Methods, based on a genetic algorithm, for configuring parameters of an array of multiple components for cooperative operation to achieve a desired performance result

• US 6,627,900 B2
• Filed: 02/16/2001
• Issued: 09/30/2003
• Est. Priority Date: 02/18/2000
• Status: Expired due to Fees

• Current Assignee: Nikon Corporation
• Original Assignee: Nikon Corporation
• Inventors: Fukui, Saori
• Primary Examiner(s): Lee, John R.
• Assistant Examiner(s): SOUW, BERNARD E
• Application Number:
  US09/785,943
• Publication Number:
  US 20010030289A1
• Time in Patent Office: 956 Days
• Field of Search: 250/492.22, 250/492.23, 250/400, 706/13
• US Class Current: 250/396.00R
• CPC Class Codes: G06N 3/126 Evolutionary algorithms, e.g. genetic algorithms or genetic programming
• CPC Class Codes: H01J 37/3023 Programme control

Abstract

Methods are disclosed for determining respective values of system parameters of, e.g., a charged-particle-beam (CPB) optical system of a CPB microlithography apparatus. The methods, based on a genetic algorithm, yield optimal combinations of the values without converging to local, rather than optimal, solutions. In an example involving six deflectors energized with respective current ratios and producing respective magnetic fields, respective values of each parameter are represented as respective genes (total=12 genes). Each parameter combination is a respective species having a chromosome containing the 12 genes. From an initial group of species having random genes as initial values, a specified number of species having high evaluation values are selected. Species having recombined chromosomes are produced by crossing selected “parents,” and a specified number of “children” having higher evaluation values are selected for further matings. Repeated matings and weighting of offspring yield an individual having an optimal evaluation value.

Claims

1. A method, based on a genetic algorithm, for optimizing parameters of an optical system used in a charged-particle-beam (CPB) optical system, the method 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 N_A 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 N_B species (wherein N_B≦

N_A) 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 C_ND, in which each group includes N_C individuals, to produce a group D including N_D 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 C_ND;

(g) producing the group D of N_D species from the groups C_ND;

(h) from the group D, selecting a new group B including N_B 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.

2. The method of claim 1, wherein, in step (f), the group C_ND of individuals is selected in a manner such that species having higher respective values of the evaluation function have a higher probability of being selected.

3. The method of claim 2, wherein, for a given species, the respective probability is expressed as a ratio of the respective value of the evaluation function to a sum of respective values of the evaluation function among the species N_B of group B.

4. The method of claim 1, further comprising the step of substituting a specified number N_E (wherein N_E<

N_D) of species, having lower respective values of the evaluation function, in the group D with the specified number N_E of species, having higher respective values of the evaluation function, in the group B.

5. The method of claim 1, further comprising the step of forming a group (D+F) of species by adding a specified number N_F of species, having higher respective values of the evaluation function, in the group B to the species in group D, wherein, in step (h), the (D+F) group is substituted for the group A.

6. The method of claim 1, wherein, in step (f), the genes are recombined according to a weighted average of respective values, of the evaluation function, of the genes.

7. The method of claim 1, further comprising the step, after step (j), of executing a hill-climbing technique on the determined respective values of at least some of the parameters to obtain a combination of respective values of the parameters having an optimal respective value of the evaluation function.

8. The method of claim 1, wherein step (f) further comprises changing the genes in the respective chromosomes of at least some of the species N_D in group D by respective specified values randomly selected from a group of values within a specified range, or to respective values randomly selected from a group of values within a specified range.

9. The method of claim 8, wherein, in step (f), the group of species having respective chromosomes containing genes tat are recombined into chromosomes of species in group D is reduced, before the recombining of genes, by excluding species having higher respective values of the evaluation function.

10. The method of claim 1, further comprising the steps, between steps (i) and (j) of:

defining a second evaluation function, wherein values of the second evaluation function are related to respective qualities of a performance characteristic of the CPB optical system, and establishing a threshold value forte second evaluation function; and

repeating steps (e)-(h) a predetermined number of times or until a species is produced in group D having a respective value of the second evaluation function that exceeds the threshold for the second evaluation function.

11. The method of claim 10, further comprising the step, after the final step, of executing a hill-climbing technique on the determined respective values of at least some of the parameters to obtain a combination of respective values of the parameters having a maximal respective value of the evaluation function.

12. A charged-particle-beam (CPB) optical system, comprising multiple components of which respective parameters have respective values configured according to a method as recited in claim 1.

13. A charged-particle-beam (CPB) microlithography apparatus, comprising the CPB optical system of claim 12.

16. A microelectronic-device fabrication process, comprising the steps of:

(a) preparing a wafer;

(b) processing the wafer; and

(c) assembling devices formed on the wafer during steps (a) and (b), wherein step (b) comprises the steps of (i) applying a resist to the wafer;

(ii) exposing the resist and (iii) developing the resist; and

step (iii) comprises providing a CPB microlithography apparatus as recited in claim 13, and using the CPB microlithography apparatus to expose the resist with the pattern defined on the reticle.

14. A divided-reticle charged-particle-beam (CPB) projection-microlithography apparatus, comprising:

(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 2, relative to respective standard values listed in Table 1, wherein (i) the respective current ratios and field angles listed in Table 1 are as optimized for the CPB optical system by analysis, using a genetic algorithm, of evaluation functions H₂=1/(10<sup>−

5</sup>+α

_a), H₃=1/(1+d+b), and H₄=1/(10<sup>−

5</sup>+α

_r), in which α

_a is angle of incidence of the beam at the beam-shaping aperture, α

_r is angle of incidence of the beam at the reticle, d is distortion in μ

m at a subfield level, and b is beam blur in μ

m, (ii) the current ratios and magnetic field angles listed in Table 2 are respective percents of corresponding values listed in Table 1, (iii) axial positions are in mm units along a CPB-optical-system axis, and (iv) the axial position of the beam-shaping aperture is zero from which a charged particle beam propagates in a positive direction.

17. A microelectronic-device fabrication process, comprising the steps of:

(a) preparing a wafer;

(b) processing the wafer; and

(c) assembling devices formed on the wafer during steps (a) and (b), wherein step (b) comprises the steps of (i) applying a resist to the wafer;

(ii) exposing the resist and (iii) developing the resist; and

step (iii) comprises providing a CPB projection-microlithography apparatus as recited in claim 14, and using the CPB projection-microlithography apparatus to expose the resist with the pattern defined on the reticle.

15. A divided-reticle charged-particle-beam (CPB) projection-microlithography apparatus, comprising:

(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 4, relative to respective standard values listed in Table 3 wherein (i) the respective current ratios and field angles listed in Table 3 are as optimized for the CPB optical system by analysis, using a genetic algorithm, of evaluation functions H₂=1/(10<sup>−

5</sup>+α

_a), H₄=1/(10<sup>−

5</sup>+α

_r) and H₅=1/(1+|4.9−

d|+|0.9−

b|), in which a is angle of incidence of the beam at the beam-shaping aperture, α

_r is angle of incidence of the beam at the reticle, d is distortion in μ

m at a subfield level, and b is beam blur in μ

m, (ii) the current ratios and magnetic field angles listed in Table 4 are respective percents of corresponding values listed in Table 3, (iii) axial positions are in mm units along a CPB-optical-system axis, and (iv) the axial position of the beam-shaping aperture is zero from which a charged particle beam propagates in a positive direction.

18. A microelectronic-device fabrication process, comprising the steps of:

(a) preparing a wafer;

(b) processing the wafer; and

(c) assembling devices formed on the wafer during steps (a) and (b), wherein step (b) comprises the steps of (i) applying a resist to the wafer;

(ii) exposing the resist; and

(iii) developing the resist; and

step (iii) comprises providing a CPB projection-microlithography apparatus as recited in claim 15, and using the CPB projection-microlithography apparatus to expose the resist with the pattern defined on the reticle.