Abstract

Using morphological and optical simulations of 1D tantalum photonic crystals at 1200K, surface diffusion was determined to gradually reduce the efficiency of selective emitters. This was attributed to shifting resonance peaks and declining emissivity caused by changes to the cavity dimensions and the aperture width. Decreasing the structure’s curvature through larger periods and smaller cavity widths, as well as generating smoother transitions in curvature through the introduction of rounded cavities, was found to alleviate this degradation. An optimized structure, that shows both high efficiency selective emissivity and resistance to surface diffusion, was presented.

© 2015 Optical Society of America

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2014 (2)

A. Lenert, D. M. Bierman, Y. Nam, W. R. Chan, I. Celanović, M. Soljacic, and E. N. Wang, “A nanophotonic solar thermophotovoltaic device,” Nat. Nanotechnol. 9, 126–130 (2014).
[Crossref] [PubMed]

V. Rinnerbauer, A. Lenert, D. M. Bierman, Y. X. Yeng, W. R. Chan, R. D. Geil, J. J. Senkevich, J. D. Joannopoulos, E. N. Wang, M. Soljacic, and I. Celanovic, “Metallic photonic crystal absorber-emitter for efficient spectral control in high-temperature solar thermophotovoltaics,” Adv. Energy Mater. 4, 1400334 (2014).
[Crossref]

2013 (7)

K. Sudoh, R. Hiruta, and H. Kuribayashi, “Shape evolution of high aspect ratio holes on Si(001) during hydrogen annealing,” J. Appl. Phys. 114, 183512 (2013).
[Crossref]

V. Rinnerbauer, S. Ndao, Y. X. Yeng, J. J. Senkevich, K. F. Jensen, J. D. Joannopoulos, M. Soljacic, I. Celanovic, and R. D. Geil, “Large-area fabrication of high aspect ratio tantalum photonic crystals for high-temperature selective emitters,” J. Vac. Sci. Technol. B 31, 011802 (2013).
[Crossref]

Y. X. Yeng, W. R. Chan, V. Rinnerbauer, J. D. Joannopoulos, M. Soljačić, and I. Celanovic, “Performance analysis of experimentally viable photonic crystal enhanced thermophotovoltaic systems,” Opt. Express 21, A1035–A1051 (2013).
[Crossref]

K. A. Arpin, M. D. Losego, A. N. Cloud, H. Ning, J. Mallek, N. P. Sergeant, L. Zhu, Z. Yu, B. Kalanyan, G. N. Parsons, G. S. Girolami, J. R. Abelson, S. Fan, and P. V. Braun, “Three-dimensional self-assembled photonic crystals with high temperature stability for thermal emission modification,” Nat. Commun. 4, 2630 (2013).
[Crossref] [PubMed]

H.-J. Lee, K. Smyth, S. Bathurst, J. Chou, M. Ghebrebrhan, J. Joannopoulos, N. Saka, and S.-G. Kim, “Hafnia-plugged microcavities for thermal stability of selective emitters,” Appl. Phys. Lett. 102, 241904 (2013).
[Crossref]

V. Rinnerbauer, Y. X. Yeng, W. R. Chan, J. J. Senkevich, J. D. Joannopoulos, M. Soljacic, and I. Celanovic, “High-temperature stability and selective thermal emission of polycrystalline tantalum photonic crystals,” Opt. Express 21, 11482–11491 (2013).
[Crossref] [PubMed]

V. Stelmakh, V. Rinnerbauer, R. D. Geil, P. R. Aimone, J. J. Senkevich, J. D. Joannopoulos, M. Soljacic, and I. Celanovic, “High-temperature tantalum tungsten alloy photonic crystals: Stability, optical properties, and fabrication,” Appl. Phys. Lett. 103, 123903 (2013).
[Crossref]

2012 (4)

Y. X. Yeng, M. Ghebrebrhan, P. Bermel, W. R. Chan, J. D. Joannopoulos, M. Soljacic, and I. Celanovic, “Enabling high-temperature nanophotonics for energy applications,” Proc. Natl. Acad. Sci. U. S. A. 109, 2280–2285 (2012).
[Crossref] [PubMed]

V. Rinnerbauer, S. Ndao, Y. X. Yeng, W. R. Chan, J. J. Senkevich, J. D. Joannopoulos, M. Soljacic, and I. Celanovic, “Recent developments in high-temperature photonic crystals for energy conversion,” Energy Environ. Sci. 5, 8815–8823 (2012).
[Crossref]

S. G. Rudisill, Z. Wang, and A. Stein, “Maintaining the structure of templated porous materials for reactive and high-temperature applications,” Langmuir 28, 7310–7324 (2012).
[Crossref] [PubMed]

M. A. Madrid, R. C. Salvarezza, and M. F. Castez, “One-dimensional gratings evolving through high-temperature annealing: sine-generated solutions,” J. Phys.: Condens. Matter 24, 015001 (2012).

2011 (4)

P. Bermel, M. Ghebrebrhan, M. Harradon, Y. X. Yeng, I. Celanovic, J. D. Joannopoulos, and M. Soljacic, “Tailoring photonic metamaterial resonances for thermal radiation,” Nanoscale Res. Lett. 6, 549 (2011).
[Crossref] [PubMed]

P. Nagpal, D. P. Josephson, N. R. Denny, J. DeWilde, D. J. Norris, and A. Stein, “Fabrication of carbon/refractory metal nanocomposites as thermally stable metallic photonic crystals,” J. Mater. Chem. 21, 10836–10843 (2011).
[Crossref]

K. A. Arpin, M. D. Losego, and P. V. Braun, “Electrodeposited 3D tungsten photonic crystals with enhanced thermal stability,” Chem. Mater. 23, 4783–4788 (2011).
[Crossref]

M. Ghebrebrhan, P. Bermel, Y. X. Yeng, I. Celanovic, M. Soljacic, and J. D. Joannopoulos, “Tailoring thermal emission via Q matching of photonic crystal resonances,” Phys. Rev. A 83, 033810 (2011).
[Crossref]

2010 (5)

N. R. Denny, F. Li, D. J. Norris, and A. Stein, “In situ high temperature TEM analysis of sintering in nanostructured tungsten and tungsten–molybdenum alloy photonic crystals,” J. Mater. Chem. 20, 1538–1545 (2010).
[Crossref]

P. Bermel, M. Ghebrebrhan, W. Chan, Y. X. Yeng, M. Araghchini, R. Hamam, C. H. Marton, K. F. Jensen, M. Soljačić, J. D. Joannopoulos, S. G. Johnson, and C. Ivan, “Design and global optimization of high-efficiency thermophotovoltaic systems,” Opt. Express 18, A314–A334 (2010).
[Crossref] [PubMed]

M. F. Castez, “Surface-diffusion-driven decay of patterns: beyond the small slopes approximation,” J. Phys. Condens. Mat. 22, 345007 (2010).
[Crossref]

M. F. Castez, R. C. Salvarezza, J. Nakamura, and K. Sudoh, “A theoretical framework to obtain interface’s shapes during the high-temperature annealing of high-aspect-ratio gratings,” Appl. Phys. Lett. 97, 123104 (2010).
[Crossref]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

2009 (2)

2008 (1)

I. Celanovic, N. Jovanovic, and J. Kassakian, “Two-dimensional tungsten photonic crystals as selective thermal emitters,” Appl. Phys. Lett. 92, 193101 (2008).
[Crossref]

2007 (2)

N. R. Denny, S. E. Han, D. J. Norris, and A. Stein, “Effects of thermal processes on the structure of monolithic tungsten and tungsten alloy photonic crystals,” Chem. Mater. 19, 4563–4569 (2007).
[Crossref]

J. Nakamura, K. Sudoh, and H. Iwasaki, “Evolution of one-dimensional gratings with high aspect ratios on Si(001) surfaces by high-temperature annealing,” Jpn. J. Appl. Phys. 46, 7194–7197 (2007).
[Crossref]

2006 (3)

J.-M. Zhang, D.-D. Wang, and K.-W. Xu, “Calculation of the surface energy of bcc transition metals by using the second nearest-neighbor modified embedded atom method,” Appl. Surf. Sci. 252, 8217–8222 (2006).
[Crossref]

D. L. C. Chan, M. Soljacic, and J. D. Joannopoulos, “Thermal emission and design in 2D-periodic metallic photonic crystal slabs,” Opt. Express 14, 8785–8796 (2006).
[Crossref] [PubMed]

D. L. C. Chan, M. Soljacic, and J. D. Joannopoulos, “Thermal emission and design in one-dimensional periodic metallic photonic crystal slabs,” Phys. Rev. E 74, 016609 (2006).
[Crossref]

2005 (1)

I. Celanovic, D. Perreault, and J. Kassakian, “Resonant-cavity enhanced thermal emission,” Phys. Rev. B 72, 075127 (2005).
[Crossref]

2004 (2)

A. Dewaele, P. Loubeyre, and M. Mezouar, “Refinement of the equation of state of tantalum,” Phys. Rev. B 69, 092106 (2004).
[Crossref]

H. Sai and H. Yugami, “Thermophotovoltaic generation with selective radiators based on tungsten surface gratings,” Appl. Phys. Lett. 85, 3399–3401 (2004).
[Crossref]

2003 (3)

H. Sai, Y. Kanamori, and H. Yugami, “High-temperature resistive surface grating for spectral control of thermal radiation,” Appl. Phys. Lett. 82, 1685–1687 (2003).
[Crossref]

C. Schlemmer, J. Aschaber, V. Boerner, and J. Luther, “Thermal stability of micro-structured selective tungsten emitters,” AIP Conf. Proc. 653, 164–173 (2003).
[Crossref]

J.-M. Zhang, F. Ma, and K.-W. Xu, “Calculation of the surface energy of bcc metals by using the modified embedded-atom method,” Surf. Interface Anal. 35, 662–666 (2003).
[Crossref]

2002 (1)

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature 417, 52–55 (2002).
[Crossref] [PubMed]

2001 (1)

S. Maruyama, T. Kashiwa, H. Yugami, and M. Esashi, “Thermal radiation from two-dimensionally confined modes in microcavities,” Appl. Phys. Lett. 79, 1393–1395 (2001).
[Crossref]

2000 (1)

A. Heinzel, V. Boerner, A. Gombert, B. Bläsi, V. Wittwer, and J. Luther, “Radiation filters and emitters for the NIR based on periodically structured metal surfaces,” J. Mod. Opt. 47, 2399–2419 (2000).
[Crossref]

1998 (1)

L. Vitos, A. V. Ruban, H. L. Skriver, and J. Kollar, “The surface energy of metals,” Surf. Sci. 411, 186–202 (1998).
[Crossref]

1997 (2)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[Crossref]

J. W. Bullard, “Digital-image-based models of two-dimensional microstructural evolution by surface diffusion and vapor transport,” J. Appl. Phys. 81, 159–168 (1997).
[Crossref]

1996 (1)

M. J. Mehl and D. A. Papaconstantopoulos, “Applications of a tight-binding total-energy method for transition and noble metals: Elastic constants, vacancies, and surfaces of monatomic metals,” Phys. Rev. B 54, 4519 (1996).
[Crossref]

1995 (2)

W. C. Carter, A. R. Roosen, J. W. Cahn, and J. E. Taylor, “Shape evolution by surface diffusion and surface attachment limited kinetics on completely faceted surfaces,” Acta Metall. Mater. 43, 4309–4323 (1995).
[Crossref]

E. G. Seebauer and C. E. Allen, “Estimating surface diffusion coefficients,” Prog. Surf. Sci. 49, 265–330 (1995).
[Crossref]

1994 (1)

J. W. Cahn and J. E. Taylor, “Overview no. 113 surface motion by surface diffusion,” Acta Metall. Mater. 42, 1045–1063 (1994).
[Crossref]

1992 (1)

D. S. Meek and D. J. Walton, “Clothoid spline transition spirals,” Math. Comput. 59, 117–133 (1992).
[Crossref]

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[Crossref] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
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1985 (1)

V. T. Binh and P. Melinon, “On viscous mechanism for surface diffusion at high temperature (T/Tm > 0.75) due to formation of a 2D dense fluid on metallic surfaces,” Surf. Sci. 161, 234–244 (1985).
[Crossref]

1984 (1)

C. N. Singman, “Atomic volume and allotropy of the elements,” J. Chem. Educ. 61, 137 (1984).
[Crossref]

1981 (1)

S. Hok and M. Drechsler, “A measurement of the surface self-diffusion of tantalum,” Surf. Sci. 107, L362–L366 (1981).
[Crossref]

1977 (2)

W. R. Tyson and W. A. Miller, “Surface free energies of solid metals: Estimation from liquid surface tension measurements,” Surf. Sci. 62, 267–276 (1977).
[Crossref]

M. H. Mueller, “The lattice parameter of tantalum,” Scr. Metall. 11, 693 (1977).
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1976 (1)

H. P. Bonze, “Surface diffusion of metals - a comparison of intrinsic and mass transfer measurements,” CRC Cr. Rev. Sol. State 6, 171–194 (1976).
[Crossref]

1974 (3)

P. C. Bettler, D. H. Bennum, and C. M. Case, “Effect of impurities on surface self-diffusion and surface structure,” Surf. Sci. 44, 360–376 (1974).
[Crossref]

J. L. Wang and R. Vanselow, “The activation energy for surface self-diffusion of tantalum and the influence of residual gases on this quantity in the presence of high electric fields,” Surf. Sci. 43, 21–28 (1974).
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A. Piquet, H. Roux, V. T. Binh, R. Uzan, and M. Drechsler, “Une détermination du coefficient d’auto-diffusion de surface avec des pointesàémission de champ (tungstène),” Surf. Sci. 44, 575–584 (1974).
[Crossref]

1972 (1)

M. Pichaud and M. Drechsler, “A field emission measurement of the influence of adsorption on surface self-diffusion,” Surf. Sci. 32, 341–348 (1972).
[Crossref]

1965 (1)

F. A. Nichols and W. W. Mullins, “Surface- (interface-) and volume-diffusion contributions to morphological changes driven by capillarity,” Trans. Metall. Soc. AIME 233, 1840–1848 (1965).

1960 (2)

W. Parrish, “Results of the IUCr precision lattice-parameter project,” Acta Crystallogr. 13, 838–850 (1960).
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J. P. Barbour, F. M. Charbonnier, W. W. Dolan, W. P. Dyke, E. E. Martin, and J. K. Trolan, “Determination of the surface tension and surface migration constants for tungsten,” Phys. Rev. 117, 1452 (1960).
[Crossref]

1959 (1)

W. W. Mullins, “Flattening of a nearly plane solid surface due to capillarity,” J. Appl. Phys. 30, 77–83 (1959).
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1957 (1)

W. W. Mullins, “Theory of thermal grooving,” J. Appl. Phys. 28, 333–339 (1957).
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Abelson, J. R.

K. A. Arpin, M. D. Losego, A. N. Cloud, H. Ning, J. Mallek, N. P. Sergeant, L. Zhu, Z. Yu, B. Kalanyan, G. N. Parsons, G. S. Girolami, J. R. Abelson, S. Fan, and P. V. Braun, “Three-dimensional self-assembled photonic crystals with high temperature stability for thermal emission modification,” Nat. Commun. 4, 2630 (2013).
[Crossref] [PubMed]

Aimone, P. R.

V. Stelmakh, V. Rinnerbauer, R. D. Geil, P. R. Aimone, J. J. Senkevich, J. D. Joannopoulos, M. Soljacic, and I. Celanovic, “High-temperature tantalum tungsten alloy photonic crystals: Stability, optical properties, and fabrication,” Appl. Phys. Lett. 103, 123903 (2013).
[Crossref]

Allen, C. E.

E. G. Seebauer and C. E. Allen, “Estimating surface diffusion coefficients,” Prog. Surf. Sci. 49, 265–330 (1995).
[Crossref]

Allen, S. M.

R. W. Balluffi, S. M. Allen, and W. C. Carter, Kinetics of Materials (Wiley Interscience, 2005).
[Crossref]

Araghchini, M.

Arpin, K. A.

K. A. Arpin, M. D. Losego, A. N. Cloud, H. Ning, J. Mallek, N. P. Sergeant, L. Zhu, Z. Yu, B. Kalanyan, G. N. Parsons, G. S. Girolami, J. R. Abelson, S. Fan, and P. V. Braun, “Three-dimensional self-assembled photonic crystals with high temperature stability for thermal emission modification,” Nat. Commun. 4, 2630 (2013).
[Crossref] [PubMed]

K. A. Arpin, M. D. Losego, and P. V. Braun, “Electrodeposited 3D tungsten photonic crystals with enhanced thermal stability,” Chem. Mater. 23, 4783–4788 (2011).
[Crossref]

Aschaber, J.

C. Schlemmer, J. Aschaber, V. Boerner, and J. Luther, “Thermal stability of micro-structured selective tungsten emitters,” AIP Conf. Proc. 653, 164–173 (2003).
[Crossref]

Balluffi, R. W.

R. W. Balluffi, S. M. Allen, and W. C. Carter, Kinetics of Materials (Wiley Interscience, 2005).
[Crossref]

Barbour, J. P.

J. P. Barbour, F. M. Charbonnier, W. W. Dolan, W. P. Dyke, E. E. Martin, and J. K. Trolan, “Determination of the surface tension and surface migration constants for tungsten,” Phys. Rev. 117, 1452 (1960).
[Crossref]

Bathurst, S.

H.-J. Lee, K. Smyth, S. Bathurst, J. Chou, M. Ghebrebrhan, J. Joannopoulos, N. Saka, and S.-G. Kim, “Hafnia-plugged microcavities for thermal stability of selective emitters,” Appl. Phys. Lett. 102, 241904 (2013).
[Crossref]

Bennum, D. H.

P. C. Bettler, D. H. Bennum, and C. M. Case, “Effect of impurities on surface self-diffusion and surface structure,” Surf. Sci. 44, 360–376 (1974).
[Crossref]

Bermel, P.

Y. X. Yeng, M. Ghebrebrhan, P. Bermel, W. R. Chan, J. D. Joannopoulos, M. Soljacic, and I. Celanovic, “Enabling high-temperature nanophotonics for energy applications,” Proc. Natl. Acad. Sci. U. S. A. 109, 2280–2285 (2012).
[Crossref] [PubMed]

M. Ghebrebrhan, P. Bermel, Y. X. Yeng, I. Celanovic, M. Soljacic, and J. D. Joannopoulos, “Tailoring thermal emission via Q matching of photonic crystal resonances,” Phys. Rev. A 83, 033810 (2011).
[Crossref]

P. Bermel, M. Ghebrebrhan, M. Harradon, Y. X. Yeng, I. Celanovic, J. D. Joannopoulos, and M. Soljacic, “Tailoring photonic metamaterial resonances for thermal radiation,” Nanoscale Res. Lett. 6, 549 (2011).
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P. Bermel, M. Ghebrebrhan, W. Chan, Y. X. Yeng, M. Araghchini, R. Hamam, C. H. Marton, K. F. Jensen, M. Soljačić, J. D. Joannopoulos, S. G. Johnson, and C. Ivan, “Design and global optimization of high-efficiency thermophotovoltaic systems,” Opt. Express 18, A314–A334 (2010).
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A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Bettler, P. C.

P. C. Bettler, D. H. Bennum, and C. M. Case, “Effect of impurities on surface self-diffusion and surface structure,” Surf. Sci. 44, 360–376 (1974).
[Crossref]

Bierman, D. M.

V. Rinnerbauer, A. Lenert, D. M. Bierman, Y. X. Yeng, W. R. Chan, R. D. Geil, J. J. Senkevich, J. D. Joannopoulos, E. N. Wang, M. Soljacic, and I. Celanovic, “Metallic photonic crystal absorber-emitter for efficient spectral control in high-temperature solar thermophotovoltaics,” Adv. Energy Mater. 4, 1400334 (2014).
[Crossref]

A. Lenert, D. M. Bierman, Y. Nam, W. R. Chan, I. Celanović, M. Soljacic, and E. N. Wang, “A nanophotonic solar thermophotovoltaic device,” Nat. Nanotechnol. 9, 126–130 (2014).
[Crossref] [PubMed]

Binh, V. T.

V. T. Binh and P. Melinon, “On viscous mechanism for surface diffusion at high temperature (T/Tm > 0.75) due to formation of a 2D dense fluid on metallic surfaces,” Surf. Sci. 161, 234–244 (1985).
[Crossref]

A. Piquet, H. Roux, V. T. Binh, R. Uzan, and M. Drechsler, “Une détermination du coefficient d’auto-diffusion de surface avec des pointesàémission de champ (tungstène),” Surf. Sci. 44, 575–584 (1974).
[Crossref]

Biswas, R.

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature 417, 52–55 (2002).
[Crossref] [PubMed]

Bläsi, B.

A. Heinzel, V. Boerner, A. Gombert, B. Bläsi, V. Wittwer, and J. Luther, “Radiation filters and emitters for the NIR based on periodically structured metal surfaces,” J. Mod. Opt. 47, 2399–2419 (2000).
[Crossref]

Boerner, V.

C. Schlemmer, J. Aschaber, V. Boerner, and J. Luther, “Thermal stability of micro-structured selective tungsten emitters,” AIP Conf. Proc. 653, 164–173 (2003).
[Crossref]

A. Heinzel, V. Boerner, A. Gombert, B. Bläsi, V. Wittwer, and J. Luther, “Radiation filters and emitters for the NIR based on periodically structured metal surfaces,” J. Mod. Opt. 47, 2399–2419 (2000).
[Crossref]

Bonze, H. P.

H. P. Bonze, “Surface diffusion of metals - a comparison of intrinsic and mass transfer measurements,” CRC Cr. Rev. Sol. State 6, 171–194 (1976).
[Crossref]

Braun, P. V.

K. A. Arpin, M. D. Losego, A. N. Cloud, H. Ning, J. Mallek, N. P. Sergeant, L. Zhu, Z. Yu, B. Kalanyan, G. N. Parsons, G. S. Girolami, J. R. Abelson, S. Fan, and P. V. Braun, “Three-dimensional self-assembled photonic crystals with high temperature stability for thermal emission modification,” Nat. Commun. 4, 2630 (2013).
[Crossref] [PubMed]

K. A. Arpin, M. D. Losego, and P. V. Braun, “Electrodeposited 3D tungsten photonic crystals with enhanced thermal stability,” Chem. Mater. 23, 4783–4788 (2011).
[Crossref]

Bullard, J. W.

J. W. Bullard, “Digital-image-based models of two-dimensional microstructural evolution by surface diffusion and vapor transport,” J. Appl. Phys. 81, 159–168 (1997).
[Crossref]

Cahn, J. W.

W. C. Carter, A. R. Roosen, J. W. Cahn, and J. E. Taylor, “Shape evolution by surface diffusion and surface attachment limited kinetics on completely faceted surfaces,” Acta Metall. Mater. 43, 4309–4323 (1995).
[Crossref]

J. W. Cahn and J. E. Taylor, “Overview no. 113 surface motion by surface diffusion,” Acta Metall. Mater. 42, 1045–1063 (1994).
[Crossref]

Carter, W. C.

W. C. Carter, A. R. Roosen, J. W. Cahn, and J. E. Taylor, “Shape evolution by surface diffusion and surface attachment limited kinetics on completely faceted surfaces,” Acta Metall. Mater. 43, 4309–4323 (1995).
[Crossref]

R. W. Balluffi, S. M. Allen, and W. C. Carter, Kinetics of Materials (Wiley Interscience, 2005).
[Crossref]

Case, C. M.

P. C. Bettler, D. H. Bennum, and C. M. Case, “Effect of impurities on surface self-diffusion and surface structure,” Surf. Sci. 44, 360–376 (1974).
[Crossref]

Castez, M. F.

M. A. Madrid, R. C. Salvarezza, and M. F. Castez, “One-dimensional gratings evolving through high-temperature annealing: sine-generated solutions,” J. Phys.: Condens. Matter 24, 015001 (2012).

M. F. Castez, “Surface-diffusion-driven decay of patterns: beyond the small slopes approximation,” J. Phys. Condens. Mat. 22, 345007 (2010).
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M. F. Castez, R. C. Salvarezza, J. Nakamura, and K. Sudoh, “A theoretical framework to obtain interface’s shapes during the high-temperature annealing of high-aspect-ratio gratings,” Appl. Phys. Lett. 97, 123104 (2010).
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M. F. Castez and R. C. Salvarezza, “Modeling thermal decay of high-aspect-ratio nanostructures,” Appl. Phys. Lett. 94, 053103 (2009).
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Celanovic, I.

V. Rinnerbauer, A. Lenert, D. M. Bierman, Y. X. Yeng, W. R. Chan, R. D. Geil, J. J. Senkevich, J. D. Joannopoulos, E. N. Wang, M. Soljacic, and I. Celanovic, “Metallic photonic crystal absorber-emitter for efficient spectral control in high-temperature solar thermophotovoltaics,” Adv. Energy Mater. 4, 1400334 (2014).
[Crossref]

A. Lenert, D. M. Bierman, Y. Nam, W. R. Chan, I. Celanović, M. Soljacic, and E. N. Wang, “A nanophotonic solar thermophotovoltaic device,” Nat. Nanotechnol. 9, 126–130 (2014).
[Crossref] [PubMed]

V. Stelmakh, V. Rinnerbauer, R. D. Geil, P. R. Aimone, J. J. Senkevich, J. D. Joannopoulos, M. Soljacic, and I. Celanovic, “High-temperature tantalum tungsten alloy photonic crystals: Stability, optical properties, and fabrication,” Appl. Phys. Lett. 103, 123903 (2013).
[Crossref]

V. Rinnerbauer, S. Ndao, Y. X. Yeng, J. J. Senkevich, K. F. Jensen, J. D. Joannopoulos, M. Soljacic, I. Celanovic, and R. D. Geil, “Large-area fabrication of high aspect ratio tantalum photonic crystals for high-temperature selective emitters,” J. Vac. Sci. Technol. B 31, 011802 (2013).
[Crossref]

V. Rinnerbauer, Y. X. Yeng, W. R. Chan, J. J. Senkevich, J. D. Joannopoulos, M. Soljacic, and I. Celanovic, “High-temperature stability and selective thermal emission of polycrystalline tantalum photonic crystals,” Opt. Express 21, 11482–11491 (2013).
[Crossref] [PubMed]

Y. X. Yeng, W. R. Chan, V. Rinnerbauer, J. D. Joannopoulos, M. Soljačić, and I. Celanovic, “Performance analysis of experimentally viable photonic crystal enhanced thermophotovoltaic systems,” Opt. Express 21, A1035–A1051 (2013).
[Crossref]

V. Rinnerbauer, S. Ndao, Y. X. Yeng, W. R. Chan, J. J. Senkevich, J. D. Joannopoulos, M. Soljacic, and I. Celanovic, “Recent developments in high-temperature photonic crystals for energy conversion,” Energy Environ. Sci. 5, 8815–8823 (2012).
[Crossref]

Y. X. Yeng, M. Ghebrebrhan, P. Bermel, W. R. Chan, J. D. Joannopoulos, M. Soljacic, and I. Celanovic, “Enabling high-temperature nanophotonics for energy applications,” Proc. Natl. Acad. Sci. U. S. A. 109, 2280–2285 (2012).
[Crossref] [PubMed]

M. Ghebrebrhan, P. Bermel, Y. X. Yeng, I. Celanovic, M. Soljacic, and J. D. Joannopoulos, “Tailoring thermal emission via Q matching of photonic crystal resonances,” Phys. Rev. A 83, 033810 (2011).
[Crossref]

P. Bermel, M. Ghebrebrhan, M. Harradon, Y. X. Yeng, I. Celanovic, J. D. Joannopoulos, and M. Soljacic, “Tailoring photonic metamaterial resonances for thermal radiation,” Nanoscale Res. Lett. 6, 549 (2011).
[Crossref] [PubMed]

I. Celanovic, N. Jovanovic, and J. Kassakian, “Two-dimensional tungsten photonic crystals as selective thermal emitters,” Appl. Phys. Lett. 92, 193101 (2008).
[Crossref]

I. Celanovic, D. Perreault, and J. Kassakian, “Resonant-cavity enhanced thermal emission,” Phys. Rev. B 72, 075127 (2005).
[Crossref]

Chan, D. L. C.

D. L. C. Chan, M. Soljacic, and J. D. Joannopoulos, “Thermal emission and design in one-dimensional periodic metallic photonic crystal slabs,” Phys. Rev. E 74, 016609 (2006).
[Crossref]

D. L. C. Chan, M. Soljacic, and J. D. Joannopoulos, “Thermal emission and design in 2D-periodic metallic photonic crystal slabs,” Opt. Express 14, 8785–8796 (2006).
[Crossref] [PubMed]

Chan, W.

Chan, W. R.

V. Rinnerbauer, A. Lenert, D. M. Bierman, Y. X. Yeng, W. R. Chan, R. D. Geil, J. J. Senkevich, J. D. Joannopoulos, E. N. Wang, M. Soljacic, and I. Celanovic, “Metallic photonic crystal absorber-emitter for efficient spectral control in high-temperature solar thermophotovoltaics,” Adv. Energy Mater. 4, 1400334 (2014).
[Crossref]

A. Lenert, D. M. Bierman, Y. Nam, W. R. Chan, I. Celanović, M. Soljacic, and E. N. Wang, “A nanophotonic solar thermophotovoltaic device,” Nat. Nanotechnol. 9, 126–130 (2014).
[Crossref] [PubMed]

Y. X. Yeng, W. R. Chan, V. Rinnerbauer, J. D. Joannopoulos, M. Soljačić, and I. Celanovic, “Performance analysis of experimentally viable photonic crystal enhanced thermophotovoltaic systems,” Opt. Express 21, A1035–A1051 (2013).
[Crossref]

V. Rinnerbauer, Y. X. Yeng, W. R. Chan, J. J. Senkevich, J. D. Joannopoulos, M. Soljacic, and I. Celanovic, “High-temperature stability and selective thermal emission of polycrystalline tantalum photonic crystals,” Opt. Express 21, 11482–11491 (2013).
[Crossref] [PubMed]

V. Rinnerbauer, S. Ndao, Y. X. Yeng, W. R. Chan, J. J. Senkevich, J. D. Joannopoulos, M. Soljacic, and I. Celanovic, “Recent developments in high-temperature photonic crystals for energy conversion,” Energy Environ. Sci. 5, 8815–8823 (2012).
[Crossref]

Y. X. Yeng, M. Ghebrebrhan, P. Bermel, W. R. Chan, J. D. Joannopoulos, M. Soljacic, and I. Celanovic, “Enabling high-temperature nanophotonics for energy applications,” Proc. Natl. Acad. Sci. U. S. A. 109, 2280–2285 (2012).
[Crossref] [PubMed]

Charbonnier, F. M.

J. P. Barbour, F. M. Charbonnier, W. W. Dolan, W. P. Dyke, E. E. Martin, and J. K. Trolan, “Determination of the surface tension and surface migration constants for tungsten,” Phys. Rev. 117, 1452 (1960).
[Crossref]

Chou, J.

H.-J. Lee, K. Smyth, S. Bathurst, J. Chou, M. Ghebrebrhan, J. Joannopoulos, N. Saka, and S.-G. Kim, “Hafnia-plugged microcavities for thermal stability of selective emitters,” Appl. Phys. Lett. 102, 241904 (2013).
[Crossref]

Cloud, A. N.

K. A. Arpin, M. D. Losego, A. N. Cloud, H. Ning, J. Mallek, N. P. Sergeant, L. Zhu, Z. Yu, B. Kalanyan, G. N. Parsons, G. S. Girolami, J. R. Abelson, S. Fan, and P. V. Braun, “Three-dimensional self-assembled photonic crystals with high temperature stability for thermal emission modification,” Nat. Commun. 4, 2630 (2013).
[Crossref] [PubMed]

Denny, N. R.

P. Nagpal, D. P. Josephson, N. R. Denny, J. DeWilde, D. J. Norris, and A. Stein, “Fabrication of carbon/refractory metal nanocomposites as thermally stable metallic photonic crystals,” J. Mater. Chem. 21, 10836–10843 (2011).
[Crossref]

N. R. Denny, F. Li, D. J. Norris, and A. Stein, “In situ high temperature TEM analysis of sintering in nanostructured tungsten and tungsten–molybdenum alloy photonic crystals,” J. Mater. Chem. 20, 1538–1545 (2010).
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N. R. Denny, S. E. Han, D. J. Norris, and A. Stein, “Effects of thermal processes on the structure of monolithic tungsten and tungsten alloy photonic crystals,” Chem. Mater. 19, 4563–4569 (2007).
[Crossref]

Dewaele, A.

A. Dewaele, P. Loubeyre, and M. Mezouar, “Refinement of the equation of state of tantalum,” Phys. Rev. B 69, 092106 (2004).
[Crossref]

DeWilde, J.

P. Nagpal, D. P. Josephson, N. R. Denny, J. DeWilde, D. J. Norris, and A. Stein, “Fabrication of carbon/refractory metal nanocomposites as thermally stable metallic photonic crystals,” J. Mater. Chem. 21, 10836–10843 (2011).
[Crossref]

Dolan, W. W.

J. P. Barbour, F. M. Charbonnier, W. W. Dolan, W. P. Dyke, E. E. Martin, and J. K. Trolan, “Determination of the surface tension and surface migration constants for tungsten,” Phys. Rev. 117, 1452 (1960).
[Crossref]

Drechsler, M.

S. Hok and M. Drechsler, “A measurement of the surface self-diffusion of tantalum,” Surf. Sci. 107, L362–L366 (1981).
[Crossref]

A. Piquet, H. Roux, V. T. Binh, R. Uzan, and M. Drechsler, “Une détermination du coefficient d’auto-diffusion de surface avec des pointesàémission de champ (tungstène),” Surf. Sci. 44, 575–584 (1974).
[Crossref]

M. Pichaud and M. Drechsler, “A field emission measurement of the influence of adsorption on surface self-diffusion,” Surf. Sci. 32, 341–348 (1972).
[Crossref]

Dyke, W. P.

J. P. Barbour, F. M. Charbonnier, W. W. Dolan, W. P. Dyke, E. E. Martin, and J. K. Trolan, “Determination of the surface tension and surface migration constants for tungsten,” Phys. Rev. 117, 1452 (1960).
[Crossref]

El-Kady, I.

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature 417, 52–55 (2002).
[Crossref] [PubMed]

Esashi, M.

S. Maruyama, T. Kashiwa, H. Yugami, and M. Esashi, “Thermal radiation from two-dimensionally confined modes in microcavities,” Appl. Phys. Lett. 79, 1393–1395 (2001).
[Crossref]

Fan, S.

K. A. Arpin, M. D. Losego, A. N. Cloud, H. Ning, J. Mallek, N. P. Sergeant, L. Zhu, Z. Yu, B. Kalanyan, G. N. Parsons, G. S. Girolami, J. R. Abelson, S. Fan, and P. V. Braun, “Three-dimensional self-assembled photonic crystals with high temperature stability for thermal emission modification,” Nat. Commun. 4, 2630 (2013).
[Crossref] [PubMed]

E. Rephaeli and S. Fan, “Absorber and emitter for solar thermo-photovoltaic systems to achieve efficiency exceeding the Shockley-Queisser limit,” Opt. Express 17, 15145–15159 (2009).
[Crossref] [PubMed]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[Crossref]

Fleming, J. G.

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature 417, 52–55 (2002).
[Crossref] [PubMed]

Geil, R. D.

V. Rinnerbauer, A. Lenert, D. M. Bierman, Y. X. Yeng, W. R. Chan, R. D. Geil, J. J. Senkevich, J. D. Joannopoulos, E. N. Wang, M. Soljacic, and I. Celanovic, “Metallic photonic crystal absorber-emitter for efficient spectral control in high-temperature solar thermophotovoltaics,” Adv. Energy Mater. 4, 1400334 (2014).
[Crossref]

V. Rinnerbauer, S. Ndao, Y. X. Yeng, J. J. Senkevich, K. F. Jensen, J. D. Joannopoulos, M. Soljacic, I. Celanovic, and R. D. Geil, “Large-area fabrication of high aspect ratio tantalum photonic crystals for high-temperature selective emitters,” J. Vac. Sci. Technol. B 31, 011802 (2013).
[Crossref]

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V. Stelmakh, V. Rinnerbauer, R. D. Geil, P. R. Aimone, J. J. Senkevich, J. D. Joannopoulos, M. Soljacic, and I. Celanovic, “High-temperature tantalum tungsten alloy photonic crystals: Stability, optical properties, and fabrication,” Appl. Phys. Lett. 103, 123903 (2013).
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Figures (13)

Fig. 1
Fig. 1

Schematic representation of the 1D PhCs considered in this study.

Fig. 2
Fig. 2

Change in morphology of a 1D Ta PhC at 1200K; (a) 2D cross-section, (b) 3D projection after 0 hours, and (c) after 200 hours.

Fig. 3
Fig. 3

Change in the (a) effective depth, and (b) effective width (solid line) and aperture width (dashed line) of a 1D PhC over time.

Fig. 4
Fig. 4

The surface diffusion rate constants of tantalum (solid blue line) and tungsten (dashed red line) from 1000 to 1500K.

Fig. 5
Fig. 5

Infrared spectral emissivity of a 1D Ta PhC (solid blue line) and flat Ta (dashed black line) at 1200K.

Fig. 6
Fig. 6

Change in spectral emissivity of a 1D Ta PhC undergoing surface diffusion at 1200K.

Fig. 7
Fig. 7

Spectral emissivity of 1D Ta PhCs with cavity widths of 930 nm, and varying aperture widths wa (width of the cavity near its opening).

Fig. 8
Fig. 8

Effects of surface diffusion at 1200K on a 1D Ta PhC with depth of 5000 nm, a width of 1000 nm, and a period of (a) 1200 nm, (b) 1300 nm, and (c) 1400 nm.

Fig. 9
Fig. 9

(a) Effective depth and (b) aperture width of 1D Ta PhCs undergoing surface diffusion, with varying generalized Fresnel integral order n.

Fig. 10
Fig. 10

Change in morphology of an optimized 1D Ta PhC at 1200K; (a) rectangular structure, (b) 3rd order Fresnel integral structure.

Fig. 11
Fig. 11

Change in spectral emissivity of an optimized 1D Ta PhC undergoing surface diffusion at 1200K; (a) rectangular structure, (b) 3rd order Fresnel integral structure.

Fig. 12
Fig. 12

Comparison of the emission efficiencies (solid lines) and conversion efficiencies (dashed lines) of the initial and optimized structures.

Fig. 13
Fig. 13

PhC structures constructed from linear segments and generalized Fresnel integrals of order (a) n = 0, (b) n = 1, (c) n = 2, and (d) n = 3. Unstable positions are marked with black circles, while green circles illustrate maximum local curvature.

Tables (1)

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Table 1 Material constants of tantalum and tungsten.

Equations (8)

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v = [ Ω δ D s γ k B T ] s 2 κ n C SD s 2 κ n
λ 1 D = 2 / ( i w ) 2 + ( j d ) 2
η e ( t ) = 0 λ c ε ( λ , t ) d λ λ 5 ( exp [ h c λ k B T ] 1 ) 0 λ c d λ λ 5 ( exp [ h c λ k B T ] 1 )
η c ( t ) = 1 λ c 0 λ c ε ( λ , t ) d λ λ 4 ( exp [ h c λ k B T ] 1 ) 0 ε ( λ , t ) d λ λ 5 ( exp [ h c λ k B T ] 1 )
( x ( s ) , z ( s ) ) = B ( 0 s sin π 2 u n d u , 0 s cos π 2 u n d u )
κ = π 2 n B s n 1
s κ = π 2 n ( n 1 ) B s n 2
s 2 κ = π 2 n ( n 1 ) ( n 2 ) B 3 s n 3

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