Methods, based on a genetic algorithm, for configuring parameters of an array of multiple components for cooperative operation to achieve a desired performance result
First Claim
1. In a charged-particle-beam (CPB) optical system comprising multiple components each having at least one parameter the value of which is established so as to cause, when all such components of the CPB optical system are configured or operated in a coordinated manner according to the respective values of the parameters, the CPB optical system to operate in a manner producing a desired performance result, a method for determining the respective values of the parameters for the components, comprising:
- (a) regarding each respective value of a respective parameter as a respective gene;
(b) regarding each respective combination of values of the parameters as a respective chromosome and each respective configuration of the CPB optical system according to the respective chromosome as a respective species;
(c) each parameter having a respective initial-condition gene, wherein each of NA species in a group A comprises a respective chromosome of the initial-condition genes;
(d) defining an evaluation function, wherein values of the evaluation function are related to respective qualities of a performance characteristic of the CPB optical system, and establishing a threshold value for the evaluation function;
(e) from the group-A species, selecting a group B including NB species (wherein NB≦
NA) in which the constituent species have higher respective values of the evaluation function than species not selected to be in the group B;
(f) from the group-B species, and based on a selection criterion, selecting groups CND, in which each group includes NC individuals, to produce a group D including ND species, wherein each species in group D comprises a respective chromosome produced by recombination of one or more genes from respective chromosomes of species in the group CND;
(g) producing the group D of ND species from the groups CND;
(h) from the group D, selecting a new group B including NB species;
(i) repeating steps (e)-(h) a predetermined number of times or until a species is produced in group D having a respective value of the evaluation function that exceeds the threshold; and
(j) employing the species produced in step (i) to define the respective combination of values of the parameters for configuring the components or for operating the components in the coordinated manner.
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Abstract
Methods are disclosed for determining respective values of configurational and/or operational parameters of a system, such as a charged-particle-beam (CPB) optical system as used, e.g., in a CPB microlithography apparatus. Executing the methods provides an optimal combination of the parametric values for the system while preventing convergence to a local solution rather than an optimal solution. The methods are based on a genetic algorithm. For example, consider a subject system including six deflectors, each of which being energized with a respective current ratio and each of which producing a respective magnetic-field orientation. For each deflector, the respective values of each of these two parameters is regarded as a separate gene, yielding a total of 12 genes. Each different combination of the parameters is regarded as a species having a respective chromosome containing the 12 respective genes. A specified number of species is selected with random genes as initial values. From this initial group, a specified number of species having high evaluation values are selected. Species possessing new chromosomes in which the genes are recombined are produced by crossing selected individuals in the manner of parents. A specified number of child species having higher evaluation values are carried forward for further matings. By repeating the matings and weighting the offspring, an individual having an optimal evaluation value ultimately is produced.
6 Citations
18 Claims
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1. In a charged-particle-beam (CPB) optical system comprising multiple components each having at least one parameter the value of which is established so as to cause, when all such components of the CPB optical system are configured or operated in a coordinated manner according to the respective values of the parameters, the CPB optical system to operate in a manner producing a desired performance result, a method for determining the respective values of the parameters for the components, comprising:
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(a) regarding each respective value of a respective parameter as a respective gene;
(b) regarding each respective combination of values of the parameters as a respective chromosome and each respective configuration of the CPB optical system according to the respective chromosome as a respective species;
(c) each parameter having a respective initial-condition gene, wherein each of NA species in a group A comprises a respective chromosome of the initial-condition genes;
(d) defining an evaluation function, wherein values of the evaluation function are related to respective qualities of a performance characteristic of the CPB optical system, and establishing a threshold value for the evaluation function;
(e) from the group-A species, selecting a group B including NB species (wherein NB≦
NA) in which the constituent species have higher respective values of the evaluation function than species not selected to be in the group B;
(f) from the group-B species, and based on a selection criterion, selecting groups CND, in which each group includes NC individuals, to produce a group D including ND species, wherein each species in group D comprises a respective chromosome produced by recombination of one or more genes from respective chromosomes of species in the group CND;
(g) producing the group D of ND species from the groups CND;
(h) from the group D, selecting a new group B including NB species;
(i) repeating steps (e)-(h) a predetermined number of times or until a species is produced in group D having a respective value of the evaluation function that exceeds the threshold; and
(j) employing the species produced in step (i) to define the respective combination of values of the parameters for configuring the components or for operating the components in the coordinated manner. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16)
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14. A divided-reticle charged-particle-beam (CPB) projection-microlithography apparatus, comprising:
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(a) a CPB optical system configured (i) to impart an acceleration voltage of at least 15 keV to a charged particle beam passing through the CPB optical system, (ii) to illuminate a reticle subfield no larger than 1.2-mm square, (iii) to provide an aperture angle of the charged particle beam of no more than 1.8 mrad at the reticle, and (iv) with a lens-column length of at least 561 mm;
(b) the CPB optical system comprising a beam-shaping aperture and six deflectors, each deflector having a coil inside diameter of 34.2 mm to 37.4 mm, a coil outside diameter of 47.6 mm to 58.2 mm, an axial length of 66.4 mm to 71.2 mm, and coil angles of 12°
, 60°
, and 72°
;
(c) the deflectors being energizable with respective electrical currents to produce respective magnetic fields directed at the charged particle beam passing through the respective deflectors; and
(d) respective axial positions of the deflectors and respective magnetic field angles produced by the deflectors being within respective ranges listed in Table B relative to respective standard values listed in Table A, TABLE A Current Ratio Field Angle Deflector 1 1 −
92.68000°Deflector 2 −
0.60810−
68.73601°Deflector 3 −
1.16774−
45.37404°Deflector 4 2.92347 −
109.09496°Deflector 5 2.20169 −
93.01785°Deflector 6 −
2.82387−
134.73484°TABLE B Current Ratio Field Angle Axial Position Mini- Maxi- Mini- Maxi- Mini- Maxi- mum mum mum mum mum mum Deflector 1 −
2.9512.530 −
4.24416.892 95 111 Deflector 2 −
5.8875.183 −
14.8413.765 180 190 Deflector 3 −
5.9444.762 −
7.6442.389 255 263 Deflector 4 −
0.3460.349 −
9.7019.767 399.8 400.2 Deflector 5 −
0.2420.244 −
0.7690.776 474.8 475.2 Deflector 6 −
0.1510.154 −
0.3680.371 549.7 550.3 wherein the current ratios and magnetic field angles listed in Table B are respective percents of corresponding values listed in Table A, axial positions are in mm units along a CPB-optical-system axis, the axial position of the beam-shaping aperture is zero from which a charged particle beam propagates in a positive direction. - View Dependent Claims (17)
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15. A divided-reticle charged-particle-beam (CPB) projection-microlithography apparatus, comprising:
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(a) a CPB optical system configured (i) to impart an acceleration voltage of at least 15 keV to a charged particle beam passing through the CPB optical system, (ii) to illuminate a reticle subfield no larger than 1.8-mm square, (iii) to provide an aperture angle of the charged particle beam of no more than 2.5 mrad at the reticle, and (iv) with a lens-column length of at least 528 mm;
(b) the CPB optical system comprising a beam-shaping aperture and six deflectors, each deflector having a coil inside diameter of 34.2 mm to 38.2 mm, a coil outside diameter of 46.8 mm to 58.2 mm, an axial length of 66.4 mm to 71.2 mm, and coil angles of 12°
, 60°
, and 72°
;
(c) the deflectors being energizable with respective electrical currents to produce respective magnetic fields directed at the charged particle beam passing through the respective deflectors; and
(d) respective axial positions of the deflectors and respective magnetic field angles produced by the deflectors being within respective ranges listed in Table C relative to respective standard values listed in Table D, TABLE C Current Ratio Field Angle Deflector 1 1 −
78.83272°Deflector 2 −
0.60810−
54.88852°Deflector 3 −
1.16775−
31.52713°Deflector 4 2.39817 −
82.87136°Deflector 5 0.41115 −
131.91370°Deflector 6 −
1.28801−
137.33486°TABLE D Current Ratio Field Angle Axial Position Mini- Maxi- Mini- Maxi- Mini- Maxi- mum mum mum mum mum mum Deflector 1 −
1.4651.226 −
1.48111.746 99 109 Deflector 2 −
2.8922.554 −
10.3031.313 182 190 Deflector 3 −
2.9902.296 −
4.7120.828 257 260 Deflector 4 −
0.2600.268 −
1.0621.036 399.9 400.1 Deflector 5 −
0.8070.821 −
1.3851.330 474 475.9 Deflector 6 −
0.2060.211 −
0.2940.304 549.6 550.4 wherein the current ratios and magnetic field angles listed in Table B are respective percents of corresponding values listed in Table A, axial positions are in mm units along a CPB-optical-system axis, the axial position of the beam-shaping aperture is zero from which a charged particle beam propagates in a positive direction. - View Dependent Claims (18)
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Specification