Abstract

We investigate the accuracy of rigorous coupled-wave analysis (RCWA) for near-field computations within cylindrical GaAs nanowire solar cells and discover excellent accuracy with low computational cost at long incident wavelengths but poor accuracy at short incident wavelengths. These near fields give the carrier generation rate, and their accurate determination is essential for device modeling. We implement two techniques for increasing the accuracy of the near fields generated by RCWA and give some guidance on parameters required for convergence along with an estimate of their associated computation times. The first improvement removes Gibbs phenomenon artifacts from the RCWA fields, and the second uses the extremely well-converged far-field absorption to rescale the local fields. These improvements allow a computational speedup between 30 and 1000 times for spectrally integrated calculations, depending on the density of the near fields desired. Some spectrally resolved quantities, especially at short wavelengths, remain expensive, but RCWA is still an excellent method for performing those calculations. These improvements open up the possibility of using RCWA for low-cost optical modeling in a full optoelectronic device model of nanowire solar cells.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

M. T. Borgström, M. H. Magnusson, F. Dimroth, G. Siefer, O. Höhn, H. Riel, H. Schmid, S. Wirths, M. Björk, I. Åberg, W. Peijnenburg, M. Vijver, M. Tchernycheva, V. Piazza, and L. Samuelson, “Towards nanowire tandem junction solar cells on silicon,” IEEE Journal of Photovoltaics 8, 733–740 (2018).

2017 (1)

D. Wu, X. Tang, K. Wang, and X. Li, “An analytic approach for optimal geometrical design of GaAs nanowires for maximal light harvesting in photovoltaic cells,” Scientific Reports 7, 46504 (2017).
[Crossref] [PubMed]

2016 (3)

O. M. Ghahfarokhi, N. Anttu, L. Samuelson, and I. Åberg, “Performance of GaAs nanowire array solar cells for varying incidence angles,” IEEE Journal of Photovoltaics 6, 1502–1508 (2016).
[Crossref]

A. H. Trojnar, C. E. Valdivia, R. R. LaPierre, K. Hinzer, and J. J. Krich, “Optimizations of GaAs nanowire solar cells,” IEEE Journal of Photovoltaics 6, 1494–1501 (2016).
[Crossref]

C. Epstein and M. O’Neil, “Smoothed corners and scattered waves,” SIAM J. Sci. Comput. 38, A2665–A2698 (2016).
[Crossref]

2015 (2)

M. Weismann, D. F. Gallagher, and N. C. Panoiu, “Accurate near-field calculation in the rigorous coupled-wave analysis method,” Journal of Optics 17, 125612 (2015).
[Crossref]

K. M. Azizur-Rahman and R. R. LaPierre, “Wavelength-selective absorptance in GaAs, InP and InAs nanowire arrays,” Nanotechnology 26, 295202 (2015).
[Crossref] [PubMed]

2014 (2)

K. T. Fountaine, W. S. Whitney, and H. A. Atwater, “Resonant absorption in semiconductor nanowires and nanowire arrays: Relating leaky waveguide modes to bloch photonic crystal modes,” Journal of Applied Physics 116, 153106 (2014).
[Crossref]

B. C. P. Sturmberg, K. B. Dossou, L. C. Botten, A. A. Asatryan, C. G. Poulton, R. C. McPhedran, and C. M. de Sterke, “Optimizing photovoltaic charge generation of nanowire arrays: A simple semi-analytic approach,” ACS Photonics 1, 683–689 (2014).
[Crossref]

2013 (1)

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Aberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, and M. T. Borgström, “InP nanowire array solar cells achieving 13.8% efficiency by exceeding the ray optics limit,” Science 339, 1057–1060 (2013).
[Crossref]

2012 (3)

Y. Hu, R. R. LaPierre, M. Li, K. Chen, and J.-J. He, “Optical characteristics of GaAs nanowire solar cells,” Journal of Applied Physics 112, 104311 (2012).
[Crossref]

E. A. Bezus and L. L. Doskolovich, “Stable algorithm for the computation of the electromagnetic field distribution of eigenmodes of periodic diffraction structures,” Journal of the Optical Society of America A 29, 2307–2313 (2012).
[Crossref]

V. Liu and S. Fan, “S4: A free electromagnetic solver for layered periodic structures,” Computer Physics Communications 183, 2233–2244 (2012).
[Crossref]

2011 (2)

R. C. Rumpf, “Improved formulation of scattering matrices for semi-analytical methods that is consistent with convention,” Progress In Electromagnetics Research B 35, 241–261 (2011).
[Crossref]

Q. G. Du, C. H. Kam, H. V. Demir, H. Y. Yu, and X. W. Sun, “Broadband absorption enhancement in randomly positioned silicon nanowire arrays for solar cell applications,” Optics Letters 36, 1884–1886 (2011).
[Crossref]

2010 (3)

K. H. Brenner, “Aspects for calculating local absorption with the rigorous coupled-wave method,” Optics Express 18, 10369–10376 (2010).
[Crossref]

K. L. Kavanagh, “Misfit dislocations in nanowire heterostructures,” Semiconductor Science and Technology 25, 024006 (2010).
[Crossref]

J. Kupec, R. L. Stoop, and B. Witzigmann, “Light absorption and emission in nanowire array solar cells,” Optics Express 18, 27589–27605 (2010).
[Crossref]

2008 (1)

P. Götz, T. Schuster, K. Frenner, S. Rafler, and W. Osten, “Normal vector method for the RCWA with automated vector field generation,” Optics express 16, 17295–17301 (2008).
[Crossref] [PubMed]

2007 (1)

H. Kim, I. Lee, and B. Lee, “Extended scattering-matrix method for efficient full parallel implementation of rigorous coupled-wave analysis,” Journal of the Optical Society of America A 24, 2313 (2007).
[Crossref]

2006 (1)

2000 (1)

M. Costabel and M. Dauge, “Singularities of electromagnetic fields in polyhedral domains,” Archive for Rational Mechanics and Analysis 151, 221–276 (2000).
[Crossref]

1999 (1)

D. M. Whittaker and I. S. Culshaw, “Scattering-matrix treatment of patterned multilayer photonic structures,” Physical Review B 60, 2610–2618 (1999).
[Crossref]

1998 (1)

P. Lalanne and M. P. Jurek, “Computation of the near-field pattern with the coupled-wave method for transverse magnetic polarization,” Journal of Modern Optics 45, 1357–1374 (1998).
[Crossref]

1996 (2)

L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” Journal of the Optical Society of America A 13, 1870–1876 (1996).
[Crossref]

L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” Journal of the Optical Society of America A 13, 1024 (1996).
[Crossref]

1995 (1)

M. G. Moharam, T. K. Gaylord, E. B. Grann, and D. A. Pommet, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” Journal of the Optical Society of America A 12, 1068–1076 (1995).
[Crossref]

Aberg, I.

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Aberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, and M. T. Borgström, “InP nanowire array solar cells achieving 13.8% efficiency by exceeding the ray optics limit,” Science 339, 1057–1060 (2013).
[Crossref]

Åberg, I.

M. T. Borgström, M. H. Magnusson, F. Dimroth, G. Siefer, O. Höhn, H. Riel, H. Schmid, S. Wirths, M. Björk, I. Åberg, W. Peijnenburg, M. Vijver, M. Tchernycheva, V. Piazza, and L. Samuelson, “Towards nanowire tandem junction solar cells on silicon,” IEEE Journal of Photovoltaics 8, 733–740 (2018).

O. M. Ghahfarokhi, N. Anttu, L. Samuelson, and I. Åberg, “Performance of GaAs nanowire array solar cells for varying incidence angles,” IEEE Journal of Photovoltaics 6, 1502–1508 (2016).
[Crossref]

Adachi, S.

S. Adachi, Optical Constants of Crystalline and Amorphous Semiconductors: Numerical Data and Graphical Information(SpringerUS, 1999), 1st ed.

Anttu, N.

O. M. Ghahfarokhi, N. Anttu, L. Samuelson, and I. Åberg, “Performance of GaAs nanowire array solar cells for varying incidence angles,” IEEE Journal of Photovoltaics 6, 1502–1508 (2016).
[Crossref]

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Aberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, and M. T. Borgström, “InP nanowire array solar cells achieving 13.8% efficiency by exceeding the ray optics limit,” Science 339, 1057–1060 (2013).
[Crossref]

Asatryan, A. A.

B. C. P. Sturmberg, K. B. Dossou, L. C. Botten, A. A. Asatryan, C. G. Poulton, R. C. McPhedran, and C. M. de Sterke, “Optimizing photovoltaic charge generation of nanowire arrays: A simple semi-analytic approach,” ACS Photonics 1, 683–689 (2014).
[Crossref]

Asoli, D.

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Aberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, and M. T. Borgström, “InP nanowire array solar cells achieving 13.8% efficiency by exceeding the ray optics limit,” Science 339, 1057–1060 (2013).
[Crossref]

Atwater, H. A.

K. T. Fountaine, W. S. Whitney, and H. A. Atwater, “Resonant absorption in semiconductor nanowires and nanowire arrays: Relating leaky waveguide modes to bloch photonic crystal modes,” Journal of Applied Physics 116, 153106 (2014).
[Crossref]

Azizur-Rahman, K. M.

K. M. Azizur-Rahman and R. R. LaPierre, “Wavelength-selective absorptance in GaAs, InP and InAs nanowire arrays,” Nanotechnology 26, 295202 (2015).
[Crossref] [PubMed]

Bermel, P.

Bezus, E. A.

E. A. Bezus and L. L. Doskolovich, “Stable algorithm for the computation of the electromagnetic field distribution of eigenmodes of periodic diffraction structures,” Journal of the Optical Society of America A 29, 2307–2313 (2012).
[Crossref]

Björk, M.

M. T. Borgström, M. H. Magnusson, F. Dimroth, G. Siefer, O. Höhn, H. Riel, H. Schmid, S. Wirths, M. Björk, I. Åberg, W. Peijnenburg, M. Vijver, M. Tchernycheva, V. Piazza, and L. Samuelson, “Towards nanowire tandem junction solar cells on silicon,” IEEE Journal of Photovoltaics 8, 733–740 (2018).

Borgström, M. T.

M. T. Borgström, M. H. Magnusson, F. Dimroth, G. Siefer, O. Höhn, H. Riel, H. Schmid, S. Wirths, M. Björk, I. Åberg, W. Peijnenburg, M. Vijver, M. Tchernycheva, V. Piazza, and L. Samuelson, “Towards nanowire tandem junction solar cells on silicon,” IEEE Journal of Photovoltaics 8, 733–740 (2018).

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Aberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, and M. T. Borgström, “InP nanowire array solar cells achieving 13.8% efficiency by exceeding the ray optics limit,” Science 339, 1057–1060 (2013).
[Crossref]

Botten, L. C.

B. C. P. Sturmberg, K. B. Dossou, L. C. Botten, A. A. Asatryan, C. G. Poulton, R. C. McPhedran, and C. M. de Sterke, “Optimizing photovoltaic charge generation of nanowire arrays: A simple semi-analytic approach,” ACS Photonics 1, 683–689 (2014).
[Crossref]

Brenner, K. H.

K. H. Brenner, “Aspects for calculating local absorption with the rigorous coupled-wave method,” Optics Express 18, 10369–10376 (2010).
[Crossref]

Burr, G. W.

Chen, K.

Y. Hu, R. R. LaPierre, M. Li, K. Chen, and J.-J. He, “Optical characteristics of GaAs nanowire solar cells,” Journal of Applied Physics 112, 104311 (2012).
[Crossref]

Costabel, M.

M. Costabel and M. Dauge, “Singularities of electromagnetic fields in polyhedral domains,” Archive for Rational Mechanics and Analysis 151, 221–276 (2000).
[Crossref]

Culshaw, I. S.

D. M. Whittaker and I. S. Culshaw, “Scattering-matrix treatment of patterned multilayer photonic structures,” Physical Review B 60, 2610–2618 (1999).
[Crossref]

Dauge, M.

M. Costabel and M. Dauge, “Singularities of electromagnetic fields in polyhedral domains,” Archive for Rational Mechanics and Analysis 151, 221–276 (2000).
[Crossref]

de Sterke, C. M.

B. C. P. Sturmberg, K. B. Dossou, L. C. Botten, A. A. Asatryan, C. G. Poulton, R. C. McPhedran, and C. M. de Sterke, “Optimizing photovoltaic charge generation of nanowire arrays: A simple semi-analytic approach,” ACS Photonics 1, 683–689 (2014).
[Crossref]

Demir, H. V.

Q. G. Du, C. H. Kam, H. V. Demir, H. Y. Yu, and X. W. Sun, “Broadband absorption enhancement in randomly positioned silicon nanowire arrays for solar cell applications,” Optics Letters 36, 1884–1886 (2011).
[Crossref]

Deppert, K.

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Aberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, and M. T. Borgström, “InP nanowire array solar cells achieving 13.8% efficiency by exceeding the ray optics limit,” Science 339, 1057–1060 (2013).
[Crossref]

Dimroth, F.

M. T. Borgström, M. H. Magnusson, F. Dimroth, G. Siefer, O. Höhn, H. Riel, H. Schmid, S. Wirths, M. Björk, I. Åberg, W. Peijnenburg, M. Vijver, M. Tchernycheva, V. Piazza, and L. Samuelson, “Towards nanowire tandem junction solar cells on silicon,” IEEE Journal of Photovoltaics 8, 733–740 (2018).

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Aberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, and M. T. Borgström, “InP nanowire array solar cells achieving 13.8% efficiency by exceeding the ray optics limit,” Science 339, 1057–1060 (2013).
[Crossref]

Doskolovich, L. L.

E. A. Bezus and L. L. Doskolovich, “Stable algorithm for the computation of the electromagnetic field distribution of eigenmodes of periodic diffraction structures,” Journal of the Optical Society of America A 29, 2307–2313 (2012).
[Crossref]

Dossou, K. B.

B. C. P. Sturmberg, K. B. Dossou, L. C. Botten, A. A. Asatryan, C. G. Poulton, R. C. McPhedran, and C. M. de Sterke, “Optimizing photovoltaic charge generation of nanowire arrays: A simple semi-analytic approach,” ACS Photonics 1, 683–689 (2014).
[Crossref]

Du, Q. G.

Q. G. Du, C. H. Kam, H. V. Demir, H. Y. Yu, and X. W. Sun, “Broadband absorption enhancement in randomly positioned silicon nanowire arrays for solar cell applications,” Optics Letters 36, 1884–1886 (2011).
[Crossref]

Epstein, C.

C. Epstein and M. O’Neil, “Smoothed corners and scattered waves,” SIAM J. Sci. Comput. 38, A2665–A2698 (2016).
[Crossref]

Fan, S.

V. Liu and S. Fan, “S4: A free electromagnetic solver for layered periodic structures,” Computer Physics Communications 183, 2233–2244 (2012).
[Crossref]

Farjadpour, A.

Fountaine, K. T.

K. T. Fountaine, W. S. Whitney, and H. A. Atwater, “Resonant absorption in semiconductor nanowires and nanowire arrays: Relating leaky waveguide modes to bloch photonic crystal modes,” Journal of Applied Physics 116, 153106 (2014).
[Crossref]

Frenner, K.

P. Götz, T. Schuster, K. Frenner, S. Rafler, and W. Osten, “Normal vector method for the RCWA with automated vector field generation,” Optics express 16, 17295–17301 (2008).
[Crossref] [PubMed]

Fuss-Kailuweit, P.

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Aberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, and M. T. Borgström, “InP nanowire array solar cells achieving 13.8% efficiency by exceeding the ray optics limit,” Science 339, 1057–1060 (2013).
[Crossref]

Gallagher, D. F.

M. Weismann, D. F. Gallagher, and N. C. Panoiu, “Accurate near-field calculation in the rigorous coupled-wave analysis method,” Journal of Optics 17, 125612 (2015).
[Crossref]

Gaylord, T. K.

M. G. Moharam, T. K. Gaylord, E. B. Grann, and D. A. Pommet, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” Journal of the Optical Society of America A 12, 1068–1076 (1995).
[Crossref]

Ghahfarokhi, O. M.

O. M. Ghahfarokhi, N. Anttu, L. Samuelson, and I. Åberg, “Performance of GaAs nanowire array solar cells for varying incidence angles,” IEEE Journal of Photovoltaics 6, 1502–1508 (2016).
[Crossref]

Götz, P.

P. Götz, T. Schuster, K. Frenner, S. Rafler, and W. Osten, “Normal vector method for the RCWA with automated vector field generation,” Optics express 16, 17295–17301 (2008).
[Crossref] [PubMed]

Grann, E. B.

M. G. Moharam, T. K. Gaylord, E. B. Grann, and D. A. Pommet, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” Journal of the Optical Society of America A 12, 1068–1076 (1995).
[Crossref]

Greenwell, A. B.

M. G. Moharam and A. B. Greenwell, “Rigorous analysis of field distribution and power flow in grating coupler of finite length,” in Diffractive Optics and Micro-Optics, (Optical Society of America, 2004), p. DMC5.
[Crossref]

He, J.-J.

Y. Hu, R. R. LaPierre, M. Li, K. Chen, and J.-J. He, “Optical characteristics of GaAs nanowire solar cells,” Journal of Applied Physics 112, 104311 (2012).
[Crossref]

Heinrich, W.

N. Huynh and W. Heinrich, “FDTD accuracy improvement by incorporation of 3D edge singularities,” in 1999 IEEE MTT-S International Microwave Symposium Digest (Cat. No.99CH36282) (IEEE, 1999), pp. 1573–1576.
[Crossref]

Hinzer, K.

A. H. Trojnar, C. E. Valdivia, R. R. LaPierre, K. Hinzer, and J. J. Krich, “Optimizations of GaAs nanowire solar cells,” IEEE Journal of Photovoltaics 6, 1494–1501 (2016).
[Crossref]

Höhn, O.

M. T. Borgström, M. H. Magnusson, F. Dimroth, G. Siefer, O. Höhn, H. Riel, H. Schmid, S. Wirths, M. Björk, I. Åberg, W. Peijnenburg, M. Vijver, M. Tchernycheva, V. Piazza, and L. Samuelson, “Towards nanowire tandem junction solar cells on silicon,” IEEE Journal of Photovoltaics 8, 733–740 (2018).

Hu, Y.

Y. Hu, R. R. LaPierre, M. Li, K. Chen, and J.-J. He, “Optical characteristics of GaAs nanowire solar cells,” Journal of Applied Physics 112, 104311 (2012).
[Crossref]

Huffman, M.

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Aberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, and M. T. Borgström, “InP nanowire array solar cells achieving 13.8% efficiency by exceeding the ray optics limit,” Science 339, 1057–1060 (2013).
[Crossref]

Huynh, N.

N. Huynh and W. Heinrich, “FDTD accuracy improvement by incorporation of 3D edge singularities,” in 1999 IEEE MTT-S International Microwave Symposium Digest (Cat. No.99CH36282) (IEEE, 1999), pp. 1573–1576.
[Crossref]

Ibanescu, M.

Joannopoulos, J. D.

Johnson, S. G.

Jurek, M. P.

P. Lalanne and M. P. Jurek, “Computation of the near-field pattern with the coupled-wave method for transverse magnetic polarization,” Journal of Modern Optics 45, 1357–1374 (1998).
[Crossref]

Kam, C. H.

Q. G. Du, C. H. Kam, H. V. Demir, H. Y. Yu, and X. W. Sun, “Broadband absorption enhancement in randomly positioned silicon nanowire arrays for solar cell applications,” Optics Letters 36, 1884–1886 (2011).
[Crossref]

Kavanagh, K. L.

K. L. Kavanagh, “Misfit dislocations in nanowire heterostructures,” Semiconductor Science and Technology 25, 024006 (2010).
[Crossref]

Kim, H.

H. Kim, I. Lee, and B. Lee, “Extended scattering-matrix method for efficient full parallel implementation of rigorous coupled-wave analysis,” Journal of the Optical Society of America A 24, 2313 (2007).
[Crossref]

Krich, J. J.

A. H. Trojnar, C. E. Valdivia, R. R. LaPierre, K. Hinzer, and J. J. Krich, “Optimizations of GaAs nanowire solar cells,” IEEE Journal of Photovoltaics 6, 1494–1501 (2016).
[Crossref]

K. W. Robertson, R. R. LaPierre, and J. J. Krich, “Optical optimization of passivated GaAs nanowire solar cells,” in 2017 IEEE 44th Photovoltaic Specialist Conference (IEEE, 2017), pp. 1294–1298.

Kupec, J.

J. Kupec, R. L. Stoop, and B. Witzigmann, “Light absorption and emission in nanowire array solar cells,” Optics Express 18, 27589–27605 (2010).
[Crossref]

Lalanne, P.

P. Lalanne and M. P. Jurek, “Computation of the near-field pattern with the coupled-wave method for transverse magnetic polarization,” Journal of Modern Optics 45, 1357–1374 (1998).
[Crossref]

LaPierre, R. R.

A. H. Trojnar, C. E. Valdivia, R. R. LaPierre, K. Hinzer, and J. J. Krich, “Optimizations of GaAs nanowire solar cells,” IEEE Journal of Photovoltaics 6, 1494–1501 (2016).
[Crossref]

K. M. Azizur-Rahman and R. R. LaPierre, “Wavelength-selective absorptance in GaAs, InP and InAs nanowire arrays,” Nanotechnology 26, 295202 (2015).
[Crossref] [PubMed]

Y. Hu, R. R. LaPierre, M. Li, K. Chen, and J.-J. He, “Optical characteristics of GaAs nanowire solar cells,” Journal of Applied Physics 112, 104311 (2012).
[Crossref]

K. W. Robertson, R. R. LaPierre, and J. J. Krich, “Optical optimization of passivated GaAs nanowire solar cells,” in 2017 IEEE 44th Photovoltaic Specialist Conference (IEEE, 2017), pp. 1294–1298.

Lee, B.

H. Kim, I. Lee, and B. Lee, “Extended scattering-matrix method for efficient full parallel implementation of rigorous coupled-wave analysis,” Journal of the Optical Society of America A 24, 2313 (2007).
[Crossref]

Lee, I.

H. Kim, I. Lee, and B. Lee, “Extended scattering-matrix method for efficient full parallel implementation of rigorous coupled-wave analysis,” Journal of the Optical Society of America A 24, 2313 (2007).
[Crossref]

Li, L.

L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” Journal of the Optical Society of America A 13, 1024 (1996).
[Crossref]

L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” Journal of the Optical Society of America A 13, 1870–1876 (1996).
[Crossref]

Li, M.

Y. Hu, R. R. LaPierre, M. Li, K. Chen, and J.-J. He, “Optical characteristics of GaAs nanowire solar cells,” Journal of Applied Physics 112, 104311 (2012).
[Crossref]

Li, X.

D. Wu, X. Tang, K. Wang, and X. Li, “An analytic approach for optimal geometrical design of GaAs nanowires for maximal light harvesting in photovoltaic cells,” Scientific Reports 7, 46504 (2017).
[Crossref] [PubMed]

Liu, V.

V. Liu and S. Fan, “S4: A free electromagnetic solver for layered periodic structures,” Computer Physics Communications 183, 2233–2244 (2012).
[Crossref]

Magnusson, M. H.

M. T. Borgström, M. H. Magnusson, F. Dimroth, G. Siefer, O. Höhn, H. Riel, H. Schmid, S. Wirths, M. Björk, I. Åberg, W. Peijnenburg, M. Vijver, M. Tchernycheva, V. Piazza, and L. Samuelson, “Towards nanowire tandem junction solar cells on silicon,” IEEE Journal of Photovoltaics 8, 733–740 (2018).

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Aberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, and M. T. Borgström, “InP nanowire array solar cells achieving 13.8% efficiency by exceeding the ray optics limit,” Science 339, 1057–1060 (2013).
[Crossref]

McPhedran, R. C.

B. C. P. Sturmberg, K. B. Dossou, L. C. Botten, A. A. Asatryan, C. G. Poulton, R. C. McPhedran, and C. M. de Sterke, “Optimizing photovoltaic charge generation of nanowire arrays: A simple semi-analytic approach,” ACS Photonics 1, 683–689 (2014).
[Crossref]

Moharam, M. G.

M. G. Moharam, T. K. Gaylord, E. B. Grann, and D. A. Pommet, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” Journal of the Optical Society of America A 12, 1068–1076 (1995).
[Crossref]

M. G. Moharam and A. B. Greenwell, “Rigorous analysis of field distribution and power flow in grating coupler of finite length,” in Diffractive Optics and Micro-Optics, (Optical Society of America, 2004), p. DMC5.
[Crossref]

O’Neil, M.

C. Epstein and M. O’Neil, “Smoothed corners and scattered waves,” SIAM J. Sci. Comput. 38, A2665–A2698 (2016).
[Crossref]

Osten, W.

P. Götz, T. Schuster, K. Frenner, S. Rafler, and W. Osten, “Normal vector method for the RCWA with automated vector field generation,” Optics express 16, 17295–17301 (2008).
[Crossref] [PubMed]

Panoiu, N. C.

M. Weismann, D. F. Gallagher, and N. C. Panoiu, “Accurate near-field calculation in the rigorous coupled-wave analysis method,” Journal of Optics 17, 125612 (2015).
[Crossref]

Peijnenburg, W.

M. T. Borgström, M. H. Magnusson, F. Dimroth, G. Siefer, O. Höhn, H. Riel, H. Schmid, S. Wirths, M. Björk, I. Åberg, W. Peijnenburg, M. Vijver, M. Tchernycheva, V. Piazza, and L. Samuelson, “Towards nanowire tandem junction solar cells on silicon,” IEEE Journal of Photovoltaics 8, 733–740 (2018).

Piazza, V.

M. T. Borgström, M. H. Magnusson, F. Dimroth, G. Siefer, O. Höhn, H. Riel, H. Schmid, S. Wirths, M. Björk, I. Åberg, W. Peijnenburg, M. Vijver, M. Tchernycheva, V. Piazza, and L. Samuelson, “Towards nanowire tandem junction solar cells on silicon,” IEEE Journal of Photovoltaics 8, 733–740 (2018).

Pommet, D. A.

M. G. Moharam, T. K. Gaylord, E. B. Grann, and D. A. Pommet, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” Journal of the Optical Society of America A 12, 1068–1076 (1995).
[Crossref]

Poulton, C. G.

B. C. P. Sturmberg, K. B. Dossou, L. C. Botten, A. A. Asatryan, C. G. Poulton, R. C. McPhedran, and C. M. de Sterke, “Optimizing photovoltaic charge generation of nanowire arrays: A simple semi-analytic approach,” ACS Photonics 1, 683–689 (2014).
[Crossref]

Rafler, S.

P. Götz, T. Schuster, K. Frenner, S. Rafler, and W. Osten, “Normal vector method for the RCWA with automated vector field generation,” Optics express 16, 17295–17301 (2008).
[Crossref] [PubMed]

Riel, H.

M. T. Borgström, M. H. Magnusson, F. Dimroth, G. Siefer, O. Höhn, H. Riel, H. Schmid, S. Wirths, M. Björk, I. Åberg, W. Peijnenburg, M. Vijver, M. Tchernycheva, V. Piazza, and L. Samuelson, “Towards nanowire tandem junction solar cells on silicon,” IEEE Journal of Photovoltaics 8, 733–740 (2018).

Robertson, K. W.

K. W. Robertson, R. R. LaPierre, and J. J. Krich, “Optical optimization of passivated GaAs nanowire solar cells,” in 2017 IEEE 44th Photovoltaic Specialist Conference (IEEE, 2017), pp. 1294–1298.

Rodriguez, A.

Roundy, D.

Rumpf, R. C.

R. C. Rumpf, “Improved formulation of scattering matrices for semi-analytical methods that is consistent with convention,” Progress In Electromagnetics Research B 35, 241–261 (2011).
[Crossref]

Samuelson, L.

M. T. Borgström, M. H. Magnusson, F. Dimroth, G. Siefer, O. Höhn, H. Riel, H. Schmid, S. Wirths, M. Björk, I. Åberg, W. Peijnenburg, M. Vijver, M. Tchernycheva, V. Piazza, and L. Samuelson, “Towards nanowire tandem junction solar cells on silicon,” IEEE Journal of Photovoltaics 8, 733–740 (2018).

O. M. Ghahfarokhi, N. Anttu, L. Samuelson, and I. Åberg, “Performance of GaAs nanowire array solar cells for varying incidence angles,” IEEE Journal of Photovoltaics 6, 1502–1508 (2016).
[Crossref]

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Aberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, and M. T. Borgström, “InP nanowire array solar cells achieving 13.8% efficiency by exceeding the ray optics limit,” Science 339, 1057–1060 (2013).
[Crossref]

Schmid, H.

M. T. Borgström, M. H. Magnusson, F. Dimroth, G. Siefer, O. Höhn, H. Riel, H. Schmid, S. Wirths, M. Björk, I. Åberg, W. Peijnenburg, M. Vijver, M. Tchernycheva, V. Piazza, and L. Samuelson, “Towards nanowire tandem junction solar cells on silicon,” IEEE Journal of Photovoltaics 8, 733–740 (2018).

Schuster, T.

P. Götz, T. Schuster, K. Frenner, S. Rafler, and W. Osten, “Normal vector method for the RCWA with automated vector field generation,” Optics express 16, 17295–17301 (2008).
[Crossref] [PubMed]

Siefer, G.

M. T. Borgström, M. H. Magnusson, F. Dimroth, G. Siefer, O. Höhn, H. Riel, H. Schmid, S. Wirths, M. Björk, I. Åberg, W. Peijnenburg, M. Vijver, M. Tchernycheva, V. Piazza, and L. Samuelson, “Towards nanowire tandem junction solar cells on silicon,” IEEE Journal of Photovoltaics 8, 733–740 (2018).

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Aberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, and M. T. Borgström, “InP nanowire array solar cells achieving 13.8% efficiency by exceeding the ray optics limit,” Science 339, 1057–1060 (2013).
[Crossref]

Stoop, R. L.

J. Kupec, R. L. Stoop, and B. Witzigmann, “Light absorption and emission in nanowire array solar cells,” Optics Express 18, 27589–27605 (2010).
[Crossref]

Sturmberg, B. C. P.

B. C. P. Sturmberg, K. B. Dossou, L. C. Botten, A. A. Asatryan, C. G. Poulton, R. C. McPhedran, and C. M. de Sterke, “Optimizing photovoltaic charge generation of nanowire arrays: A simple semi-analytic approach,” ACS Photonics 1, 683–689 (2014).
[Crossref]

Sun, X. W.

Q. G. Du, C. H. Kam, H. V. Demir, H. Y. Yu, and X. W. Sun, “Broadband absorption enhancement in randomly positioned silicon nanowire arrays for solar cell applications,” Optics Letters 36, 1884–1886 (2011).
[Crossref]

Tang, X.

D. Wu, X. Tang, K. Wang, and X. Li, “An analytic approach for optimal geometrical design of GaAs nanowires for maximal light harvesting in photovoltaic cells,” Scientific Reports 7, 46504 (2017).
[Crossref] [PubMed]

Tchernycheva, M.

M. T. Borgström, M. H. Magnusson, F. Dimroth, G. Siefer, O. Höhn, H. Riel, H. Schmid, S. Wirths, M. Björk, I. Åberg, W. Peijnenburg, M. Vijver, M. Tchernycheva, V. Piazza, and L. Samuelson, “Towards nanowire tandem junction solar cells on silicon,” IEEE Journal of Photovoltaics 8, 733–740 (2018).

Trojnar, A. H.

A. H. Trojnar, C. E. Valdivia, R. R. LaPierre, K. Hinzer, and J. J. Krich, “Optimizations of GaAs nanowire solar cells,” IEEE Journal of Photovoltaics 6, 1494–1501 (2016).
[Crossref]

Valdivia, C. E.

A. H. Trojnar, C. E. Valdivia, R. R. LaPierre, K. Hinzer, and J. J. Krich, “Optimizations of GaAs nanowire solar cells,” IEEE Journal of Photovoltaics 6, 1494–1501 (2016).
[Crossref]

Vijver, M.

M. T. Borgström, M. H. Magnusson, F. Dimroth, G. Siefer, O. Höhn, H. Riel, H. Schmid, S. Wirths, M. Björk, I. Åberg, W. Peijnenburg, M. Vijver, M. Tchernycheva, V. Piazza, and L. Samuelson, “Towards nanowire tandem junction solar cells on silicon,” IEEE Journal of Photovoltaics 8, 733–740 (2018).

Wallentin, J.

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Aberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, and M. T. Borgström, “InP nanowire array solar cells achieving 13.8% efficiency by exceeding the ray optics limit,” Science 339, 1057–1060 (2013).
[Crossref]

Wang, K.

D. Wu, X. Tang, K. Wang, and X. Li, “An analytic approach for optimal geometrical design of GaAs nanowires for maximal light harvesting in photovoltaic cells,” Scientific Reports 7, 46504 (2017).
[Crossref] [PubMed]

Weismann, M.

M. Weismann, D. F. Gallagher, and N. C. Panoiu, “Accurate near-field calculation in the rigorous coupled-wave analysis method,” Journal of Optics 17, 125612 (2015).
[Crossref]

Whitney, W. S.

K. T. Fountaine, W. S. Whitney, and H. A. Atwater, “Resonant absorption in semiconductor nanowires and nanowire arrays: Relating leaky waveguide modes to bloch photonic crystal modes,” Journal of Applied Physics 116, 153106 (2014).
[Crossref]

Whittaker, D. M.

D. M. Whittaker and I. S. Culshaw, “Scattering-matrix treatment of patterned multilayer photonic structures,” Physical Review B 60, 2610–2618 (1999).
[Crossref]

Wirths, S.

M. T. Borgström, M. H. Magnusson, F. Dimroth, G. Siefer, O. Höhn, H. Riel, H. Schmid, S. Wirths, M. Björk, I. Åberg, W. Peijnenburg, M. Vijver, M. Tchernycheva, V. Piazza, and L. Samuelson, “Towards nanowire tandem junction solar cells on silicon,” IEEE Journal of Photovoltaics 8, 733–740 (2018).

Witzigmann, B.

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Aberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, and M. T. Borgström, “InP nanowire array solar cells achieving 13.8% efficiency by exceeding the ray optics limit,” Science 339, 1057–1060 (2013).
[Crossref]

J. Kupec, R. L. Stoop, and B. Witzigmann, “Light absorption and emission in nanowire array solar cells,” Optics Express 18, 27589–27605 (2010).
[Crossref]

Wu, D.

D. Wu, X. Tang, K. Wang, and X. Li, “An analytic approach for optimal geometrical design of GaAs nanowires for maximal light harvesting in photovoltaic cells,” Scientific Reports 7, 46504 (2017).
[Crossref] [PubMed]

Xu, H. Q.

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Aberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, and M. T. Borgström, “InP nanowire array solar cells achieving 13.8% efficiency by exceeding the ray optics limit,” Science 339, 1057–1060 (2013).
[Crossref]

Yu, H. Y.

Q. G. Du, C. H. Kam, H. V. Demir, H. Y. Yu, and X. W. Sun, “Broadband absorption enhancement in randomly positioned silicon nanowire arrays for solar cell applications,” Optics Letters 36, 1884–1886 (2011).
[Crossref]

ACS Photonics (1)

B. C. P. Sturmberg, K. B. Dossou, L. C. Botten, A. A. Asatryan, C. G. Poulton, R. C. McPhedran, and C. M. de Sterke, “Optimizing photovoltaic charge generation of nanowire arrays: A simple semi-analytic approach,” ACS Photonics 1, 683–689 (2014).
[Crossref]

Archive for Rational Mechanics and Analysis (1)

M. Costabel and M. Dauge, “Singularities of electromagnetic fields in polyhedral domains,” Archive for Rational Mechanics and Analysis 151, 221–276 (2000).
[Crossref]

Computer Physics Communications (1)

V. Liu and S. Fan, “S4: A free electromagnetic solver for layered periodic structures,” Computer Physics Communications 183, 2233–2244 (2012).
[Crossref]

IEEE Journal of Photovoltaics (3)

O. M. Ghahfarokhi, N. Anttu, L. Samuelson, and I. Åberg, “Performance of GaAs nanowire array solar cells for varying incidence angles,” IEEE Journal of Photovoltaics 6, 1502–1508 (2016).
[Crossref]

M. T. Borgström, M. H. Magnusson, F. Dimroth, G. Siefer, O. Höhn, H. Riel, H. Schmid, S. Wirths, M. Björk, I. Åberg, W. Peijnenburg, M. Vijver, M. Tchernycheva, V. Piazza, and L. Samuelson, “Towards nanowire tandem junction solar cells on silicon,” IEEE Journal of Photovoltaics 8, 733–740 (2018).

A. H. Trojnar, C. E. Valdivia, R. R. LaPierre, K. Hinzer, and J. J. Krich, “Optimizations of GaAs nanowire solar cells,” IEEE Journal of Photovoltaics 6, 1494–1501 (2016).
[Crossref]

Journal of Applied Physics (2)

K. T. Fountaine, W. S. Whitney, and H. A. Atwater, “Resonant absorption in semiconductor nanowires and nanowire arrays: Relating leaky waveguide modes to bloch photonic crystal modes,” Journal of Applied Physics 116, 153106 (2014).
[Crossref]

Y. Hu, R. R. LaPierre, M. Li, K. Chen, and J.-J. He, “Optical characteristics of GaAs nanowire solar cells,” Journal of Applied Physics 112, 104311 (2012).
[Crossref]

Journal of Modern Optics (1)

P. Lalanne and M. P. Jurek, “Computation of the near-field pattern with the coupled-wave method for transverse magnetic polarization,” Journal of Modern Optics 45, 1357–1374 (1998).
[Crossref]

Journal of Optics (1)

M. Weismann, D. F. Gallagher, and N. C. Panoiu, “Accurate near-field calculation in the rigorous coupled-wave analysis method,” Journal of Optics 17, 125612 (2015).
[Crossref]

Journal of the Optical Society of America A (5)

M. G. Moharam, T. K. Gaylord, E. B. Grann, and D. A. Pommet, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” Journal of the Optical Society of America A 12, 1068–1076 (1995).
[Crossref]

E. A. Bezus and L. L. Doskolovich, “Stable algorithm for the computation of the electromagnetic field distribution of eigenmodes of periodic diffraction structures,” Journal of the Optical Society of America A 29, 2307–2313 (2012).
[Crossref]

L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” Journal of the Optical Society of America A 13, 1024 (1996).
[Crossref]

H. Kim, I. Lee, and B. Lee, “Extended scattering-matrix method for efficient full parallel implementation of rigorous coupled-wave analysis,” Journal of the Optical Society of America A 24, 2313 (2007).
[Crossref]

L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” Journal of the Optical Society of America A 13, 1870–1876 (1996).
[Crossref]

Nanotechnology (1)

K. M. Azizur-Rahman and R. R. LaPierre, “Wavelength-selective absorptance in GaAs, InP and InAs nanowire arrays,” Nanotechnology 26, 295202 (2015).
[Crossref] [PubMed]

Opt. Lett. (1)

Optics express (1)

P. Götz, T. Schuster, K. Frenner, S. Rafler, and W. Osten, “Normal vector method for the RCWA with automated vector field generation,” Optics express 16, 17295–17301 (2008).
[Crossref] [PubMed]

K. H. Brenner, “Aspects for calculating local absorption with the rigorous coupled-wave method,” Optics Express 18, 10369–10376 (2010).
[Crossref]

J. Kupec, R. L. Stoop, and B. Witzigmann, “Light absorption and emission in nanowire array solar cells,” Optics Express 18, 27589–27605 (2010).
[Crossref]

Optics Letters (1)

Q. G. Du, C. H. Kam, H. V. Demir, H. Y. Yu, and X. W. Sun, “Broadband absorption enhancement in randomly positioned silicon nanowire arrays for solar cell applications,” Optics Letters 36, 1884–1886 (2011).
[Crossref]

Physical Review B (1)

D. M. Whittaker and I. S. Culshaw, “Scattering-matrix treatment of patterned multilayer photonic structures,” Physical Review B 60, 2610–2618 (1999).
[Crossref]

Progress In Electromagnetics Research B (1)

R. C. Rumpf, “Improved formulation of scattering matrices for semi-analytical methods that is consistent with convention,” Progress In Electromagnetics Research B 35, 241–261 (2011).
[Crossref]

Science (1)

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Aberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, and M. T. Borgström, “InP nanowire array solar cells achieving 13.8% efficiency by exceeding the ray optics limit,” Science 339, 1057–1060 (2013).
[Crossref]

Scientific Reports (1)

D. Wu, X. Tang, K. Wang, and X. Li, “An analytic approach for optimal geometrical design of GaAs nanowires for maximal light harvesting in photovoltaic cells,” Scientific Reports 7, 46504 (2017).
[Crossref] [PubMed]

Semiconductor Science and Technology (1)

K. L. Kavanagh, “Misfit dislocations in nanowire heterostructures,” Semiconductor Science and Technology 25, 024006 (2010).
[Crossref]

SIAM J. Sci. Comput. (1)

C. Epstein and M. O’Neil, “Smoothed corners and scattered waves,” SIAM J. Sci. Comput. 38, A2665–A2698 (2016).
[Crossref]

Other (6)

M. G. Moharam and A. B. Greenwell, “Rigorous analysis of field distribution and power flow in grating coupler of finite length,” in Diffractive Optics and Micro-Optics, (Optical Society of America, 2004), p. DMC5.
[Crossref]

N. Huynh and W. Heinrich, “FDTD accuracy improvement by incorporation of 3D edge singularities,” in 1999 IEEE MTT-S International Microwave Symposium Digest (Cat. No.99CH36282) (IEEE, 1999), pp. 1573–1576.
[Crossref]

S. Adachi, Optical Constants of Crystalline and Amorphous Semiconductors: Numerical Data and Graphical Information(SpringerUS, 1999), 1st ed.

“Standard tables for reference solar spectral irradiances: Direct normal and hemispherical on 37° tilted surface,” Tech. rep., ASTM International (2012).

O. Tange, “Gnu parallel 2018,” https://doi.org/10.5281/zenodo.1146014 (2018).

K. W. Robertson, R. R. LaPierre, and J. J. Krich, “Optical optimization of passivated GaAs nanowire solar cells,” in 2017 IEEE 44th Photovoltaic Specialist Conference (IEEE, 2017), pp. 1294–1298.

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Figures (10)

Fig. 1
Fig. 1 The test device used for assessment of RCWA. Left: A single unit cell in a square nanowire array containing a cylindrical GasAs nanowire passivated by an AlInP shell on a GaAs substrate, planarized by a cyclotene dielectric, and top-contacted with a layer of indium tin oxide. A thin layer of SiO2, surrounding the GaAs core but lacking the AlInP shell, exists between the cyclotene and substrate. Right: A top down view of the unit cell, demonstrating the piecewise constant material parameters in the plane.
Fig. 2
Fig. 2 Absorptance of the entire device calculated using the far field fluxes, Eqs. (7)(11). The markers for all values of NG lie nearly on top of one another, indicating convergence at low numbers of basis terms. The dashed black line shows the portion of the absorptance that occurs in the GaAs substrate (calculated with NG = 997), which is negligible at shorter wavelengths, becoming more significant at longer wavelengths.
Fig. 3
Fig. 3 Absorptance calculated from near fields using Eqs. (12)(13) (circles). Far field absorptance at NG = 997 (triangles). a) S4 implementation of RCWA. b) Continuous variable formulation. Gray background shows the AM1.5 solar spectrum. The CVF shows significant improvement, especially at short wavelengths.
Fig. 4
Fig. 4 Convergence of the spectrally integrated and wavelength resolved A far field, A near field using the CVF fields, and A near field using the unmodified fields. Blue box indicates 1% error bars around the NG = 997 far field absorptance, showing that the far field absorptance is self-converged in all cases; at short wavelengths, neither near field absorptance line is converged. The CVF fields improve accuracy at all wavelengths.
Fig. 5
Fig. 5 Line cuts of | E x | 2 (left) and | E y | 2 (right) along the x-direction through the center of the nanowire 101 nm from the top of the nanowire with and without use of the CVF with an incident wavelength of 453 nm and NG = 997. The CVF formulation reduces the Gibbs oscillations in Ex and introduces proper discontinuities while maintaining the continuity of Ey.
Fig. 6
Fig. 6 Relative difference between the far field and near field calculations of A with NG = 997. Orange line uses the unmodified fields in Eq. 13, blue line uses the CVF fields. Gray background shows the AM1.5G solar spectrum, which is strongest in the region of good convergence. Black dashed line indicates the 1% mark.
Fig. 7
Fig. 7 Rescaled generation rate on a line cut along the x direction through the center of the nanowire 83 nm from the top of the nanowire layer. The spectrally integrated and λ = 487 nm case are clearly converged even at NG = 197, while the longer and shorter wavelengths need high NG to remove all the Gibbs oscillations.
Fig. 8
Fig. 8 Rescaled generation rate on a line cut along the z direction through the center of the nanowire core. As in Fig. 7, the spectrally integrated results are well converged at low NG while the shortest and longest wavelengths require higher NG for convergence.
Fig. 9
Fig. 9 Left: Spectrally integrated generation rate with AM1.5G spectrum along a cut through the middle of the nanowire using the rescaled fields with NG = 197. Right: Absolute difference between the generation rate shown at left and the well-converged, rescaled generation rate at NG = 997. The deviations between the two generation maps are small. White regions are areas of vacuum and SiO2, where the generation rate is zero. Area within the solid contour indicates the location of peak generation, greater than 2.75 × 10 22 cm 3 s 1, while the differences there are much smaller. Dashed lines indicate line cuts shown in Figs. 7 and 8.
Fig. 10
Fig. 10 Run time of a single simulation as a function of basis terms with and without computation of the local fields. Field computations dominate the runtime at small NG. A least-squares fit to the blue line yields a slope of 3.06, consistent with the N G 3 scaling of the QR algorithm for solving eigenvalue problems. Dashed lines are guides to the eye.

Tables (1)

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Table 1 Numerical values for all geometric parameters in the test device.

Equations (25)

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× H = i ω ϵ E + J f
× E = i ω μ H
B = 0
D = ρ f
H ( r , z ) = G H G ( z ) e i ( k + G ) r ,
H G ( z ) = [ ϕ G , x x ^ + ϕ G , y y ^ ( k x + G x ) ϕ G , x + ( k y + G y ) ϕ G , y q z ^ ] e i q z ,
P up i ( ω ) = top S z ( ω ) d A
P down i ( ω ) = bottom S z ( ω ) d A ,
R ( ω ) = P up 1 ( ω ) P in ( ω )
T ( ω ) = P down n ( ω ) P in ( ω ) ,
A far field ( ω ) = 1 R ( ω ) T ( ω ) .
P abs ( ω ) = ϵ 0 ω n ( x , y , z ; ω ) k ( x , y , z ; ω ) | E ( x , y , z ; ω ) | 2 d V
A near field = P abs P in .
D = ϵ E
[ E T , x ( r ) E T , y ( r ) ] = T ( r ) [ E x ( r ) E y ( r ) ]
[ D N , x ( r ) D N , y ( r ) ] = N ( r ) [ D x ( r ) D y ( r ) ] ,
[ E x ( r ) E y ( r ) ] = [ E T , x ( r ) E T , y ( r ) ] + [ E N , x ( r ) E N , y ( r ) ] .
[ e T , x e T , y ] = [ [ T ] ] [ e x e y ] ,
[ [ 1 ϵ ] ] 1 [ d N ] = [ e N ] ,
[ d N , x d N , y ] = 1 2 ( [ [ N ] ] [ [ 1 ϵ ] ] 1 + [ [ 1 ϵ ] ] 1 [ [ N ] ] ) [ e x e y ] ,
E N ( r ) = F 1 ( d N ) ϵ 0 ϵ r ( r ) ,
E y ( r ) = F 1 ( d N , y ) ϵ 0 ϵ r ( r ) + F 1 ( e T , y )
E x ( r ) = F 1 ( d N , x ) ϵ 0 ϵ r ( r ) + F 1 ( e T , x ) .
F i ( ω ) = A far field i ( ω ) A near field i ( ω ) .
E rescaled ( ω ) = F i ( ω ) E ( ω )

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