# US 10,872,188 B2 · Tool to provide integrated circuit masks with accurate dimensional compensation of patterns

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- Number: US 10,872,188 B2
- Document ID: US10872188B2
- Status: Granted
- Kind: B2
- Application number: 16/426,204
- Filed: 2019-05-30
- Published: 2020-03-05
- Granted: 2020-12-22
- Earliest claimed: 2015-11-25
- Assignees: International Business Machines Corporation
- Applicants: International Business Machines Corporation
- Inventors: Alan E. Rosenbluth
- Web page: https://patentgrep.com/patent/US10872188B2

## CPC

- G06F 30/367: Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
- G03F 1/36: Masks having proximity correction features; Preparation thereof, e.g. optical proximity correction [OPC] design processes
- G03F 7/70091: {Illumination settings, i.e. intensity distribution in the pupil plane or angular distribution in the field plane; On-axis or off-axis settings, e.g. annular, dipole or quadrupole settings; Partial coherence control, i.e. sigma or numerical aperture [NA]}
- G03F 7/70283: {Mask effects on the imaging process}
- G03F 7/705: {Modelling or simulating from physical phenomena up to complete wafer processes or whole workflow in wafer productions}
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- G03F: PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR; (phototypographic composing devices B41B; photosensitive materials or processes for photographic purposes G03C; electrophotography, sensitive layers or processes therefor G03G)

## Abstract

Disclosed are mask definition tools, apparatus, methods, systems and computer program products configured to process data representing a semiconductor fabrication mask. A non-limiting example of a method includes performing a decomposition process on a full Transmission Cross Coefficient (TCC) using coherent optimal coherent systems (OCS) kernels; isolating a residual TCC that remains after some number of coherent kernels are extracted from the full TCC; and performing at least one decomposition process on the residual TCC using at least one loxicoherent system. The loxicoherent system uses a plurality of distinct non-coherent kernel functions and is a compound system containing a paired coherent system and an incoherent system that act in sequence. An output of the coherent system is input as a self-luminous quantity to the incoherent system, and the output of the incoherent system is an output of the loxicoherent system.

## Claims

### Claim 1

A photomask for optical lithography, the photomask comprising mask shapes containing a reduced number of edges enabling the mask shapes to be decomposed into a reduced number of shots of an electron beam mask writer that creates the photomask, where the reduced number of edges is reduced compared with an overall number of edges in a full optical lithography layout associated with the photomask, where the reduced number of shots is reduced compared with a number of shots associated with the full optical lithography layout.

### Claim 2 (depends on 1)

The photomask as in claim 1, where performance goals and requirements are specified in a constrained problem formulation that is solved using an Augmented Lagrangian method, with a set of edge variables being redefined at a commencement of each iteration cycle of outer loops so as to lock into alignment coordinates of suitable edge endpoints, where the suitable edge endpoints are associated with parallel edges that at least partially face each other.

### Claim 3 (depends on 2)

The photomask as in claim 2, where at least one loxicoherent system is used during execution of each iteration cycle of the outer loops; and where the at least one loxicoherent system is a compound system comprised of a paired coherent system and an incoherent system that act in sequence, where an output of the coherent system is input as a self-luminous quantity to the incoherent system of the pair, and where an output of the incoherent system is an output of the loxicoherent system.

### Claim 4 (depends on 3)

The photomask as in claim 3, where the edge endpoint coordinates that are suitable for locking into alignment are first adjusted for exact equalization, and subsequently kept equal by use of a single common variable to control respective coordinates of the suitable edge endpoints during a next set of inner loops.

### Claim 5 (depends on 4)

The photomask as in claim 4, where two edge endpoints of parallel edges within each mask shape that partially face each other across the shape are locked into alignment whenever a difference between coordinate values of the two edge endpoints is lower than a locking threshold, and where a common coordinate given to the locked edge endpoints is initially set to a midpoint of their coordinate values prior to locking, as weighted by respective lengths of corresponding connector edges that also intersect the two edge endpoints of the two facing parallel edges.

### Claim 6

A method comprising:
receiving a full optical lithography layout; and
producing a photomask for optical lithography, the photomask comprising mask shapes containing a reduced number of edges enabling the mask shapes to be decomposed into a reduced number of shots of an electron beam mask writer that creates the photomask, where the reduced number of edges is reduced compared with an overall number of edges in the full optical lithography layout associated with the photomask, where the reduced number of shots is reduced compared with a number of shots associated with the full optical lithography layout.

### Claim 7 (depends on 6)

The method as in claim 6, where the producing of the photomask comprises:
using performance goals and requirements that are specified in a constrained problem formulation that is solved using an Augmented Lagrangian method, with a set of edge variables being redefined at a commencement of each iteration cycle of outer loops so as to lock into alignment coordinates of suitable edge endpoints, where the suitable edge endpoints are associated with parallel edges that at least partially face each other.

### Claim 8 (depends on 7)

The method as in claim 7, where at least one loxicoherent system is used during execution of each iteration cycle of the outer loops; and where the at least one loxicoherent system is a compound system comprised of a paired coherent system and an incoherent system that act in sequence, where an output of the coherent system is input as a self-luminous quantity to the incoherent system of the pair, and where an output of the incoherent system is an output of the loxicoherent system.

### Claim 9 (depends on 8)

The method as in claim 8, where the edge endpoint coordinates that are suitable for locking into alignment are first adjusted for exact equalization, and subsequently kept equal by use of a single common variable to control respective coordinates of the suitable edge endpoints during a next set of inner loops.

### Claim 10 (depends on 9)

The method as in claim 9, where two edge endpoints of parallel edges within each mask shape that partially face each other across the shape are locked into alignment whenever a difference between coordinate values of the two edge endpoints is lower than a locking threshold, and where a common coordinate given to the locked edge endpoints is initially set to a midpoint of their coordinate values prior to locking, as weighted by respective lengths of corresponding connector edges that also intersect the two edge endpoints of the two facing parallel edges.

### Claim 11

An apparatus comprising at least one processor and at least one non-transitory memory including computer program code, the at least one memory and computer program code configured to with the at least one processor cause the apparatus at least to:
produce a photomask for optical lithography, the photomask comprising mask shapes containing a reduced number of edges enabling the mask shapes to be decomposed into a reduced number of shots, where the reduced number of edges is reduced compared with an overall number of edges in a full optical lithography layout associated with the photomask, where the reduced number of shots is reduced compared with a number of shots associated with the full optical lithography layout.

### Claim 12 (depends on 11)

The apparatus as in claim 11, where producing the photomask comprises the at least one memory and computer program code further configured to with the at least one processor cause the apparatus at least to:
use performance goals and requirements that are specified in a constrained problem formulation that is solved using an Augmented Lagrangian method, with a set of edge variables being redefined at a commencement of each iteration cycle of outer loops so as to lock into alignment coordinates of suitable edge endpoints, where the suitable edge endpoints are associated with parallel edges that at least partially face each other.

### Claim 13 (depends on 12)

The apparatus as in claim 12, where at least one loxicoherent system is used during execution of each iteration cycle of the outer loops; and where the at least one loxicoherent system is a compound system comprised of a paired coherent system and an incoherent system that act in sequence, where an output of the coherent system is input as a self-luminous quantity to the incoherent system of the pair, and where an output of the incoherent system is an output of the loxicoherent system.

### Claim 14 (depends on 13)

The apparatus as in claim 13, where the edge endpoint coordinates that are suitable for locking into alignment are first adjusted for exact equalization, and subsequently kept equal by use of a single common variable to control respective coordinates of the suitable edge endpoints during a next set of inner loops.

### Claim 15 (depends on 14)

The apparatus as in claim 14, where two edge endpoints of parallel edges within each mask shape that partially face each other across the shape are locked into alignment whenever a difference between coordinate values of the two edge endpoints is lower than a locking threshold, and where a common coordinate given to the locked edge endpoints is initially set to a midpoint of their coordinate values prior to locking, as weighted by respective lengths of corresponding connector edges that also intersect the two edge endpoints of the two facing parallel edges.