Abstract

We investigate the dielectric properties of the 4H and 6H polytypes of silicon carbide in the 0.1-19 THz range, below the fundamental transverse-optical phonons. Folding of the Brillouin zone due to the specific superlattice structure of the two polytypes leads to activation of acoustic phonon modes. We use a combination of ultrabroadband terahertz time-domain spectroscopy and simulations based on density-functional perturbation theory to observe and characterize these modes, including band splitting due to the dissimilar carbon and silicon sublattices of the structures, and an indirect measurement of the anisotropic sound velocities in the two polytypes.

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

Full Article  |  PDF Article
OSA Recommended Articles
Accurate measurements of second-order nonlinear optical coefficients of 6H and 4H silicon carbide

Hiroaki Sato, Makoto Abe, Ichiro Shoji, Jun Suda, and Takashi Kondo
J. Opt. Soc. Am. B 26(10) 1892-1896 (2009)

Terahertz time-domain spectroscopy characterization of the far-infrared absorption and index of refraction of high-resistivity, float-zone silicon

Jianming Dai, Jiangquan Zhang, Weili Zhang, and D. Grischkowsky
J. Opt. Soc. Am. B 21(7) 1379-1386 (2004)

High-quality factor, high-confinement microring resonators in 4H-silicon carbide-on-insulator

Yi Zheng, Minhao Pu, Ailun Yi, Bingdong Chang, Tiangui You, Kai Huang, Ayman N. Kamel, Martin R. Henriksen, Asbjørn A. Jørgensen, Xin Ou, and Haiyan Ou
Opt. Express 27(9) 13053-13060 (2019)

References

  • View by:
  • |
  • |
  • |

  1. T. Kimoto, and J. A. Cooper, Fundamentals of silicon carbide technology (John Wiley & Sons Singapore Pte. Ltd, 2014).
  2. H. Ou, Y. Ou, A. Argyraki, S. Schimmel, M. Kaiser, P. Wellmann, M. K. Linnarsson, V. Jokubavicius, J. Sun, R. Liljedahl, and M. Syväjärvi, “Advances in wide bandgap SiC for optoelectronics,” Eur. Phys. J. B 87(3), 58 (2014).
    [Crossref]
  3. I. Aharonovich, D. Englund, and M. Toth, “Solid-state single-photon emitters,” Nat. Photonics 10(10), 631–641 (2016).
    [Crossref]
  4. K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater. 8(3), 203–207 (2009).
    [Crossref] [PubMed]
  5. J. Baringhaus, M. Ruan, F. Edler, A. Tejeda, M. Sicot, A. Taleb-Ibrahimi, A.-P. Li, Z. Jiang, E. H. Conrad, C. Berger, C. Tegenkamp, and W. A. de Heer, “Exceptional ballistic transport in epitaxial graphene nanoribbons,” Nature 506(7488), 349–354 (2014).
    [Crossref] [PubMed]
  6. J. D. Caldwell, L. Lindsay, V. Giannini, I. Vurgaftman, T. L. Reinecke, S. A. Maier, and O. J. Glembocki, “Low-loss, infrared and terahertz nanophotonics using surface phonon polaritons,” Nanophotonics 4(1), 44–68 (2015).
    [Crossref]
  7. H.-T. Fan, C.-H. Xu, Z.-H. Wang, G. Wang, C.-J. Liu, J.-K. Liang, X.-L. Chen, and Z.-Y. Wei, “Generation of broadband 17-μJ mid-infrared femtosecond pulses at 3.75 μm by silicon carbide crystal,” Opt. Lett. 39(21), 6249–6252 (2014).
    [Crossref] [PubMed]
  8. M. P. Fischer, J. Bühler, G. Fitzky, T. Kurihara, S. Eggert, A. Leitenstorfer, and D. Brida, “Coherent field transients below 15 THz from phase-matched difference frequency generation in 4H-SiC,” Opt. Lett. 42(14), 2687–2690 (2017).
    [Crossref] [PubMed]
  9. V. I. Sankin, A. V. Andrianov, A. O. Zakhar’in, and A. G. Petrov, “Terahertz electroluminescence from 6H-SiC structures with natural superlattice,” Appl. Phys. Lett. 100(11), 111109 (2012).
    [Crossref]
  10. M. Kruskopf, D. M. Pakdehi, K. Pierz, S. Wundrack, R. Stosch, T. Dziomba, M. Gotz, J. Baringhaus, J. Aprojanz, C. Tegenkamp, J. Lidzba, T. Seyller, F. Hohls, F. J. Ahlers, and H. W. Schumacher, “Comeback of epitaxial graphene for electronics: large-area growth of bilayer-free graphene on SiC,” 2D Mater. 3, 041002 (2016).
    [Crossref]
  11. J. Aprojanz, S. R. Power, P. Bampoulis, S. Roche, A.-P. Jauho, H. J. W. Zandvliet, A. A. Zakharov, and C. Tegenkamp, “Ballistic tracks in graphene nanoribbons,” Nat. Commun. 9(1), 4426 (2018).
    [Crossref] [PubMed]
  12. D. W. Feldman, J. H. Parker, W. J. Choyke, and L. Patrick, “Phonon dispersion curves by Raman scattering in SiC, polytypes 3C, 4H, 6H, 15R, and 21R,” Phys. Rev. 173(3), 787–793 (1968).
    [Crossref]
  13. S. Nakashima and H. Harima, “Raman investigation of SiC polytypes,” Phys. Status Solidi, A Appl. Res. 162(1), 39–64 (1997).
    [Crossref]
  14. A. S. Barker, J. L. Merz, and A. C. Gossard, “Study of zone-folding effects on phonons in alternating monolayers of GaAs-AlAs,” Phys. Rev. B Condens. Matter 17(8), 3181–3196 (1978).
    [Crossref]
  15. A. Polian, K. Kunc, and A. Kuhn, “Low-frequency lattice vibrations of δ-GaSe compared to ϵ- and γ-polytypes,” Solid State Commun. 19(11), 1079–1082 (1976).
    [Crossref]
  16. M. Naftaly, J. F. Molloy, B. Magnusson, Y. M. Andreev, and G. V. Lanskii, “Silicon carbide--a high-transparency nonlinear material for THz applications,” Opt. Express 24(3), 2590–2595 (2016).
    [Crossref] [PubMed]
  17. B. Ellis and T. S. Moss, “The conduction bands in 6H and 15R silicon carbide. II. Absorption measurements,” Proc. R. Soc. Lond. A Math. Phys. Sci. 299, 393–404 (1967).
  18. J. Dai, X. Xie, and X. C. Zhang, “Detection of broadband terahertz waves with a laser-induced plasma in gases,” Phys. Rev. Lett. 97(10), 103903 (2006).
    [Crossref] [PubMed]
  19. T. Wang, K. Iwaszczuk, E. A. Wrisberg, E. V. Denning, and P. U. Jepsen, “Linearity of Air-Biased Coherent Detection for Terahertz Time-Domain Spectroscopy,” J. Infrared Millim. Terahertz Waves 37(6), 592–604 (2016).
    [Crossref]
  20. P. Kužel, H. Němec, F. Kadlec, and C. Kadlec, “Gouy shift correction for highly accurate refractive index retrieval in time-domain terahertz spectroscopy,” Opt. Express 18(15), 15338–15348 (2010).
    [Crossref] [PubMed]
  21. P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging – Modern techniques and applications,” Laser Photonics Rev. 5(1), 124–166 (2011).
    [Crossref]
  22. S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. J. Probert, K. Refson, and M. C. Payne, “First principles methods using CASTEP,” Z. Kristallogr. 220, 567–570 (2005).
  23. K. Refson, P. R. Tulip, and S. J. Clark, “Variational density-functional perturbation theory for dielectrics and lattice dynamics,” Phys. Rev. B Condens. Matter Mater. Phys. 73(15), 155114 (2006).
    [Crossref]
  24. M. Walther, B. M. Fischer, and P. U. Jepsen, “Noncovalent intermolecular forces in polycrystalline and amorphous saccharides in the far infrared,” Chem. Phys. 288(2-3), 261–268 (2003).
    [Crossref]
  25. Z. Li and R. C. Bradt, “Thermal expansion of the hexagonal (6H) polytype of silicon carbide,” J. Am. Ceram. Soc. 69(12), 863–866 (1986).
    [Crossref]
  26. B. H. Cheong, K. J. Chang, and M. L. Cohen, “Pressure dependences of band gaps and optical-phonon frequency in cubic SiC,” Phys. Rev. B Condens. Matter 44(3), 1053–1056 (1991).
    [Crossref] [PubMed]
  27. K. Kamitani, M. Grimsditch, J. C. Nipko, C.-K. Loong, M. Okada, and I. Kimura, “The elastic constants of silicon carbide: A Brillouin-scattering study of 4H and 6H SiC single crystals,” J. Appl. Phys. 82(6), 3152–3154 (1997).
    [Crossref]
  28. G. Arlt and G. R. Schodder, “Some elastic constants of silicon carbide,” J. Acoust. Soc. Am. 37(2), 384–386 (1965).
    [Crossref]
  29. M. Stockmeier, R. Müller, S. A. Sakwe, P. J. Wellmann, and A. Magerl, “On the lattice parameters of silicon carbide,” J. Appl. Phys. 105(3), 033511 (2009).
    [Crossref]

2018 (1)

J. Aprojanz, S. R. Power, P. Bampoulis, S. Roche, A.-P. Jauho, H. J. W. Zandvliet, A. A. Zakharov, and C. Tegenkamp, “Ballistic tracks in graphene nanoribbons,” Nat. Commun. 9(1), 4426 (2018).
[Crossref] [PubMed]

2017 (1)

2016 (3)

I. Aharonovich, D. Englund, and M. Toth, “Solid-state single-photon emitters,” Nat. Photonics 10(10), 631–641 (2016).
[Crossref]

M. Naftaly, J. F. Molloy, B. Magnusson, Y. M. Andreev, and G. V. Lanskii, “Silicon carbide--a high-transparency nonlinear material for THz applications,” Opt. Express 24(3), 2590–2595 (2016).
[Crossref] [PubMed]

T. Wang, K. Iwaszczuk, E. A. Wrisberg, E. V. Denning, and P. U. Jepsen, “Linearity of Air-Biased Coherent Detection for Terahertz Time-Domain Spectroscopy,” J. Infrared Millim. Terahertz Waves 37(6), 592–604 (2016).
[Crossref]

2015 (1)

J. D. Caldwell, L. Lindsay, V. Giannini, I. Vurgaftman, T. L. Reinecke, S. A. Maier, and O. J. Glembocki, “Low-loss, infrared and terahertz nanophotonics using surface phonon polaritons,” Nanophotonics 4(1), 44–68 (2015).
[Crossref]

2014 (3)

H.-T. Fan, C.-H. Xu, Z.-H. Wang, G. Wang, C.-J. Liu, J.-K. Liang, X.-L. Chen, and Z.-Y. Wei, “Generation of broadband 17-μJ mid-infrared femtosecond pulses at 3.75 μm by silicon carbide crystal,” Opt. Lett. 39(21), 6249–6252 (2014).
[Crossref] [PubMed]

H. Ou, Y. Ou, A. Argyraki, S. Schimmel, M. Kaiser, P. Wellmann, M. K. Linnarsson, V. Jokubavicius, J. Sun, R. Liljedahl, and M. Syväjärvi, “Advances in wide bandgap SiC for optoelectronics,” Eur. Phys. J. B 87(3), 58 (2014).
[Crossref]

J. Baringhaus, M. Ruan, F. Edler, A. Tejeda, M. Sicot, A. Taleb-Ibrahimi, A.-P. Li, Z. Jiang, E. H. Conrad, C. Berger, C. Tegenkamp, and W. A. de Heer, “Exceptional ballistic transport in epitaxial graphene nanoribbons,” Nature 506(7488), 349–354 (2014).
[Crossref] [PubMed]

2012 (1)

V. I. Sankin, A. V. Andrianov, A. O. Zakhar’in, and A. G. Petrov, “Terahertz electroluminescence from 6H-SiC structures with natural superlattice,” Appl. Phys. Lett. 100(11), 111109 (2012).
[Crossref]

2011 (1)

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging – Modern techniques and applications,” Laser Photonics Rev. 5(1), 124–166 (2011).
[Crossref]

2010 (1)

2009 (2)

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater. 8(3), 203–207 (2009).
[Crossref] [PubMed]

M. Stockmeier, R. Müller, S. A. Sakwe, P. J. Wellmann, and A. Magerl, “On the lattice parameters of silicon carbide,” J. Appl. Phys. 105(3), 033511 (2009).
[Crossref]

2006 (2)

K. Refson, P. R. Tulip, and S. J. Clark, “Variational density-functional perturbation theory for dielectrics and lattice dynamics,” Phys. Rev. B Condens. Matter Mater. Phys. 73(15), 155114 (2006).
[Crossref]

J. Dai, X. Xie, and X. C. Zhang, “Detection of broadband terahertz waves with a laser-induced plasma in gases,” Phys. Rev. Lett. 97(10), 103903 (2006).
[Crossref] [PubMed]

2005 (1)

S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. J. Probert, K. Refson, and M. C. Payne, “First principles methods using CASTEP,” Z. Kristallogr. 220, 567–570 (2005).

2003 (1)

M. Walther, B. M. Fischer, and P. U. Jepsen, “Noncovalent intermolecular forces in polycrystalline and amorphous saccharides in the far infrared,” Chem. Phys. 288(2-3), 261–268 (2003).
[Crossref]

1997 (2)

K. Kamitani, M. Grimsditch, J. C. Nipko, C.-K. Loong, M. Okada, and I. Kimura, “The elastic constants of silicon carbide: A Brillouin-scattering study of 4H and 6H SiC single crystals,” J. Appl. Phys. 82(6), 3152–3154 (1997).
[Crossref]

S. Nakashima and H. Harima, “Raman investigation of SiC polytypes,” Phys. Status Solidi, A Appl. Res. 162(1), 39–64 (1997).
[Crossref]

1991 (1)

B. H. Cheong, K. J. Chang, and M. L. Cohen, “Pressure dependences of band gaps and optical-phonon frequency in cubic SiC,” Phys. Rev. B Condens. Matter 44(3), 1053–1056 (1991).
[Crossref] [PubMed]

1986 (1)

Z. Li and R. C. Bradt, “Thermal expansion of the hexagonal (6H) polytype of silicon carbide,” J. Am. Ceram. Soc. 69(12), 863–866 (1986).
[Crossref]

1978 (1)

A. S. Barker, J. L. Merz, and A. C. Gossard, “Study of zone-folding effects on phonons in alternating monolayers of GaAs-AlAs,” Phys. Rev. B Condens. Matter 17(8), 3181–3196 (1978).
[Crossref]

1976 (1)

A. Polian, K. Kunc, and A. Kuhn, “Low-frequency lattice vibrations of δ-GaSe compared to ϵ- and γ-polytypes,” Solid State Commun. 19(11), 1079–1082 (1976).
[Crossref]

1968 (1)

D. W. Feldman, J. H. Parker, W. J. Choyke, and L. Patrick, “Phonon dispersion curves by Raman scattering in SiC, polytypes 3C, 4H, 6H, 15R, and 21R,” Phys. Rev. 173(3), 787–793 (1968).
[Crossref]

1967 (1)

B. Ellis and T. S. Moss, “The conduction bands in 6H and 15R silicon carbide. II. Absorption measurements,” Proc. R. Soc. Lond. A Math. Phys. Sci. 299, 393–404 (1967).

1965 (1)

G. Arlt and G. R. Schodder, “Some elastic constants of silicon carbide,” J. Acoust. Soc. Am. 37(2), 384–386 (1965).
[Crossref]

Aharonovich, I.

I. Aharonovich, D. Englund, and M. Toth, “Solid-state single-photon emitters,” Nat. Photonics 10(10), 631–641 (2016).
[Crossref]

Andreev, Y. M.

Andrianov, A. V.

V. I. Sankin, A. V. Andrianov, A. O. Zakhar’in, and A. G. Petrov, “Terahertz electroluminescence from 6H-SiC structures with natural superlattice,” Appl. Phys. Lett. 100(11), 111109 (2012).
[Crossref]

Aprojanz, J.

J. Aprojanz, S. R. Power, P. Bampoulis, S. Roche, A.-P. Jauho, H. J. W. Zandvliet, A. A. Zakharov, and C. Tegenkamp, “Ballistic tracks in graphene nanoribbons,” Nat. Commun. 9(1), 4426 (2018).
[Crossref] [PubMed]

Argyraki, A.

H. Ou, Y. Ou, A. Argyraki, S. Schimmel, M. Kaiser, P. Wellmann, M. K. Linnarsson, V. Jokubavicius, J. Sun, R. Liljedahl, and M. Syväjärvi, “Advances in wide bandgap SiC for optoelectronics,” Eur. Phys. J. B 87(3), 58 (2014).
[Crossref]

Arlt, G.

G. Arlt and G. R. Schodder, “Some elastic constants of silicon carbide,” J. Acoust. Soc. Am. 37(2), 384–386 (1965).
[Crossref]

Bampoulis, P.

J. Aprojanz, S. R. Power, P. Bampoulis, S. Roche, A.-P. Jauho, H. J. W. Zandvliet, A. A. Zakharov, and C. Tegenkamp, “Ballistic tracks in graphene nanoribbons,” Nat. Commun. 9(1), 4426 (2018).
[Crossref] [PubMed]

Baringhaus, J.

J. Baringhaus, M. Ruan, F. Edler, A. Tejeda, M. Sicot, A. Taleb-Ibrahimi, A.-P. Li, Z. Jiang, E. H. Conrad, C. Berger, C. Tegenkamp, and W. A. de Heer, “Exceptional ballistic transport in epitaxial graphene nanoribbons,” Nature 506(7488), 349–354 (2014).
[Crossref] [PubMed]

Barker, A. S.

A. S. Barker, J. L. Merz, and A. C. Gossard, “Study of zone-folding effects on phonons in alternating monolayers of GaAs-AlAs,” Phys. Rev. B Condens. Matter 17(8), 3181–3196 (1978).
[Crossref]

Berger, C.

J. Baringhaus, M. Ruan, F. Edler, A. Tejeda, M. Sicot, A. Taleb-Ibrahimi, A.-P. Li, Z. Jiang, E. H. Conrad, C. Berger, C. Tegenkamp, and W. A. de Heer, “Exceptional ballistic transport in epitaxial graphene nanoribbons,” Nature 506(7488), 349–354 (2014).
[Crossref] [PubMed]

Bostwick, A.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater. 8(3), 203–207 (2009).
[Crossref] [PubMed]

Bradt, R. C.

Z. Li and R. C. Bradt, “Thermal expansion of the hexagonal (6H) polytype of silicon carbide,” J. Am. Ceram. Soc. 69(12), 863–866 (1986).
[Crossref]

Brida, D.

Bühler, J.

Caldwell, J. D.

J. D. Caldwell, L. Lindsay, V. Giannini, I. Vurgaftman, T. L. Reinecke, S. A. Maier, and O. J. Glembocki, “Low-loss, infrared and terahertz nanophotonics using surface phonon polaritons,” Nanophotonics 4(1), 44–68 (2015).
[Crossref]

Chang, K. J.

B. H. Cheong, K. J. Chang, and M. L. Cohen, “Pressure dependences of band gaps and optical-phonon frequency in cubic SiC,” Phys. Rev. B Condens. Matter 44(3), 1053–1056 (1991).
[Crossref] [PubMed]

Chen, X.-L.

Cheong, B. H.

B. H. Cheong, K. J. Chang, and M. L. Cohen, “Pressure dependences of band gaps and optical-phonon frequency in cubic SiC,” Phys. Rev. B Condens. Matter 44(3), 1053–1056 (1991).
[Crossref] [PubMed]

Choyke, W. J.

D. W. Feldman, J. H. Parker, W. J. Choyke, and L. Patrick, “Phonon dispersion curves by Raman scattering in SiC, polytypes 3C, 4H, 6H, 15R, and 21R,” Phys. Rev. 173(3), 787–793 (1968).
[Crossref]

Clark, S. J.

K. Refson, P. R. Tulip, and S. J. Clark, “Variational density-functional perturbation theory for dielectrics and lattice dynamics,” Phys. Rev. B Condens. Matter Mater. Phys. 73(15), 155114 (2006).
[Crossref]

S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. J. Probert, K. Refson, and M. C. Payne, “First principles methods using CASTEP,” Z. Kristallogr. 220, 567–570 (2005).

Cohen, M. L.

B. H. Cheong, K. J. Chang, and M. L. Cohen, “Pressure dependences of band gaps and optical-phonon frequency in cubic SiC,” Phys. Rev. B Condens. Matter 44(3), 1053–1056 (1991).
[Crossref] [PubMed]

Conrad, E. H.

J. Baringhaus, M. Ruan, F. Edler, A. Tejeda, M. Sicot, A. Taleb-Ibrahimi, A.-P. Li, Z. Jiang, E. H. Conrad, C. Berger, C. Tegenkamp, and W. A. de Heer, “Exceptional ballistic transport in epitaxial graphene nanoribbons,” Nature 506(7488), 349–354 (2014).
[Crossref] [PubMed]

Cooke, D. G.

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging – Modern techniques and applications,” Laser Photonics Rev. 5(1), 124–166 (2011).
[Crossref]

Dai, J.

J. Dai, X. Xie, and X. C. Zhang, “Detection of broadband terahertz waves with a laser-induced plasma in gases,” Phys. Rev. Lett. 97(10), 103903 (2006).
[Crossref] [PubMed]

de Heer, W. A.

J. Baringhaus, M. Ruan, F. Edler, A. Tejeda, M. Sicot, A. Taleb-Ibrahimi, A.-P. Li, Z. Jiang, E. H. Conrad, C. Berger, C. Tegenkamp, and W. A. de Heer, “Exceptional ballistic transport in epitaxial graphene nanoribbons,” Nature 506(7488), 349–354 (2014).
[Crossref] [PubMed]

Denning, E. V.

T. Wang, K. Iwaszczuk, E. A. Wrisberg, E. V. Denning, and P. U. Jepsen, “Linearity of Air-Biased Coherent Detection for Terahertz Time-Domain Spectroscopy,” J. Infrared Millim. Terahertz Waves 37(6), 592–604 (2016).
[Crossref]

Edler, F.

J. Baringhaus, M. Ruan, F. Edler, A. Tejeda, M. Sicot, A. Taleb-Ibrahimi, A.-P. Li, Z. Jiang, E. H. Conrad, C. Berger, C. Tegenkamp, and W. A. de Heer, “Exceptional ballistic transport in epitaxial graphene nanoribbons,” Nature 506(7488), 349–354 (2014).
[Crossref] [PubMed]

Eggert, S.

Ellis, B.

B. Ellis and T. S. Moss, “The conduction bands in 6H and 15R silicon carbide. II. Absorption measurements,” Proc. R. Soc. Lond. A Math. Phys. Sci. 299, 393–404 (1967).

Emtsev, K. V.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater. 8(3), 203–207 (2009).
[Crossref] [PubMed]

Englund, D.

I. Aharonovich, D. Englund, and M. Toth, “Solid-state single-photon emitters,” Nat. Photonics 10(10), 631–641 (2016).
[Crossref]

Fan, H.-T.

Feldman, D. W.

D. W. Feldman, J. H. Parker, W. J. Choyke, and L. Patrick, “Phonon dispersion curves by Raman scattering in SiC, polytypes 3C, 4H, 6H, 15R, and 21R,” Phys. Rev. 173(3), 787–793 (1968).
[Crossref]

Fischer, B. M.

M. Walther, B. M. Fischer, and P. U. Jepsen, “Noncovalent intermolecular forces in polycrystalline and amorphous saccharides in the far infrared,” Chem. Phys. 288(2-3), 261–268 (2003).
[Crossref]

Fischer, M. P.

Fitzky, G.

Giannini, V.

J. D. Caldwell, L. Lindsay, V. Giannini, I. Vurgaftman, T. L. Reinecke, S. A. Maier, and O. J. Glembocki, “Low-loss, infrared and terahertz nanophotonics using surface phonon polaritons,” Nanophotonics 4(1), 44–68 (2015).
[Crossref]

Glembocki, O. J.

J. D. Caldwell, L. Lindsay, V. Giannini, I. Vurgaftman, T. L. Reinecke, S. A. Maier, and O. J. Glembocki, “Low-loss, infrared and terahertz nanophotonics using surface phonon polaritons,” Nanophotonics 4(1), 44–68 (2015).
[Crossref]

Gossard, A. C.

A. S. Barker, J. L. Merz, and A. C. Gossard, “Study of zone-folding effects on phonons in alternating monolayers of GaAs-AlAs,” Phys. Rev. B Condens. Matter 17(8), 3181–3196 (1978).
[Crossref]

Grimsditch, M.

K. Kamitani, M. Grimsditch, J. C. Nipko, C.-K. Loong, M. Okada, and I. Kimura, “The elastic constants of silicon carbide: A Brillouin-scattering study of 4H and 6H SiC single crystals,” J. Appl. Phys. 82(6), 3152–3154 (1997).
[Crossref]

Harima, H.

S. Nakashima and H. Harima, “Raman investigation of SiC polytypes,” Phys. Status Solidi, A Appl. Res. 162(1), 39–64 (1997).
[Crossref]

Hasnip, P. J.

S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. J. Probert, K. Refson, and M. C. Payne, “First principles methods using CASTEP,” Z. Kristallogr. 220, 567–570 (2005).

Horn, K.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater. 8(3), 203–207 (2009).
[Crossref] [PubMed]

Iwaszczuk, K.

T. Wang, K. Iwaszczuk, E. A. Wrisberg, E. V. Denning, and P. U. Jepsen, “Linearity of Air-Biased Coherent Detection for Terahertz Time-Domain Spectroscopy,” J. Infrared Millim. Terahertz Waves 37(6), 592–604 (2016).
[Crossref]

Jauho, A.-P.

J. Aprojanz, S. R. Power, P. Bampoulis, S. Roche, A.-P. Jauho, H. J. W. Zandvliet, A. A. Zakharov, and C. Tegenkamp, “Ballistic tracks in graphene nanoribbons,” Nat. Commun. 9(1), 4426 (2018).
[Crossref] [PubMed]

Jepsen, P. U.

T. Wang, K. Iwaszczuk, E. A. Wrisberg, E. V. Denning, and P. U. Jepsen, “Linearity of Air-Biased Coherent Detection for Terahertz Time-Domain Spectroscopy,” J. Infrared Millim. Terahertz Waves 37(6), 592–604 (2016).
[Crossref]

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging – Modern techniques and applications,” Laser Photonics Rev. 5(1), 124–166 (2011).
[Crossref]

M. Walther, B. M. Fischer, and P. U. Jepsen, “Noncovalent intermolecular forces in polycrystalline and amorphous saccharides in the far infrared,” Chem. Phys. 288(2-3), 261–268 (2003).
[Crossref]

Jiang, Z.

J. Baringhaus, M. Ruan, F. Edler, A. Tejeda, M. Sicot, A. Taleb-Ibrahimi, A.-P. Li, Z. Jiang, E. H. Conrad, C. Berger, C. Tegenkamp, and W. A. de Heer, “Exceptional ballistic transport in epitaxial graphene nanoribbons,” Nature 506(7488), 349–354 (2014).
[Crossref] [PubMed]

Jobst, J.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater. 8(3), 203–207 (2009).
[Crossref] [PubMed]

Jokubavicius, V.

H. Ou, Y. Ou, A. Argyraki, S. Schimmel, M. Kaiser, P. Wellmann, M. K. Linnarsson, V. Jokubavicius, J. Sun, R. Liljedahl, and M. Syväjärvi, “Advances in wide bandgap SiC for optoelectronics,” Eur. Phys. J. B 87(3), 58 (2014).
[Crossref]

Kadlec, C.

Kadlec, F.

Kaiser, M.

H. Ou, Y. Ou, A. Argyraki, S. Schimmel, M. Kaiser, P. Wellmann, M. K. Linnarsson, V. Jokubavicius, J. Sun, R. Liljedahl, and M. Syväjärvi, “Advances in wide bandgap SiC for optoelectronics,” Eur. Phys. J. B 87(3), 58 (2014).
[Crossref]

Kamitani, K.

K. Kamitani, M. Grimsditch, J. C. Nipko, C.-K. Loong, M. Okada, and I. Kimura, “The elastic constants of silicon carbide: A Brillouin-scattering study of 4H and 6H SiC single crystals,” J. Appl. Phys. 82(6), 3152–3154 (1997).
[Crossref]

Kellogg, G. L.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater. 8(3), 203–207 (2009).
[Crossref] [PubMed]

Kimura, I.

K. Kamitani, M. Grimsditch, J. C. Nipko, C.-K. Loong, M. Okada, and I. Kimura, “The elastic constants of silicon carbide: A Brillouin-scattering study of 4H and 6H SiC single crystals,” J. Appl. Phys. 82(6), 3152–3154 (1997).
[Crossref]

Koch, M.

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging – Modern techniques and applications,” Laser Photonics Rev. 5(1), 124–166 (2011).
[Crossref]

Kuhn, A.

A. Polian, K. Kunc, and A. Kuhn, “Low-frequency lattice vibrations of δ-GaSe compared to ϵ- and γ-polytypes,” Solid State Commun. 19(11), 1079–1082 (1976).
[Crossref]

Kunc, K.

A. Polian, K. Kunc, and A. Kuhn, “Low-frequency lattice vibrations of δ-GaSe compared to ϵ- and γ-polytypes,” Solid State Commun. 19(11), 1079–1082 (1976).
[Crossref]

Kurihara, T.

Kužel, P.

Lanskii, G. V.

Leitenstorfer, A.

Ley, L.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater. 8(3), 203–207 (2009).
[Crossref] [PubMed]

Li, A.-P.

J. Baringhaus, M. Ruan, F. Edler, A. Tejeda, M. Sicot, A. Taleb-Ibrahimi, A.-P. Li, Z. Jiang, E. H. Conrad, C. Berger, C. Tegenkamp, and W. A. de Heer, “Exceptional ballistic transport in epitaxial graphene nanoribbons,” Nature 506(7488), 349–354 (2014).
[Crossref] [PubMed]

Li, Z.

Z. Li and R. C. Bradt, “Thermal expansion of the hexagonal (6H) polytype of silicon carbide,” J. Am. Ceram. Soc. 69(12), 863–866 (1986).
[Crossref]

Liang, J.-K.

Liljedahl, R.

H. Ou, Y. Ou, A. Argyraki, S. Schimmel, M. Kaiser, P. Wellmann, M. K. Linnarsson, V. Jokubavicius, J. Sun, R. Liljedahl, and M. Syväjärvi, “Advances in wide bandgap SiC for optoelectronics,” Eur. Phys. J. B 87(3), 58 (2014).
[Crossref]

Lindsay, L.

J. D. Caldwell, L. Lindsay, V. Giannini, I. Vurgaftman, T. L. Reinecke, S. A. Maier, and O. J. Glembocki, “Low-loss, infrared and terahertz nanophotonics using surface phonon polaritons,” Nanophotonics 4(1), 44–68 (2015).
[Crossref]

Linnarsson, M. K.

H. Ou, Y. Ou, A. Argyraki, S. Schimmel, M. Kaiser, P. Wellmann, M. K. Linnarsson, V. Jokubavicius, J. Sun, R. Liljedahl, and M. Syväjärvi, “Advances in wide bandgap SiC for optoelectronics,” Eur. Phys. J. B 87(3), 58 (2014).
[Crossref]

Liu, C.-J.

Loong, C.-K.

K. Kamitani, M. Grimsditch, J. C. Nipko, C.-K. Loong, M. Okada, and I. Kimura, “The elastic constants of silicon carbide: A Brillouin-scattering study of 4H and 6H SiC single crystals,” J. Appl. Phys. 82(6), 3152–3154 (1997).
[Crossref]

Magerl, A.

M. Stockmeier, R. Müller, S. A. Sakwe, P. J. Wellmann, and A. Magerl, “On the lattice parameters of silicon carbide,” J. Appl. Phys. 105(3), 033511 (2009).
[Crossref]

Magnusson, B.

Maier, S. A.

J. D. Caldwell, L. Lindsay, V. Giannini, I. Vurgaftman, T. L. Reinecke, S. A. Maier, and O. J. Glembocki, “Low-loss, infrared and terahertz nanophotonics using surface phonon polaritons,” Nanophotonics 4(1), 44–68 (2015).
[Crossref]

McChesney, J. L.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater. 8(3), 203–207 (2009).
[Crossref] [PubMed]

Merz, J. L.

A. S. Barker, J. L. Merz, and A. C. Gossard, “Study of zone-folding effects on phonons in alternating monolayers of GaAs-AlAs,” Phys. Rev. B Condens. Matter 17(8), 3181–3196 (1978).
[Crossref]

Molloy, J. F.

Moss, T. S.

B. Ellis and T. S. Moss, “The conduction bands in 6H and 15R silicon carbide. II. Absorption measurements,” Proc. R. Soc. Lond. A Math. Phys. Sci. 299, 393–404 (1967).

Müller, R.

M. Stockmeier, R. Müller, S. A. Sakwe, P. J. Wellmann, and A. Magerl, “On the lattice parameters of silicon carbide,” J. Appl. Phys. 105(3), 033511 (2009).
[Crossref]

Naftaly, M.

Nakashima, S.

S. Nakashima and H. Harima, “Raman investigation of SiC polytypes,” Phys. Status Solidi, A Appl. Res. 162(1), 39–64 (1997).
[Crossref]

Nemec, H.

Nipko, J. C.

K. Kamitani, M. Grimsditch, J. C. Nipko, C.-K. Loong, M. Okada, and I. Kimura, “The elastic constants of silicon carbide: A Brillouin-scattering study of 4H and 6H SiC single crystals,” J. Appl. Phys. 82(6), 3152–3154 (1997).
[Crossref]

Ohta, T.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater. 8(3), 203–207 (2009).
[Crossref] [PubMed]

Okada, M.

K. Kamitani, M. Grimsditch, J. C. Nipko, C.-K. Loong, M. Okada, and I. Kimura, “The elastic constants of silicon carbide: A Brillouin-scattering study of 4H and 6H SiC single crystals,” J. Appl. Phys. 82(6), 3152–3154 (1997).
[Crossref]

Ou, H.

H. Ou, Y. Ou, A. Argyraki, S. Schimmel, M. Kaiser, P. Wellmann, M. K. Linnarsson, V. Jokubavicius, J. Sun, R. Liljedahl, and M. Syväjärvi, “Advances in wide bandgap SiC for optoelectronics,” Eur. Phys. J. B 87(3), 58 (2014).
[Crossref]

Ou, Y.

H. Ou, Y. Ou, A. Argyraki, S. Schimmel, M. Kaiser, P. Wellmann, M. K. Linnarsson, V. Jokubavicius, J. Sun, R. Liljedahl, and M. Syväjärvi, “Advances in wide bandgap SiC for optoelectronics,” Eur. Phys. J. B 87(3), 58 (2014).
[Crossref]

Parker, J. H.

D. W. Feldman, J. H. Parker, W. J. Choyke, and L. Patrick, “Phonon dispersion curves by Raman scattering in SiC, polytypes 3C, 4H, 6H, 15R, and 21R,” Phys. Rev. 173(3), 787–793 (1968).
[Crossref]

Patrick, L.

D. W. Feldman, J. H. Parker, W. J. Choyke, and L. Patrick, “Phonon dispersion curves by Raman scattering in SiC, polytypes 3C, 4H, 6H, 15R, and 21R,” Phys. Rev. 173(3), 787–793 (1968).
[Crossref]

Payne, M. C.

S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. J. Probert, K. Refson, and M. C. Payne, “First principles methods using CASTEP,” Z. Kristallogr. 220, 567–570 (2005).

Petrov, A. G.

V. I. Sankin, A. V. Andrianov, A. O. Zakhar’in, and A. G. Petrov, “Terahertz electroluminescence from 6H-SiC structures with natural superlattice,” Appl. Phys. Lett. 100(11), 111109 (2012).
[Crossref]

Pickard, C. J.

S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. J. Probert, K. Refson, and M. C. Payne, “First principles methods using CASTEP,” Z. Kristallogr. 220, 567–570 (2005).

Polian, A.

A. Polian, K. Kunc, and A. Kuhn, “Low-frequency lattice vibrations of δ-GaSe compared to ϵ- and γ-polytypes,” Solid State Commun. 19(11), 1079–1082 (1976).
[Crossref]

Power, S. R.

J. Aprojanz, S. R. Power, P. Bampoulis, S. Roche, A.-P. Jauho, H. J. W. Zandvliet, A. A. Zakharov, and C. Tegenkamp, “Ballistic tracks in graphene nanoribbons,” Nat. Commun. 9(1), 4426 (2018).
[Crossref] [PubMed]

Probert, M. J.

S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. J. Probert, K. Refson, and M. C. Payne, “First principles methods using CASTEP,” Z. Kristallogr. 220, 567–570 (2005).

Refson, K.

K. Refson, P. R. Tulip, and S. J. Clark, “Variational density-functional perturbation theory for dielectrics and lattice dynamics,” Phys. Rev. B Condens. Matter Mater. Phys. 73(15), 155114 (2006).
[Crossref]

S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. J. Probert, K. Refson, and M. C. Payne, “First principles methods using CASTEP,” Z. Kristallogr. 220, 567–570 (2005).

Reinecke, T. L.

J. D. Caldwell, L. Lindsay, V. Giannini, I. Vurgaftman, T. L. Reinecke, S. A. Maier, and O. J. Glembocki, “Low-loss, infrared and terahertz nanophotonics using surface phonon polaritons,” Nanophotonics 4(1), 44–68 (2015).
[Crossref]

Reshanov, S. A.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater. 8(3), 203–207 (2009).
[Crossref] [PubMed]

Roche, S.

J. Aprojanz, S. R. Power, P. Bampoulis, S. Roche, A.-P. Jauho, H. J. W. Zandvliet, A. A. Zakharov, and C. Tegenkamp, “Ballistic tracks in graphene nanoribbons,” Nat. Commun. 9(1), 4426 (2018).
[Crossref] [PubMed]

Röhrl, J.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater. 8(3), 203–207 (2009).
[Crossref] [PubMed]

Rotenberg, E.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater. 8(3), 203–207 (2009).
[Crossref] [PubMed]

Ruan, M.

J. Baringhaus, M. Ruan, F. Edler, A. Tejeda, M. Sicot, A. Taleb-Ibrahimi, A.-P. Li, Z. Jiang, E. H. Conrad, C. Berger, C. Tegenkamp, and W. A. de Heer, “Exceptional ballistic transport in epitaxial graphene nanoribbons,” Nature 506(7488), 349–354 (2014).
[Crossref] [PubMed]

Sakwe, S. A.

M. Stockmeier, R. Müller, S. A. Sakwe, P. J. Wellmann, and A. Magerl, “On the lattice parameters of silicon carbide,” J. Appl. Phys. 105(3), 033511 (2009).
[Crossref]

Sankin, V. I.

V. I. Sankin, A. V. Andrianov, A. O. Zakhar’in, and A. G. Petrov, “Terahertz electroluminescence from 6H-SiC structures with natural superlattice,” Appl. Phys. Lett. 100(11), 111109 (2012).
[Crossref]

Schimmel, S.

H. Ou, Y. Ou, A. Argyraki, S. Schimmel, M. Kaiser, P. Wellmann, M. K. Linnarsson, V. Jokubavicius, J. Sun, R. Liljedahl, and M. Syväjärvi, “Advances in wide bandgap SiC for optoelectronics,” Eur. Phys. J. B 87(3), 58 (2014).
[Crossref]

Schmid, A. K.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater. 8(3), 203–207 (2009).
[Crossref] [PubMed]

Schodder, G. R.

G. Arlt and G. R. Schodder, “Some elastic constants of silicon carbide,” J. Acoust. Soc. Am. 37(2), 384–386 (1965).
[Crossref]

Segall, M. D.

S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. J. Probert, K. Refson, and M. C. Payne, “First principles methods using CASTEP,” Z. Kristallogr. 220, 567–570 (2005).

Seyller, T.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater. 8(3), 203–207 (2009).
[Crossref] [PubMed]

Sicot, M.

J. Baringhaus, M. Ruan, F. Edler, A. Tejeda, M. Sicot, A. Taleb-Ibrahimi, A.-P. Li, Z. Jiang, E. H. Conrad, C. Berger, C. Tegenkamp, and W. A. de Heer, “Exceptional ballistic transport in epitaxial graphene nanoribbons,” Nature 506(7488), 349–354 (2014).
[Crossref] [PubMed]

Stockmeier, M.

M. Stockmeier, R. Müller, S. A. Sakwe, P. J. Wellmann, and A. Magerl, “On the lattice parameters of silicon carbide,” J. Appl. Phys. 105(3), 033511 (2009).
[Crossref]

Sun, J.

H. Ou, Y. Ou, A. Argyraki, S. Schimmel, M. Kaiser, P. Wellmann, M. K. Linnarsson, V. Jokubavicius, J. Sun, R. Liljedahl, and M. Syväjärvi, “Advances in wide bandgap SiC for optoelectronics,” Eur. Phys. J. B 87(3), 58 (2014).
[Crossref]

Syväjärvi, M.

H. Ou, Y. Ou, A. Argyraki, S. Schimmel, M. Kaiser, P. Wellmann, M. K. Linnarsson, V. Jokubavicius, J. Sun, R. Liljedahl, and M. Syväjärvi, “Advances in wide bandgap SiC for optoelectronics,” Eur. Phys. J. B 87(3), 58 (2014).
[Crossref]

Taleb-Ibrahimi, A.

J. Baringhaus, M. Ruan, F. Edler, A. Tejeda, M. Sicot, A. Taleb-Ibrahimi, A.-P. Li, Z. Jiang, E. H. Conrad, C. Berger, C. Tegenkamp, and W. A. de Heer, “Exceptional ballistic transport in epitaxial graphene nanoribbons,” Nature 506(7488), 349–354 (2014).
[Crossref] [PubMed]

Tegenkamp, C.

J. Aprojanz, S. R. Power, P. Bampoulis, S. Roche, A.-P. Jauho, H. J. W. Zandvliet, A. A. Zakharov, and C. Tegenkamp, “Ballistic tracks in graphene nanoribbons,” Nat. Commun. 9(1), 4426 (2018).
[Crossref] [PubMed]

J. Baringhaus, M. Ruan, F. Edler, A. Tejeda, M. Sicot, A. Taleb-Ibrahimi, A.-P. Li, Z. Jiang, E. H. Conrad, C. Berger, C. Tegenkamp, and W. A. de Heer, “Exceptional ballistic transport in epitaxial graphene nanoribbons,” Nature 506(7488), 349–354 (2014).
[Crossref] [PubMed]

Tejeda, A.

J. Baringhaus, M. Ruan, F. Edler, A. Tejeda, M. Sicot, A. Taleb-Ibrahimi, A.-P. Li, Z. Jiang, E. H. Conrad, C. Berger, C. Tegenkamp, and W. A. de Heer, “Exceptional ballistic transport in epitaxial graphene nanoribbons,” Nature 506(7488), 349–354 (2014).
[Crossref] [PubMed]

Toth, M.

I. Aharonovich, D. Englund, and M. Toth, “Solid-state single-photon emitters,” Nat. Photonics 10(10), 631–641 (2016).
[Crossref]

Tulip, P. R.

K. Refson, P. R. Tulip, and S. J. Clark, “Variational density-functional perturbation theory for dielectrics and lattice dynamics,” Phys. Rev. B Condens. Matter Mater. Phys. 73(15), 155114 (2006).
[Crossref]

Vurgaftman, I.

J. D. Caldwell, L. Lindsay, V. Giannini, I. Vurgaftman, T. L. Reinecke, S. A. Maier, and O. J. Glembocki, “Low-loss, infrared and terahertz nanophotonics using surface phonon polaritons,” Nanophotonics 4(1), 44–68 (2015).
[Crossref]

Waldmann, D.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater. 8(3), 203–207 (2009).
[Crossref] [PubMed]

Walther, M.

M. Walther, B. M. Fischer, and P. U. Jepsen, “Noncovalent intermolecular forces in polycrystalline and amorphous saccharides in the far infrared,” Chem. Phys. 288(2-3), 261–268 (2003).
[Crossref]

Wang, G.

Wang, T.

T. Wang, K. Iwaszczuk, E. A. Wrisberg, E. V. Denning, and P. U. Jepsen, “Linearity of Air-Biased Coherent Detection for Terahertz Time-Domain Spectroscopy,” J. Infrared Millim. Terahertz Waves 37(6), 592–604 (2016).
[Crossref]

Wang, Z.-H.

Weber, H. B.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater. 8(3), 203–207 (2009).
[Crossref] [PubMed]

Wei, Z.-Y.

Wellmann, P.

H. Ou, Y. Ou, A. Argyraki, S. Schimmel, M. Kaiser, P. Wellmann, M. K. Linnarsson, V. Jokubavicius, J. Sun, R. Liljedahl, and M. Syväjärvi, “Advances in wide bandgap SiC for optoelectronics,” Eur. Phys. J. B 87(3), 58 (2014).
[Crossref]

Wellmann, P. J.

M. Stockmeier, R. Müller, S. A. Sakwe, P. J. Wellmann, and A. Magerl, “On the lattice parameters of silicon carbide,” J. Appl. Phys. 105(3), 033511 (2009).
[Crossref]

Wrisberg, E. A.

T. Wang, K. Iwaszczuk, E. A. Wrisberg, E. V. Denning, and P. U. Jepsen, “Linearity of Air-Biased Coherent Detection for Terahertz Time-Domain Spectroscopy,” J. Infrared Millim. Terahertz Waves 37(6), 592–604 (2016).
[Crossref]

Xie, X.

J. Dai, X. Xie, and X. C. Zhang, “Detection of broadband terahertz waves with a laser-induced plasma in gases,” Phys. Rev. Lett. 97(10), 103903 (2006).
[Crossref] [PubMed]

Xu, C.-H.

Zakhar’in, A. O.

V. I. Sankin, A. V. Andrianov, A. O. Zakhar’in, and A. G. Petrov, “Terahertz electroluminescence from 6H-SiC structures with natural superlattice,” Appl. Phys. Lett. 100(11), 111109 (2012).
[Crossref]

Zakharov, A. A.

J. Aprojanz, S. R. Power, P. Bampoulis, S. Roche, A.-P. Jauho, H. J. W. Zandvliet, A. A. Zakharov, and C. Tegenkamp, “Ballistic tracks in graphene nanoribbons,” Nat. Commun. 9(1), 4426 (2018).
[Crossref] [PubMed]

Zandvliet, H. J. W.

J. Aprojanz, S. R. Power, P. Bampoulis, S. Roche, A.-P. Jauho, H. J. W. Zandvliet, A. A. Zakharov, and C. Tegenkamp, “Ballistic tracks in graphene nanoribbons,” Nat. Commun. 9(1), 4426 (2018).
[Crossref] [PubMed]

Zhang, X. C.

J. Dai, X. Xie, and X. C. Zhang, “Detection of broadband terahertz waves with a laser-induced plasma in gases,” Phys. Rev. Lett. 97(10), 103903 (2006).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

V. I. Sankin, A. V. Andrianov, A. O. Zakhar’in, and A. G. Petrov, “Terahertz electroluminescence from 6H-SiC structures with natural superlattice,” Appl. Phys. Lett. 100(11), 111109 (2012).
[Crossref]

Chem. Phys. (1)

M. Walther, B. M. Fischer, and P. U. Jepsen, “Noncovalent intermolecular forces in polycrystalline and amorphous saccharides in the far infrared,” Chem. Phys. 288(2-3), 261–268 (2003).
[Crossref]

Eur. Phys. J. B (1)

H. Ou, Y. Ou, A. Argyraki, S. Schimmel, M. Kaiser, P. Wellmann, M. K. Linnarsson, V. Jokubavicius, J. Sun, R. Liljedahl, and M. Syväjärvi, “Advances in wide bandgap SiC for optoelectronics,” Eur. Phys. J. B 87(3), 58 (2014).
[Crossref]

J. Acoust. Soc. Am. (1)

G. Arlt and G. R. Schodder, “Some elastic constants of silicon carbide,” J. Acoust. Soc. Am. 37(2), 384–386 (1965).
[Crossref]

J. Am. Ceram. Soc. (1)

Z. Li and R. C. Bradt, “Thermal expansion of the hexagonal (6H) polytype of silicon carbide,” J. Am. Ceram. Soc. 69(12), 863–866 (1986).
[Crossref]

J. Appl. Phys. (2)

K. Kamitani, M. Grimsditch, J. C. Nipko, C.-K. Loong, M. Okada, and I. Kimura, “The elastic constants of silicon carbide: A Brillouin-scattering study of 4H and 6H SiC single crystals,” J. Appl. Phys. 82(6), 3152–3154 (1997).
[Crossref]

M. Stockmeier, R. Müller, S. A. Sakwe, P. J. Wellmann, and A. Magerl, “On the lattice parameters of silicon carbide,” J. Appl. Phys. 105(3), 033511 (2009).
[Crossref]

J. Infrared Millim. Terahertz Waves (1)

T. Wang, K. Iwaszczuk, E. A. Wrisberg, E. V. Denning, and P. U. Jepsen, “Linearity of Air-Biased Coherent Detection for Terahertz Time-Domain Spectroscopy,” J. Infrared Millim. Terahertz Waves 37(6), 592–604 (2016).
[Crossref]

Laser Photonics Rev. (1)

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging – Modern techniques and applications,” Laser Photonics Rev. 5(1), 124–166 (2011).
[Crossref]

Nanophotonics (1)

J. D. Caldwell, L. Lindsay, V. Giannini, I. Vurgaftman, T. L. Reinecke, S. A. Maier, and O. J. Glembocki, “Low-loss, infrared and terahertz nanophotonics using surface phonon polaritons,” Nanophotonics 4(1), 44–68 (2015).
[Crossref]

Nat. Commun. (1)

J. Aprojanz, S. R. Power, P. Bampoulis, S. Roche, A.-P. Jauho, H. J. W. Zandvliet, A. A. Zakharov, and C. Tegenkamp, “Ballistic tracks in graphene nanoribbons,” Nat. Commun. 9(1), 4426 (2018).
[Crossref] [PubMed]

Nat. Mater. (1)

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater. 8(3), 203–207 (2009).
[Crossref] [PubMed]

Nat. Photonics (1)

I. Aharonovich, D. Englund, and M. Toth, “Solid-state single-photon emitters,” Nat. Photonics 10(10), 631–641 (2016).
[Crossref]

Nature (1)

J. Baringhaus, M. Ruan, F. Edler, A. Tejeda, M. Sicot, A. Taleb-Ibrahimi, A.-P. Li, Z. Jiang, E. H. Conrad, C. Berger, C. Tegenkamp, and W. A. de Heer, “Exceptional ballistic transport in epitaxial graphene nanoribbons,” Nature 506(7488), 349–354 (2014).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. (1)

D. W. Feldman, J. H. Parker, W. J. Choyke, and L. Patrick, “Phonon dispersion curves by Raman scattering in SiC, polytypes 3C, 4H, 6H, 15R, and 21R,” Phys. Rev. 173(3), 787–793 (1968).
[Crossref]

Phys. Rev. B Condens. Matter (2)

A. S. Barker, J. L. Merz, and A. C. Gossard, “Study of zone-folding effects on phonons in alternating monolayers of GaAs-AlAs,” Phys. Rev. B Condens. Matter 17(8), 3181–3196 (1978).
[Crossref]

B. H. Cheong, K. J. Chang, and M. L. Cohen, “Pressure dependences of band gaps and optical-phonon frequency in cubic SiC,” Phys. Rev. B Condens. Matter 44(3), 1053–1056 (1991).
[Crossref] [PubMed]

Phys. Rev. B Condens. Matter Mater. Phys. (1)

K. Refson, P. R. Tulip, and S. J. Clark, “Variational density-functional perturbation theory for dielectrics and lattice dynamics,” Phys. Rev. B Condens. Matter Mater. Phys. 73(15), 155114 (2006).
[Crossref]

Phys. Rev. Lett. (1)

J. Dai, X. Xie, and X. C. Zhang, “Detection of broadband terahertz waves with a laser-induced plasma in gases,” Phys. Rev. Lett. 97(10), 103903 (2006).
[Crossref] [PubMed]

Phys. Status Solidi, A Appl. Res. (1)

S. Nakashima and H. Harima, “Raman investigation of SiC polytypes,” Phys. Status Solidi, A Appl. Res. 162(1), 39–64 (1997).
[Crossref]

Proc. R. Soc. Lond. A Math. Phys. Sci. (1)

B. Ellis and T. S. Moss, “The conduction bands in 6H and 15R silicon carbide. II. Absorption measurements,” Proc. R. Soc. Lond. A Math. Phys. Sci. 299, 393–404 (1967).

Solid State Commun. (1)

A. Polian, K. Kunc, and A. Kuhn, “Low-frequency lattice vibrations of δ-GaSe compared to ϵ- and γ-polytypes,” Solid State Commun. 19(11), 1079–1082 (1976).
[Crossref]

Z. Kristallogr. (1)

S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. J. Probert, K. Refson, and M. C. Payne, “First principles methods using CASTEP,” Z. Kristallogr. 220, 567–570 (2005).

Other (2)

T. Kimoto, and J. A. Cooper, Fundamentals of silicon carbide technology (John Wiley & Sons Singapore Pte. Ltd, 2014).

M. Kruskopf, D. M. Pakdehi, K. Pierz, S. Wundrack, R. Stosch, T. Dziomba, M. Gotz, J. Baringhaus, J. Aprojanz, C. Tegenkamp, J. Lidzba, T. Seyller, F. Hohls, F. J. Ahlers, and H. W. Schumacher, “Comeback of epitaxial graphene for electronics: large-area growth of bilayer-free graphene on SiC,” 2D Mater. 3, 041002 (2016).
[Crossref]

Supplementary Material (6)

NameDescription
» Visualization 1       Visualization of the transverse acoustic mode at 7.8 THz in 4H SiC, activated by zone folding.
» Visualization 2       Visualization of the transverse acoustic mode at 6.87 THz in 6H SiC, activated by zone folding.
» Visualization 3       Visualization of the transverse acoustic mode at 7.0 THz in 6H SiC, activated by zone folding.
» Visualization 4       Visualization of the longitudinal acoustic phonon mode at 15.1 THz in 6H SiC, activated by zone folding.
» Visualization 5       Visualization of the longitudinal acoustic phonon mode at 18.2 THz in 4H SiC, activated by zone folding.
» Visualization 6       Visualization of the longitudinal acoustic phonon mode at 15.4 THz in 6H SiC, activated by zone folding.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1 Experimental setup. BS – R/T 80/20 beamsplitter; SHG – second harmonic generation crystal; HWP – dual wavelength half-wave plate; Si – silicon plate; BD – beam dump; BPF – 400-nm band pass filter; APD – avalanche photodiode; L – focusing lenses. The setup is driven by 35-fs, 800 nm, 1.5 mJ laser pulses at 1 kHz repetition rate.
Fig. 2
Fig. 2 Time-domain THz electric field transients (reference: black; sample: red) for (a) 4H SiC and (b) 6H SiC. Insets show the spectral amplitudes of each trace, with zoom on the narrow resonance features. Error bars indicate the standard deviation of 5 sequential measurements of each sample.
Fig. 3
Fig. 3 (a) Real and (b) imaginary part of the permittivity of 4H (blue curves) and 6H (red curves) SiC. The insets show a zoom onto the resonant modes in the 6.5-8.5 THz region. Dashed curves in insets are Lorentz fits to the measurements. (c) Imaginary part of permittivity measured at 70 degrees incidence angle with longitudinal phonons at 18.4 THz (4H) and 15.2 THz (6H). The shaded areas around each curve indicate the standard deviation of the measurements.
Fig. 4
Fig. 4 Index of refraction of 4H (blue) and 6H (red) SiC (ordinary axis) as function of wavelength, together with Sellmeier fits in the range 15-300 µm. Shaded areas indicate standard deviation of the experimental data. Top panel shows deviation between experimental data and fits, with RMS deviations indicated in the legend. Dashed and dashed-dotted curves show the Sellmeier fits from [8,16], respectively (4H SiC).
Fig. 5
Fig. 5 Acoustic phonon dispersion diagrams of (a) 4H and (b) 6H SiC, calculated by DFT. Red and blue symbols represent transverse and longitudinal zone-folded acoustic branches, respectively. Grey bars indicate IR intensities (upper logarithmic scale) predicted by DFPT. Solid, black lines indicate the linear dispersion relation and speed of sound for the transverse and longitudinal directions.
Fig. 6
Fig. 6 Representative potential energy curves calculated by DFPT for the 4H SiC TA mode at 7.83 THz (red symbols) and the second 6H TA mode at 7.00 THz (blue symbols). Dashed lines are harmonic fits.
Fig. 7
Fig. 7 Eigenmode motion of the zone-folded transverse (a-c) and longitudinal (d-f) acoustic modes of 4H SiC at 7.8 and 18.2 THz (a + d) and the split 6H SiC modes at 6.87 + 7.00 THz (b + c) and 15.1 + 15.4 THz (e + f). The bars indicate amplitude and polarization of the motion of the individual ions in the unit cell. See also Visualization 1, Visualization 2, Visualization 3, Visualization 4, Visualization 5, and Visualization 6 (1: 4H TA; 2: 6H TA1; 3: 6H TA2; 4: 4H LA; 5: 6H LA1; 6: 6H LA2).

Tables (3)

Tables Icon

Table 1 Lorentzian fitting parameters for 4H and 6H SiC

Tables Icon

Table 2 Experimental and DFT phonon frequencies [THz]

Tables Icon

Table 3 Planar (vT) and axial (vL) sound velocities (km/s) in 4H and 6H SiC, compared with literature values.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

ε(ω)= ε + k W k ω 0,k 2 ω 2 iω/τ ,
n o,4H 2 =6.588+ 3.174 λ 2 λ 2 157.1 ,
n o,6H 2 =6.649+ 3.152 λ 2 λ 2 158.0 ,

Metrics