reduce solution Between search；(3) position for suturing (stitch) is not local optimum, and good suture location can reduce disaggregated cost.Cause This, in order to obtain more preferable decomposition result, replaces line projection to be projected as conflict, local punching is first found before dyeing by the use of face projection It is prominent, and it is necessary to find the algorithm of the suture location of a local optimum.
The content of the invention
In view of this, it is an object of the invention to provide a kind of three pattern photoetching for being minimized and being legalized based on disaggregated cost Layout decomposition method, it is reasonable that this method is decomposed, and efficiently quick, decomposition result is good.
The present invention is realized using following scheme：A kind of three pattern photomask layouts for minimizing and legalizing based on disaggregated cost Decomposition method, comprise the following steps：
Step S1：Layout is converted into non-directed graph；
Step S2：Point is deleted using figure reduction method, and stored；
Step S3：The figure reduction method first step in the step S2 is less than 3 point for deletion degree；
Step S4：Figure reduction method second step in the step S2 includes a little for deletion；
Step S5：The step of figure reduction method the 3rd in the step S2 is solution connected component；
Step S6：Repeating said steps S3- steps S5 three times, produces multiple connected components；
Step S7：Face conflict projecting method inspection is used whether each to put representative pattern for the pattern that conflicts；
Step S8：To assigning power a little, it is 1 that the point for the pattern that conflicts, which assigns power, and the point tax power to non conflicting pattern is α=0.1；
Step S9：Using 3 dyeing solutions of connected component's subgraph of non-linear Zero-one integer programming model solution point cum rights；
Step S10：Suture is judged or inserted with suture insertion algorithm to each pattern represented that is unstained；
Step S11：Connected component where not having the pluggable pattern of suture in the step S10 is obtained with retrogressive method To another more preferable 3 dyeing solution, the step S10 is returned to, until the connected component does not have legal relaxation dyeing solution；
Step S12：The step S3 is dyed with the point deleted in step S4.
Further, the specific implementation of the step S1 is：Layout is dyed spacing Rule Expression according to minimum For undirected conflict graph G (V, E), wherein V=(v1,v2,...,vn) represent layout in pattern set, E={ e1,e2,…,en} Represent side collection；The minimum dyeing spacing rule is if the gap between two patterns is less than mincs, then described two patterns Between have a line, wherein mincsIt is a constant, represents minimum dyeing gap；For three pattern photoetching resolution problems, give One two-dimentional layout plate, it is laid out in plate and contains n nonoverlapping patterns, there is certain gap, and each figure between pattern Sample pi(i=1,2 ..., geometry n) be orthogonal, aiFor its area, then two pattern piAnd pjBetween gap For：
Wherein (xi,yi),(xj,yj) it is p respectivelyiAnd pjCoordinate；According to the gap d (p between patterni,pj) and minimum dye Color gap mincs, undirected conflict graph G (V, E) can be constructed.
Further, all connected components are calculated in the step S3 has point viThe degree d of (i=1,2 ..., n)i, delete Except all degree di＜ 3 point vi, and be stored to and delete in point set RV.
Further, figure G (V, E) is given in the step S4, for each pair point vi,vj∈ V haveAndWherein A (vi),A(vj) represent viAnd vjConsecutive points form set；Represent viPhase Adjoint point collection is included in vjConsecutive points concentrate, then claim viIt is comprised in vjIn, i.e. viTo include a little；The specific bag of the step S4 Include following steps：
Step S41：To obtained each connected subgraph Gc(V, E) is calculated and is stored vi(i=1,2's ..., n) is adjacent Point arrives set A (vi)；
Step S42：The point that selection one is not labeledJudge it is all withNon-conterminous point vj, i.e., With the presence or absence of A (vj),(j≠ik) so thatIf it is present from GcPoint is deleted in (V, E)And its it is connected Side, and it is stored to RV；Otherwise markJudge to finish；
Step S43：Update Gc(V, E), return to step S43, finished until all points are all judged；
The each point i ∈ V of traversal, judge whether it is included by some and the non-conterminous summits of i, if it is, point i will be by Delete, be stored to and delete point set RV.
Further, the step S5 solves its connected component using BFS BFS methods, for different companies Reduction of fractions to a common denominator branch, dyeing solution are independent of each other, and only need to independently solve the dyeing solution of each connected component.
Further, the face used in the step S7 conflicts projecting method to differentiate pattern piAnd pjWhether conflict, The specific implementation of the face conflict projecting method is as follows：For pattern pi(i=1,2 ..., n), its conflict area regiIt is One two-dimentional round rectangle, the border of the round rectangle to pattern piThe distance on border is mincs, i.e.,
Wherein coordinate (xi,yi) it is pattern piBorderline point；The step S7 specifically includes following steps：
Step S71：Each connected subgraph G obtained to the step S6cPattern layout figure corresponding to (V, E), meter Calculate all pattern piThe conflict area reg of (i=1,2 ..., n)i；
Step S72：The pattern that selection one is not labeledJudgeIt is upper to cause with the presence or absence of a region in the area There are three or the adjacent pattern of more than three on domainConflict areaOverlapping phase Hand over；If it is, into the step S73；Otherwise the step S74 is entered；
Step S73：Judge patternWithWhether the spanning subgraph that l+1 points are formed altogether is that 3 can not contaminate 's；If it is, mark patternFor the pattern that conflicts；Otherwise step S74 is entered；
Step S74：MarkFor non conflicting pattern, return to step S72, until all patterns are examined.
Further, the step S9 uses connected component's subgraph of non-linear Zero-one integer programming model solution point cum rights 3 dyeing solutions, to minimize the weights sum of undyed point, it is same that constraints is that two points for having side connected are not allocated A kind of color, uses C1,C2,C3Color class point set 1,2,3 and R are represented respectively4The set being unstained a little is represented, then can be obtained Optimized model：
Wherein wiFor point viWeight.
Optimized model (3) is converted into non-linear Zero-one integer programming model：
Dyeing solution C can be obtained by solving non-linear Zero-one integer programming model (4) with branch and bound method1,C2,C3,R4。
Further, the step S10 introduces conflict rectangle, pattern piOn by adjacent pattern pjCaused by conflict rectangle, i.e., Include pi∩regjThe minimum enclosed rectangle rtg in regioni←j；The step S10 specifically includes following steps：
Step S101：In the point set R that is unstained4One pattern p of middle selectioni；
Step S102：Calculate by piAll adjacent patterns cause piOn conflict rectangle, be stored to piConflict square Shape collection Rtgi；
Step S103：To piConflict rectangular set RtgiIn each conflict rectangle four edges, extend this four edges to scheme Sample piBorder, the side of generation is cut edge, is stored to cut edge collection CSEi；
Step S104：Judge cut edge collection CSEiIn every cut edge whether simultaneously meet condition 1, condition 2 and condition 3； If it is satisfied, then the cut edge sutures for candidate, stored to candidate and suture collection CSi；
Step S101：The step S101 is returned to, until R4In all pattern pi(i=1,2 ..., m) all judge Finish；
Condition 1 in wherein described step S104, condition 2 and condition 3 are respectively：
Condition 1：Pattern piTwo sub-pattern p caused by after being split by cut edgei1And pi2Minimum dimension be both greater than minimal graph Sample ruler cun minfs；
Condition 2：Cut edge is not in pattern piCorner；
Condition 3：Pattern piTwo sub-pattern p caused by after being split by cut edgei1And pi2, pi1And pi2Adjacent pattern face Color is not more than 2 kinds, i.e. pi1And pi2It can be colored and conflict will not be produced.
Further, retrogressive method specifically includes following steps in the step S11：
Step S1101：Initialize connected component G, the dyeing solution X=(C to be recalled1,C2,C3,R4)；
Step S1102：Take subgraph Gm=G/R4；
Step S1103：G is obtained with traversal methodmIt is all it is legal 3 dyeing solution；
Step S1104：From GmIt is all 3 dyeing solutions in take out one solution (C1',C2',C3'), and use the step S10 In seam insertion algorithm carry out insertion suture；
Step S1105：If solve (C1',C2',C3',R4) meet R4In all non conflicting patterns can be inserted into suture Conflict is eliminated, i.e.,So obtain backtracking solution X*=(C1',C2',C3',R4), output backtracking solution X*；Otherwise, return To the step S1104；
Step S1106：G all legal solution X "=(C are obtained with traversal method1”,C2”,C3”,R4"), wherein R4”≠R4； And calculate disaggregated cost cost (X ")=| C |+α | S |；
Step S1101：The solution X " of minimal decomposition cost is taken, makes X*=X ", output backtracking solution X*。
Further, the collection RV that the step S12 is formed to the point deleted in the step S3 and step S4 is dyed, and is obtained The color of minimum cost；Deletion order of the dyeing sequentially with point deleted in the step S3 and step S4 is on the contrary, specific wrap Include following steps：
Step S1201：Level=k, wherein k are the total degree for deleting point；
Step S1202：To the point set RV of the level times deletionlevelIn each point represent pattern pi(1=1, 2,...,|RVlevel|), calculate it and contaminate the cost cost_c of kth kind colork；
Step S1203：Take so that cost_ckMinimum color is as pattern piColor；
Step S1204：Level=level-1；
Step S1205：The step S1202 is returned to, until level=0.
Segmentation to point and 3 colouring problems of figure relaxation are non-linear Zero-one integer programming problem by the present invention, and then with repairing Positive branch-bound algorithm obtains the decomposition result of highly effective.The basic thought of layout decomposition method is directly conflict and suture Decomposed simultaneously in view of triple pattern photoetching, problem solution space can be caused to become very big, be unfavorable for solving, and it is provided by the invention Method be first by problem relaxation into only consider conflict optimization problem, the exponential reduction of solution space；Optimal pine to obtaining again Solution of relaxing carries out legal chemical conversion feasible solution.With the decomposition thought of two steps, a solution space can be obtained and greatly reduced, performance is excellent Layout decomposition method more.
Compared to prior art, the beneficial effects of the invention are as follows：(1) a kind of new non conflicting pattern delet method is used. (2) adequate condition of an identification local conflicts is provided, for layout decomposition.(3) thought of discrete relaxation is used, by former problem Solution space scale be substantially reduced, and obtain optimal discrete relaxation solution with improved Branch-and-bound method.(4) when suturing insertion Consider optimal insertion position, be easy to solve to conflict.Through the comparative experiments with ISCAS-85＆89, the results showed that of the invention three Multigraph sample layout decomposition method, is effectively for the intensive example of pattern.
Brief description of the drawings
Fig. 1 is the flow for the three pattern photomask layout decomposition methods that the present invention is minimized and legalized based on disaggregated cost Figure.
Fig. 2 is the layout of a specific embodiment of the invention.
Fig. 3 is the decomposition coloration result of the layout of a specific embodiment of the invention.
Embodiment
Below in conjunction with the accompanying drawings and embodiment the present invention will be further described.
The present embodiment provides a kind of three pattern photomask layout decomposition methods for being minimized and being legalized based on disaggregated cost, will Three pattern photomask layout resolution problems are divided into two stages solutions.Initial pattern layout (pattern layout) is turned first Non-directed graph G (V, E) is turned to, problem scale is then reduced using figure reduction method, the first stage optimizes mould using a relaxation Type is dyed (coloring) to pattern (patterns), and second stage considers to introduce suture (stitch) by a pattern point The modes of multiple sub-patterns is cut into eliminate conflict (conflict) as much as possible, realizes final dyeing；As shown in figure 1, tool Body comprises the following steps：
Step S1：Layout is converted into non-directed graph；
Step S2：Point is deleted using figure reduction method, and stored；
Step S3：The figure reduction method first step in the step S2 is less than 3 point for deletion degree；
Step S4：Figure reduction method second step in the step S2 includes a little for deletion；
Step S5：The step of figure reduction method the 3rd in the step S2 is solution connected component；
Step S6：Repeating said steps S3- steps S5 three times, produces multiple connected components；
Step S7：Face conflict projecting method inspection is used whether each to put representative pattern for the pattern that conflicts；
Step S8：To assigning power a little, it is 1 that the point for the pattern that conflicts, which assigns power, and the point tax power to non conflicting pattern is α=0.1；
Step S9：Using 3 dyeing solutions of connected component's subgraph of non-linear Zero-one integer programming model solution point cum rights；
Step S10：Suture is judged or inserted with suture insertion algorithm to each pattern represented that is unstained；
Step S11：Connected component where not having the pluggable pattern of suture in the step S10 is obtained with retrogressive method To another more preferable 3 dyeing solution, the step S10 is returned to, until the connected component does not have legal relaxation dyeing solution；
Step S12：The step S3 is dyed with the point deleted in step S4.
In the present embodiment, as shown in 102 parts in Fig. 1, the specific implementation of the step S1 is：Layout root Undirected conflict graph G (V, E), wherein V=(v are expressed as according to minimum dyeing spacing rule1,v2,...,vn) represent layout in figure Sample set, E={ e1,e2,…,enRepresent side collection；The minimum dyeing spacing rule is if the gap between two patterns is small In mincs, then have a line, wherein min between described two patternscsIt is a constant, represents minimum dyeing gap；For three Pattern photoetching resolution problem, a two-dimentional layout plate is given, be laid out in plate and contain n nonoverlapping patterns, between pattern There are certain gap, and each pattern pi(i=1,2 ..., geometry n) be orthogonal, aiFor its area, then two Individual pattern piAnd pjBetween gap be：
Wherein (xi,yi),(xj,yj) it is p respectivelyiAnd pjCoordinate；According to the gap d (p between patterni,pj) and minimum dye Color gap mincs, undirected conflict graph G (V, E) can be constructed.
In the present embodiment, as shown in 104 parts in Fig. 1, the institute of all connected components is calculated in the step S3 a little viThe degree d of (i=1,2 ..., n)i, delete all degree di＜ 3 point vi, and be stored to and delete in point set RV.
In the present embodiment, as shown in 105 parts in Fig. 1, figure G (V, E) is given in the step S4, for each pair point vi,vj∈ V haveAndWherein A (vi),A(vj) represent viAnd vjConsecutive points form set；Represent viAdjacent point set be included in vjConsecutive points concentrate, then claim viIt is comprised in vjIn, i.e. viTo include Point；The step S4's specifically includes following steps：
Step S41：To obtained each connected subgraph Gc(V, E) is calculated and is stored vi(i=1,2's ..., n) is adjacent Point arrives set A (vi)；
Step S42：The point that selection one is not labeledJudge it is all withNon-conterminous point vj, i.e., With the presence or absence of A (vj),(j≠ik) so thatIf it is present from GcPoint is deleted in (V, E)And its it is connected Side, and it is stored to RV；Otherwise markJudge to finish；
Step S43：Update Gc(V, E), return to step S43, finished until all points are all judged；
The each point i ∈ V of traversal, judge whether it is included by some and the non-conterminous summits of i, if it is, point i will be by Delete, be stored to and delete point set RV.
In the present embodiment, as shown in 106 parts in Fig. 1, the step S5 is solved using BFS BFS methods Its connected component, for different connected components, dyeing solution is independent of each other, and only need to independently solve the dyeing of each connected component Solution.
In the present embodiment, as shown in 107 parts in Fig. 1, the face that is used in step S7 conflict projecting method to Differentiate pattern piAnd pjWhether conflict, the specific implementation of the face conflict projecting method is as follows：For pattern pi(i=1, 2 ..., n), its conflict area regiIt is a two-dimentional round rectangle, the border of the round rectangle to pattern piThe distance on border For mincs, i.e.,
Wherein coordinate (xi,yi) it is pattern piBorderline point；The step S7 specifically includes following steps：
Step S71：Each connected subgraph G obtained to the step S6cPattern layout figure corresponding to (V, E), meter Calculate all pattern piThe conflict area reg of (i=1,2 ..., n)i；
Step S72：The pattern that selection one is not labeledJudgeIt is upper to cause with the presence or absence of a region in the area There are three or the adjacent pattern of more than three on domainConflict areaOverlapping phase Hand over；If it is, into the step S73；Otherwise the step S74 is entered；
Step S73：Judge patternWithWhether the spanning subgraph that l+1 points are formed altogether is that 3 can not contaminate 's；If it is, mark patternFor the pattern that conflicts；Otherwise step S74 is entered；
Step S74：MarkFor non conflicting pattern, return to step S72, until all patterns are examined.
In the present embodiment, as shown in 111 parts in Fig. 1, the step S9 is asked using non-linear Zero-one integer programming model 3 dyeing solutions of connected component's subgraph of solution point cum rights, to minimize the weights sum of undyed point, constraints is to have side Two connected points are not allocated same color, use C1,C2,C3Color class point set 1,2,3 and R are represented respectively4Expression does not contaminate The set of color dot, then it can obtain Optimized model：
Wherein wiFor point viWeight.
Optimized model (3) is converted into non-linear Zero-one integer programming model：
Dyeing solution C can be obtained by solving non-linear Zero-one integer programming model (4) with branch and bound method1,C2,C3,R4。
In the present embodiment, as shown in 112 parts in Fig. 1, the step S10 introduces conflict rectangle, pattern piOn by phase Adjacent pattern pjCaused by conflict rectangle, i.e., comprising pi∩regjThe minimum enclosed rectangle rtg in regioni←j；The step S10 is specifically wrapped Include following steps：
Step S101：In the point set R that is unstained4One pattern p of middle selectioni；
Step S102：Calculate by piAll adjacent patterns cause piOn conflict rectangle, be stored to piConflict square Shape collection Rtgi；
Step S103：To piConflict rectangular set RtgiIn each conflict rectangle four edges, extend this four edges to scheme Sample piBorder, the side of generation is cut edge, is stored to cut edge collection CSEi；
Step S104：Judge cut edge collection CSEiIn every cut edge whether simultaneously meet condition 1, condition 2 and condition 3； If it is satisfied, then the cut edge sutures for candidate, stored to candidate and suture collection CSi；
Step S101：The step S101 is returned to, until R4In all pattern pi(i=1,2 ..., m) all judge Finish；
Condition 1 in wherein described step S104, condition 2 and condition 3 are respectively：
Condition 1：Pattern piTwo sub-pattern p caused by after being split by cut edgei1And pi2Minimum dimension be both greater than minimal graph Sample ruler cun minfs；
Condition 2：Cut edge is not in pattern piCorner；
Condition 3：Pattern piTwo sub-pattern p caused by after being split by cut edgei1And pi2, pi1And pi2Adjacent pattern face Color is not more than 2 kinds, i.e. pi1And pi2It can be colored and conflict will not be produced.
In the present embodiment, as shown in 114 parts in Fig. 1, retrogressive method specifically includes following step in the step S11 Suddenly：
Step S1101：Initialize connected component G, the dyeing solution X=(C to be recalled1,C2,C3,R4)；
Step S1102：Take subgraph Gm=G/R4；
Step S1103：G is obtained with traversal methodmIt is all it is legal 3 dyeing solution；
Step S1104：From GmIt is all 3 dyeing solutions in take out one solution (C1',C2',C3'), and use the step S10 In seam insertion algorithm carry out insertion suture；
Step S1105：If solve (C1',C2',C3',R4) meet R4In all non conflicting patterns can be inserted into suture Conflict is eliminated, i.e.,So obtain backtracking solution X*=(C1',C2',C3',R4), output backtracking solution X*；Otherwise, return To the step S1104；
Step S1106：G all legal solution X "=(C are obtained with traversal method1”,C2”,C3”,R4"), wherein R4”≠R4； And calculate disaggregated cost cost (X ")=| C |+α | S |；
Step S1101：The solution X " of minimal decomposition cost is taken, makes X*=X ", output backtracking solution X*。
In the present embodiment, as shown in 116 parts in Fig. 1, the step S12 in the step S3 and step S4 to deleting Point form collection RV dyeing, obtain the color of minimum cost；Dyeing order is with being deleted in the step S3 and step S4 The deletion order of point is on the contrary, specifically include following steps：
Step S1201：Level=k, wherein k are the total degree for deleting point；
Step S1202：To the point set RV of the level times deletionlevelIn each point represent pattern pi(1=1, 2,...,|RVlevel|), calculate it and contaminate the cost cost_c of kth kind colork；
Step S1203：Take so that cost_ckMinimum color is as pattern piColor；
Step S1204：Level=level-1；
Step S1205：The step S1202 is returned to, until level=0.
According to above method, Fig. 2 layout can be subjected to decomposition dyeing, as a result as shown in Figure 3.
The foregoing is only presently preferred embodiments of the present invention, all equivalent changes done according to scope of the present invention patent with Modification, it should all belong to the covering scope of the present invention.

Claims (1)

  1. Minimized 1. a kind of based on disaggregated cost and the three pattern photomask layout decomposition methods that legalize, it is characterised in that including with Lower step：
    Step S1：Layout is converted into non-directed graph；
    Step S2：Point is deleted using figure reduction method, and stored；
    Step S3：The figure reduction method first step in the step S2 is less than 3 point for deletion degree；
    Step S4：Figure reduction method second step in the step S2 includes a little for deletion；
    Step S5：The step of figure reduction method the 3rd in the step S2 is solution connected component；
    Step S6：Repeating said steps S3- steps S5 three times, produces multiple connected components；
    Step S7：Face conflict projecting method inspection is used whether each to put representative pattern for the pattern that conflicts；
    Step S8：To assigning power a little, it is 1 that the point for the pattern that conflicts, which assigns power, and the point tax power to non conflicting pattern is α=0.1；
    Step S9：Using 3 dyeing solutions of connected component's subgraph of non-linear Zero-one integer programming model solution point cum rights；
    Step S10：Suture is judged or inserted with suture insertion algorithm to each pattern represented that is unstained；
    Step S11：Connected component where not having the pluggable pattern of suture in the step S10 is obtained separately with retrogressive method One more preferable 3 dyeing solution, returns to the step S10, until the connected component does not have legal relaxation dyeing solution；
    Step S12：The step S3 is dyed with the point deleted in step S4；
    The specific implementation of the step S1 is：Layout is expressed as undirected conflict graph G according to minimum dyeing spacing rule (V, E), wherein V=(v1,v2,...,vn) represent layout in pattern set, E={ e1,e2,…,enRepresent side collection；It is described Minimum dyeing spacing rule is if the gap between two patterns is less than mincs, then there is a line between described two patterns, Wherein mincsIt is a constant, represents minimum dyeing gap；For three pattern photoetching resolution problems, a two-dimentional layout is given Plate, it is laid out in plate and contains n nonoverlapping patterns, there is certain gap, and each pattern p between patterni(i=1, 2 ..., geometry n) be orthogonal, aiFor its area, then two pattern piAnd pjBetween gap be：
    Wherein (xi,yi),(xj,yj) it is p respectivelyiAnd pjCoordinate；According to the gap d (p between patterni,pj) and minimum dyeing Gap mincs, undirected conflict graph G (V, E) can be constructed；
    All connected components are calculated in the step S3 has point viThe degree d of (i=1,2 ..., n)i, delete all degree di＜ 3 Point vi, and be stored to and delete in point set RV；
    Figure G (V, E) is given in the step S4, for each pair point vi,vj∈ V haveAndWherein A (vi),A(vj) represent viAnd vjConsecutive points form set；Represent viAdjacent point set be included in vjPhase Adjoint point is concentrated, then claims viIt is comprised in vjIn, i.e. viTo include a little；The step S4's specifically includes following steps：
    Step S41：To obtained each connected subgraph Gc(V, E) is calculated and is stored viThe consecutive points of (i=1,2 ..., n) arrive Set A (vi)；
    Step S42：The point that selection one is not labeledJudge it is all withNon-conterminous point vj, i.e.,Whether A (v be presentj),(j≠ik) so thatIf it is present from GcPoint is deleted in (V, E)And its connected side, and It is stored to RV；Otherwise markJudge to finish；
    Step S43：Update Gc(V, E), return to step S43, finished until all points are all judged；
    The each point i ∈ V of traversal, judge whether it is included by some and the non-conterminous summits of i, if it is, point i will be deleted Remove, be stored to and delete point set RV；
    The step S5 solves its connected component using BFS BFS methods, for different connected components, dyeing solution It is independent of each other, only need to independently solves the dyeing solution of each connected component；
    The face used in the step S7 conflicts projecting method to differentiate pattern piAnd pjWhether conflict, the face conflict is thrown The specific implementation of image method is as follows：For pattern pi(i=1,2 ..., n), its conflict area regiIt is a two-dimentional fillet Rectangle, the border of the round rectangle to pattern piThe distance on border is mincs, i.e.,
    Wherein coordinate (xi,yi) it is pattern piBorderline point；The step S7 specifically includes following steps：
    Step S71：Each connected subgraph G obtained to the step S6cPattern layout figure corresponding to (V, E), calculate institute There is pattern piThe conflict area reg of (i=1,2 ..., n)i；
    Step S72：The pattern that selection one is not labeledJudgeIt is upper to cause have over the region with the presence or absence of a region Three or the adjacent pattern of more than threeConflict areaIt is overlapping intersecting；Such as Fruit is, then into step S73；Otherwise step S74 is entered；
    Step S73：Judge patternWithWhether the spanning subgraph that l+1 points are formed altogether is that 3 can not contaminate；Such as Fruit is then to mark patternFor the pattern that conflicts；Otherwise step S74 is entered；
    Step S74：MarkFor non conflicting pattern, return to step S72, until all patterns are examined；The step S9 is used 3 dyeing solutions of connected component's subgraph of non-linear Zero-one integer programming model solution point cum rights, to minimize undyed point Weights sum, constraints are that two points for having side connected are not allocated same color, use C1,C2,C3Color class is represented respectively Point set 1,2,3 and R4The set being unstained a little is represented, then can obtain Optimized model：
    Wherein wiFor point viWeight；
    Optimized model (3) is converted into non-linear Zero-one integer programming model：
    Dyeing solution C can be obtained by solving non-linear Zero-one integer programming model (4) with branch and bound method1,C2,C3,R4；The step Rapid S10 introduces conflict rectangle, pattern piOn by adjacent pattern pjCaused by conflict rectangle, i.e., comprising pi∩regjThe minimum in region Boundary rectangle rtgi←j；The step S10 specifically includes following steps：
    Step S101：In the point set R that is unstained4One pattern p of middle selectioni；
    Step S102：Calculate by piAll adjacent patterns cause piOn conflict rectangle, be stored to piConflict rectangular set Rtgi；
    Step S103：To piConflict rectangular set RtgiIn each conflict rectangle four edges, extend this four edges to pattern pi Border, the side of generation is cut edge, is stored to cut edge collection CSEi；
    Step S104：Judge cut edge collection CSEiIn every cut edge whether simultaneously meet condition 1, condition 2 and condition 3；It is if full Foot, then the cut edge is candidate's suture, is stored to candidate and sutures collection CSi；
    Step S101：The step S101 is returned to, until R4In all pattern pi(i=1,2 ..., m) all judge to finish；
    Condition 1 in wherein described step S104, condition 2 and condition 3 are respectively：
    Condition 1：Pattern piTwo sub-pattern p caused by after being split by cut edgei1And pi2Minimum dimension be both greater than minimal graph sample ruler Very little minfs；
    Condition 2：Cut edge is not in pattern piCorner；
    Condition 3：Pattern piTwo sub-pattern p caused by after being split by cut edgei1And pi2, pi1And pi2Adjacent pattern color not More than 2 kinds, i.e. pi1And pi2It can be colored and conflict will not be produced；
    Retrogressive method specifically includes following steps in the step S11：
    Step S1101：Initialize connected component G, the dyeing solution X=(C to be recalled1,C2,C3,R4)；
    Step S1102：Take subgraph Gm=G/R4；
    Step S1103：G is obtained with traversal methodmIt is all it is legal 3 dyeing solution；
    Step S1104：From GmIt is all 3 dyeing solutions in take out one solution (C1',C2',C3'), and using in the step S10 Seam insertion algorithm carries out insertion suture；
    Step S1105：If solve (C1',C2',C3',R4) meet R4In all non conflicting patterns can be inserted into suture eliminate Conflict, i.e.,So obtain backtracking solution X*=(C1',C2',C3',R4), output backtracking solution X*；Otherwise, institute is returned to State step S1104；
    Step S1106：G all legal solution X "=(C are obtained with traversal method1”,C2”,C3”,R4"), wherein R4”≠R4；And count Calculation disaggregated cost cost (X ")=| C |+α | S |；
    Step S1101：The solution X " of minimal decomposition cost is taken, makes X*=X ", output backtracking solution X*；
    The collection RV that the step S12 is formed to the point deleted in the step S3 and step S4 is dyed, and obtains the face of minimum cost Color；Deletion order of the dyeing sequentially with point deleted in the step S3 and step S4 is on the contrary, specifically include following steps：
    Step S1201：Level=k, wherein k are the total degree for deleting point；
    Step S1202：To the point set RV of the level times deletionlevelIn each point represent pattern pi(1=1,2 ..., | RVlevel|), calculate it and contaminate the cost cost_c of kth kind colork；
    Step S1203：Take so that cost_ckMinimum color is as pattern piColor；
    Step S1204：Level=level-1；
    Step S1205：The step S1202 is returned to, until level=0.
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