US 8,028,254 B2Granted

Determining manufacturability of lithographic mask using continuous derivatives characterizing the manufacturability on a continuous scale

AssigneeInternational Business Machines Corporation

InventorsTadanobu Inoue, David O. Melville, Hidemasa Muta, Kehan Tian, Masaharu Sakamoto, Alan E. Rosenbluth

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Abstract

The manufacturability of a lithographic mask employed in fabricating instances of a semiconductor device is determined. Target edge pairs are selected from mask layout data of the lithographic mask, for determining a manufacturing penalty in making the lithographic mask. The mask layout data includes polygons, where each polygon has a number of edges. Each target edge pair is defined by two of the edges of one or more of the polygons. The manufacturability of the lithographic mask, including the manufacturing penalty in making the lithographic mask, is determined. Determining the manufacturing penalty is based on the target edge pairs as selected. Determining the manufacturability of the lithographic mask uses continuous derivatives characterizing the manufacturability of the lithographic mask on a continuous scale. The manufacturability of the lithographic mask is output. The manufacturability of the lithographic mask is dependent on the manufacturing penalty in making the lithographic mask.

Claims18

Dependent claims

A method for determining manufacturability of a lithographic mask employed in fabricating instances of a semiconductor device, comprising:

selecting a plurality of target edge pairs from mask layout data of the lithographic mask, for determining a manufacturing penalty in making the lithographic mask, the mask layout data comprising a plurality of polygons, each polygon having a plurality of edges, each target edge pair defined by two of the edges of one or more of the polygons;
determining the manufacturability of the lithographic mask by a computer, including determining the manufacturing penalty in making the lithographic mask, where determining the manufacturing penalty is based on the target edge pairs as selected, and where determining the manufacturability of the lithographic mask comprises using continuous derivatives characterizing the manufacturability of the lithographic mask on a continuous scale;
and,
outputting the manufacturability of the lithographic mask by the computer, where the manufacturability of the lithographic mask is dependent on the manufacturing penalty in making the lithographic mask,
wherein determining the manufacturability of the lithographic mask, including determining the manufacturing penalty in making the lithographic mask, comprises:
for a selected target edge pair having a first edge and a second edge that belong to a same polygon and that are at least substantially parallel to one another,
determining a manufacturing shape penalty resulting from the selected target edge pair, the manufacturing shape penalty related to a penalty incurred in manufacturing the lithographic mask due to a shape of the same polygon,
wherein determining the manufacturing shape penalty comprises evaluating
Pshape=Pgap—size×Pjog—stair×Paspect—ratio—i—a×Paspect—ratio—j—a×Poverlap,
where Pshape denotes the manufacturing shape penalty, Pgap size denotes a manufacturing penalty owing to a size of a gap between the first and the second edges, Pjog—stair denotes a manufacturing penalty owing to whether the first and the second edges define a jog shape or a stair shape, Paspect—ratio—i—a denotes a manufacturing penalty owing to an aspect ratio of the first edge denoted as i relative to a size of a gap between the two edges i and j, Paspect—ratio—j—a denotes a manufacturing penalty owing to an aspect ratio of the second edge denoted as j relative to the size of a gap between the two edges i and j, and Poverlap denotes a manufacturing penalty owing to a degree of overlap between the first and the second edges,
and wherein Pshape, Pgap—size, Pjog—stair, Paspect—ratio—i—a, Paspect—ratio—j—a, and Poverlap are smoothly varying continuous functions, as opposed to non-smoothly varying discontinuous functions.

8 more elements

A method for determining manufacturability of a lithographic mask employed in fabricating instances of a semiconductor device, comprising:

selecting a plurality of target edge pairs from mask layout data of the lithographic mask, for determining a manufacturing penalty in making the lithographic mask, the mask layout data comprising a plurality of polygons, each polygon having a plurality of edges, each target edge pair defined by two of the edges of one or more of the polygons;
determining the manufacturability of the lithographic mask by a computer, including determining the manufacturing penalty in making the lithographic mask, where determining the manufacturing penalty is based on the target edge pairs as selected, and where determining the manufacturability of the lithographic mask comprises using continuous derivatives characterizing the manufacturability of the lithographic mask on a continuous scale;
and,
outputting the manufacturability of the lithographic mask by the computer, where the manufacturability of the lithographic mask is dependent on the manufacturing penalty in making the lithographic mask,
wherein determining the manufacturability of the lithographic mask, including determining the manufacturing penalty in making the lithographic mask, comprises:
for a selected target edge pair having a first edge belong to a first polygon and a second edge belonging to a second polygon that is different than the first polygon, the first and the second edges being at least substantially parallel to one another,
determining a manufacturing gap penalty resulting from the selected target edge pair, the manufacturing gap penalty related to a penalty incurred in manufacturing the lithographic mask due to a gap between the first and the second polygons,
wherein determining the manufacturing gap penalty comprises evaluating
Pgap=Pgap—size×Poverlap,
where Pgap denotes the manufacturing gap penalty, Pgap—size denotes a manufacturing penalty owing to a size of a gap between the first and the second edges, Poverlap denotes a manufacturing penalty owing to a degree of overlap between the first and the second edges,
and wherein Pgap, Pgap—size, and Poverlap are smoothly varying continuous functions, as opposed to non-smoothly varying discontinuous functions.

8 more elements

A method for determining manufacturability of a lithographic mask employed in fabricating instances of a semiconductor device, comprising:

selecting a plurality of target edge pairs from mask layout data of the lithographic mask, for determining a manufacturing penalty in making the lithographic mask, the mask layout data comprising a plurality of polygons, each polygon having a plurality of edges, each target edge pair defined by two of the edges of one or more of the polygons;
determining the manufacturability of the lithographic mask by a computer, including determining the manufacturing penalty in making the lithographic mask, where determining the manufacturing penalty is based on the target edge pairs as selected, and where determining the manufacturability of the lithographic mask comprises using continuous derivatives characterizing the manufacturability of the lithographic mask on a continuous scale;
and,
outputting the manufacturability of the lithographic mask by the computer, where the manufacturability of the lithographic mask is dependent on the manufacturing penalty in making the lithographic mask,
wherein determining the manufacturability of the lithographic mask, including determining the manufacturing penalty in making the lithographic mask, comprises:
for a selected target edge pair having a first edge belong to a first polygon and a second edge belonging to a second polygon that is different than the first polygon, the first and the second edges being at least substantially perpendicular to one another,
determining a manufacturing crossing penalty resulting from the selected target edge pair, the manufacturing gap penalty related to a penalty incurred in manufacturing the lithographic mask due to potential overlap between the first and the second polygons,
wherein determining the manufacturing crossing penalty comprises evaluating
Pcrossing=wcrossing×Pcrossing—i—j×Pcrossing—j—i,
where Pcrossing denotes the manufacturing crossing penalty, wcrossing denotes a weight coefficient, Pcrossing—i—j denotes a manufacturing penalty owing to the first edge denoted as i crossing the second edge denoted as j, and Pcrossing—j—i denotes a manufacturing penalty owing to the second edge denoted as j crossing the first edge denoted as i,
and wherein Pcrossing, Pcrossing—i—j,and Pcrossing—j—i are smoothly varying continuous functions, as opposed to non-smoothly varying discontinuous functions.

8 more elements

A non-transitory computer-readable medium having one or more computer programs stored in the medium, such that execution of the one or more computer programs by a computer causes a method to be performed, wherein the method is for determining manufacturability of a lithographic mask employed in fabricating instances of a semiconductor device, the method comprising:

selecting a plurality of target edge pairs from mask layout data of the lithographic mask, for determining a manufacturing penalty in making the lithographic mask, the mask layout data comprising a plurality of polygons, each polygon having a plurality of edges, each target edge pair defined by two of the edges of one or more of the polygons;
determining the manufacturability of the lithographic mask, including determining the manufacturing penalty in making the lithographic mask, where determining the manufacturing penalty is based on the target edge pairs as selected, and where determining the manufacturability of the lithographic mask comprises using continuous derivatives characterizing the manufacturability of the lithographic mask on a continuous scale by using smoothly varying assessment functions representing the manufacturing penalty in making the lithographic mask,
wherein determining the manufacturability of the lithographic mask is achieved by performing one or more of:
(a) for a first selected target edge pair having a first edge and a second edge that belong to a same polygon and that are at least substantially parallel to one another,
determining a manufacturing shape penalty resulting from the first selected target edge pair, the manufacturing shape penalty related to a penalty incurred in manufacturing the lithographic mask due to a shape of the same polygon;
(b) for a second selected target edge pair having a third edge belong to a third polygon and a fourth edge belonging to a fourth polygon that is different than the third polygon, the third and the fourth edges being at least substantially parallel to one another,
determining a manufacturing gap penalty resulting from the second selected target edge pair, the manufacturing gap penalty related to a penalty incurred in manufacturing the lithographic mask due to a gap between the third and the fourth polygons;
and,
(c) for a third selected target edge pair having a fifth edge belong to a fifth polygon and a sixth edge belonging to a sixth polygon that is different than the fifth polygon, the fifth and the sixth edges being at least substantially perpendicular to one another,
determining a manufacturing crossing penalty resulting from the third selected target edge pair, the manufacturing gap penalty related to a penalty incurred in manufacturing the lithographic mask due to potential overlap between the fifth and the sixth polygons,
and wherein determining the manufacturing shape penalty comprises evaluating one or more of:
Pshape=Pgap—size×Pjog—stair×Paspect—ratio—i—a×Paspect—ratio—j—a×Poverlap, where Pshape denotes the manufacturing shape penalty, Pgap—size denotes a manufacturing penalty owing to a size of a gap between the first and the second edges, Pjog—stair denotes a manufacturing penalty owing to whether the first and the second edges define a jog shape or a stair shape, Paspect—ratio—i—a denotes a manufacturing penalty owing to an aspect ratio of the first edge denoted as i relative to a size of a gap between the two edges i and j, Paspect—ratio—j—a denotes a manufacturing penalty owing to an aspect ratio of the second edge denoted as j relative to the size of a gap between the two edges i and j, and Poverlap denotes a manufacturing penalty owing to a degree of overlap between the first and the second edges, and where Pshape, Pgap—size, Pjog—stair, Paspect—ratio—i—a, Paspect—ratio—j—a, and Poverlap are smoothly varying continuous functions, as opposed to non-smoothly varying discontinuous functions;
Pgap=Pgap—size×Poverlap, where Pgap—size denotes the manufacturing gap penalty, Pgap—size denotes a manufacturing penalty owing to a size of a gap between the third and the fourth edges, Poverlap denotes a manufacturing penalty owing to a degree of overlap between the third and the fourth edges, and where Pgap, Pgap—size, and Poverlap are smoothly varying continuous functions, as opposed to non-smoothly varying discontinuous functions;
Pcrossing=wcrossing×Pcrossing—i—j×Pcrossing—j—i, where Pcrossing denotes the manufacturing crossing penalty, wcrossing denotes a weight coefficient, Pcrossing—i—j denotes a manufacturing penalty owing to the fifth edge denoted as i crossing the sixth edge denoted as j, and Pcrossing—j—i denotes a manufacturing penalty owing to the sixth edge denoted as j crossing the fifth edge denoted as i, and where Pcrossing, Pcrossing—i—j, and Pcrossing—j—i are smoothly varying continuous functions, as opposed to non-smoothly varying discontinuous functions.

11 more elements

selecting a plurality of target edge pairs from mask layout data of the lithographic mask, for determining a manufacturing penalty in making the lithographic mask, the mask layout data comprising a plurality of polygons, each polygon having a plurality of edges, each target edge pair defined by two of the edges of one or more of the polygons;
determining the manufacturability of the lithographic mask, including determining the manufacturing penalty in making the lithographic mask, where determining the manufacturing penalty is based on the target edge pairs as selected, and where determining the manufacturability of the lithographic mask comprises using continuous derivatives characterizing the manufacturability of the lithographic mask on a continuous scale by using smoothly varying assessment functions representing the manufacturing penalty in making the lithographic mask,
wherein determining the manufacturability of the lithographic mask is achieved by performing all of:
(a) for a first selected target edge pair having a first edge and a second edge that belong to a same polygon and that are at least substantially parallel to one another,
determining a manufacturing shape penalty resulting from the first selected target edge pair, the manufacturing shape penalty related to a penalty incurred in manufacturing the lithographic mask due to a shape of the same polygon;
(b) for a second selected target edge pair having a third edge belong to a third polygon and a fourth edge belonging to a fourth polygon that is different than the third polygon, the third and the fourth edges being at least substantially parallel to one another,
determining a manufacturing gap penalty resulting from the second selected target edge pair, the manufacturing gap penalty related to a penalty incurred in manufacturing the lithographic mask due to a gap between the third and the fourth polygons;
and,
(c) for a third selected target edge pair having a fifth edge belong to a fifth polygon and a sixth edge belonging to a sixth polygon that is different than the fifth polygon, the fifth and the sixth edges being at least substantially perpendicular to one another,
determining a manufacturing crossing penalty resulting from the third selected target edge pair, the manufacturing gap penalty related to a penalty incurred in manufacturing the lithographic mask due to potential overlap between the fifth and the sixth polygons,
(a) wherein determining the manufacturing shape penalty comprises evaluating
Pshape=Pgap—size×Pjog—stair×Paspect—ratio—i—a×Paspect—ratio—j—a×Poverlap,
where Pshape denotes the manufacturing shape penalty, Pgap—size denotes a manufacturing penalty owing to a size of a gap between the first and the second edges, Pjog—stair denotes a manufacturing penalty owing to whether the first and the second edges define a jog shape or a stair shape, Paspect—ratio—i—a denotes a manufacturing penalty owing to an aspect ratio of the first edge denoted as i relative to a size of a gap between the two edges i and j, Paspect—ratio—j—a denotes a manufacturing penalty owing to an aspect ratio of the second edge denoted as j relative to the size of a gap between the two edges i and j, and Poverlap denotes a manufacturing penalty owing to a degree of overlap between the first and the second edges,
and where Pshape, Pgap—size, Pjog—stair, Paspect—ratio—i—a, Paspect—ratio—j—a, and Poverlap are smoothly varying continuous functions, as opposed to non-smoothly varying discontinuous functions,
(b) wherein determining the manufacturing gap penalty comprises evaluating
Pgap=Pgap—size×Poverlap,
where Pgap denotes the manufacturing gap penalty, Pgap—size denotes a manufacturing penalty owing to a size of a gap between the third and the fourth edges, Poverlap denotes a manufacturing penalty owing to a degree of overlap between the third and the fourth edges,
and where Pgap, Pgap—size, and Poverlap are smoothly varying continuous functions, as opposed to non-smoothly varying discontinuous functions,
(c) and wherein determining the manufacturing crossing penalty comprises evaluating
Pcrossing=wcrossing×Pcrossing—i—j×Pcrossing—j—i,
where Pcrossing denotes the manufacturing crossing penalty, wcrossing denotes a constant, Pcrossing—i—j denotes a manufacturing penalty owing to the fifth edge denoted as i crossing the sixth edge denoted as j, and Pcrossing—j—i denotes a manufacturing penalty owing to the sixth edge denoted as j crossing the fifth edge denoted as i,
and where Pcrossing, Pcrossing—i—j, and Pcrossing—j—i are smoothly varying continuous functions, as opposed to non-smoothly varying discontinuous functions.

19 more elements

Dependencies are inferred from the claim text.