Abstract

Atomic layers of hexagonal boron nitride (h-BN) crystal, primarily serving as atomically-smooth dielectric layers in two-dimensional (2D) electronics and structural materials in 2D nanoelectromechanical systems (NEMS), have recently emerged as a promising platform for nanoscale optics and photonics. Ultrawide bandgap (~5.9 eV) of h-BN promises ultraviolet (UV) and deep ultraviolet (DUV) responsivity; it can host defect states related to single photon generation. Meanwhile, it also gives rise to the visibility challenge of these atomically-thin crystals, because of the optical transparency in the visible range. In this work, we conduct a comprehensive study, synergizing numerical modeling and experimental efforts, to reveal the optical contrast signatures of h-BN on various substrates. We demonstrate that the visualization and thickness identification based on optical contrast are applicable to mechanically suspended h-BN crystals, without interference enhancement from the commonly used oxidized silicon (SiO2 on Si) wafer. The understanding and protocols developed here offer a non-contact, rapid thickness estimation method for h-BN thin films on suspended device platforms, where conventional contact methods such as scanning probes are incapable or cumbersome. The results and methods presented here also serve as valuable guidelines for engineering the h-BN platform towards 2D nanophotonic and optoelectronic applications.

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

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2018 (4)

M. Atatüre, D. Englund, N. Vamivakas, S. Y. Lee, and J. Wrachtrup, “Material platforms for spin-based photonic quantum technologies,” Nat. Rev. Mater. 3(5), 38–51 (2018).
[Crossref]

A. Sajid, J. R. Reimers, and M. J. Ford, “Defect states in hexagonal boron nitride: Assignments of observed properties and prediction of properties relevant to quantum computation,” Phys. Rev. B 97(6), 064101 (2018).
[Crossref]

L. Weston, D. Wickramaratne, M. Mackoit, A. Alkauskas, and C. G. Van de Walle, “Native point defects and impurities in hexagonal boron nitride,” Phys. Rev. B 97(21), 214104 (2018).
[Crossref]

A. Islam, W. Du, V. Pashaei, H. Jia, Z. Wang, J. Lee, G. J. Ye, X. H. Chen, and P. X.-L. Feng, “Discerning Black Phosphorus Crystal Orientation and Anisotropy by Polarized Reflectance Measurement,” ACS Appl. Mater. Interfaces 10(30), 25629–25637 (2018).
[Crossref] [PubMed]

2017 (2)

X. Li, G. D. Shepard, A. Cupo, N. Camporeale, K. Shayan, Y. Luo, V. Meunier, and S. Strauf, “Nonmagnetic quantum emitters in boron nitride with ultranarrow and sideband-free emission spectra,” ACS Nano 11(7), 6652–6660 (2017).
[Crossref] [PubMed]

X.-Q. Zheng, J. Lee, and P. X.-L. Feng, “Hexagonal boron nitride nanomechanical resonators with spatially visualized motion,” Microsyst. Nanoeng. 3, 17038 (2017).
[Crossref]

2016 (2)

T. T. Tran, K. Bray, M. J. Ford, M. Toth, and I. Aharonovich, “Quantum emission from hexagonal boron nitride monolayers,” Nat. Nanotechnol. 11(1), 37–41 (2016).
[Crossref] [PubMed]

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

2015 (2)

D. H. Lien, J. S. Kang, M. Amani, K. Chen, M. Tosun, H. P. Wang, T. Roy, M. S. Eggleston, M. C. Wu, M. Dubey, S. C. Lee, J. H. He, and A. Javey, “Engineering light outcoupling in 2D materials,” Nano Lett. 15(2), 1356–1361 (2015).
[Crossref] [PubMed]

P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015).
[Crossref] [PubMed]

2014 (2)

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

R. Yang, X.-Q. Zheng, Z. Wang, C. J. Miller, and P. X.-L. Feng, “Multilayer MoS2 transistors enabled by a facile dry-transfer technique and thermal annealing,” J. Vac. Sci. Technol. B 32(6), 061203 (2014).
[Crossref]

2013 (6)

I. Jo, M. T. Pettes, J. Kim, K. Watanabe, T. Taniguchi, Z. Yao, and L. Shi, “Thermal conductivity and phonon transport in suspended few-layer hexagonal boron nitride,” Nano Lett. 13(2), 550–554 (2013).
[Crossref] [PubMed]

D. Golla, K. Chattrakun, K. Watanabe, T. Taniguchi, B. J. LeRoy, and A. Sandhu, “Optical thickness determination of hexagonal boron nitride flakes,” Appl. Phys. Lett. 102(16), 161906 (2013).
[Crossref]

Z. Liu, Y. Gong, W. Zhou, L. Ma, J. Yu, J. C. Idrobo, J. Jung, A. H. MacDonald, R. Vajtai, J. Lou, and P. M. Ajayan, “Ultrathin high-temperature oxidation-resistant coatings of hexagonal boron nitride,” Nat. Commun. 4(1), 2541 (2013).
[Crossref] [PubMed]

J. Wu, B. Wang, Y. Wei, R. Yang, and M. Dresselhaus, “Mechanics and mechanically tunable band gap in single-layer hexagonal boron-nitride,” Mater. Res. Lett. 1(4), 200–206 (2013).
[Crossref]

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

A. C. Ferrari and D. M. Basko, “Raman spectroscopy as a versatile tool for studying the properties of graphene,” Nat. Nanotechnol. 8(4), 235–246 (2013).
[Crossref] [PubMed]

2012 (2)

L. Wang, Z. Chen, C. R. Dean, T. Taniguchi, K. Watanabe, L. E. Brus, and J. Hone, “Negligible environmental sensitivity of graphene in a hexagonal boron nitride/graphene/h-BN sandwich structure,” ACS Nano 6(10), 9314–9319 (2012).
[Crossref] [PubMed]

Y. Y. Wang, R. X. Gao, Z. H. Ni, H. He, S. P. Guo, H. P. Yang, C. X. Cong, and T. Yu, “Thickness identification of two-dimensional materials by optical imaging,” Nanotechnology 23(49), 495713 (2012).
[Crossref] [PubMed]

2011 (2)

M. M. Benameur, B. Radisavljevic, J. S. Héron, S. Sahoo, H. Berger, and A. Kis, “Visibility of dichalcogenide nanolayers,” Nanotechnology 22(12), 125706 (2011).
[Crossref] [PubMed]

R. V. Gorbachev, I. Riaz, R. R. Nair, R. Jalil, L. Britnell, B. D. Belle, E. W. Hill, K. S. Novoselov, K. Watanabe, T. Taniguchi, A. K. Geim, and P. Blake, “Hunting for monolayer boron nitride: Optical and Raman signatures,” Small 7(4), 465–468 (2011).
[Crossref] [PubMed]

2010 (3)

A. Castellanos-Gomez, N. Agraït, and G. Rubio-Bollinger, “Optical identification of atomically thin dichalcogenide crystals,” Appl. Phys. Lett. 96(21), 213116 (2010).
[Crossref]

L. Song, L. Ci, H. Lu, P. B. Sorokin, C. Jin, J. Ni, A. G. Kvashnin, D. G. Kvashnin, J. Lou, B. I. Yakobson, and P. M. Ajayan, “Large scale growth and characterization of atomic hexagonal boron nitride layers,” Nano Lett. 10(8), 3209–3215 (2010).
[Crossref] [PubMed]

K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically thin MoS2: A new direct-gap semiconductor,” Phys. Rev. Lett. 105(13), 136805 (2010).
[Crossref] [PubMed]

2009 (2)

S. Berciaud, S. Ryu, L. E. Brus, and T. F. Heinz, “Probing the intrinsic properties of exfoliated graphene: Raman spectroscopy of free-standing monolayers,” Nano Lett. 9(1), 346–352 (2009).
[Crossref] [PubMed]

X. Wang, M. Zhao, and D. D. Nolte, “Optical contrast and clarity of graphene on an arbitrary substrate,” Appl. Phys. Lett. 95(8), 081102 (2009).
[Crossref]

2008 (1)

D. Pacile, J. C. Meyer, Ç. Ö. Girit, and A. Zettl, “The two-dimensional phase of boron nitride: Few-atomic-layer sheets and suspended membranes,” Appl. Phys. Lett. 92(13), 133107 (2008).
[Crossref]

2007 (2)

P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91(6), 063124 (2007).
[Crossref]

Y. Kubota, K. Watanabe, O. Tsuda, and T. Taniguchi, “Deep ultraviolet light-emitting hexagonal boron nitride synthesized at atmospheric pressure,” Science 317(5840), 932–934 (2007).
[Crossref] [PubMed]

1984 (1)

1983 (1)

D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B Condens. Matter 27(2), 985–1009 (1983).
[Crossref]

Agraït, N.

A. Castellanos-Gomez, N. Agraït, and G. Rubio-Bollinger, “Optical identification of atomically thin dichalcogenide crystals,” Appl. Phys. Lett. 96(21), 213116 (2010).
[Crossref]

Aharonovich, I.

T. T. Tran, K. Bray, M. J. Ford, M. Toth, and I. Aharonovich, “Quantum emission from hexagonal boron nitride monolayers,” Nat. Nanotechnol. 11(1), 37–41 (2016).
[Crossref] [PubMed]

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

Ajayan, P. M.

Z. Liu, Y. Gong, W. Zhou, L. Ma, J. Yu, J. C. Idrobo, J. Jung, A. H. MacDonald, R. Vajtai, J. Lou, and P. M. Ajayan, “Ultrathin high-temperature oxidation-resistant coatings of hexagonal boron nitride,” Nat. Commun. 4(1), 2541 (2013).
[Crossref] [PubMed]

L. Song, L. Ci, H. Lu, P. B. Sorokin, C. Jin, J. Ni, A. G. Kvashnin, D. G. Kvashnin, J. Lou, B. I. Yakobson, and P. M. Ajayan, “Large scale growth and characterization of atomic hexagonal boron nitride layers,” Nano Lett. 10(8), 3209–3215 (2010).
[Crossref] [PubMed]

Alkauskas, A.

L. Weston, D. Wickramaratne, M. Mackoit, A. Alkauskas, and C. G. Van de Walle, “Native point defects and impurities in hexagonal boron nitride,” Phys. Rev. B 97(21), 214104 (2018).
[Crossref]

Amani, M.

D. H. Lien, J. S. Kang, M. Amani, K. Chen, M. Tosun, H. P. Wang, T. Roy, M. S. Eggleston, M. C. Wu, M. Dubey, S. C. Lee, J. H. He, and A. Javey, “Engineering light outcoupling in 2D materials,” Nano Lett. 15(2), 1356–1361 (2015).
[Crossref] [PubMed]

Aspnes, D. E.

D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B Condens. Matter 27(2), 985–1009 (1983).
[Crossref]

Atatüre, M.

M. Atatüre, D. Englund, N. Vamivakas, S. Y. Lee, and J. Wrachtrup, “Material platforms for spin-based photonic quantum technologies,” Nat. Rev. Mater. 3(5), 38–51 (2018).
[Crossref]

Basko, D. M.

A. C. Ferrari and D. M. Basko, “Raman spectroscopy as a versatile tool for studying the properties of graphene,” Nat. Nanotechnol. 8(4), 235–246 (2013).
[Crossref] [PubMed]

Basov, D. N.

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Belle, B. D.

R. V. Gorbachev, I. Riaz, R. R. Nair, R. Jalil, L. Britnell, B. D. Belle, E. W. Hill, K. S. Novoselov, K. Watanabe, T. Taniguchi, A. K. Geim, and P. Blake, “Hunting for monolayer boron nitride: Optical and Raman signatures,” Small 7(4), 465–468 (2011).
[Crossref] [PubMed]

Belov, P.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

Benameur, M. M.

M. M. Benameur, B. Radisavljevic, J. S. Héron, S. Sahoo, H. Berger, and A. Kis, “Visibility of dichalcogenide nanolayers,” Nanotechnology 22(12), 125706 (2011).
[Crossref] [PubMed]

Berciaud, S.

S. Berciaud, S. Ryu, L. E. Brus, and T. F. Heinz, “Probing the intrinsic properties of exfoliated graphene: Raman spectroscopy of free-standing monolayers,” Nano Lett. 9(1), 346–352 (2009).
[Crossref] [PubMed]

Berger, H.

M. M. Benameur, B. Radisavljevic, J. S. Héron, S. Sahoo, H. Berger, and A. Kis, “Visibility of dichalcogenide nanolayers,” Nanotechnology 22(12), 125706 (2011).
[Crossref] [PubMed]

Blake, P.

R. V. Gorbachev, I. Riaz, R. R. Nair, R. Jalil, L. Britnell, B. D. Belle, E. W. Hill, K. S. Novoselov, K. Watanabe, T. Taniguchi, A. K. Geim, and P. Blake, “Hunting for monolayer boron nitride: Optical and Raman signatures,” Small 7(4), 465–468 (2011).
[Crossref] [PubMed]

P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91(6), 063124 (2007).
[Crossref]

Booth, T. J.

P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91(6), 063124 (2007).
[Crossref]

Bray, K.

T. T. Tran, K. Bray, M. J. Ford, M. Toth, and I. Aharonovich, “Quantum emission from hexagonal boron nitride monolayers,” Nat. Nanotechnol. 11(1), 37–41 (2016).
[Crossref] [PubMed]

Britnell, L.

R. V. Gorbachev, I. Riaz, R. R. Nair, R. Jalil, L. Britnell, B. D. Belle, E. W. Hill, K. S. Novoselov, K. Watanabe, T. Taniguchi, A. K. Geim, and P. Blake, “Hunting for monolayer boron nitride: Optical and Raman signatures,” Small 7(4), 465–468 (2011).
[Crossref] [PubMed]

Brus, L. E.

L. Wang, Z. Chen, C. R. Dean, T. Taniguchi, K. Watanabe, L. E. Brus, and J. Hone, “Negligible environmental sensitivity of graphene in a hexagonal boron nitride/graphene/h-BN sandwich structure,” ACS Nano 6(10), 9314–9319 (2012).
[Crossref] [PubMed]

S. Berciaud, S. Ryu, L. E. Brus, and T. F. Heinz, “Probing the intrinsic properties of exfoliated graphene: Raman spectroscopy of free-standing monolayers,” Nano Lett. 9(1), 346–352 (2009).
[Crossref] [PubMed]

Caldwell, J. D.

P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015).
[Crossref] [PubMed]

Camporeale, N.

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[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

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[Crossref]

I. Jo, M. T. Pettes, J. Kim, K. Watanabe, T. Taniguchi, Z. Yao, and L. Shi, “Thermal conductivity and phonon transport in suspended few-layer hexagonal boron nitride,” Nano Lett. 13(2), 550–554 (2013).
[Crossref] [PubMed]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

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J. Wu, B. Wang, Y. Wei, R. Yang, and M. Dresselhaus, “Mechanics and mechanically tunable band gap in single-layer hexagonal boron-nitride,” Mater. Res. Lett. 1(4), 200–206 (2013).
[Crossref]

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L. Weston, D. Wickramaratne, M. Mackoit, A. Alkauskas, and C. G. Van de Walle, “Native point defects and impurities in hexagonal boron nitride,” Phys. Rev. B 97(21), 214104 (2018).
[Crossref]

Wickramaratne, D.

L. Weston, D. Wickramaratne, M. Mackoit, A. Alkauskas, and C. G. Van de Walle, “Native point defects and impurities in hexagonal boron nitride,” Phys. Rev. B 97(21), 214104 (2018).
[Crossref]

Wrachtrup, J.

M. Atatüre, D. Englund, N. Vamivakas, S. Y. Lee, and J. Wrachtrup, “Material platforms for spin-based photonic quantum technologies,” Nat. Rev. Mater. 3(5), 38–51 (2018).
[Crossref]

Wu, J.

J. Wu, B. Wang, Y. Wei, R. Yang, and M. Dresselhaus, “Mechanics and mechanically tunable band gap in single-layer hexagonal boron-nitride,” Mater. Res. Lett. 1(4), 200–206 (2013).
[Crossref]

Wu, M. C.

D. H. Lien, J. S. Kang, M. Amani, K. Chen, M. Tosun, H. P. Wang, T. Roy, M. S. Eggleston, M. C. Wu, M. Dubey, S. C. Lee, J. H. He, and A. Javey, “Engineering light outcoupling in 2D materials,” Nano Lett. 15(2), 1356–1361 (2015).
[Crossref] [PubMed]

Yakobson, B. I.

L. Song, L. Ci, H. Lu, P. B. Sorokin, C. Jin, J. Ni, A. G. Kvashnin, D. G. Kvashnin, J. Lou, B. I. Yakobson, and P. M. Ajayan, “Large scale growth and characterization of atomic hexagonal boron nitride layers,” Nano Lett. 10(8), 3209–3215 (2010).
[Crossref] [PubMed]

Yang, H. P.

Y. Y. Wang, R. X. Gao, Z. H. Ni, H. He, S. P. Guo, H. P. Yang, C. X. Cong, and T. Yu, “Thickness identification of two-dimensional materials by optical imaging,” Nanotechnology 23(49), 495713 (2012).
[Crossref] [PubMed]

Yang, R.

R. Yang, X.-Q. Zheng, Z. Wang, C. J. Miller, and P. X.-L. Feng, “Multilayer MoS2 transistors enabled by a facile dry-transfer technique and thermal annealing,” J. Vac. Sci. Technol. B 32(6), 061203 (2014).
[Crossref]

J. Wu, B. Wang, Y. Wei, R. Yang, and M. Dresselhaus, “Mechanics and mechanically tunable band gap in single-layer hexagonal boron-nitride,” Mater. Res. Lett. 1(4), 200–206 (2013).
[Crossref]

P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91(6), 063124 (2007).
[Crossref]

Yao, Z.

I. Jo, M. T. Pettes, J. Kim, K. Watanabe, T. Taniguchi, Z. Yao, and L. Shi, “Thermal conductivity and phonon transport in suspended few-layer hexagonal boron nitride,” Nano Lett. 13(2), 550–554 (2013).
[Crossref] [PubMed]

Ye, G. J.

A. Islam, W. Du, V. Pashaei, H. Jia, Z. Wang, J. Lee, G. J. Ye, X. H. Chen, and P. X.-L. Feng, “Discerning Black Phosphorus Crystal Orientation and Anisotropy by Polarized Reflectance Measurement,” ACS Appl. Mater. Interfaces 10(30), 25629–25637 (2018).
[Crossref] [PubMed]

Yu, J.

Z. Liu, Y. Gong, W. Zhou, L. Ma, J. Yu, J. C. Idrobo, J. Jung, A. H. MacDonald, R. Vajtai, J. Lou, and P. M. Ajayan, “Ultrathin high-temperature oxidation-resistant coatings of hexagonal boron nitride,” Nat. Commun. 4(1), 2541 (2013).
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Yu, T.

Y. Y. Wang, R. X. Gao, Z. H. Ni, H. He, S. P. Guo, H. P. Yang, C. X. Cong, and T. Yu, “Thickness identification of two-dimensional materials by optical imaging,” Nanotechnology 23(49), 495713 (2012).
[Crossref] [PubMed]

Zettl, A.

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
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D. Pacile, J. C. Meyer, Ç. Ö. Girit, and A. Zettl, “The two-dimensional phase of boron nitride: Few-atomic-layer sheets and suspended membranes,” Appl. Phys. Lett. 92(13), 133107 (2008).
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Zhao, M.

X. Wang, M. Zhao, and D. D. Nolte, “Optical contrast and clarity of graphene on an arbitrary substrate,” Appl. Phys. Lett. 95(8), 081102 (2009).
[Crossref]

Zheng, X.-Q.

X.-Q. Zheng, J. Lee, and P. X.-L. Feng, “Hexagonal boron nitride nanomechanical resonators with spatially visualized motion,” Microsyst. Nanoeng. 3, 17038 (2017).
[Crossref]

R. Yang, X.-Q. Zheng, Z. Wang, C. J. Miller, and P. X.-L. Feng, “Multilayer MoS2 transistors enabled by a facile dry-transfer technique and thermal annealing,” J. Vac. Sci. Technol. B 32(6), 061203 (2014).
[Crossref]

Zhou, W.

Z. Liu, Y. Gong, W. Zhou, L. Ma, J. Yu, J. C. Idrobo, J. Jung, A. H. MacDonald, R. Vajtai, J. Lou, and P. M. Ajayan, “Ultrathin high-temperature oxidation-resistant coatings of hexagonal boron nitride,” Nat. Commun. 4(1), 2541 (2013).
[Crossref] [PubMed]

ACS Appl. Mater. Interfaces (1)

A. Islam, W. Du, V. Pashaei, H. Jia, Z. Wang, J. Lee, G. J. Ye, X. H. Chen, and P. X.-L. Feng, “Discerning Black Phosphorus Crystal Orientation and Anisotropy by Polarized Reflectance Measurement,” ACS Appl. Mater. Interfaces 10(30), 25629–25637 (2018).
[Crossref] [PubMed]

ACS Nano (2)

X. Li, G. D. Shepard, A. Cupo, N. Camporeale, K. Shayan, Y. Luo, V. Meunier, and S. Strauf, “Nonmagnetic quantum emitters in boron nitride with ultranarrow and sideband-free emission spectra,” ACS Nano 11(7), 6652–6660 (2017).
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L. Wang, Z. Chen, C. R. Dean, T. Taniguchi, K. Watanabe, L. E. Brus, and J. Hone, “Negligible environmental sensitivity of graphene in a hexagonal boron nitride/graphene/h-BN sandwich structure,” ACS Nano 6(10), 9314–9319 (2012).
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Appl. Opt. (1)

Appl. Phys. Lett. (5)

D. Pacile, J. C. Meyer, Ç. Ö. Girit, and A. Zettl, “The two-dimensional phase of boron nitride: Few-atomic-layer sheets and suspended membranes,” Appl. Phys. Lett. 92(13), 133107 (2008).
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D. Golla, K. Chattrakun, K. Watanabe, T. Taniguchi, B. J. LeRoy, and A. Sandhu, “Optical thickness determination of hexagonal boron nitride flakes,” Appl. Phys. Lett. 102(16), 161906 (2013).
[Crossref]

P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91(6), 063124 (2007).
[Crossref]

X. Wang, M. Zhao, and D. D. Nolte, “Optical contrast and clarity of graphene on an arbitrary substrate,” Appl. Phys. Lett. 95(8), 081102 (2009).
[Crossref]

A. Castellanos-Gomez, N. Agraït, and G. Rubio-Bollinger, “Optical identification of atomically thin dichalcogenide crystals,” Appl. Phys. Lett. 96(21), 213116 (2010).
[Crossref]

J. Vac. Sci. Technol. B (1)

R. Yang, X.-Q. Zheng, Z. Wang, C. J. Miller, and P. X.-L. Feng, “Multilayer MoS2 transistors enabled by a facile dry-transfer technique and thermal annealing,” J. Vac. Sci. Technol. B 32(6), 061203 (2014).
[Crossref]

Mater. Res. Lett. (1)

J. Wu, B. Wang, Y. Wei, R. Yang, and M. Dresselhaus, “Mechanics and mechanically tunable band gap in single-layer hexagonal boron-nitride,” Mater. Res. Lett. 1(4), 200–206 (2013).
[Crossref]

Microsyst. Nanoeng. (1)

X.-Q. Zheng, J. Lee, and P. X.-L. Feng, “Hexagonal boron nitride nanomechanical resonators with spatially visualized motion,” Microsyst. Nanoeng. 3, 17038 (2017).
[Crossref]

Nano Lett. (4)

L. Song, L. Ci, H. Lu, P. B. Sorokin, C. Jin, J. Ni, A. G. Kvashnin, D. G. Kvashnin, J. Lou, B. I. Yakobson, and P. M. Ajayan, “Large scale growth and characterization of atomic hexagonal boron nitride layers,” Nano Lett. 10(8), 3209–3215 (2010).
[Crossref] [PubMed]

D. H. Lien, J. S. Kang, M. Amani, K. Chen, M. Tosun, H. P. Wang, T. Roy, M. S. Eggleston, M. C. Wu, M. Dubey, S. C. Lee, J. H. He, and A. Javey, “Engineering light outcoupling in 2D materials,” Nano Lett. 15(2), 1356–1361 (2015).
[Crossref] [PubMed]

S. Berciaud, S. Ryu, L. E. Brus, and T. F. Heinz, “Probing the intrinsic properties of exfoliated graphene: Raman spectroscopy of free-standing monolayers,” Nano Lett. 9(1), 346–352 (2009).
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I. Jo, M. T. Pettes, J. Kim, K. Watanabe, T. Taniguchi, Z. Yao, and L. Shi, “Thermal conductivity and phonon transport in suspended few-layer hexagonal boron nitride,” Nano Lett. 13(2), 550–554 (2013).
[Crossref] [PubMed]

Nanotechnology (2)

Y. Y. Wang, R. X. Gao, Z. H. Ni, H. He, S. P. Guo, H. P. Yang, C. X. Cong, and T. Yu, “Thickness identification of two-dimensional materials by optical imaging,” Nanotechnology 23(49), 495713 (2012).
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M. M. Benameur, B. Radisavljevic, J. S. Héron, S. Sahoo, H. Berger, and A. Kis, “Visibility of dichalcogenide nanolayers,” Nanotechnology 22(12), 125706 (2011).
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Nat. Commun. (2)

Z. Liu, Y. Gong, W. Zhou, L. Ma, J. Yu, J. C. Idrobo, J. Jung, A. H. MacDonald, R. Vajtai, J. Lou, and P. M. Ajayan, “Ultrathin high-temperature oxidation-resistant coatings of hexagonal boron nitride,” Nat. Commun. 4(1), 2541 (2013).
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P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015).
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Nat. Nanotechnol. (2)

T. T. Tran, K. Bray, M. J. Ford, M. Toth, and I. Aharonovich, “Quantum emission from hexagonal boron nitride monolayers,” Nat. Nanotechnol. 11(1), 37–41 (2016).
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A. C. Ferrari and D. M. Basko, “Raman spectroscopy as a versatile tool for studying the properties of graphene,” Nat. Nanotechnol. 8(4), 235–246 (2013).
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Nat. Photonics (2)

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

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

Nat. Rev. Mater. (1)

M. Atatüre, D. Englund, N. Vamivakas, S. Y. Lee, and J. Wrachtrup, “Material platforms for spin-based photonic quantum technologies,” Nat. Rev. Mater. 3(5), 38–51 (2018).
[Crossref]

Phys. Rev. B (2)

A. Sajid, J. R. Reimers, and M. J. Ford, “Defect states in hexagonal boron nitride: Assignments of observed properties and prediction of properties relevant to quantum computation,” Phys. Rev. B 97(6), 064101 (2018).
[Crossref]

L. Weston, D. Wickramaratne, M. Mackoit, A. Alkauskas, and C. G. Van de Walle, “Native point defects and impurities in hexagonal boron nitride,” Phys. Rev. B 97(21), 214104 (2018).
[Crossref]

Phys. Rev. B Condens. Matter (1)

D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B Condens. Matter 27(2), 985–1009 (1983).
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Phys. Rev. Lett. (1)

K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically thin MoS2: A new direct-gap semiconductor,” Phys. Rev. Lett. 105(13), 136805 (2010).
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S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
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R. V. Gorbachev, I. Riaz, R. R. Nair, R. Jalil, L. Britnell, B. D. Belle, E. W. Hill, K. S. Novoselov, K. Watanabe, T. Taniguchi, A. K. Geim, and P. Blake, “Hunting for monolayer boron nitride: Optical and Raman signatures,” Small 7(4), 465–468 (2011).
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Other (1)

X.-Q. Zheng, J. Lee, and P. X.-L. Feng, “Hexagonal boron nitride (h-BN) nanomechanical resonators with temperature-dependent multimode operations”, in Tech. Digest, The 18th Int.Conf. on Solid-State Sensors, Actuators & Microsystems (Transducers’15), 1393–1396, Anchorage, Alaska, June 21–25 (2017).

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Figures (5)

Fig. 1
Fig. 1 (a) Real color and inverted color microscopy images of a h-BN flake, and schematic illustration of PDMS assisted dry transferring of h-BN crystals onto pre-patterned device platform. The color difference comes from the thickness variation of the flake. (b)-(d) Schematic diagrams of multi-reflection model for h-BN on PDMS, bare Si, 290 nm SiO2/Si and corresponding color contour plots of the optical contrast as a function of both h-BN thickness and excitation wavelength calculated by the Fresnel equations. The schematic light path is simplified without refraction for the nearly normal incident condition.
Fig. 2
Fig. 2 Typical modeling results of h-BN supported on a SiO2/Si substrate. (a) Reflectance spectra of 1–10 layers of h-BN calculated from Eq. (2). (b) Contrast spectra of 1–10 layers of h-BN calculated from Eq. (1). (c) Integrated contrast spectra of 1–1000 layers of h-BN over RGB channels and zoom-in spectra for 1–10 layers. (d)–(f) The dependence of optical contrast on the dielectric SiO2 layer thickness and air gap thickness under different sample configurations. The thickness of h-BN is set as 15 nm (45 layers) for (d), 30 nm (91 layers) for (e), and 188 nm (570 layers) for (f).
Fig. 3
Fig. 3 Optical microscopy images (splitting channels) of a h-BN flake on (a) PDMS and transferred onto (b) the patterned SiO2/Si substrate. (c) Gray values measured from each channel along the orange dashed line in (a) & (b). (d) Atomic force microscopy trace of the flake on SiO2/Si along an identical line as the orange dashed line. (e) Measured optical contrast traces of each channel derived from SiO2/Si data shown in (c). (f) The theoretical and experimental optical contrast of h-BN on PDMS and SiO2/Si. The red triangles, green circles, and blue squares with error bars mark the measured optical contrast values averaged over the h-BN region highlighted in (c) & (e) for channel R, G, B, respectively. The SiO2 thickness of 287 nm is used for the theoretical calculation, giving a better match. The black dashed line indicates the thickness of 15 nm (45 layers) position in the contrast spectra. The scale bar represents 10 µm.
Fig. 4
Fig. 4 Schematic diagrams of multi-reflection model and optical microscopy images of h-BN suspended over patterned (a) SiO2/Si and (b) Si substrates. (c)–(d) Optical contrast plots of suspended h-BN in configuration (b). (e)–(f) Optical contrast plots of suspended h-BN in configuration (a). The schematic light path is simplified without refraction for the nearly normal incident condition. The scale bar represents 20 µm.
Fig. 5
Fig. 5 Optical microscopy images (splitting channels) of h-BN flakes suspended over patterned (a) SiO2/Si and (e) Si substrates. Measured contrast traces of (b) & (f) supported areas and (c) & (g) suspended areas along the orange dashed lines in optical images. (d) and (h) Calculated contrast plots with solid lines (solid symbols) for supported cases and dashed lines (open symbols) for suspended cases. The red triangles, green circles, and blue squares with error bars mark the measured contrast values averaged over the h-BN region highlighted in (b)–(c) & (f)–(g) for channel R, G, and B, respectively. The SiO2 thickness of 287 nm is used for the theoretical calculation, giving a better match than using the nominal 290 nm. The black dashed lines indicate the thickness of 30 nm (91 layers) position in (d) and 188 nm (570 layers) position in (h). The scale bar represents 10 µm.

Equations (5)

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C( λ )=  R( n 1 = n 0 )R( n 1 )  R( n 1 =1 ) ;
R( n 1 )= | r 1 e i( Φ 1 + Φ 2 ) + r 2 e i( Φ 1 Φ 2 ) + r 3 e i( Φ 1 + Φ 2 ) + r 1 r 2 r 3 e i( Φ 1 Φ 2 ) ( e i( Φ 1 + Φ 2 ) + r 1 r 2 e i( Φ 1 Φ 2 ) + r 1 r 3 e i( Φ 1 + Φ 2 ) + r 2 r 3 e i( Φ 1 Φ 2 ) ) | 2 ;
r 1 =  n 0 n 1 n 0 + n 1 , r 2 = n 1 n 2 n 1 + n 2 , r 3 = n 2 n 3 n 2 + n 3 ;
Φ 1 = 2π n 1 d 1 λ , Φ 2 = 2π n 2 d 2 λ .
C( R )= I (R) 0 I(R) I (R) 0 ,C( G )= I (G) 0 I(G) I (G) 0 ,C( B )= I (B) 0 I(B) I (B) 0 .

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