Abstract

Nano-texturization provides sensitive routes for selection of preferred phonon modes. Biomimetic gallium arsenide (GaAs) nano-tips, with a pencil-like structure, prepared by an electron cyclotron resonance plasma etching of planar GaAs wafer demonstrates tunable strength of the surface optic (SO), and long wavelength transverse optic and longitudinal optic phonon modes. These modes can be tuned as a function of the length (L) of the nano-tips enabling phonon engineering. Invalidation of symmetry rules due to nano-texturization results in the excitation of a SO mode that can also be tuned, in strength and position, with L. Red shift of this mode with a change in the dielectric constant of the medium (air to aniline) confirms the SO nature. The theoretically estimated length scales indicate that the diameter modulated apexes of the nano-tips, whose length (L’) increases consistently with L, could be responsible in transferring the required momentum to the SO phonons.

© 2011 OSA

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    [CrossRef]
  25. S. Hayashi and H. Kanamori, “Raman scattering from the surface phonon mode in GaP microcrystals,” Phys. Rev. B 26(12), 7079–7082 (1982).
    [CrossRef]

2011

G. Liu, H. Zhao, J. Zhang, J. H. Park, L. J. Mawst, and N. Tansu, “Selective area epitaxy of ultra-high density InGaN quantum dots by diblock copolymer lithography,” Nanoscale Res. Lett. 6(1), 342 (2011).
[CrossRef] [PubMed]

2010

S. Chattopadhyay, Y. F. Huang, Y. J. Jen, A. Ganguly, K. H. Chen, and L. C. Chen, “Antireflecting and photonic nanostructures,” Mater. Sci. Eng. Rep. 69(1-3), 1–35 (2010).
[CrossRef]

T. F. Kuech and L. J. Mawst, “Nanofabrication of III-V semiconductors employing diblock copolymer lithography,” J. Phys. D Appl. Phys. 43(18), 183001 (2010).
[CrossRef]

2007

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

2006

K. W. Adu, Q. Xiong, H. R. Gutierrez, G. Chen, and P. C. Eklund, “Raman scattering as a probe of phonon confinement and surface optical modes in semiconducting nano-wires,” Appl. Phys., A Mater. Sci. Process. 85(3), 287–297 (2006).
[CrossRef]

C. H. Hsu, Y. F. Huang, L. C. Chen, S. Chattopadhyay, K. H. Chen, H. C. Lo, and C. F. Chen, “Morphology control of silicon nano-tips fabricated by electron cyclotron resonance plasma etching,” J. Vac. Sci. Technol. B 24(1), 308–311 (2006).
[CrossRef]

2004

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, K. H. Chen, and L. C. Chen, “Generally applicable self-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

2003

G. D. Mahan, R. Gupta, Q. Xiong, C. K. Adu, and P. C. Eklund, “Optical phonons in polar semiconductor nano-wires,” Phys. Rev. B 68(7), 073402 (2003).
[CrossRef]

R. Gupta, Q. Xiong, G. D. Mahan, and P. C. Eklund, “Surface optical phonons in gallium phosphide nano-wires,” Nano Lett. 3(12), 1745–1750 (2003).
[CrossRef]

2001

A. Sarua, J. Monecke, G. Irmer, I. M. Tiginyanu, G. Gärtner, and H. L. Hartnagel, “Fröhlich modes in porous III–V semiconductors,” J. Phys. Condens. Matter 13(31), 6687–6706 (2001).
[CrossRef]

I. M. Tiginyanu, A. Sarua, G. Irmer, J. Monecke, S. M. Hubbard, D. Pavlidis, and V. Valiaev, “Fröhlich modes in GaN columnar nanostructures,” Phys. Rev. B 64(23), 233317 (2001).
[CrossRef]

1999

F. J. P. Schuurmans, D. Vanmaekelbergh, and A. Lagendijk, “Strongly photonic macroporous gallium phosphide networks,” Science 284(5411), 141–143 (1999).
[CrossRef] [PubMed]

1998

S. W. Silva, J. C. Galzerani, D. I. Lubyshev, and P. Basmaji, “Surface phonon observed in GaAs wire crystals grown on porous Si,” J. Phys. Condens. Matter 10(43), 9687–9690 (1998).
[CrossRef]

1997

A. G. Cullis, L. T. Canham, and P. D. J. Calcott, “The structural and luminescence properties of porous silicon,” J. Appl. Phys. 82(3), 909–965 (1997).
[CrossRef]

I. M. Tiginyanu, G. Irmer, J. Monecke, and H. L. Hartnagel, “Micro-Raman-scattering study of surface-related phonon modes in porous GaP,” Phys. Rev. B 55(11), 6739–6742 (1997).
[CrossRef]

1996

I. M. Tiginyanu, V. V. Ursaki, V. A. Karavanskii, V. N. Sokolov, Y. S. Raptis, and E. Anastassakis, “Surface-related phonon mode in porous GaP,” Solid State Commun. 97(8), 675–678 (1996).
[CrossRef]

T. D. Krauss, F. W. Wise, and D. B. Tanner, “Observation of coupled vibrational modes of a semiconductor nanocrystal,” Phys. Rev. Lett. 76(8), 1376–1379 (1996).
[CrossRef] [PubMed]

1994

E. Roca, C. Trallero-Giner, and M. Cardona, “Polar optical vibrational modes in quantum dots,” Phys. Rev. B Condens. Matter 49(19), 13704–13711 (1994).
[CrossRef] [PubMed]

1990

M. Watt, C. M. S. Torres, H. E. G. Arnot, and S. P. Beaumont, “Surface phonons in GaAs cylinders,” Semicond. Sci. Technol. 5(4), 285–290 (1990).
[CrossRef]

1982

S. Hayashi and H. Kanamori, “Raman scattering from the surface phonon mode in GaP microcrystals,” Phys. Rev. B 26(12), 7079–7082 (1982).
[CrossRef]

1981

B. Jusserand and J. Sapriel, “Raman investigation of anharmonicity and disorder-induced effects in Ga1-xAlxAs epitaxial layers,” Phys. Rev. B 24(12), 7194–7205 (1981).
[CrossRef]

H. Richter, Z. P. Wang, and L. Ley, “The one phonon Raman spectrum in microcrystalline silicon,” Solid State Commun. 39(5), 625–629 (1981).
[CrossRef]

1970

R. Ruppin and R. Englman, “Optical phonons of small crystals,” Rep. Prog. Phys. 33(1), 149–196 (1970).
[CrossRef]

1935

D. A. G. Bruggeman, “Berechnung Verschiedener Physikalischer Konstanten von Heterogenen Substanzen, I. Dielektrizitatskonstanten und Leitfahigkeiten der Mischkorper aus Isotropen Substanzen,” Ann. Phys. 416(7), 636–664 (1935).
[CrossRef]

Adu, C. K.

G. D. Mahan, R. Gupta, Q. Xiong, C. K. Adu, and P. C. Eklund, “Optical phonons in polar semiconductor nano-wires,” Phys. Rev. B 68(7), 073402 (2003).
[CrossRef]

Adu, K. W.

K. W. Adu, Q. Xiong, H. R. Gutierrez, G. Chen, and P. C. Eklund, “Raman scattering as a probe of phonon confinement and surface optical modes in semiconducting nano-wires,” Appl. Phys., A Mater. Sci. Process. 85(3), 287–297 (2006).
[CrossRef]

Anastassakis, E.

I. M. Tiginyanu, V. V. Ursaki, V. A. Karavanskii, V. N. Sokolov, Y. S. Raptis, and E. Anastassakis, “Surface-related phonon mode in porous GaP,” Solid State Commun. 97(8), 675–678 (1996).
[CrossRef]

Arnot, H. E. G.

M. Watt, C. M. S. Torres, H. E. G. Arnot, and S. P. Beaumont, “Surface phonons in GaAs cylinders,” Semicond. Sci. Technol. 5(4), 285–290 (1990).
[CrossRef]

Basmaji, P.

S. W. Silva, J. C. Galzerani, D. I. Lubyshev, and P. Basmaji, “Surface phonon observed in GaAs wire crystals grown on porous Si,” J. Phys. Condens. Matter 10(43), 9687–9690 (1998).
[CrossRef]

Beaumont, S. P.

M. Watt, C. M. S. Torres, H. E. G. Arnot, and S. P. Beaumont, “Surface phonons in GaAs cylinders,” Semicond. Sci. Technol. 5(4), 285–290 (1990).
[CrossRef]

Bruggeman, D. A. G.

D. A. G. Bruggeman, “Berechnung Verschiedener Physikalischer Konstanten von Heterogenen Substanzen, I. Dielektrizitatskonstanten und Leitfahigkeiten der Mischkorper aus Isotropen Substanzen,” Ann. Phys. 416(7), 636–664 (1935).
[CrossRef]

Calcott, P. D. J.

A. G. Cullis, L. T. Canham, and P. D. J. Calcott, “The structural and luminescence properties of porous silicon,” J. Appl. Phys. 82(3), 909–965 (1997).
[CrossRef]

Canham, L. T.

A. G. Cullis, L. T. Canham, and P. D. J. Calcott, “The structural and luminescence properties of porous silicon,” J. Appl. Phys. 82(3), 909–965 (1997).
[CrossRef]

Cardona, M.

E. Roca, C. Trallero-Giner, and M. Cardona, “Polar optical vibrational modes in quantum dots,” Phys. Rev. B Condens. Matter 49(19), 13704–13711 (1994).
[CrossRef] [PubMed]

Chang, Y. H.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

Chattopadhyay, S.

S. Chattopadhyay, Y. F. Huang, Y. J. Jen, A. Ganguly, K. H. Chen, and L. C. Chen, “Antireflecting and photonic nanostructures,” Mater. Sci. Eng. Rep. 69(1-3), 1–35 (2010).
[CrossRef]

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

C. H. Hsu, Y. F. Huang, L. C. Chen, S. Chattopadhyay, K. H. Chen, H. C. Lo, and C. F. Chen, “Morphology control of silicon nano-tips fabricated by electron cyclotron resonance plasma etching,” J. Vac. Sci. Technol. B 24(1), 308–311 (2006).
[CrossRef]

Chen, C. F.

C. H. Hsu, Y. F. Huang, L. C. Chen, S. Chattopadhyay, K. H. Chen, H. C. Lo, and C. F. Chen, “Morphology control of silicon nano-tips fabricated by electron cyclotron resonance plasma etching,” J. Vac. Sci. Technol. B 24(1), 308–311 (2006).
[CrossRef]

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, K. H. Chen, and L. C. Chen, “Generally applicable self-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Chen, G.

K. W. Adu, Q. Xiong, H. R. Gutierrez, G. Chen, and P. C. Eklund, “Raman scattering as a probe of phonon confinement and surface optical modes in semiconducting nano-wires,” Appl. Phys., A Mater. Sci. Process. 85(3), 287–297 (2006).
[CrossRef]

Chen, K. H.

S. Chattopadhyay, Y. F. Huang, Y. J. Jen, A. Ganguly, K. H. Chen, and L. C. Chen, “Antireflecting and photonic nanostructures,” Mater. Sci. Eng. Rep. 69(1-3), 1–35 (2010).
[CrossRef]

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

C. H. Hsu, Y. F. Huang, L. C. Chen, S. Chattopadhyay, K. H. Chen, H. C. Lo, and C. F. Chen, “Morphology control of silicon nano-tips fabricated by electron cyclotron resonance plasma etching,” J. Vac. Sci. Technol. B 24(1), 308–311 (2006).
[CrossRef]

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, K. H. Chen, and L. C. Chen, “Generally applicable self-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Chen, L. C.

S. Chattopadhyay, Y. F. Huang, Y. J. Jen, A. Ganguly, K. H. Chen, and L. C. Chen, “Antireflecting and photonic nanostructures,” Mater. Sci. Eng. Rep. 69(1-3), 1–35 (2010).
[CrossRef]

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

C. H. Hsu, Y. F. Huang, L. C. Chen, S. Chattopadhyay, K. H. Chen, H. C. Lo, and C. F. Chen, “Morphology control of silicon nano-tips fabricated by electron cyclotron resonance plasma etching,” J. Vac. Sci. Technol. B 24(1), 308–311 (2006).
[CrossRef]

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, K. H. Chen, and L. C. Chen, “Generally applicable self-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Cullis, A. G.

A. G. Cullis, L. T. Canham, and P. D. J. Calcott, “The structural and luminescence properties of porous silicon,” J. Appl. Phys. 82(3), 909–965 (1997).
[CrossRef]

Das, D.

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, K. H. Chen, and L. C. Chen, “Generally applicable self-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Eklund, P. C.

K. W. Adu, Q. Xiong, H. R. Gutierrez, G. Chen, and P. C. Eklund, “Raman scattering as a probe of phonon confinement and surface optical modes in semiconducting nano-wires,” Appl. Phys., A Mater. Sci. Process. 85(3), 287–297 (2006).
[CrossRef]

G. D. Mahan, R. Gupta, Q. Xiong, C. K. Adu, and P. C. Eklund, “Optical phonons in polar semiconductor nano-wires,” Phys. Rev. B 68(7), 073402 (2003).
[CrossRef]

R. Gupta, Q. Xiong, G. D. Mahan, and P. C. Eklund, “Surface optical phonons in gallium phosphide nano-wires,” Nano Lett. 3(12), 1745–1750 (2003).
[CrossRef]

Englman, R.

R. Ruppin and R. Englman, “Optical phonons of small crystals,” Rep. Prog. Phys. 33(1), 149–196 (1970).
[CrossRef]

Galzerani, J. C.

S. W. Silva, J. C. Galzerani, D. I. Lubyshev, and P. Basmaji, “Surface phonon observed in GaAs wire crystals grown on porous Si,” J. Phys. Condens. Matter 10(43), 9687–9690 (1998).
[CrossRef]

Ganguly, A.

S. Chattopadhyay, Y. F. Huang, Y. J. Jen, A. Ganguly, K. H. Chen, and L. C. Chen, “Antireflecting and photonic nanostructures,” Mater. Sci. Eng. Rep. 69(1-3), 1–35 (2010).
[CrossRef]

Gärtner, G.

A. Sarua, J. Monecke, G. Irmer, I. M. Tiginyanu, G. Gärtner, and H. L. Hartnagel, “Fröhlich modes in porous III–V semiconductors,” J. Phys. Condens. Matter 13(31), 6687–6706 (2001).
[CrossRef]

Gupta, R.

R. Gupta, Q. Xiong, G. D. Mahan, and P. C. Eklund, “Surface optical phonons in gallium phosphide nano-wires,” Nano Lett. 3(12), 1745–1750 (2003).
[CrossRef]

G. D. Mahan, R. Gupta, Q. Xiong, C. K. Adu, and P. C. Eklund, “Optical phonons in polar semiconductor nano-wires,” Phys. Rev. B 68(7), 073402 (2003).
[CrossRef]

Gutierrez, H. R.

K. W. Adu, Q. Xiong, H. R. Gutierrez, G. Chen, and P. C. Eklund, “Raman scattering as a probe of phonon confinement and surface optical modes in semiconducting nano-wires,” Appl. Phys., A Mater. Sci. Process. 85(3), 287–297 (2006).
[CrossRef]

Hartnagel, H. L.

A. Sarua, J. Monecke, G. Irmer, I. M. Tiginyanu, G. Gärtner, and H. L. Hartnagel, “Fröhlich modes in porous III–V semiconductors,” J. Phys. Condens. Matter 13(31), 6687–6706 (2001).
[CrossRef]

I. M. Tiginyanu, G. Irmer, J. Monecke, and H. L. Hartnagel, “Micro-Raman-scattering study of surface-related phonon modes in porous GaP,” Phys. Rev. B 55(11), 6739–6742 (1997).
[CrossRef]

Hayashi, S.

S. Hayashi and H. Kanamori, “Raman scattering from the surface phonon mode in GaP microcrystals,” Phys. Rev. B 26(12), 7079–7082 (1982).
[CrossRef]

Hsu, C. H.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

C. H. Hsu, Y. F. Huang, L. C. Chen, S. Chattopadhyay, K. H. Chen, H. C. Lo, and C. F. Chen, “Morphology control of silicon nano-tips fabricated by electron cyclotron resonance plasma etching,” J. Vac. Sci. Technol. B 24(1), 308–311 (2006).
[CrossRef]

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, K. H. Chen, and L. C. Chen, “Generally applicable self-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Hsu, Y. K.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

Huang, Y. F.

S. Chattopadhyay, Y. F. Huang, Y. J. Jen, A. Ganguly, K. H. Chen, and L. C. Chen, “Antireflecting and photonic nanostructures,” Mater. Sci. Eng. Rep. 69(1-3), 1–35 (2010).
[CrossRef]

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

C. H. Hsu, Y. F. Huang, L. C. Chen, S. Chattopadhyay, K. H. Chen, H. C. Lo, and C. F. Chen, “Morphology control of silicon nano-tips fabricated by electron cyclotron resonance plasma etching,” J. Vac. Sci. Technol. B 24(1), 308–311 (2006).
[CrossRef]

Hubbard, S. M.

I. M. Tiginyanu, A. Sarua, G. Irmer, J. Monecke, S. M. Hubbard, D. Pavlidis, and V. Valiaev, “Fröhlich modes in GaN columnar nanostructures,” Phys. Rev. B 64(23), 233317 (2001).
[CrossRef]

Hwang, J. S.

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, K. H. Chen, and L. C. Chen, “Generally applicable self-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Irmer, G.

A. Sarua, J. Monecke, G. Irmer, I. M. Tiginyanu, G. Gärtner, and H. L. Hartnagel, “Fröhlich modes in porous III–V semiconductors,” J. Phys. Condens. Matter 13(31), 6687–6706 (2001).
[CrossRef]

I. M. Tiginyanu, A. Sarua, G. Irmer, J. Monecke, S. M. Hubbard, D. Pavlidis, and V. Valiaev, “Fröhlich modes in GaN columnar nanostructures,” Phys. Rev. B 64(23), 233317 (2001).
[CrossRef]

I. M. Tiginyanu, G. Irmer, J. Monecke, and H. L. Hartnagel, “Micro-Raman-scattering study of surface-related phonon modes in porous GaP,” Phys. Rev. B 55(11), 6739–6742 (1997).
[CrossRef]

Jen, Y. J.

S. Chattopadhyay, Y. F. Huang, Y. J. Jen, A. Ganguly, K. H. Chen, and L. C. Chen, “Antireflecting and photonic nanostructures,” Mater. Sci. Eng. Rep. 69(1-3), 1–35 (2010).
[CrossRef]

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

Jusserand, B.

B. Jusserand and J. Sapriel, “Raman investigation of anharmonicity and disorder-induced effects in Ga1-xAlxAs epitaxial layers,” Phys. Rev. B 24(12), 7194–7205 (1981).
[CrossRef]

Kanamori, H.

S. Hayashi and H. Kanamori, “Raman scattering from the surface phonon mode in GaP microcrystals,” Phys. Rev. B 26(12), 7079–7082 (1982).
[CrossRef]

Karavanskii, V. A.

I. M. Tiginyanu, V. V. Ursaki, V. A. Karavanskii, V. N. Sokolov, Y. S. Raptis, and E. Anastassakis, “Surface-related phonon mode in porous GaP,” Solid State Commun. 97(8), 675–678 (1996).
[CrossRef]

Krauss, T. D.

T. D. Krauss, F. W. Wise, and D. B. Tanner, “Observation of coupled vibrational modes of a semiconductor nanocrystal,” Phys. Rev. Lett. 76(8), 1376–1379 (1996).
[CrossRef] [PubMed]

Kuech, T. F.

T. F. Kuech and L. J. Mawst, “Nanofabrication of III-V semiconductors employing diblock copolymer lithography,” J. Phys. D Appl. Phys. 43(18), 183001 (2010).
[CrossRef]

Lagendijk, A.

F. J. P. Schuurmans, D. Vanmaekelbergh, and A. Lagendijk, “Strongly photonic macroporous gallium phosphide networks,” Science 284(5411), 141–143 (1999).
[CrossRef] [PubMed]

Lee, C. S.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

Ley, L.

H. Richter, Z. P. Wang, and L. Ley, “The one phonon Raman spectrum in microcrystalline silicon,” Solid State Commun. 39(5), 625–629 (1981).
[CrossRef]

Liu, G.

G. Liu, H. Zhao, J. Zhang, J. H. Park, L. J. Mawst, and N. Tansu, “Selective area epitaxy of ultra-high density InGaN quantum dots by diblock copolymer lithography,” Nanoscale Res. Lett. 6(1), 342 (2011).
[CrossRef] [PubMed]

Liu, T. A.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

Lo, H. C.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

C. H. Hsu, Y. F. Huang, L. C. Chen, S. Chattopadhyay, K. H. Chen, H. C. Lo, and C. F. Chen, “Morphology control of silicon nano-tips fabricated by electron cyclotron resonance plasma etching,” J. Vac. Sci. Technol. B 24(1), 308–311 (2006).
[CrossRef]

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, K. H. Chen, and L. C. Chen, “Generally applicable self-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Lubyshev, D. I.

S. W. Silva, J. C. Galzerani, D. I. Lubyshev, and P. Basmaji, “Surface phonon observed in GaAs wire crystals grown on porous Si,” J. Phys. Condens. Matter 10(43), 9687–9690 (1998).
[CrossRef]

Mahan, G. D.

G. D. Mahan, R. Gupta, Q. Xiong, C. K. Adu, and P. C. Eklund, “Optical phonons in polar semiconductor nano-wires,” Phys. Rev. B 68(7), 073402 (2003).
[CrossRef]

R. Gupta, Q. Xiong, G. D. Mahan, and P. C. Eklund, “Surface optical phonons in gallium phosphide nano-wires,” Nano Lett. 3(12), 1745–1750 (2003).
[CrossRef]

Mawst, L. J.

G. Liu, H. Zhao, J. Zhang, J. H. Park, L. J. Mawst, and N. Tansu, “Selective area epitaxy of ultra-high density InGaN quantum dots by diblock copolymer lithography,” Nanoscale Res. Lett. 6(1), 342 (2011).
[CrossRef] [PubMed]

T. F. Kuech and L. J. Mawst, “Nanofabrication of III-V semiconductors employing diblock copolymer lithography,” J. Phys. D Appl. Phys. 43(18), 183001 (2010).
[CrossRef]

Monecke, J.

I. M. Tiginyanu, A. Sarua, G. Irmer, J. Monecke, S. M. Hubbard, D. Pavlidis, and V. Valiaev, “Fröhlich modes in GaN columnar nanostructures,” Phys. Rev. B 64(23), 233317 (2001).
[CrossRef]

A. Sarua, J. Monecke, G. Irmer, I. M. Tiginyanu, G. Gärtner, and H. L. Hartnagel, “Fröhlich modes in porous III–V semiconductors,” J. Phys. Condens. Matter 13(31), 6687–6706 (2001).
[CrossRef]

I. M. Tiginyanu, G. Irmer, J. Monecke, and H. L. Hartnagel, “Micro-Raman-scattering study of surface-related phonon modes in porous GaP,” Phys. Rev. B 55(11), 6739–6742 (1997).
[CrossRef]

Pan, C. L.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

Park, J. H.

G. Liu, H. Zhao, J. Zhang, J. H. Park, L. J. Mawst, and N. Tansu, “Selective area epitaxy of ultra-high density InGaN quantum dots by diblock copolymer lithography,” Nanoscale Res. Lett. 6(1), 342 (2011).
[CrossRef] [PubMed]

Pavlidis, D.

I. M. Tiginyanu, A. Sarua, G. Irmer, J. Monecke, S. M. Hubbard, D. Pavlidis, and V. Valiaev, “Fröhlich modes in GaN columnar nanostructures,” Phys. Rev. B 64(23), 233317 (2001).
[CrossRef]

Peng, C. Y.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

Raptis, Y. S.

I. M. Tiginyanu, V. V. Ursaki, V. A. Karavanskii, V. N. Sokolov, Y. S. Raptis, and E. Anastassakis, “Surface-related phonon mode in porous GaP,” Solid State Commun. 97(8), 675–678 (1996).
[CrossRef]

Richter, H.

H. Richter, Z. P. Wang, and L. Ley, “The one phonon Raman spectrum in microcrystalline silicon,” Solid State Commun. 39(5), 625–629 (1981).
[CrossRef]

Roca, E.

E. Roca, C. Trallero-Giner, and M. Cardona, “Polar optical vibrational modes in quantum dots,” Phys. Rev. B Condens. Matter 49(19), 13704–13711 (1994).
[CrossRef] [PubMed]

Ruppin, R.

R. Ruppin and R. Englman, “Optical phonons of small crystals,” Rep. Prog. Phys. 33(1), 149–196 (1970).
[CrossRef]

Sapriel, J.

B. Jusserand and J. Sapriel, “Raman investigation of anharmonicity and disorder-induced effects in Ga1-xAlxAs epitaxial layers,” Phys. Rev. B 24(12), 7194–7205 (1981).
[CrossRef]

Sarua, A.

A. Sarua, J. Monecke, G. Irmer, I. M. Tiginyanu, G. Gärtner, and H. L. Hartnagel, “Fröhlich modes in porous III–V semiconductors,” J. Phys. Condens. Matter 13(31), 6687–6706 (2001).
[CrossRef]

I. M. Tiginyanu, A. Sarua, G. Irmer, J. Monecke, S. M. Hubbard, D. Pavlidis, and V. Valiaev, “Fröhlich modes in GaN columnar nanostructures,” Phys. Rev. B 64(23), 233317 (2001).
[CrossRef]

Schuurmans, F. J. P.

F. J. P. Schuurmans, D. Vanmaekelbergh, and A. Lagendijk, “Strongly photonic macroporous gallium phosphide networks,” Science 284(5411), 141–143 (1999).
[CrossRef] [PubMed]

Silva, S. W.

S. W. Silva, J. C. Galzerani, D. I. Lubyshev, and P. Basmaji, “Surface phonon observed in GaAs wire crystals grown on porous Si,” J. Phys. Condens. Matter 10(43), 9687–9690 (1998).
[CrossRef]

Sokolov, V. N.

I. M. Tiginyanu, V. V. Ursaki, V. A. Karavanskii, V. N. Sokolov, Y. S. Raptis, and E. Anastassakis, “Surface-related phonon mode in porous GaP,” Solid State Commun. 97(8), 675–678 (1996).
[CrossRef]

Tanner, D. B.

T. D. Krauss, F. W. Wise, and D. B. Tanner, “Observation of coupled vibrational modes of a semiconductor nanocrystal,” Phys. Rev. Lett. 76(8), 1376–1379 (1996).
[CrossRef] [PubMed]

Tansu, N.

G. Liu, H. Zhao, J. Zhang, J. H. Park, L. J. Mawst, and N. Tansu, “Selective area epitaxy of ultra-high density InGaN quantum dots by diblock copolymer lithography,” Nanoscale Res. Lett. 6(1), 342 (2011).
[CrossRef] [PubMed]

Tiginyanu, I. M.

A. Sarua, J. Monecke, G. Irmer, I. M. Tiginyanu, G. Gärtner, and H. L. Hartnagel, “Fröhlich modes in porous III–V semiconductors,” J. Phys. Condens. Matter 13(31), 6687–6706 (2001).
[CrossRef]

I. M. Tiginyanu, A. Sarua, G. Irmer, J. Monecke, S. M. Hubbard, D. Pavlidis, and V. Valiaev, “Fröhlich modes in GaN columnar nanostructures,” Phys. Rev. B 64(23), 233317 (2001).
[CrossRef]

I. M. Tiginyanu, G. Irmer, J. Monecke, and H. L. Hartnagel, “Micro-Raman-scattering study of surface-related phonon modes in porous GaP,” Phys. Rev. B 55(11), 6739–6742 (1997).
[CrossRef]

I. M. Tiginyanu, V. V. Ursaki, V. A. Karavanskii, V. N. Sokolov, Y. S. Raptis, and E. Anastassakis, “Surface-related phonon mode in porous GaP,” Solid State Commun. 97(8), 675–678 (1996).
[CrossRef]

Torres, C. M. S.

M. Watt, C. M. S. Torres, H. E. G. Arnot, and S. P. Beaumont, “Surface phonons in GaAs cylinders,” Semicond. Sci. Technol. 5(4), 285–290 (1990).
[CrossRef]

Trallero-Giner, C.

E. Roca, C. Trallero-Giner, and M. Cardona, “Polar optical vibrational modes in quantum dots,” Phys. Rev. B Condens. Matter 49(19), 13704–13711 (1994).
[CrossRef] [PubMed]

Tsai, J.

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, K. H. Chen, and L. C. Chen, “Generally applicable self-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Ursaki, V. V.

I. M. Tiginyanu, V. V. Ursaki, V. A. Karavanskii, V. N. Sokolov, Y. S. Raptis, and E. Anastassakis, “Surface-related phonon mode in porous GaP,” Solid State Commun. 97(8), 675–678 (1996).
[CrossRef]

Valiaev, V.

I. M. Tiginyanu, A. Sarua, G. Irmer, J. Monecke, S. M. Hubbard, D. Pavlidis, and V. Valiaev, “Fröhlich modes in GaN columnar nanostructures,” Phys. Rev. B 64(23), 233317 (2001).
[CrossRef]

Vanmaekelbergh, D.

F. J. P. Schuurmans, D. Vanmaekelbergh, and A. Lagendijk, “Strongly photonic macroporous gallium phosphide networks,” Science 284(5411), 141–143 (1999).
[CrossRef] [PubMed]

Wang, Z. P.

H. Richter, Z. P. Wang, and L. Ley, “The one phonon Raman spectrum in microcrystalline silicon,” Solid State Commun. 39(5), 625–629 (1981).
[CrossRef]

Watt, M.

M. Watt, C. M. S. Torres, H. E. G. Arnot, and S. P. Beaumont, “Surface phonons in GaAs cylinders,” Semicond. Sci. Technol. 5(4), 285–290 (1990).
[CrossRef]

Wise, F. W.

T. D. Krauss, F. W. Wise, and D. B. Tanner, “Observation of coupled vibrational modes of a semiconductor nanocrystal,” Phys. Rev. Lett. 76(8), 1376–1379 (1996).
[CrossRef] [PubMed]

Wu, C. T.

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, K. H. Chen, and L. C. Chen, “Generally applicable self-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Xiong, Q.

K. W. Adu, Q. Xiong, H. R. Gutierrez, G. Chen, and P. C. Eklund, “Raman scattering as a probe of phonon confinement and surface optical modes in semiconducting nano-wires,” Appl. Phys., A Mater. Sci. Process. 85(3), 287–297 (2006).
[CrossRef]

G. D. Mahan, R. Gupta, Q. Xiong, C. K. Adu, and P. C. Eklund, “Optical phonons in polar semiconductor nano-wires,” Phys. Rev. B 68(7), 073402 (2003).
[CrossRef]

R. Gupta, Q. Xiong, G. D. Mahan, and P. C. Eklund, “Surface optical phonons in gallium phosphide nano-wires,” Nano Lett. 3(12), 1745–1750 (2003).
[CrossRef]

Zhang, J.

G. Liu, H. Zhao, J. Zhang, J. H. Park, L. J. Mawst, and N. Tansu, “Selective area epitaxy of ultra-high density InGaN quantum dots by diblock copolymer lithography,” Nanoscale Res. Lett. 6(1), 342 (2011).
[CrossRef] [PubMed]

Zhao, H.

G. Liu, H. Zhao, J. Zhang, J. H. Park, L. J. Mawst, and N. Tansu, “Selective area epitaxy of ultra-high density InGaN quantum dots by diblock copolymer lithography,” Nanoscale Res. Lett. 6(1), 342 (2011).
[CrossRef] [PubMed]

Ann. Phys.

D. A. G. Bruggeman, “Berechnung Verschiedener Physikalischer Konstanten von Heterogenen Substanzen, I. Dielektrizitatskonstanten und Leitfahigkeiten der Mischkorper aus Isotropen Substanzen,” Ann. Phys. 416(7), 636–664 (1935).
[CrossRef]

Appl. Phys., A Mater. Sci. Process.

K. W. Adu, Q. Xiong, H. R. Gutierrez, G. Chen, and P. C. Eklund, “Raman scattering as a probe of phonon confinement and surface optical modes in semiconducting nano-wires,” Appl. Phys., A Mater. Sci. Process. 85(3), 287–297 (2006).
[CrossRef]

J. Appl. Phys.

A. G. Cullis, L. T. Canham, and P. D. J. Calcott, “The structural and luminescence properties of porous silicon,” J. Appl. Phys. 82(3), 909–965 (1997).
[CrossRef]

J. Phys. Condens. Matter

A. Sarua, J. Monecke, G. Irmer, I. M. Tiginyanu, G. Gärtner, and H. L. Hartnagel, “Fröhlich modes in porous III–V semiconductors,” J. Phys. Condens. Matter 13(31), 6687–6706 (2001).
[CrossRef]

S. W. Silva, J. C. Galzerani, D. I. Lubyshev, and P. Basmaji, “Surface phonon observed in GaAs wire crystals grown on porous Si,” J. Phys. Condens. Matter 10(43), 9687–9690 (1998).
[CrossRef]

J. Phys. D Appl. Phys.

T. F. Kuech and L. J. Mawst, “Nanofabrication of III-V semiconductors employing diblock copolymer lithography,” J. Phys. D Appl. Phys. 43(18), 183001 (2010).
[CrossRef]

J. Vac. Sci. Technol. B

C. H. Hsu, Y. F. Huang, L. C. Chen, S. Chattopadhyay, K. H. Chen, H. C. Lo, and C. F. Chen, “Morphology control of silicon nano-tips fabricated by electron cyclotron resonance plasma etching,” J. Vac. Sci. Technol. B 24(1), 308–311 (2006).
[CrossRef]

Mater. Sci. Eng. Rep.

S. Chattopadhyay, Y. F. Huang, Y. J. Jen, A. Ganguly, K. H. Chen, and L. C. Chen, “Antireflecting and photonic nanostructures,” Mater. Sci. Eng. Rep. 69(1-3), 1–35 (2010).
[CrossRef]

Nano Lett.

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, K. H. Chen, and L. C. Chen, “Generally applicable self-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

R. Gupta, Q. Xiong, G. D. Mahan, and P. C. Eklund, “Surface optical phonons in gallium phosphide nano-wires,” Nano Lett. 3(12), 1745–1750 (2003).
[CrossRef]

Nanoscale Res. Lett.

G. Liu, H. Zhao, J. Zhang, J. H. Park, L. J. Mawst, and N. Tansu, “Selective area epitaxy of ultra-high density InGaN quantum dots by diblock copolymer lithography,” Nanoscale Res. Lett. 6(1), 342 (2011).
[CrossRef] [PubMed]

Nat. Nanotechnol.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

Phys. Rev. B

I. M. Tiginyanu, G. Irmer, J. Monecke, and H. L. Hartnagel, “Micro-Raman-scattering study of surface-related phonon modes in porous GaP,” Phys. Rev. B 55(11), 6739–6742 (1997).
[CrossRef]

I. M. Tiginyanu, A. Sarua, G. Irmer, J. Monecke, S. M. Hubbard, D. Pavlidis, and V. Valiaev, “Fröhlich modes in GaN columnar nanostructures,” Phys. Rev. B 64(23), 233317 (2001).
[CrossRef]

G. D. Mahan, R. Gupta, Q. Xiong, C. K. Adu, and P. C. Eklund, “Optical phonons in polar semiconductor nano-wires,” Phys. Rev. B 68(7), 073402 (2003).
[CrossRef]

B. Jusserand and J. Sapriel, “Raman investigation of anharmonicity and disorder-induced effects in Ga1-xAlxAs epitaxial layers,” Phys. Rev. B 24(12), 7194–7205 (1981).
[CrossRef]

S. Hayashi and H. Kanamori, “Raman scattering from the surface phonon mode in GaP microcrystals,” Phys. Rev. B 26(12), 7079–7082 (1982).
[CrossRef]

Phys. Rev. B Condens. Matter

E. Roca, C. Trallero-Giner, and M. Cardona, “Polar optical vibrational modes in quantum dots,” Phys. Rev. B Condens. Matter 49(19), 13704–13711 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett.

T. D. Krauss, F. W. Wise, and D. B. Tanner, “Observation of coupled vibrational modes of a semiconductor nanocrystal,” Phys. Rev. Lett. 76(8), 1376–1379 (1996).
[CrossRef] [PubMed]

Rep. Prog. Phys.

R. Ruppin and R. Englman, “Optical phonons of small crystals,” Rep. Prog. Phys. 33(1), 149–196 (1970).
[CrossRef]

Science

F. J. P. Schuurmans, D. Vanmaekelbergh, and A. Lagendijk, “Strongly photonic macroporous gallium phosphide networks,” Science 284(5411), 141–143 (1999).
[CrossRef] [PubMed]

Semicond. Sci. Technol.

M. Watt, C. M. S. Torres, H. E. G. Arnot, and S. P. Beaumont, “Surface phonons in GaAs cylinders,” Semicond. Sci. Technol. 5(4), 285–290 (1990).
[CrossRef]

Solid State Commun.

H. Richter, Z. P. Wang, and L. Ley, “The one phonon Raman spectrum in microcrystalline silicon,” Solid State Commun. 39(5), 625–629 (1981).
[CrossRef]

I. M. Tiginyanu, V. V. Ursaki, V. A. Karavanskii, V. N. Sokolov, Y. S. Raptis, and E. Anastassakis, “Surface-related phonon mode in porous GaP,” Solid State Commun. 97(8), 675–678 (1996).
[CrossRef]

Other

M. A. Stroscio and M. Dutta, Phonons in Nanostructures (Cambridge University Press, 2001).

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Figures (5)

Fig. 1
Fig. 1

(a) Cross-section SEM image of a 3.1 μm long GaAs array; (b) bright field TEM image of a single long GaAs nanotip near the apex region showing a GaAs core, with large number of morphological defects (marked by arrows), and a thin, predominantly, SiC sheath; (c) Bright field HRTEM of the GaAs core showing morphological defects (marked by an arrow); (d) Dark field TEM image and (e) schematic drawn with (d) as model showing the crystalline core and nanocomposite sheath for the structure near the apex of the GaAs nanotip.

Fig. 2
Fig. 2

High resolution bright field TEM images of short ~50 nm GaAs nano-tips- (a) the body, (b) near the apex of the nanotip, showing no significant morphological defects.

Fig. 3
Fig. 3

Room temperature Raman spectroscopy data, measured in air, showing the LO, TO modes in (a) commercial GaAs wafer, with an additional SO mode in GaAs nanotip arrays of length (b) 0.7, (c) 2.0, and (d) 3.1 μm. The TO, LO and SO modes were deconvoluted and shown in each panel of the spectra. Scatter data points and the underlying solid line in each panel represent convoluted spectrum and actual experimental data, respectively. Raman spectroscopy data of the 3.1 µm long GaAs nanotip array, measured in (e) air and in (f) aniline, showing the clear shift of the surface optic mode.

Fig. 4
Fig. 4

(a) Length dependent integrated Raman band strength and surface optic mode dispersion. (a) The variation of the (left axis) ratio of the integrated intensity of the LO to TO modes (ILO/ITO), and (right axis) the ratio of the integrated intensity of the SO mode to the sum of the TO and LO mode (ISO/(ITO + ILO)), as a function of the GaAs nanotip array length. Data obtained from Fig. 3. Line joining the points is a guide to the eye only. (b) Theoretical dispersion of the SO mode shown with respect to the dispersion-less TO and LO modes (horizontal lines). The height (along vertical axis) of the grey boxes indicates the range within which the LO and TO modes varied in our study. The dashed line over the linear part of the SO dispersion curve shows the spread of experimental data for SO mode frequencies obtained for the GaAs nano-tips.

Fig. 5
Fig. 5

Schematic of the GaAs nanotip array. (a) A schematic of the nanotip array showing the total length L (line 1-line 4), SO active apex length L’ (line 2-line 5) and maximum crystal dimension (d = 2r) above which SO mode is not excited. Total apex length is line 5-line 6. (b) A tilted top view SEM image showing the apex part for GaAs nanotip with L = 3.1µm.

Equations (3)

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ϖ S O 2 = ϖ T O 2 + ϖ p 2 ε + ε m f ( x ) ,
ϖ L O 2 = ϖ T O 2 + ϖ p 2 ε ,
f ( x ) = I 0 ( x ) I 1 ( x ) K 1 ( x ) K 0 ( x ) ,

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