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  • Editor: Christian Seassal
  • Vol. 22, Iss. S4 — Jun. 30, 2014
  • pp: A1137–A1144
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Design of broadband omnidirectional antireflection coatings using ant colony algorithm

X. Guo, H. Y. Zhou, S. Guo, X. X. Luan, W. K. Cui, Y. F. Ma, and L. Shi  »View Author Affiliations


Optics Express, Vol. 22, Issue S4, pp. A1137-A1144 (2014)
http://dx.doi.org/10.1364/OE.22.0A1137


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Abstract

Optimization method which is based on the ant colony algorithm (ACA) is described to optimize antireflection (AR) coating system with broadband omnidirectional characteristics for silicon solar cells incorporated with the solar spectrum (AM1.5 radiation). It’s the first time to use ACA method for optimizing the AR coating system. In this paper, for the wavelength range from 400 nm to 1100 nm, the optimized three-layer AR coating system could provide an average reflectance of 2.98% for incident angles from R ave θ+ to 80° and 6.56% for incident angles from 0° to 90° .

© 2014 Optical Society of America

1. Introduction

With the increasing urgent demands in clean energy, solar cells have been gaining much attention in recent years. One of the key problems for solar cells is how to decrease the surface reflection due to the large refractive index discontinuity between the semiconductor and the air. On the basis of destructive interference between the incident and reflected light, the reflection loss of the antireflection (AR) coating system, which was applied on the crystalline silicon solar cells, can be achieved less than 5% for one specific wavelength under the normal incidence [1

1. T. Lohmüller, M. Helgert, M. Sundermann, R. Brunner, and J. P. Spatz, “Biomimetic interfaces for high-performance optics in the deep-UV light range,” Nano Lett. 8(5), 1429–1433 (2008). [CrossRef] [PubMed]

3

3. Y. Liu, S. H. Sun, J. Xu, L. Zhao, H. C. Sun, J. Li, W. W. Mu, L. Xu, and K. J. Chen, “Broadband antireflection and absorption enhancement by forming nano-patterned Si structures for solar cells,” Opt. Express 19(S5Suppl 5), A1051–A1056 (2011). [CrossRef] [PubMed]

]. Broadband AR coating system over a wide incident angle range are highly desirable for solar cells, which can increase light absorption in the active region up to a factor of 4n2 in a relative wide wavelength range, where n is the refractive index of the material [4

4. K. Choi, S. H. Park, Y. M. Song, Y. T. Lee, C. K. Hwangbo, H. Yang, and H. S. Lee, “Nano-tailoring the surface structure for the monolithic high-performance antireflection polymer film,” Adv. Mater. 22(33), 3713–3718 (2010). [CrossRef] [PubMed]

, 5

5. E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. 29(2), 300–305 (1982). [CrossRef]

].

By now, various approaches for broadband and omnidirectional AR coating system design have been reported. They include the use of multilayer porous films [6

6. M. L. Kuo, D. J. Poxson, Y. S. Kim, F. W. Mont, J. K. Kim, E. F. Schubert, and S. Y. Lin, “Realization of a near-perfect antireflection coating for silicon solar energy utilization,” Opt. Lett. 33(21), 2527–2529 (2008). [CrossRef] [PubMed]

], the biomimetic moth’s eye structure [7

7. Y. M. Song, S. J. Jang, J. S. Yu, and Y. T. Lee, “Bioinspired parabola subwavelength structures for improved broadband antireflection,” Small 6(9), 984–987 (2010). [CrossRef] [PubMed]

, 8

8. H. Park, D. Shin, G. Kang, S. Baek, K. Kim, and W. J. Padilla, “Broadband optical antireflection enhancement by integrating antireflective nanoislands with silicon nanoconical-frustum arrays,” Adv. Mater. 23(48), 5796–5800 (2011). [CrossRef] [PubMed]

], subwavelength surface Mie resonators [9

9. P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface mie resonators,” Nat Commun 3, 692 (2012). [CrossRef] [PubMed]

], and etc.. Recently, a step-graded graded-refractive-index (GRIN) AR coating system with a refractive index as low as 1.05 has been demonstrated which could eliminate Fresnel reflection [10

10. J. Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S. Y. Lin, W. Liu, and J. A. Smart, “Optical thin-film materials with low refractive index for broadband elimination of fresnel reflection,” Nat. Photonics 1, 176 (2007).

]. However, it is difficult to optimize the GRIN profiles, because the parameter space generally includes many local minima, which makes it unsuitable to find the local minima for deterministic optimization schemes. To meet this challenge, computational genetic algorithm (GA) [2

2. D. J. Poxson, M. F. Schubert, F. W. Mont, E. F. Schubert, and J. K. Kim, “Broadband omnidirectional antireflection coatings optimized by genetic algorithm,” Opt. Lett. 34(6), 728–730 (2009). [CrossRef] [PubMed]

, 11

11. M. F. Schubert, F. W. Mont, S. Chhajed, D. J. Poxson, J. K. Kim, and E. F. Schubert, “Design of multilayer antireflection coatings made from co-sputtered and low-refractive-index materials by genetic algorithm,” Opt. Express 16(8), 5290–5298 (2008). [CrossRef] [PubMed]

13

13. S. Martin, J. Rivory, and M. Schoenauer, “Synthesis of optical multilayer systems using genetic algorithms,” Appl. Opt. 34(13), 2247–2254 (1995). [CrossRef] [PubMed]

] and simulated annealing algorithm (SA) [14

14. Y. J. Chang and Y. T. Chen, “Broadband omnidirectional antireflection coatings for metal-backed solar cells optimized using simulated annealing algorithm incorporated with solar spectrum,” Opt. Express 19(S4Suppl 4), A875–A887 (2011). [CrossRef] [PubMed]

] methods have been applied in order to design optimized GRIN profiles for AR coating system.

The ant colony algorithm (ACA) is a heuristic optimization method, which was developed to solve traveling salesman problem (TSP) by Dorigo [15

15. M. Dorigo and L. M. Gambardella, “Ant colonies for the travelling salesman problem,” Biosystems 43(2), 73–81 (1997). [CrossRef] [PubMed]

, 16

16. M. Dorigo and L. M. Gambardella, “Ant colony system: a cooperative learning approach to the traveling salesman problem,” IEEE T Evolut. Comput. 1, 53 (1997).

]. The searching mechanism of ACA is based on the ants’ capability of finding the shortest path from a food source to their nest. The global optimum found by ACA is insensitive to the initial values which are often critical in conventional optimization algorithms. ACA has been proved to be a useful technique to solve optimization problems in feeder bus network design [17

17. S. N. Kuan, H. L. Ong, and K. M. Ng, “Solving the feeder bus network design problem by genetic algorithms and ant colony optimization,” Adv. Eng. Softw. 37(6), 351–359 (2006). [CrossRef]

].

In this paper, according to the demands for the broadband and omnidirectional AR coating system, the iterative method of ACA was applied to optimize the AR coating system for silicon-based solar cells, with the objective of minimizing the average reflectivity over the 400 nm to 1100 nm which can be absorbed by silicon [14

14. Y. J. Chang and Y. T. Chen, “Broadband omnidirectional antireflection coatings for metal-backed solar cells optimized using simulated annealing algorithm incorporated with solar spectrum,” Opt. Express 19(S4Suppl 4), A875–A887 (2011). [CrossRef] [PubMed]

] from 0° to 90° of all the incident angle ranges.

2. Optimization algorithm

Fig. 1 Schematic cross section of AR coating system on a silicon substrate for the reflectance calculation by ACA-based method.
Figure 1 depicts a multilayer structure used in this paper. Each layer in this structure is assumed to be homogeneous and is characterized by its thickness di with the refractive index ni, i = {1, 2, …, N}. A plane wave is incident from the semi-infinite air region with refractive index n0. For simplicity, the entire absorption layer is assumed by the bottom silicon substrate with the refractive index nSi.

Assuming the possible maximal thickness of each layer is dmax, and the refractive index range is [nmin, nmax], the refractive index of the ith layer can be calculated by [18

18. W. Wang, S. Guo, N. Chang, and W. Yang, “Optimum buckling design of composite stiffened panels using ant colony algorithm,” Compos. Struct. 92(3), 712–719 (2010). [CrossRef]

]:
ni=(nmaxnmin)j=1scij2j12s1+nmin,
(1)
in which the s-bit binary numberCi=ci1ci2cis, cijis 0 or 1, j = 1, 2, ..., s. Similarly, the thickness of the ith layer Di the m-bit binary number, can be written as:
Di=di1di2dim,
(2)
in which dij is 0 or 1, j = 1,2, ..., m. The thickness of the ith layer can be calculated by:
di=dmaxj=1mdij2m12m1.
(3)
Then the n-layer AR coating system can be expressed by a string of binary number:
L=C1D1C2D2CNDN.
(4)
As a result, we can use a (Ns + Nm)-bit binary number to describe a film structure as shown in Fig. 1. Assuming s = m = g, the film structure could be simplified to be 2Ng-bit binary number. Then, the L was reordered as follow:
L=c11d11c12d12...c1gd1gc21d21c22d22...cijdij...cNgdNg,
(5)
the value of cijdij which can be {00, 01, 10, 11}, was expressed by {A, B, C, D}.

The intensity of trail information, which was used to simulate the pheromone of ants, was denoted between city i in the dthcity-layer and city j in the (d+1)th layer as τ(d,i,j), where d = {1, 2, ..., Ng-1}, i = {1, 2, 3, 4}, j = {1, 2, 3, 4}. Since the prior trail information was not available, the intensity matrix of trail information was first initiated as a fixed number τ0. All the ants with the number of K were randomly placed in the cities in the first city-layer. For any ant in the city i of the dth city-layer, the probability to visit the city j in the (d+1)th city-layer can be written in a formula as follows [18

18. W. Wang, S. Guo, N. Chang, and W. Yang, “Optimum buckling design of composite stiffened panels using ant colony algorithm,” Compos. Struct. 92(3), 712–719 (2010). [CrossRef]

]:
j={argmax[τ(d,i,j)]ifqq0Potherwise,
(7)
where q was a random number within [0,1], q0 was an experienced parameter, and P was a random variable selected according to the following probability distribution [18

18. W. Wang, S. Guo, N. Chang, and W. Yang, “Optimum buckling design of composite stiffened panels using ant colony algorithm,” Compos. Struct. 92(3), 712–719 (2010). [CrossRef]

]:

P(d,i,j)=τ(d,i,j)jτ(d,i,j).
(8)

The pheromone trail now could be expressed by:
τ(i,j)=(1ρ)τ(i,j)+Δτ(i,j)+eΔτe(i,j),
(9)
where ρ was a random number within [0,1], e was the number of elite ants, and the updated amount of pheromone Δτ was

Δτ(i,j)=k=1KΔτk(i,j).
(10)

For the kth ant,
Δτk(i,j)={Q/Raveθif(i,j)tour0otherwise,
(11)
Δτe(i,j)={Q/Raveθ+if(i,j)theshortesttour0otherwise,
(12)
where Q was an experienced parameter, Raveθ stood for the traveled distance of the tour of each ant, while Raveθ+ was for the shortest traveled distance of all the tours. According to the local update principle, each ant updated the amount of pheromone on the visited path in its tour while the other pheromone was volatilized to disappear gradually. The updated amount of pheromone Δτ deposited on each visited path by one ant was inversely proportional to the traveled distance of its tour. According to the global update principle, the Δτe was enhanced amount of pheromone on the shortest path.

The calculation procedure using ACA can be described as following with its implementation of the AR coating system optimization, as illustrated in Fig. 3
Fig. 3 Flow chart for ACA-based broadband omnidirectional AR coating system optimization method.
.

The main six steps were:

  1. Setting up the parameters and initializing the pheromone trails,
  2. Putting the ants to the first city-layer,
  3. Each ant must go to the next city through a chosen path in available paths depending on the probability given in Eq. (7),
  4. Calculating the thickness and refractive index of the n-layer AR coating system by the traveled distance of all ant paths, and getting the value of Raveθ,
  5. According to the local and global update principles, updating the pheromone according to Eqs. (9)-(12), to calculate the shorter travelled distance of the tours for the smaller Raveθ,
  6. If the iteration cyclecounter reached the maximum value, stop the process, otherwise repeat steps 2-5. Raveθ+ was obtained when the iteration process finished.

3. Numerical results

Using the ACA method incorporated with the solar spectrum (AM1.5G radiation), AR coating system for bulk crystalline silicon solar cells with three layers was optimized while the spectral range was from 400 nm to 1100 nm and incident angle range was 0° to 90°. The detailed structure was shown in Table 4.

Table 4. Structure parameters and average reflectances of the three-layer AR coating system on silicon designed by ACA method for wavelength from 400 nm to 1100 nm

table-icon
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Fig. 5 Simulation results of the reflectance performance of optimized AR coating system designed by ACA method as a function of wavelength from 400nm to 1100nm and incident angle from 0°to 90°.
The calculated reflectance performance was shown in Fig. 5. It can be seen that the overall reflectance was less than 10% over the incident angle less than 80°. The reflectance increased when the incident angle was larger than 85°. In Fig. 5, there were three areas with the reflectance less than 1%, one of which located the peak of solar spectrum at 495 nm. The optimized average reflectance Raveθ+ was 6.56% for λ = [400, 1100] nm and θ = [0°, 90°], and 2.98% for λ = [400, 1100] nm and θ = [0°, 80°], as opposed to 3.40% for the same wavelength and incident angle ranges reported in [14

14. Y. J. Chang and Y. T. Chen, “Broadband omnidirectional antireflection coatings for metal-backed solar cells optimized using simulated annealing algorithm incorporated with solar spectrum,” Opt. Express 19(S4Suppl 4), A875–A887 (2011). [CrossRef] [PubMed]

] by using SA method.

4. Conclusion

In this paper, the ACA-based design method for broadband and omnidirectional AR coating system by optimizing the thickness and refractive index of each layer was theoretically demonstrated. The calculated reflectance performance showed that the ACA optimized AR coating system for silicon solar cells could in general minimize and flatten the angle-averaged reflectance over the spectral range from 400nm to 1100nm, which dominated the whole solar spectrum. The optimized three-layer AR coating system was shown to reduce the average reflectance to 6.56% over λ = [400, 1100] nm and θ = [0°, 90°], and 2.98% over λ = [400, 1100] nm and θ = [0°, 80°], respectively. The results obtained for this study showed that ACA-based optimization method was a very efficient design tool for the AR coating system design, which was applicable to other wavebands and material systems for solar cells or photodetectors.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 61222501 and 61335004).

References and links

1.

T. Lohmüller, M. Helgert, M. Sundermann, R. Brunner, and J. P. Spatz, “Biomimetic interfaces for high-performance optics in the deep-UV light range,” Nano Lett. 8(5), 1429–1433 (2008). [CrossRef] [PubMed]

2.

D. J. Poxson, M. F. Schubert, F. W. Mont, E. F. Schubert, and J. K. Kim, “Broadband omnidirectional antireflection coatings optimized by genetic algorithm,” Opt. Lett. 34(6), 728–730 (2009). [CrossRef] [PubMed]

3.

Y. Liu, S. H. Sun, J. Xu, L. Zhao, H. C. Sun, J. Li, W. W. Mu, L. Xu, and K. J. Chen, “Broadband antireflection and absorption enhancement by forming nano-patterned Si structures for solar cells,” Opt. Express 19(S5Suppl 5), A1051–A1056 (2011). [CrossRef] [PubMed]

4.

K. Choi, S. H. Park, Y. M. Song, Y. T. Lee, C. K. Hwangbo, H. Yang, and H. S. Lee, “Nano-tailoring the surface structure for the monolithic high-performance antireflection polymer film,” Adv. Mater. 22(33), 3713–3718 (2010). [CrossRef] [PubMed]

5.

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. 29(2), 300–305 (1982). [CrossRef]

6.

M. L. Kuo, D. J. Poxson, Y. S. Kim, F. W. Mont, J. K. Kim, E. F. Schubert, and S. Y. Lin, “Realization of a near-perfect antireflection coating for silicon solar energy utilization,” Opt. Lett. 33(21), 2527–2529 (2008). [CrossRef] [PubMed]

7.

Y. M. Song, S. J. Jang, J. S. Yu, and Y. T. Lee, “Bioinspired parabola subwavelength structures for improved broadband antireflection,” Small 6(9), 984–987 (2010). [CrossRef] [PubMed]

8.

H. Park, D. Shin, G. Kang, S. Baek, K. Kim, and W. J. Padilla, “Broadband optical antireflection enhancement by integrating antireflective nanoislands with silicon nanoconical-frustum arrays,” Adv. Mater. 23(48), 5796–5800 (2011). [CrossRef] [PubMed]

9.

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface mie resonators,” Nat Commun 3, 692 (2012). [CrossRef] [PubMed]

10.

J. Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S. Y. Lin, W. Liu, and J. A. Smart, “Optical thin-film materials with low refractive index for broadband elimination of fresnel reflection,” Nat. Photonics 1, 176 (2007).

11.

M. F. Schubert, F. W. Mont, S. Chhajed, D. J. Poxson, J. K. Kim, and E. F. Schubert, “Design of multilayer antireflection coatings made from co-sputtered and low-refractive-index materials by genetic algorithm,” Opt. Express 16(8), 5290–5298 (2008). [CrossRef] [PubMed]

12.

H. Greiner, “Robust optical coating design with evolutionary strategies,” Appl. Opt. 35(28), 5477–5483 (1996). [CrossRef] [PubMed]

13.

S. Martin, J. Rivory, and M. Schoenauer, “Synthesis of optical multilayer systems using genetic algorithms,” Appl. Opt. 34(13), 2247–2254 (1995). [CrossRef] [PubMed]

14.

Y. J. Chang and Y. T. Chen, “Broadband omnidirectional antireflection coatings for metal-backed solar cells optimized using simulated annealing algorithm incorporated with solar spectrum,” Opt. Express 19(S4Suppl 4), A875–A887 (2011). [CrossRef] [PubMed]

15.

M. Dorigo and L. M. Gambardella, “Ant colonies for the travelling salesman problem,” Biosystems 43(2), 73–81 (1997). [CrossRef] [PubMed]

16.

M. Dorigo and L. M. Gambardella, “Ant colony system: a cooperative learning approach to the traveling salesman problem,” IEEE T Evolut. Comput. 1, 53 (1997).

17.

S. N. Kuan, H. L. Ong, and K. M. Ng, “Solving the feeder bus network design problem by genetic algorithms and ant colony optimization,” Adv. Eng. Softw. 37(6), 351–359 (2006). [CrossRef]

18.

W. Wang, S. Guo, N. Chang, and W. Yang, “Optimum buckling design of composite stiffened panels using ant colony algorithm,” Compos. Struct. 92(3), 712–719 (2010). [CrossRef]

19.

H. A. Macleod, Thin-Film Optical Filters, (CRC, Bristol, 2001, Chap. 4).

20.

S. Chhajed, M. F. Schubert, J. K. Kim, and E. F. Schubert, “Nanostructured multilayer graded-index antireflection coating for Si solar cells with broadband and omnidirectional characteristics,” Appl. Phys. Lett. 93(25), 251108 (2008). [CrossRef]

21.

E. D. Palik, “Doped n-Type Silicon (n-Si),” in Handbook of Optical Constants of Solids, (Academic, 1998).

22.

H. B. Duan, The Theory and Application of Ant Colony Algorithm (Science, 2005), Chap. 4.

OCIS Codes
(310.0310) Thin films : Thin films
(310.1210) Thin films : Antireflection coatings
(350.6050) Other areas of optics : Solar energy

ToC Category:
Light Trapping for Photovoltaics

History
Original Manuscript: February 10, 2014
Revised Manuscript: May 22, 2014
Manuscript Accepted: May 23, 2014
Published: June 6, 2014

Citation
X. Guo, H. Y. Zhou, S. Guo, X. X. Luan, W. K. Cui, Y. F. Ma, and L. Shi, "Design of broadband omnidirectional antireflection coatings using ant colony algorithm," Opt. Express 22, A1137-A1144 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-S4-A1137


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References

  1. T. Lohmüller, M. Helgert, M. Sundermann, R. Brunner, and J. P. Spatz, “Biomimetic interfaces for high-performance optics in the deep-UV light range,” Nano Lett.8(5), 1429–1433 (2008). [CrossRef] [PubMed]
  2. D. J. Poxson, M. F. Schubert, F. W. Mont, E. F. Schubert, and J. K. Kim, “Broadband omnidirectional antireflection coatings optimized by genetic algorithm,” Opt. Lett.34(6), 728–730 (2009). [CrossRef] [PubMed]
  3. Y. Liu, S. H. Sun, J. Xu, L. Zhao, H. C. Sun, J. Li, W. W. Mu, L. Xu, and K. J. Chen, “Broadband antireflection and absorption enhancement by forming nano-patterned Si structures for solar cells,” Opt. Express19(S5Suppl 5), A1051–A1056 (2011). [CrossRef] [PubMed]
  4. K. Choi, S. H. Park, Y. M. Song, Y. T. Lee, C. K. Hwangbo, H. Yang, and H. S. Lee, “Nano-tailoring the surface structure for the monolithic high-performance antireflection polymer film,” Adv. Mater.22(33), 3713–3718 (2010). [CrossRef] [PubMed]
  5. E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev.29(2), 300–305 (1982). [CrossRef]
  6. M. L. Kuo, D. J. Poxson, Y. S. Kim, F. W. Mont, J. K. Kim, E. F. Schubert, and S. Y. Lin, “Realization of a near-perfect antireflection coating for silicon solar energy utilization,” Opt. Lett.33(21), 2527–2529 (2008). [CrossRef] [PubMed]
  7. Y. M. Song, S. J. Jang, J. S. Yu, and Y. T. Lee, “Bioinspired parabola subwavelength structures for improved broadband antireflection,” Small6(9), 984–987 (2010). [CrossRef] [PubMed]
  8. H. Park, D. Shin, G. Kang, S. Baek, K. Kim, and W. J. Padilla, “Broadband optical antireflection enhancement by integrating antireflective nanoislands with silicon nanoconical-frustum arrays,” Adv. Mater.23(48), 5796–5800 (2011). [CrossRef] [PubMed]
  9. P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface mie resonators,” Nat Commun3, 692 (2012). [CrossRef] [PubMed]
  10. J. Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S. Y. Lin, W. Liu, and J. A. Smart, “Optical thin-film materials with low refractive index for broadband elimination of fresnel reflection,” Nat. Photonics1, 176 (2007).
  11. M. F. Schubert, F. W. Mont, S. Chhajed, D. J. Poxson, J. K. Kim, and E. F. Schubert, “Design of multilayer antireflection coatings made from co-sputtered and low-refractive-index materials by genetic algorithm,” Opt. Express16(8), 5290–5298 (2008). [CrossRef] [PubMed]
  12. H. Greiner, “Robust optical coating design with evolutionary strategies,” Appl. Opt.35(28), 5477–5483 (1996). [CrossRef] [PubMed]
  13. S. Martin, J. Rivory, and M. Schoenauer, “Synthesis of optical multilayer systems using genetic algorithms,” Appl. Opt.34(13), 2247–2254 (1995). [CrossRef] [PubMed]
  14. Y. J. Chang and Y. T. Chen, “Broadband omnidirectional antireflection coatings for metal-backed solar cells optimized using simulated annealing algorithm incorporated with solar spectrum,” Opt. Express19(S4Suppl 4), A875–A887 (2011). [CrossRef] [PubMed]
  15. M. Dorigo and L. M. Gambardella, “Ant colonies for the travelling salesman problem,” Biosystems43(2), 73–81 (1997). [CrossRef] [PubMed]
  16. M. Dorigo and L. M. Gambardella, “Ant colony system: a cooperative learning approach to the traveling salesman problem,” IEEE T Evolut. Comput.1, 53 (1997).
  17. S. N. Kuan, H. L. Ong, and K. M. Ng, “Solving the feeder bus network design problem by genetic algorithms and ant colony optimization,” Adv. Eng. Softw.37(6), 351–359 (2006). [CrossRef]
  18. W. Wang, S. Guo, N. Chang, and W. Yang, “Optimum buckling design of composite stiffened panels using ant colony algorithm,” Compos. Struct.92(3), 712–719 (2010). [CrossRef]
  19. H. A. Macleod, Thin-Film Optical Filters, (CRC, Bristol, 2001, Chap. 4).
  20. S. Chhajed, M. F. Schubert, J. K. Kim, and E. F. Schubert, “Nanostructured multilayer graded-index antireflection coating for Si solar cells with broadband and omnidirectional characteristics,” Appl. Phys. Lett.93(25), 251108 (2008). [CrossRef]
  21. E. D. Palik, “Doped n-Type Silicon (n-Si),” in Handbook of Optical Constants of Solids, (Academic, 1998).
  22. H. B. Duan, The Theory and Application of Ant Colony Algorithm (Science, 2005), Chap. 4.

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