Abstract

Phase-change materials, such as the well-known ternary alloy Ge2Sb2Te5, are essential to many types of photonic devices, from re-writeable optical disk memories to more recent developments such as phase-change displays, reconfigurable optical metasurfaces, and integrated phase-change photonic devices and systems. The successful design and development of such applications and devices requires accurate knowledge of the complex refractive index of the phase-change material being used. To this end, it is common practice to rely on published experimental refractive index data. However, published values can vary quite significantly for notionally the same composition, no doubt due to variations in fabrication/deposition processes. Rather than rely on published data, a more reliable approach to index determination is to measure the properties of as-fabricated films, and this is usually carried out using specialized and dedicated ellipsometric equipment. In this paper, we propose a simple and effective alternative to ellipsometry, based on spectroscopic reflectance measurements of Fabry–Perot phase-change nanocavities. We describe this alternative approach in detail, apply it to measurement of the complex index of the archetypal phase-change materials Ge2Sb2Te5 and GeTe, and compare the results to those obtained using conventional ellipsometry, where we find good agreement.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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Corrections

1 July 2020: Typographical corrections were made to the body text and Fig. 6 was replaced.

References

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2019 (5)

S. García-Cuevas Carrillo, L. Trimby, Y.-Y. Au, K. Nagareddy, G. Rodriguez-Hernandez, P. Hosseini, C. Rios, H. Bhaskaran, and C. D. Wright, “A Nonvolatile Phase-Change Metamaterial Color Display,” Adv. Opt. Mater. 7(18), 1801782 (2019).
[Crossref]

E. Gemo, S. García-Cuevas Carrillo, C. Ruiz De Galarreta, A. Baldycheva, H. Hayat, N. Youngblood, H. Bhaskaran, W. H. P. Pernice, and C. D. Wright, “Plasmonically-enhanced all-optical integrated phase-change memory,” Opt. Express 27(17), 24724–24737 (2019).
[Crossref]

J. Feldmann, N. Youngblood, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “All-optical spiking neurosynaptic networks with self-learning capabilities,” Nature 569(7755), 208–214 (2019).
[Crossref]

C. Ríos, N. Youngblood, Z. Cheng, M. Le Gallo, W. H. P. Pernice, C. D. Wright, A. Sebastian, and H. Bhaskaran, “In-memory computing on a photonic platform,” Sci. Adv. 5(2), eaau5759 (2019).
[Crossref]

C. Wu, H. Yu, H. Li, X. Zhang, I. Takeuchi, and M. Li, “Low-Loss Integrated Photonic Switch Using Subwavelength Patterned Phase Change Material,” ACS Photonics 6(1), 87–92 (2019).
[Crossref]

2018 (3)

Y. Qu, Q. Li, L. Cai, M. Pan, P. Ghosh, K. Du, and M. Qiu, “Thermal camouflage based on the phase-changing material GST,” Light: Sci. Appl. 7(1), 1–10 (2018).
[Crossref]

S. García-Cuevas Carrillo, A. M. Alexeev, Y.-Y. Au, and C. D. Wright, “Reconfigurable phase-change meta-absorbers with on-demand quality factor control,” Opt. Express 26(20), 25567–25581 (2018).
[Crossref]

C. Ruiz de Galarreta, A. M. Alexeev, Y.-Y. Au, M. Lopez-Garcia, M. Klemm, M. Cryan, J. Bertolotti, and C. D. Wright, “Nonvolatile reconfigurable phase-change metadevices for beam steering in the near infrared,” Adv. Funct. Mater. 28(10), 1704993 (2018).
[Crossref]

2017 (1)

M. Wuttig, H. Bhaskaran, and T. Taubner, “Phase-Change materials for non-volatile photonic applications,” Nat. Photonics 11(8), 465–476 (2017).
[Crossref]

2016 (3)

G. W. Burr, S. Kim, M. Brightsky, A. Sebastian, H.-L. Lung, H.-Y. Cheng, N. E. S. Cortes, J. Y. Wu, H. Pozidis, and C. Lam, “Recent progress in Phase change memory technology,” IEEE J. Emerg. Sel. Topics Circuits Syst. 6(2), 146–162 (2016).
[Crossref]

M. Jafari and M. Rais-Zadeh, “Zero-static-power phase-change optical modulator,” Opt. Lett. 41(6), 1177–1180 (2016).
[Crossref]

A. Kats and F. Capasso, “Optical absorbers based on strong interference in ultra-thin films,” Laser Photonics Rev. 10(5), 735–749 (2016).
[Crossref]

2014 (1)

P. Hosseini, C. D. Wright, and H. Bhaskaran, “An optoelectronic framework enabled by low-dimensional phase-change films,” Nature 511(7508), 206–211 (2014).
[Crossref]

2013 (2)

B. Gholipour, J. Zhang, K. F. MacDonald, D. W. Hewak, and N. I. Zheludev, “An all-optical, non-volatile, bidirectional, phase-change meta-switch,” Adv. Mater. 25(22), 3050–3054 (2013).
[Crossref]

M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12(1), 20–24 (2013).
[Crossref]

2012 (3)

W. H. P. Pernice and H. Bhaskaran, “Photonic non-volatile memories using phase change materials,” Appl. Phys. Lett. 101(17), 171101 (2012).
[Crossref]

L. Gao, F. Lemarchand, and M. Lequime, “Exploitation of multiple incidences spectrometric measurements for thin film reverse engineering,” Opt. Express 20(14), 15734–15751 (2012).
[Crossref]

D. Loke, T. H. Lee, W. J. Wang, L. P. Shi, R. Zhao, Y. C. Yeo, T. C. Chong, and S. R. Elliott, “Breaking the speed limits of phase-change memory,” Science 336(6088), 1566–1569 (2012).
[Crossref]

2011 (2)

T. Welzel and K. Ellmer, “The influence of the target age on laterally resolved ion distributions in reactive planar magnetron sputtering,” Surf. Coat. Technol. 205(2), S294–S298 (2011).
[Crossref]

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

2008 (2)

K. Shportko, S. Kremers, M. Woda, D. Lencer, J. Robertson, and M. Wuttig, “Resonant bonding in crystalline phase-change materials,” Nat. Mater. 7(8), 653–658 (2008).
[Crossref]

M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300K including temperature coefficients,” Sol. Energy Mater. Sol. Cells 92(11), 1305–1310 (2008).
[Crossref]

2007 (1)

M. Wuttig and N. Yamada, “Phase-change materials for rewriteable data storage,” Nat. Mater. 6(11), 824–832 (2007).
[Crossref]

2005 (1)

H. Dieker and M. Wuttig, “Influence of deposition parameters on the properties of sputtered Ge2Sb2Te5 films,” Thin Solid Films 478(1-2), 248–251 (2005).
[Crossref]

2001 (2)

T. P. Leervad Pedersen, J. Kalb, W. K. Njoroge, D. Wamwangi, and M. Wuttig, “Mechanical stresses upon crystallisation in phase change materials,” Appl. Phys. Lett. 79(22), 3597–3599 (2001).
[Crossref]

P. Hlubina, “White light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica,” Opt. Commun. 193(1-6), 1–7 (2001).
[Crossref]

1999 (2)

J. Siegel, C. N. Afonso, and J. Solis, “Dynamics of ultrafast reversible phase transitions in GeSb films triggered by picosecond laser pulses,” Appl. Phys. Lett. 75(20), 3102–3104 (1999).
[Crossref]

J. Aarik, A. Aidla, A.-A. Kiisler, T. Uustare, and V. Sammelseg, “Influence of substrate temperature on atomic layer growth and properties of HfO2 thin films,” Thin Solid Films 340(1-2), 110–116 (1999).
[Crossref]

1998 (2)

M. Bender, W. Seeling, C. Daube, H. Frankenberger, B. Ocker, and J. Stollenwerk, “Dependence of film composition and thicknesses on optical and electrical properties of ITO-metal-ITO multilayers,” Thin Solid Films 326(1-2), 67–71 (1998).
[Crossref]

A. D. Rakić, A. B. Djurišic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998).
[Crossref]

1996 (2)

L. Duvillaret, F. Garet, and J. L. Coutaz, “A Reliable Method for Extraction of Material Parameters in Terahertz Time-Domain Spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2(3), 739–746 (1996).
[Crossref]

W. Rieger, T. Metzger, H. Angerer, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Influence of substrate-induced biaxial stress on the optical properties of thin GaN films,” Appl. Phys. Lett. 68(7), 970–972 (1996).
[Crossref]

1995 (1)

1990 (1)

Z. Bor, K. Osvay, B. Racz, and G. Szabo, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78(2), 109–112 (1990).
[Crossref]

1971 (1)

A. G. Mathewson and H. P. Myers, “Absolute values of the optical constants of some pure metals,” Phys. Scr. 4(6), 291–292 (1971).
[Crossref]

1965 (1)

Aarik, J.

J. Aarik, A. Aidla, A.-A. Kiisler, T. Uustare, and V. Sammelseg, “Influence of substrate temperature on atomic layer growth and properties of HfO2 thin films,” Thin Solid Films 340(1-2), 110–116 (1999).
[Crossref]

Afonso, C. N.

J. Siegel, C. N. Afonso, and J. Solis, “Dynamics of ultrafast reversible phase transitions in GeSb films triggered by picosecond laser pulses,” Appl. Phys. Lett. 75(20), 3102–3104 (1999).
[Crossref]

Aidla, A.

J. Aarik, A. Aidla, A.-A. Kiisler, T. Uustare, and V. Sammelseg, “Influence of substrate temperature on atomic layer growth and properties of HfO2 thin films,” Thin Solid Films 340(1-2), 110–116 (1999).
[Crossref]

Alexeev, A. M.

S. García-Cuevas Carrillo, A. M. Alexeev, Y.-Y. Au, and C. D. Wright, “Reconfigurable phase-change meta-absorbers with on-demand quality factor control,” Opt. Express 26(20), 25567–25581 (2018).
[Crossref]

C. Ruiz de Galarreta, A. M. Alexeev, Y.-Y. Au, M. Lopez-Garcia, M. Klemm, M. Cryan, J. Bertolotti, and C. D. Wright, “Nonvolatile reconfigurable phase-change metadevices for beam steering in the near infrared,” Adv. Funct. Mater. 28(10), 1704993 (2018).
[Crossref]

Ambacher, O.

W. Rieger, T. Metzger, H. Angerer, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Influence of substrate-induced biaxial stress on the optical properties of thin GaN films,” Appl. Phys. Lett. 68(7), 970–972 (1996).
[Crossref]

Angerer, H.

W. Rieger, T. Metzger, H. Angerer, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Influence of substrate-induced biaxial stress on the optical properties of thin GaN films,” Appl. Phys. Lett. 68(7), 970–972 (1996).
[Crossref]

Au, Y.-Y.

S. García-Cuevas Carrillo, L. Trimby, Y.-Y. Au, K. Nagareddy, G. Rodriguez-Hernandez, P. Hosseini, C. Rios, H. Bhaskaran, and C. D. Wright, “A Nonvolatile Phase-Change Metamaterial Color Display,” Adv. Opt. Mater. 7(18), 1801782 (2019).
[Crossref]

S. García-Cuevas Carrillo, A. M. Alexeev, Y.-Y. Au, and C. D. Wright, “Reconfigurable phase-change meta-absorbers with on-demand quality factor control,” Opt. Express 26(20), 25567–25581 (2018).
[Crossref]

C. Ruiz de Galarreta, A. M. Alexeev, Y.-Y. Au, M. Lopez-Garcia, M. Klemm, M. Cryan, J. Bertolotti, and C. D. Wright, “Nonvolatile reconfigurable phase-change metadevices for beam steering in the near infrared,” Adv. Funct. Mater. 28(10), 1704993 (2018).
[Crossref]

Baldycheva, A.

Bender, M.

M. Bender, W. Seeling, C. Daube, H. Frankenberger, B. Ocker, and J. Stollenwerk, “Dependence of film composition and thicknesses on optical and electrical properties of ITO-metal-ITO multilayers,” Thin Solid Films 326(1-2), 67–71 (1998).
[Crossref]

Bertolotti, J.

C. Ruiz de Galarreta, A. M. Alexeev, Y.-Y. Au, M. Lopez-Garcia, M. Klemm, M. Cryan, J. Bertolotti, and C. D. Wright, “Nonvolatile reconfigurable phase-change metadevices for beam steering in the near infrared,” Adv. Funct. Mater. 28(10), 1704993 (2018).
[Crossref]

Bhaskaran, H.

E. Gemo, S. García-Cuevas Carrillo, C. Ruiz De Galarreta, A. Baldycheva, H. Hayat, N. Youngblood, H. Bhaskaran, W. H. P. Pernice, and C. D. Wright, “Plasmonically-enhanced all-optical integrated phase-change memory,” Opt. Express 27(17), 24724–24737 (2019).
[Crossref]

S. García-Cuevas Carrillo, L. Trimby, Y.-Y. Au, K. Nagareddy, G. Rodriguez-Hernandez, P. Hosseini, C. Rios, H. Bhaskaran, and C. D. Wright, “A Nonvolatile Phase-Change Metamaterial Color Display,” Adv. Opt. Mater. 7(18), 1801782 (2019).
[Crossref]

J. Feldmann, N. Youngblood, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “All-optical spiking neurosynaptic networks with self-learning capabilities,” Nature 569(7755), 208–214 (2019).
[Crossref]

C. Ríos, N. Youngblood, Z. Cheng, M. Le Gallo, W. H. P. Pernice, C. D. Wright, A. Sebastian, and H. Bhaskaran, “In-memory computing on a photonic platform,” Sci. Adv. 5(2), eaau5759 (2019).
[Crossref]

M. Wuttig, H. Bhaskaran, and T. Taubner, “Phase-Change materials for non-volatile photonic applications,” Nat. Photonics 11(8), 465–476 (2017).
[Crossref]

P. Hosseini, C. D. Wright, and H. Bhaskaran, “An optoelectronic framework enabled by low-dimensional phase-change films,” Nature 511(7508), 206–211 (2014).
[Crossref]

W. H. P. Pernice and H. Bhaskaran, “Photonic non-volatile memories using phase change materials,” Appl. Phys. Lett. 101(17), 171101 (2012).
[Crossref]

Blanchard, R.

M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12(1), 20–24 (2013).
[Crossref]

Bor, Z.

Z. Bor, K. Osvay, B. Racz, and G. Szabo, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78(2), 109–112 (1990).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Elsevier, 2013).

Brightsky, M.

G. W. Burr, S. Kim, M. Brightsky, A. Sebastian, H.-L. Lung, H.-Y. Cheng, N. E. S. Cortes, J. Y. Wu, H. Pozidis, and C. Lam, “Recent progress in Phase change memory technology,” IEEE J. Emerg. Sel. Topics Circuits Syst. 6(2), 146–162 (2016).
[Crossref]

W. Kim, M. BrightSky, T. Masuda, N. Sosa, S. Kim, R. Bruce, F. Carta, G. Fraczak, H. Y. Cheng, A. Ray, Y. Zhu, H. L. Lung, K. Suu, and C. Lam, “ALD-based confined PCM with a metallic liner toward unlimited endurance,” IEDM Tech. Dig., 4.2.1–4.2.4 (2016).
[Crossref]

Bruce, R.

W. Kim, M. BrightSky, T. Masuda, N. Sosa, S. Kim, R. Bruce, F. Carta, G. Fraczak, H. Y. Cheng, A. Ray, Y. Zhu, H. L. Lung, K. Suu, and C. Lam, “ALD-based confined PCM with a metallic liner toward unlimited endurance,” IEDM Tech. Dig., 4.2.1–4.2.4 (2016).
[Crossref]

Burr, G. W.

G. W. Burr, S. Kim, M. Brightsky, A. Sebastian, H.-L. Lung, H.-Y. Cheng, N. E. S. Cortes, J. Y. Wu, H. Pozidis, and C. Lam, “Recent progress in Phase change memory technology,” IEEE J. Emerg. Sel. Topics Circuits Syst. 6(2), 146–162 (2016).
[Crossref]

Cai, L.

Y. Qu, Q. Li, L. Cai, M. Pan, P. Ghosh, K. Du, and M. Qiu, “Thermal camouflage based on the phase-changing material GST,” Light: Sci. Appl. 7(1), 1–10 (2018).
[Crossref]

Capasso, F.

A. Kats and F. Capasso, “Optical absorbers based on strong interference in ultra-thin films,” Laser Photonics Rev. 10(5), 735–749 (2016).
[Crossref]

M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12(1), 20–24 (2013).
[Crossref]

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K. Shportko, S. Kremers, M. Woda, D. Lencer, J. Robertson, and M. Wuttig, “Resonant bonding in crystalline phase-change materials,” Nat. Mater. 7(8), 653–658 (2008).
[Crossref]

Siegel, J.

J. Siegel, C. N. Afonso, and J. Solis, “Dynamics of ultrafast reversible phase transitions in GeSb films triggered by picosecond laser pulses,” Appl. Phys. Lett. 75(20), 3102–3104 (1999).
[Crossref]

Solis, J.

J. Siegel, C. N. Afonso, and J. Solis, “Dynamics of ultrafast reversible phase transitions in GeSb films triggered by picosecond laser pulses,” Appl. Phys. Lett. 75(20), 3102–3104 (1999).
[Crossref]

Sosa, N.

W. Kim, M. BrightSky, T. Masuda, N. Sosa, S. Kim, R. Bruce, F. Carta, G. Fraczak, H. Y. Cheng, A. Ray, Y. Zhu, H. L. Lung, K. Suu, and C. Lam, “ALD-based confined PCM with a metallic liner toward unlimited endurance,” IEDM Tech. Dig., 4.2.1–4.2.4 (2016).
[Crossref]

Stollenwerk, J.

M. Bender, W. Seeling, C. Daube, H. Frankenberger, B. Ocker, and J. Stollenwerk, “Dependence of film composition and thicknesses on optical and electrical properties of ITO-metal-ITO multilayers,” Thin Solid Films 326(1-2), 67–71 (1998).
[Crossref]

Stutzmann, M.

W. Rieger, T. Metzger, H. Angerer, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Influence of substrate-induced biaxial stress on the optical properties of thin GaN films,” Appl. Phys. Lett. 68(7), 970–972 (1996).
[Crossref]

Suu, K.

W. Kim, M. BrightSky, T. Masuda, N. Sosa, S. Kim, R. Bruce, F. Carta, G. Fraczak, H. Y. Cheng, A. Ray, Y. Zhu, H. L. Lung, K. Suu, and C. Lam, “ALD-based confined PCM with a metallic liner toward unlimited endurance,” IEDM Tech. Dig., 4.2.1–4.2.4 (2016).
[Crossref]

Szabo, G.

Z. Bor, K. Osvay, B. Racz, and G. Szabo, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78(2), 109–112 (1990).
[Crossref]

Takeuchi, I.

C. Wu, H. Yu, H. Li, X. Zhang, I. Takeuchi, and M. Li, “Low-Loss Integrated Photonic Switch Using Subwavelength Patterned Phase Change Material,” ACS Photonics 6(1), 87–92 (2019).
[Crossref]

Taubner, T.

M. Wuttig, H. Bhaskaran, and T. Taubner, “Phase-Change materials for non-volatile photonic applications,” Nat. Photonics 11(8), 465–476 (2017).
[Crossref]

Trimby, L.

S. García-Cuevas Carrillo, L. Trimby, Y.-Y. Au, K. Nagareddy, G. Rodriguez-Hernandez, P. Hosseini, C. Rios, H. Bhaskaran, and C. D. Wright, “A Nonvolatile Phase-Change Metamaterial Color Display,” Adv. Opt. Mater. 7(18), 1801782 (2019).
[Crossref]

Uustare, T.

J. Aarik, A. Aidla, A.-A. Kiisler, T. Uustare, and V. Sammelseg, “Influence of substrate temperature on atomic layer growth and properties of HfO2 thin films,” Thin Solid Films 340(1-2), 110–116 (1999).
[Crossref]

Wamwangi, D.

T. P. Leervad Pedersen, J. Kalb, W. K. Njoroge, D. Wamwangi, and M. Wuttig, “Mechanical stresses upon crystallisation in phase change materials,” Appl. Phys. Lett. 79(22), 3597–3599 (2001).
[Crossref]

Wang, W. J.

D. Loke, T. H. Lee, W. J. Wang, L. P. Shi, R. Zhao, Y. C. Yeo, T. C. Chong, and S. R. Elliott, “Breaking the speed limits of phase-change memory,” Science 336(6088), 1566–1569 (2012).
[Crossref]

Welzel, T.

T. Welzel and K. Ellmer, “The influence of the target age on laterally resolved ion distributions in reactive planar magnetron sputtering,” Surf. Coat. Technol. 205(2), S294–S298 (2011).
[Crossref]

Woda, M.

K. Shportko, S. Kremers, M. Woda, D. Lencer, J. Robertson, and M. Wuttig, “Resonant bonding in crystalline phase-change materials,” Nat. Mater. 7(8), 653–658 (2008).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Elsevier, 2013).

Wright, C. D.

J. Feldmann, N. Youngblood, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “All-optical spiking neurosynaptic networks with self-learning capabilities,” Nature 569(7755), 208–214 (2019).
[Crossref]

C. Ríos, N. Youngblood, Z. Cheng, M. Le Gallo, W. H. P. Pernice, C. D. Wright, A. Sebastian, and H. Bhaskaran, “In-memory computing on a photonic platform,” Sci. Adv. 5(2), eaau5759 (2019).
[Crossref]

S. García-Cuevas Carrillo, L. Trimby, Y.-Y. Au, K. Nagareddy, G. Rodriguez-Hernandez, P. Hosseini, C. Rios, H. Bhaskaran, and C. D. Wright, “A Nonvolatile Phase-Change Metamaterial Color Display,” Adv. Opt. Mater. 7(18), 1801782 (2019).
[Crossref]

E. Gemo, S. García-Cuevas Carrillo, C. Ruiz De Galarreta, A. Baldycheva, H. Hayat, N. Youngblood, H. Bhaskaran, W. H. P. Pernice, and C. D. Wright, “Plasmonically-enhanced all-optical integrated phase-change memory,” Opt. Express 27(17), 24724–24737 (2019).
[Crossref]

C. Ruiz de Galarreta, A. M. Alexeev, Y.-Y. Au, M. Lopez-Garcia, M. Klemm, M. Cryan, J. Bertolotti, and C. D. Wright, “Nonvolatile reconfigurable phase-change metadevices for beam steering in the near infrared,” Adv. Funct. Mater. 28(10), 1704993 (2018).
[Crossref]

S. García-Cuevas Carrillo, A. M. Alexeev, Y.-Y. Au, and C. D. Wright, “Reconfigurable phase-change meta-absorbers with on-demand quality factor control,” Opt. Express 26(20), 25567–25581 (2018).
[Crossref]

P. Hosseini, C. D. Wright, and H. Bhaskaran, “An optoelectronic framework enabled by low-dimensional phase-change films,” Nature 511(7508), 206–211 (2014).
[Crossref]

Wu, C.

C. Wu, H. Yu, H. Li, X. Zhang, I. Takeuchi, and M. Li, “Low-Loss Integrated Photonic Switch Using Subwavelength Patterned Phase Change Material,” ACS Photonics 6(1), 87–92 (2019).
[Crossref]

Wu, J. Y.

G. W. Burr, S. Kim, M. Brightsky, A. Sebastian, H.-L. Lung, H.-Y. Cheng, N. E. S. Cortes, J. Y. Wu, H. Pozidis, and C. Lam, “Recent progress in Phase change memory technology,” IEEE J. Emerg. Sel. Topics Circuits Syst. 6(2), 146–162 (2016).
[Crossref]

Wuttig, M.

M. Wuttig, H. Bhaskaran, and T. Taubner, “Phase-Change materials for non-volatile photonic applications,” Nat. Photonics 11(8), 465–476 (2017).
[Crossref]

K. Shportko, S. Kremers, M. Woda, D. Lencer, J. Robertson, and M. Wuttig, “Resonant bonding in crystalline phase-change materials,” Nat. Mater. 7(8), 653–658 (2008).
[Crossref]

M. Wuttig and N. Yamada, “Phase-change materials for rewriteable data storage,” Nat. Mater. 6(11), 824–832 (2007).
[Crossref]

H. Dieker and M. Wuttig, “Influence of deposition parameters on the properties of sputtered Ge2Sb2Te5 films,” Thin Solid Films 478(1-2), 248–251 (2005).
[Crossref]

T. P. Leervad Pedersen, J. Kalb, W. K. Njoroge, D. Wamwangi, and M. Wuttig, “Mechanical stresses upon crystallisation in phase change materials,” Appl. Phys. Lett. 79(22), 3597–3599 (2001).
[Crossref]

Yadav, A.

Y. Zang, J. B. Chou, J. Li, H. Li, Q. Du, A. Yadav, S. Zhou, M. Y. Shalaginov, Z. Fang, H. Zhong, and C. Roberts, “Extreme Broadband Transparent Optical Phase Change Materials for High-Performance Nonvolatile Photonics,” arXiv preprint arXiv:1811.00526 (2018).

Yamada, N.

M. Wuttig and N. Yamada, “Phase-change materials for rewriteable data storage,” Nat. Mater. 6(11), 824–832 (2007).
[Crossref]

Yeo, Y. C.

D. Loke, T. H. Lee, W. J. Wang, L. P. Shi, R. Zhao, Y. C. Yeo, T. C. Chong, and S. R. Elliott, “Breaking the speed limits of phase-change memory,” Science 336(6088), 1566–1569 (2012).
[Crossref]

Youngblood, N.

C. Ríos, N. Youngblood, Z. Cheng, M. Le Gallo, W. H. P. Pernice, C. D. Wright, A. Sebastian, and H. Bhaskaran, “In-memory computing on a photonic platform,” Sci. Adv. 5(2), eaau5759 (2019).
[Crossref]

J. Feldmann, N. Youngblood, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “All-optical spiking neurosynaptic networks with self-learning capabilities,” Nature 569(7755), 208–214 (2019).
[Crossref]

E. Gemo, S. García-Cuevas Carrillo, C. Ruiz De Galarreta, A. Baldycheva, H. Hayat, N. Youngblood, H. Bhaskaran, W. H. P. Pernice, and C. D. Wright, “Plasmonically-enhanced all-optical integrated phase-change memory,” Opt. Express 27(17), 24724–24737 (2019).
[Crossref]

Yu, H.

C. Wu, H. Yu, H. Li, X. Zhang, I. Takeuchi, and M. Li, “Low-Loss Integrated Photonic Switch Using Subwavelength Patterned Phase Change Material,” ACS Photonics 6(1), 87–92 (2019).
[Crossref]

Zang, Y.

Y. Zang, J. B. Chou, J. Li, H. Li, Q. Du, A. Yadav, S. Zhou, M. Y. Shalaginov, Z. Fang, H. Zhong, and C. Roberts, “Extreme Broadband Transparent Optical Phase Change Materials for High-Performance Nonvolatile Photonics,” arXiv preprint arXiv:1811.00526 (2018).

Zhang, J.

B. Gholipour, J. Zhang, K. F. MacDonald, D. W. Hewak, and N. I. Zheludev, “An all-optical, non-volatile, bidirectional, phase-change meta-switch,” Adv. Mater. 25(22), 3050–3054 (2013).
[Crossref]

Zhang, X.

C. Wu, H. Yu, H. Li, X. Zhang, I. Takeuchi, and M. Li, “Low-Loss Integrated Photonic Switch Using Subwavelength Patterned Phase Change Material,” ACS Photonics 6(1), 87–92 (2019).
[Crossref]

Zhao, R.

D. Loke, T. H. Lee, W. J. Wang, L. P. Shi, R. Zhao, Y. C. Yeo, T. C. Chong, and S. R. Elliott, “Breaking the speed limits of phase-change memory,” Science 336(6088), 1566–1569 (2012).
[Crossref]

Zheludev, N. I.

B. Gholipour, J. Zhang, K. F. MacDonald, D. W. Hewak, and N. I. Zheludev, “An all-optical, non-volatile, bidirectional, phase-change meta-switch,” Adv. Mater. 25(22), 3050–3054 (2013).
[Crossref]

Zhong, H.

Y. Zang, J. B. Chou, J. Li, H. Li, Q. Du, A. Yadav, S. Zhou, M. Y. Shalaginov, Z. Fang, H. Zhong, and C. Roberts, “Extreme Broadband Transparent Optical Phase Change Materials for High-Performance Nonvolatile Photonics,” arXiv preprint arXiv:1811.00526 (2018).

Zhou, S.

Y. Zang, J. B. Chou, J. Li, H. Li, Q. Du, A. Yadav, S. Zhou, M. Y. Shalaginov, Z. Fang, H. Zhong, and C. Roberts, “Extreme Broadband Transparent Optical Phase Change Materials for High-Performance Nonvolatile Photonics,” arXiv preprint arXiv:1811.00526 (2018).

Zhu, Y.

W. Kim, M. BrightSky, T. Masuda, N. Sosa, S. Kim, R. Bruce, F. Carta, G. Fraczak, H. Y. Cheng, A. Ray, Y. Zhu, H. L. Lung, K. Suu, and C. Lam, “ALD-based confined PCM with a metallic liner toward unlimited endurance,” IEDM Tech. Dig., 4.2.1–4.2.4 (2016).
[Crossref]

ACS Photonics (1)

C. Wu, H. Yu, H. Li, X. Zhang, I. Takeuchi, and M. Li, “Low-Loss Integrated Photonic Switch Using Subwavelength Patterned Phase Change Material,” ACS Photonics 6(1), 87–92 (2019).
[Crossref]

Adv. Funct. Mater. (1)

C. Ruiz de Galarreta, A. M. Alexeev, Y.-Y. Au, M. Lopez-Garcia, M. Klemm, M. Cryan, J. Bertolotti, and C. D. Wright, “Nonvolatile reconfigurable phase-change metadevices for beam steering in the near infrared,” Adv. Funct. Mater. 28(10), 1704993 (2018).
[Crossref]

Adv. Mater. (1)

B. Gholipour, J. Zhang, K. F. MacDonald, D. W. Hewak, and N. I. Zheludev, “An all-optical, non-volatile, bidirectional, phase-change meta-switch,” Adv. Mater. 25(22), 3050–3054 (2013).
[Crossref]

Adv. Opt. Mater. (1)

S. García-Cuevas Carrillo, L. Trimby, Y.-Y. Au, K. Nagareddy, G. Rodriguez-Hernandez, P. Hosseini, C. Rios, H. Bhaskaran, and C. D. Wright, “A Nonvolatile Phase-Change Metamaterial Color Display,” Adv. Opt. Mater. 7(18), 1801782 (2019).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (4)

J. Siegel, C. N. Afonso, and J. Solis, “Dynamics of ultrafast reversible phase transitions in GeSb films triggered by picosecond laser pulses,” Appl. Phys. Lett. 75(20), 3102–3104 (1999).
[Crossref]

W. Rieger, T. Metzger, H. Angerer, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Influence of substrate-induced biaxial stress on the optical properties of thin GaN films,” Appl. Phys. Lett. 68(7), 970–972 (1996).
[Crossref]

W. H. P. Pernice and H. Bhaskaran, “Photonic non-volatile memories using phase change materials,” Appl. Phys. Lett. 101(17), 171101 (2012).
[Crossref]

T. P. Leervad Pedersen, J. Kalb, W. K. Njoroge, D. Wamwangi, and M. Wuttig, “Mechanical stresses upon crystallisation in phase change materials,” Appl. Phys. Lett. 79(22), 3597–3599 (2001).
[Crossref]

IEEE J. Emerg. Sel. Topics Circuits Syst. (1)

G. W. Burr, S. Kim, M. Brightsky, A. Sebastian, H.-L. Lung, H.-Y. Cheng, N. E. S. Cortes, J. Y. Wu, H. Pozidis, and C. Lam, “Recent progress in Phase change memory technology,” IEEE J. Emerg. Sel. Topics Circuits Syst. 6(2), 146–162 (2016).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

L. Duvillaret, F. Garet, and J. L. Coutaz, “A Reliable Method for Extraction of Material Parameters in Terahertz Time-Domain Spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2(3), 739–746 (1996).
[Crossref]

J. Opt. Soc. Am. (1)

Laser Photonics Rev. (1)

A. Kats and F. Capasso, “Optical absorbers based on strong interference in ultra-thin films,” Laser Photonics Rev. 10(5), 735–749 (2016).
[Crossref]

Light: Sci. Appl. (1)

Y. Qu, Q. Li, L. Cai, M. Pan, P. Ghosh, K. Du, and M. Qiu, “Thermal camouflage based on the phase-changing material GST,” Light: Sci. Appl. 7(1), 1–10 (2018).
[Crossref]

Nat. Mater. (3)

K. Shportko, S. Kremers, M. Woda, D. Lencer, J. Robertson, and M. Wuttig, “Resonant bonding in crystalline phase-change materials,” Nat. Mater. 7(8), 653–658 (2008).
[Crossref]

M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12(1), 20–24 (2013).
[Crossref]

M. Wuttig and N. Yamada, “Phase-change materials for rewriteable data storage,” Nat. Mater. 6(11), 824–832 (2007).
[Crossref]

Nat. Photonics (1)

M. Wuttig, H. Bhaskaran, and T. Taubner, “Phase-Change materials for non-volatile photonic applications,” Nat. Photonics 11(8), 465–476 (2017).
[Crossref]

Nature (2)

P. Hosseini, C. D. Wright, and H. Bhaskaran, “An optoelectronic framework enabled by low-dimensional phase-change films,” Nature 511(7508), 206–211 (2014).
[Crossref]

J. Feldmann, N. Youngblood, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “All-optical spiking neurosynaptic networks with self-learning capabilities,” Nature 569(7755), 208–214 (2019).
[Crossref]

Opt. Commun. (2)

Z. Bor, K. Osvay, B. Racz, and G. Szabo, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78(2), 109–112 (1990).
[Crossref]

P. Hlubina, “White light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica,” Opt. Commun. 193(1-6), 1–7 (2001).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Phys. Scr. (1)

A. G. Mathewson and H. P. Myers, “Absolute values of the optical constants of some pure metals,” Phys. Scr. 4(6), 291–292 (1971).
[Crossref]

Prog. Electromagn. Res. B (1)

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

Sci. Adv. (1)

C. Ríos, N. Youngblood, Z. Cheng, M. Le Gallo, W. H. P. Pernice, C. D. Wright, A. Sebastian, and H. Bhaskaran, “In-memory computing on a photonic platform,” Sci. Adv. 5(2), eaau5759 (2019).
[Crossref]

Science (1)

D. Loke, T. H. Lee, W. J. Wang, L. P. Shi, R. Zhao, Y. C. Yeo, T. C. Chong, and S. R. Elliott, “Breaking the speed limits of phase-change memory,” Science 336(6088), 1566–1569 (2012).
[Crossref]

Sol. Energy Mater. Sol. Cells (1)

M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300K including temperature coefficients,” Sol. Energy Mater. Sol. Cells 92(11), 1305–1310 (2008).
[Crossref]

Surf. Coat. Technol. (1)

T. Welzel and K. Ellmer, “The influence of the target age on laterally resolved ion distributions in reactive planar magnetron sputtering,” Surf. Coat. Technol. 205(2), S294–S298 (2011).
[Crossref]

Thin Solid Films (3)

J. Aarik, A. Aidla, A.-A. Kiisler, T. Uustare, and V. Sammelseg, “Influence of substrate temperature on atomic layer growth and properties of HfO2 thin films,” Thin Solid Films 340(1-2), 110–116 (1999).
[Crossref]

M. Bender, W. Seeling, C. Daube, H. Frankenberger, B. Ocker, and J. Stollenwerk, “Dependence of film composition and thicknesses on optical and electrical properties of ITO-metal-ITO multilayers,” Thin Solid Films 326(1-2), 67–71 (1998).
[Crossref]

H. Dieker and M. Wuttig, “Influence of deposition parameters on the properties of sputtered Ge2Sb2Te5 films,” Thin Solid Films 478(1-2), 248–251 (2005).
[Crossref]

Other (5)

W. Kim, M. BrightSky, T. Masuda, N. Sosa, S. Kim, R. Bruce, F. Carta, G. Fraczak, H. Y. Cheng, A. Ray, Y. Zhu, H. L. Lung, K. Suu, and C. Lam, “ALD-based confined PCM with a metallic liner toward unlimited endurance,” IEDM Tech. Dig., 4.2.1–4.2.4 (2016).
[Crossref]

Y. Zang, J. B. Chou, J. Li, H. Li, Q. Du, A. Yadav, S. Zhou, M. Y. Shalaginov, Z. Fang, H. Zhong, and C. Roberts, “Extreme Broadband Transparent Optical Phase Change Materials for High-Performance Nonvolatile Photonics,” arXiv preprint arXiv:1811.00526 (2018).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Elsevier, 2013).

H. A. Macleod, Thin-Film Optical Filters, 4 Edition (CRC Press, 2010).

https://github.com/EmanueleGemo/algorithm-for-n-k-determination-from-reflectance-spectra

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Figures (9)

Fig. 1.
Fig. 1. Optical properties (complex refractive index) for (a) amorphous and (b) crystalline (fcc) Ge2Sb2Te5, as reported in literature [14, 15]. Left axis (and blue lines) refers to the refractive index, whereas the right axis (and red lines) report the extinction coefficient. As visible, for the same material, the optical properties found in published data vary widely from reference to reference.
Fig. 2.
Fig. 2. (a) Diagram and interference working principle of a simple tri-layer Fabry-Perot cavity. (b) Characteristic features of a Fabry-Perot resonance which can be obtained via reflectance measurements, i.e. spectral position of resonance ( ${\lambda _{res}}$ ), reflectance at resonance ( $R({{\lambda_{res}}} )$ ), and Q factor.
Fig. 3.
Fig. 3. Dimensions and materials of the fabricated cavities for (a) amorphous and crystalline GST and (b) amorphous and crystalline GeTe, all fabricated using magnetron sputtering on Si/SiO2 substrates and capped by 10 nm SiO2 layer.
Fig. 4.
Fig. 4. Experimental reflectance spectra of GST Fabry-Perot cavities, compared to simulations using n and k values reported in references [14] and [15], with (a) the GST layer in the amorphous phase, and (b) in crystalline phase.
Fig. 5.
Fig. 5. (a-b) Refractive index (a) and extinction coefficient (b) for our amorphous GST, obtained with our simple method (blue solid lines) and compared to our ellipsometry measurements (blue dashed lines) and literature values from Refs. [14, 15] (grey lines). (c) Measured reflectance spectrum for amorphous GST (black line) against simulated spectra employing n and k values obtained from our simple method (blue solid line), from our ellipsometry measurements (blue dashed line) and from literature (grey lines) [14, 15].
Fig. 6.
Fig. 6. (a-b) Refractive index (a) and extinction coefficient (b) for our crystalline GST, obtained with our simple method (red solid lines) and compared to our ellipsometry measurements (pink dashed lines) and literature values from Refs. [14, 15] (grey lines). (c) Measured reflectance spectrum for crystalline GST (black line) against spectra simulated using n and $k\; $ values obtained from our simple method (red solid line), from our ellipsometry measurements (pink dashed lines) and from literature (grey lines) [14, 15].
Fig. 7.
Fig. 7. (a-b) Refractive index (a) and extinction coefficient (b), for our amorphous GeTe obtained with our simple method (blue solid lines) and compared to our ellipsometry measurements (blue dashed lines) and literature values from Refs. [14, 40] (grey lines). (c) Measured reflectance spectrum for amorphous GeTe (black solid line) against spectra simulated using n and k values obtained from our method (blue solid line), from our ellipsometry measurements (blue dashed line) and from literature (grey lines) [14, 40].
Fig. 8.
Fig. 8. (a-b) Refractive index (a) and extinction coefficient (b), for our crystalline GeTe, obtained with our simple method (red and green solid lines) and compared to our ellipsometry measurements (pink dashed lines) and literature values from Refs. [14, 40] (grey lines). (c) Measured reflectance spectrum (black solid line) against spectra simulated using n and k values obtained from our method (red and green solid lines), from our ellipsometry measurements (pink dashed lines) and from literature (grey lines) [14, 40]. (Note that the green lines shows results from the wavelength-dependent weight fitting approach, that prioritises fitting at resonance).
Fig. 9.
Fig. 9. Flowchart describing the method for determination of n and k.

Equations (6)

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

E o u t = r ~ E 0 i n
r ~ = r ~ 12 + r ~ 23 e i 2 π λ t n ~ 2 1 + r ~ 12 r ~ 23 e i 2 π λ t n ~ 2
t λ r e s 4 n 2 m
n ~ ( λ ) = i r w i n ~ i ( λ )
M S E = 1 m j m ( R c a l c ( λ j ) R e x p ( λ j ) ) 2
ζ ( q , λ ) = | ( q r ( λ ) q e l ( λ ) ) q e l ( λ ) |

Metrics