Abstract

An accurate control of the optical properties of single crystal diamond during microfabrication processes such as ion implantation plays a crucial role in the engineering of integrated photonic devices. In this work we present a systematic study of the variation of both real and imaginary parts of the refractive index of single crystal diamond, when damaged with 2 and 3 MeV protons at low-medium fluences (range: 1015 - 1017 cm−2). After implanting in 125 × 125 μm2 areas with a scanning ion microbeam, the variation of optical pathlength of the implanted regions was measured with laser interferometric microscopy, while their optical transmission was studied using a spectrometric set-up with micrometric spatial resolution. On the basis of a model taking into account the strongly non-uniform damage profile in the bulk sample, the variation of the complex refractive index as a function of damage density was evaluated.

© 2012 OSA

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2012 (1)

2011 (1)

L. Giuntini, “A review of external microbeams for ion beam analyses,” Anal. Bioanal. Chem.401(3), 785–793 (2011).
[CrossRef] [PubMed]

2010 (5)

J. F. Ziegler, M. D. Ziegler, and J. P. Biersack, “SRIM – The stopping and range of ions in matter (2010),” Nucl. Instrum. Methods Phys. Res. B268(11-12), 1818–1823 (2010).
[CrossRef]

P. Olivero, S. Calusi, L. Giuntini, S. Lagomarsino, A. Lo Giudice, M. Massi, S. Sciortino, M. Vannoni, and E. Vittone, “Controlled variation of the refractive index in ion-damaged diamond,” Diamond Related Materials19(5-6), 428–431 (2010).
[CrossRef]

A. K. Sytchkova, J. Bulir, and A. M. Piegari, “Transmittance measurements on variable coatings with enhanced spatial resolution,” Chin. Opt. Lett.8, 103–104 (2010).
[CrossRef]

I. Aharonovich, S. Castelletto, B. C. Johnson, J. C. McCallum, D. A. Simpson, A. D. Greentree, and S. Prawer, “Chromium single-photon emitters in diamond fabricated by ion implantation,” Phys. Rev. B81(12), 121201 (2010).
[CrossRef]

S. Lagomarsino, P. Olivero, F. Bosia, M. Vannoni, S. Calusi, L. Giuntini, and M. Massi, “Evidence of Light Guiding in Ion-Implanted Diamond,” Phys. Rev. Lett.105(23), 233903 (2010).
[CrossRef] [PubMed]

2009 (4)

S. Tomljenovic-Hanic, A. D. Greentree, C. M. de Sterke, and S. Prawer, “Flexible design of ultrahigh-Q microcavities in diamond-based photonic crystal slabs,” Opt. Express17(8), 6465–6475 (2009).
[CrossRef] [PubMed]

I. Aharonovich, C. Zhou, A. Stacey, J. Orwa, S. Castelletto, D. Simpson, A. D. Greentree, F. Treussart, J.-F. Roch, and S. Prawer, “Enhanced single-photon emission in the near infrared from a diamond color center,” Phys. Rev. B79(23), 235316 (2009).
[CrossRef]

M. Vannoni, G. Molesini, S. Sciortino, S. Lagomarsino, P. Olivero, and E. Vittone, “Interferometric characterization of mono-and polycrystalline CVD diamond,” Proc. SPIE7389, 738931, 738931-6 (2009).
[CrossRef]

D. P. Hickey, K. S. Jones, and R. G. Elliman, “Amorphization and graphitization of single-crystal diamond – a transmission electron microscopy study,” Diamond Related Materials18(11), 1353–1359 (2009).
[CrossRef]

2008 (5)

S. Calusi, E. Colombo, L. Giuntini, A. L. Giudice, C. Manfredotti, M. Massi, G. Pratesi, and E. Vittone, “The ionoluminescence apparatus at the LABEC external microbeam facility,” Nucl. Instrum. Methods Phys. Res. B2662306–2310 (2008).
[CrossRef]

S. Prawer and A. D. Greentree, “Applied physics. Diamond for quantum computing,” Science320(5883), 1601–1602 (2008).
[CrossRef] [PubMed]

M. P. Hiscocks, C. J. Kaalund, F. Ladouceur, S. T. Huntington, B. C. Gibson, S. Trpkovski, D. Simpson, E. Ampem-Lassen, S. Prawer, and J. E. Butler, “Reactive ion etching of waveguide structures in diamond,” Diamond Related Materials17(11), 1831–1834 (2008).
[CrossRef]

M. P. Hiscocks, K. Ganesan, B. C. Gibson, S. T. Huntington, F. Ladouceur, and S. Prawer, “Diamond waveguides fabricated by reactive ion etching,” Opt. Express16(24), 19512–19519 (2008).
[CrossRef] [PubMed]

B. A. Fairchild, P. Olivero, S. Rubanov, A. D. Greentree, F. Waldermann, R. A. Taylor, I. Walmsley, J. M. Smith, S. Huntington, B. C. Gibson, D. N. Jamieson, and S. Prawer, “Fabrication of Ultrathin Single-Crystal Diamond Membranes,” Adv. Mater. (Deerfield Beach Fla.)20(24), 4793–4798 (2008).
[CrossRef]

2007 (3)

C. F. Wang, Y.-S. Choi, J. C. Lee, E. L. Hu, J. Yang, and J. E. Butler, “Observation of whispering gallery modes in nanocrystalline diamond microdisks,” Appl. Phys. Lett.90(8), 081110 (2007).
[CrossRef]

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, “Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond,” Appl. Phys. Lett.91(20), 201112 (2007).
[CrossRef]

L. Giuntini, M. Massi, and S. Calusi, “The external scanning proton microprobe of Firenze: a comprehensive description,” Nucl. Instrum. Methods Phys. Res. A576(2-3), 266–273 (2007).
[CrossRef]

2006 (5)

A. A. Bettiol, S. V. Rao, E. J. Teo, J. A. van Kan, and F. Watt, “Fabrication of buried channel waveguides in photosensitive glass using proton beam writing,” Appl. Phys. Lett.88(17), 171106 (2006).
[CrossRef]

F. Chen, L. Wang, Y. Jiang, X.-L. Wang, K.-M. Wang, G. Fu, Q.-M. Lu, C. E. Rüter, and D. Kip, “Optical channel waveguides in Nd: YVO4 crystal produced by O+ ion implantation,” Appl. Phys. Lett.88(7), 071123 (2006).
[CrossRef]

C. Wang, C. Kurtsiefer, H. Weinfurter, and B. Burchard, “Single photon emission from SiV centres in diamond produced by ion implantation,” J. Phys. B39(1), 37–41 (2006).
[CrossRef]

P. Kok and B. W. Lovett, “Materials science: Qubits in the pink,” Nature444(7115), 49–49 (2006).
[CrossRef] [PubMed]

P. Olivero, S. Rubanov, P. Reichart, B. C. Gibson, S. T. Huntington, J. R. Rabeau, A. D. Greentree, J. Salzman, D. Moore, D. N. Jamieson, and S. Prawer, “Characterization of three-dimensional microstructures in single-crystal diamond,” Diamond Related Materials15(10), 1614–1621 (2006).
[CrossRef]

2005 (1)

A. V. Khomich, V. I. Kovalev, E. V. Zavedeev, R. A. Khmelnitskiy, and A. A. Gippius, “Spectroscopic ellipsometry study of buried graphitized layers in the ion-implanted diamond,” Vacuum78(2-4), 583–587 (2005).
[CrossRef]

2004 (1)

E. Gu, H. W. Choi, C. Liu, C. Griffin, J. M. Girkin, I. M. Watson, M. D. Dawson, G. McConnell, and A. M. Gurney, “Reflection/transmission confocal microscopy characterization of single-crystal diamond microlens arrays,” Appl. Phys. Lett.84(15), 2754–2756 (2004).
[CrossRef]

2003 (1)

Y. Fu and B. K. A. Ngoi, “Investigation of diffractive optical element fabricated on diamond film by use of focused ion beam direct milling,” Opt. Eng.42(8), 2214–2217 (2003).
[CrossRef]

2002 (3)

A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J.-P. Poizat, and P. Grangier, “Single photon quantum cryptography,” Phys. Rev. Lett.89(18), 187901 (2002).
[CrossRef] [PubMed]

M. Massi, L. Giuntini, M. Chiari, N. Gelli, and P. A. Mandò, “The external beam microprobe facility in Florence: set-up and performance,” Nucl. Instrum. Methods Phys. Res. B190(1-4), 276–282 (2002).
[CrossRef]

M. Chiari, A. Migliori, and P. A. Mandò, “Measurement of low currents in an external beam set-up,” Nucl. Instrum. Methods Phys. Res. B188, 162–165 (2002).
[CrossRef]

2000 (2)

T. Calligaro, J.-C. Dran, E. Ioannidou, B. Moignard, L. Pichon, and J. Salomon, “Development of an external beam nuclear microprobe on the Aglae facility of the Louvre museum,” Nucl. Instrum. Methods Phys. Res. B161–163, 328–333 (2000).
[CrossRef]

S. Gloor, V. Romano, W. Lüthy, H. P. Weber, V. V. Kononenko, S. M. Pimenov, V. I. Konov, and A. V. Khomich, “Antireflection structures written by excimer laser on CVD diamond,” Appl. Phys., A Mater. Sci. Process.70(5), 547–550 (2000).
[CrossRef]

1999 (1)

H. Björkman, P. Rangsten, and K. Hjort, “Diamond microstructures for optical micro electromechanical systems,” Sens. Actuators78(1), 41–47 (1999).
[CrossRef]

1998 (1)

K. L. Bhatia, S. Fabian, S. Kalbitzer, C. Klatt, W. Krätschmer, R. Stoll, and J. F. P. Sellschop, “Optical effects in carbon-ion irradiated diamond,” Thin Solid Films324(1-2), 11–18 (1998).
[CrossRef]

1995 (2)

M. G. Jubber, M. Liehr, J. L. McGrath, J. I. B. Wilson, I. C. Drummond, P. John, D. K. Milne, R. W. McCullough, J. Geddes, D. P. Higgins, and M. Schlapp, “Atom beam treatment of diamond films,” Diamond Related Materials4(4), 445–450 (1995).
[CrossRef]

C. Uzan-Saguy, C. Cytermann, R. Brener, V. Richter, M. Shaanan, and R. Kalish, “Damage threshold for ion-beam induced graphitization of diamond,” Appl. Phys. Lett.67(9), 1194–1196 (1995).
[CrossRef]

1994 (3)

W. Wu and S. Fahy, “Molecular-dynamics study of single-atom radiation damage in diamond,” Phys. Rev. B Condens. Matter49(5), 3030–3035 (1994).
[CrossRef] [PubMed]

P. A. Mandò, “Measurement of low currents in an external beam set-up,” Nucl. Instrum. Methods Phys. Res. B85, 815 (1994).

P. A. Mandò, “Advantages and limitations of external beams in applications to arts & archeology, geology and environmental problems,” Nucl. Instrum. Methods Phys. Res. B85(1-4), 815–823 (1994).
[CrossRef]

1991 (1)

L. Babsail, N. Hamelin, and P. D. Townsend, “Helium-ion implanted waveguides in zircon,” Nucl. Instrum. Methods Phys. Res. B59–60, 1219–1222 (1991).
[CrossRef]

1986 (1)

J. F. Prins, T. E. Derry, and J. P. Sellschop, “Volume expansion of diamond during ion implantation,” Phys. Rev. B Condens. Matter34(12), 8870–8874 (1986).
[CrossRef] [PubMed]

1981 (1)

E. W. Maby, C. W. Magee, and J. H. Morewood, “Volume expansion of ion-implanted diamond,” Appl. Phys. Lett.39(2), 157–158 (1981).
[CrossRef]

1974 (1)

D. T. Y. Wei, W. W. Lee, and L. R. Bloom, “Large refractive index change induced by ion implantation in lithium niobate,” Appl. Phys. Lett.25(6), 329–331 (1974).
[CrossRef]

1965 (1)

R. L. Hines, “Radiation Damage of Diamond by 20-keV Carbon Ions,” Phys. Rev.138(6A), A1747–A1751 (1965).
[CrossRef]

1960 (1)

R. L. Hines and R. Arndt, “Radiation effects of bombardment of quartz and vitreous silica by 7.5-kev to 59-kev positive ions,” Phys. Rev.119(2), 623–633 (1960).
[CrossRef]

Aharonovich, I.

I. Aharonovich, S. Castelletto, B. C. Johnson, J. C. McCallum, D. A. Simpson, A. D. Greentree, and S. Prawer, “Chromium single-photon emitters in diamond fabricated by ion implantation,” Phys. Rev. B81(12), 121201 (2010).
[CrossRef]

I. Aharonovich, C. Zhou, A. Stacey, J. Orwa, S. Castelletto, D. Simpson, A. D. Greentree, F. Treussart, J.-F. Roch, and S. Prawer, “Enhanced single-photon emission in the near infrared from a diamond color center,” Phys. Rev. B79(23), 235316 (2009).
[CrossRef]

Ampem-Lassen, E.

M. P. Hiscocks, C. J. Kaalund, F. Ladouceur, S. T. Huntington, B. C. Gibson, S. Trpkovski, D. Simpson, E. Ampem-Lassen, S. Prawer, and J. E. Butler, “Reactive ion etching of waveguide structures in diamond,” Diamond Related Materials17(11), 1831–1834 (2008).
[CrossRef]

Arndt, R.

R. L. Hines and R. Arndt, “Radiation effects of bombardment of quartz and vitreous silica by 7.5-kev to 59-kev positive ions,” Phys. Rev.119(2), 623–633 (1960).
[CrossRef]

Awschalom, D. D.

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, “Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond,” Appl. Phys. Lett.91(20), 201112 (2007).
[CrossRef]

Babsail, L.

L. Babsail, N. Hamelin, and P. D. Townsend, “Helium-ion implanted waveguides in zircon,” Nucl. Instrum. Methods Phys. Res. B59–60, 1219–1222 (1991).
[CrossRef]

Battiato, A.

Bettiol, A. A.

A. A. Bettiol, S. V. Rao, E. J. Teo, J. A. van Kan, and F. Watt, “Fabrication of buried channel waveguides in photosensitive glass using proton beam writing,” Appl. Phys. Lett.88(17), 171106 (2006).
[CrossRef]

Beveratos, A.

A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J.-P. Poizat, and P. Grangier, “Single photon quantum cryptography,” Phys. Rev. Lett.89(18), 187901 (2002).
[CrossRef] [PubMed]

Bhatia, K. L.

K. L. Bhatia, S. Fabian, S. Kalbitzer, C. Klatt, W. Krätschmer, R. Stoll, and J. F. P. Sellschop, “Optical effects in carbon-ion irradiated diamond,” Thin Solid Films324(1-2), 11–18 (1998).
[CrossRef]

Biersack, J. P.

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B. A. Fairchild, P. Olivero, S. Rubanov, A. D. Greentree, F. Waldermann, R. A. Taylor, I. Walmsley, J. M. Smith, S. Huntington, B. C. Gibson, D. N. Jamieson, and S. Prawer, “Fabrication of Ultrathin Single-Crystal Diamond Membranes,” Adv. Mater. (Deerfield Beach Fla.)20(24), 4793–4798 (2008).
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I. Aharonovich, S. Castelletto, B. C. Johnson, J. C. McCallum, D. A. Simpson, A. D. Greentree, and S. Prawer, “Chromium single-photon emitters in diamond fabricated by ion implantation,” Phys. Rev. B81(12), 121201 (2010).
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M. P. Hiscocks, C. J. Kaalund, F. Ladouceur, S. T. Huntington, B. C. Gibson, S. Trpkovski, D. Simpson, E. Ampem-Lassen, S. Prawer, and J. E. Butler, “Reactive ion etching of waveguide structures in diamond,” Diamond Related Materials17(11), 1831–1834 (2008).
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C. Uzan-Saguy, C. Cytermann, R. Brener, V. Richter, M. Shaanan, and R. Kalish, “Damage threshold for ion-beam induced graphitization of diamond,” Appl. Phys. Lett.67(9), 1194–1196 (1995).
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M. Vannoni, G. Molesini, S. Sciortino, S. Lagomarsino, P. Olivero, and E. Vittone, “Interferometric characterization of mono-and polycrystalline CVD diamond,” Proc. SPIE7389, 738931, 738931-6 (2009).
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P. Olivero, S. Rubanov, P. Reichart, B. C. Gibson, S. T. Huntington, J. R. Rabeau, A. D. Greentree, J. Salzman, D. Moore, D. N. Jamieson, and S. Prawer, “Characterization of three-dimensional microstructures in single-crystal diamond,” Diamond Related Materials15(10), 1614–1621 (2006).
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I. Aharonovich, S. Castelletto, B. C. Johnson, J. C. McCallum, D. A. Simpson, A. D. Greentree, and S. Prawer, “Chromium single-photon emitters in diamond fabricated by ion implantation,” Phys. Rev. B81(12), 121201 (2010).
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M. P. Hiscocks, K. Ganesan, B. C. Gibson, S. T. Huntington, F. Ladouceur, and S. Prawer, “Diamond waveguides fabricated by reactive ion etching,” Opt. Express16(24), 19512–19519 (2008).
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B. A. Fairchild, P. Olivero, S. Rubanov, A. D. Greentree, F. Waldermann, R. A. Taylor, I. Walmsley, J. M. Smith, S. Huntington, B. C. Gibson, D. N. Jamieson, and S. Prawer, “Fabrication of Ultrathin Single-Crystal Diamond Membranes,” Adv. Mater. (Deerfield Beach Fla.)20(24), 4793–4798 (2008).
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P. Olivero, S. Rubanov, P. Reichart, B. C. Gibson, S. T. Huntington, J. R. Rabeau, A. D. Greentree, J. Salzman, D. Moore, D. N. Jamieson, and S. Prawer, “Characterization of three-dimensional microstructures in single-crystal diamond,” Diamond Related Materials15(10), 1614–1621 (2006).
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I. Aharonovich, C. Zhou, A. Stacey, J. Orwa, S. Castelletto, D. Simpson, A. D. Greentree, F. Treussart, J.-F. Roch, and S. Prawer, “Enhanced single-photon emission in the near infrared from a diamond color center,” Phys. Rev. B79(23), 235316 (2009).
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S. Gloor, V. Romano, W. Lüthy, H. P. Weber, V. V. Kononenko, S. M. Pimenov, V. I. Konov, and A. V. Khomich, “Antireflection structures written by excimer laser on CVD diamond,” Appl. Phys., A Mater. Sci. Process.70(5), 547–550 (2000).
[CrossRef]

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B. A. Fairchild, P. Olivero, S. Rubanov, A. D. Greentree, F. Waldermann, R. A. Taylor, I. Walmsley, J. M. Smith, S. Huntington, B. C. Gibson, D. N. Jamieson, and S. Prawer, “Fabrication of Ultrathin Single-Crystal Diamond Membranes,” Adv. Mater. (Deerfield Beach Fla.)20(24), 4793–4798 (2008).
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P. Olivero, S. Rubanov, P. Reichart, B. C. Gibson, S. T. Huntington, J. R. Rabeau, A. D. Greentree, J. Salzman, D. Moore, D. N. Jamieson, and S. Prawer, “Characterization of three-dimensional microstructures in single-crystal diamond,” Diamond Related Materials15(10), 1614–1621 (2006).
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F. Chen, L. Wang, Y. Jiang, X.-L. Wang, K.-M. Wang, G. Fu, Q.-M. Lu, C. E. Rüter, and D. Kip, “Optical channel waveguides in Nd: YVO4 crystal produced by O+ ion implantation,” Appl. Phys. Lett.88(7), 071123 (2006).
[CrossRef]

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T. Calligaro, J.-C. Dran, E. Ioannidou, B. Moignard, L. Pichon, and J. Salomon, “Development of an external beam nuclear microprobe on the Aglae facility of the Louvre museum,” Nucl. Instrum. Methods Phys. Res. B161–163, 328–333 (2000).
[CrossRef]

Salzman, J.

P. Olivero, S. Rubanov, P. Reichart, B. C. Gibson, S. T. Huntington, J. R. Rabeau, A. D. Greentree, J. Salzman, D. Moore, D. N. Jamieson, and S. Prawer, “Characterization of three-dimensional microstructures in single-crystal diamond,” Diamond Related Materials15(10), 1614–1621 (2006).
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M. G. Jubber, M. Liehr, J. L. McGrath, J. I. B. Wilson, I. C. Drummond, P. John, D. K. Milne, R. W. McCullough, J. Geddes, D. P. Higgins, and M. Schlapp, “Atom beam treatment of diamond films,” Diamond Related Materials4(4), 445–450 (1995).
[CrossRef]

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P. Olivero, S. Calusi, L. Giuntini, S. Lagomarsino, A. Lo Giudice, M. Massi, S. Sciortino, M. Vannoni, and E. Vittone, “Controlled variation of the refractive index in ion-damaged diamond,” Diamond Related Materials19(5-6), 428–431 (2010).
[CrossRef]

M. Vannoni, G. Molesini, S. Sciortino, S. Lagomarsino, P. Olivero, and E. Vittone, “Interferometric characterization of mono-and polycrystalline CVD diamond,” Proc. SPIE7389, 738931, 738931-6 (2009).
[CrossRef]

Sellschop, J. F. P.

K. L. Bhatia, S. Fabian, S. Kalbitzer, C. Klatt, W. Krätschmer, R. Stoll, and J. F. P. Sellschop, “Optical effects in carbon-ion irradiated diamond,” Thin Solid Films324(1-2), 11–18 (1998).
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J. F. Prins, T. E. Derry, and J. P. Sellschop, “Volume expansion of diamond during ion implantation,” Phys. Rev. B Condens. Matter34(12), 8870–8874 (1986).
[CrossRef] [PubMed]

Shaanan, M.

C. Uzan-Saguy, C. Cytermann, R. Brener, V. Richter, M. Shaanan, and R. Kalish, “Damage threshold for ion-beam induced graphitization of diamond,” Appl. Phys. Lett.67(9), 1194–1196 (1995).
[CrossRef]

Simpson, D.

I. Aharonovich, C. Zhou, A. Stacey, J. Orwa, S. Castelletto, D. Simpson, A. D. Greentree, F. Treussart, J.-F. Roch, and S. Prawer, “Enhanced single-photon emission in the near infrared from a diamond color center,” Phys. Rev. B79(23), 235316 (2009).
[CrossRef]

M. P. Hiscocks, C. J. Kaalund, F. Ladouceur, S. T. Huntington, B. C. Gibson, S. Trpkovski, D. Simpson, E. Ampem-Lassen, S. Prawer, and J. E. Butler, “Reactive ion etching of waveguide structures in diamond,” Diamond Related Materials17(11), 1831–1834 (2008).
[CrossRef]

Simpson, D. A.

I. Aharonovich, S. Castelletto, B. C. Johnson, J. C. McCallum, D. A. Simpson, A. D. Greentree, and S. Prawer, “Chromium single-photon emitters in diamond fabricated by ion implantation,” Phys. Rev. B81(12), 121201 (2010).
[CrossRef]

Smith, J. M.

B. A. Fairchild, P. Olivero, S. Rubanov, A. D. Greentree, F. Waldermann, R. A. Taylor, I. Walmsley, J. M. Smith, S. Huntington, B. C. Gibson, D. N. Jamieson, and S. Prawer, “Fabrication of Ultrathin Single-Crystal Diamond Membranes,” Adv. Mater. (Deerfield Beach Fla.)20(24), 4793–4798 (2008).
[CrossRef]

Stacey, A.

I. Aharonovich, C. Zhou, A. Stacey, J. Orwa, S. Castelletto, D. Simpson, A. D. Greentree, F. Treussart, J.-F. Roch, and S. Prawer, “Enhanced single-photon emission in the near infrared from a diamond color center,” Phys. Rev. B79(23), 235316 (2009).
[CrossRef]

Stoll, R.

K. L. Bhatia, S. Fabian, S. Kalbitzer, C. Klatt, W. Krätschmer, R. Stoll, and J. F. P. Sellschop, “Optical effects in carbon-ion irradiated diamond,” Thin Solid Films324(1-2), 11–18 (1998).
[CrossRef]

Sytchkova, A.

Sytchkova, A. K.

Taylor, R. A.

B. A. Fairchild, P. Olivero, S. Rubanov, A. D. Greentree, F. Waldermann, R. A. Taylor, I. Walmsley, J. M. Smith, S. Huntington, B. C. Gibson, D. N. Jamieson, and S. Prawer, “Fabrication of Ultrathin Single-Crystal Diamond Membranes,” Adv. Mater. (Deerfield Beach Fla.)20(24), 4793–4798 (2008).
[CrossRef]

Teo, E. J.

A. A. Bettiol, S. V. Rao, E. J. Teo, J. A. van Kan, and F. Watt, “Fabrication of buried channel waveguides in photosensitive glass using proton beam writing,” Appl. Phys. Lett.88(17), 171106 (2006).
[CrossRef]

Tomljenovic-Hanic, S.

Townsend, P. D.

L. Babsail, N. Hamelin, and P. D. Townsend, “Helium-ion implanted waveguides in zircon,” Nucl. Instrum. Methods Phys. Res. B59–60, 1219–1222 (1991).
[CrossRef]

Treussart, F.

I. Aharonovich, C. Zhou, A. Stacey, J. Orwa, S. Castelletto, D. Simpson, A. D. Greentree, F. Treussart, J.-F. Roch, and S. Prawer, “Enhanced single-photon emission in the near infrared from a diamond color center,” Phys. Rev. B79(23), 235316 (2009).
[CrossRef]

Trpkovski, S.

M. P. Hiscocks, C. J. Kaalund, F. Ladouceur, S. T. Huntington, B. C. Gibson, S. Trpkovski, D. Simpson, E. Ampem-Lassen, S. Prawer, and J. E. Butler, “Reactive ion etching of waveguide structures in diamond,” Diamond Related Materials17(11), 1831–1834 (2008).
[CrossRef]

Uzan-Saguy, C.

C. Uzan-Saguy, C. Cytermann, R. Brener, V. Richter, M. Shaanan, and R. Kalish, “Damage threshold for ion-beam induced graphitization of diamond,” Appl. Phys. Lett.67(9), 1194–1196 (1995).
[CrossRef]

van Kan, J. A.

A. A. Bettiol, S. V. Rao, E. J. Teo, J. A. van Kan, and F. Watt, “Fabrication of buried channel waveguides in photosensitive glass using proton beam writing,” Appl. Phys. Lett.88(17), 171106 (2006).
[CrossRef]

Vannoni, M.

S. Lagomarsino, P. Olivero, F. Bosia, M. Vannoni, S. Calusi, L. Giuntini, and M. Massi, “Evidence of Light Guiding in Ion-Implanted Diamond,” Phys. Rev. Lett.105(23), 233903 (2010).
[CrossRef] [PubMed]

P. Olivero, S. Calusi, L. Giuntini, S. Lagomarsino, A. Lo Giudice, M. Massi, S. Sciortino, M. Vannoni, and E. Vittone, “Controlled variation of the refractive index in ion-damaged diamond,” Diamond Related Materials19(5-6), 428–431 (2010).
[CrossRef]

M. Vannoni, G. Molesini, S. Sciortino, S. Lagomarsino, P. Olivero, and E. Vittone, “Interferometric characterization of mono-and polycrystalline CVD diamond,” Proc. SPIE7389, 738931, 738931-6 (2009).
[CrossRef]

Villing, A.

A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J.-P. Poizat, and P. Grangier, “Single photon quantum cryptography,” Phys. Rev. Lett.89(18), 187901 (2002).
[CrossRef] [PubMed]

Vittone, E.

A. Battiato, F. Bosia, S. Ferrari, P. Olivero, A. Sytchkova, and E. Vittone, “Spectroscopic measurement of the refractive index of ion-implanted diamond,” Opt. Lett.37(4), 671–673 (2012).
[CrossRef] [PubMed]

P. Olivero, S. Calusi, L. Giuntini, S. Lagomarsino, A. Lo Giudice, M. Massi, S. Sciortino, M. Vannoni, and E. Vittone, “Controlled variation of the refractive index in ion-damaged diamond,” Diamond Related Materials19(5-6), 428–431 (2010).
[CrossRef]

M. Vannoni, G. Molesini, S. Sciortino, S. Lagomarsino, P. Olivero, and E. Vittone, “Interferometric characterization of mono-and polycrystalline CVD diamond,” Proc. SPIE7389, 738931, 738931-6 (2009).
[CrossRef]

S. Calusi, E. Colombo, L. Giuntini, A. L. Giudice, C. Manfredotti, M. Massi, G. Pratesi, and E. Vittone, “The ionoluminescence apparatus at the LABEC external microbeam facility,” Nucl. Instrum. Methods Phys. Res. B2662306–2310 (2008).
[CrossRef]

Waldermann, F.

B. A. Fairchild, P. Olivero, S. Rubanov, A. D. Greentree, F. Waldermann, R. A. Taylor, I. Walmsley, J. M. Smith, S. Huntington, B. C. Gibson, D. N. Jamieson, and S. Prawer, “Fabrication of Ultrathin Single-Crystal Diamond Membranes,” Adv. Mater. (Deerfield Beach Fla.)20(24), 4793–4798 (2008).
[CrossRef]

Walmsley, I.

B. A. Fairchild, P. Olivero, S. Rubanov, A. D. Greentree, F. Waldermann, R. A. Taylor, I. Walmsley, J. M. Smith, S. Huntington, B. C. Gibson, D. N. Jamieson, and S. Prawer, “Fabrication of Ultrathin Single-Crystal Diamond Membranes,” Adv. Mater. (Deerfield Beach Fla.)20(24), 4793–4798 (2008).
[CrossRef]

Wang, C.

C. Wang, C. Kurtsiefer, H. Weinfurter, and B. Burchard, “Single photon emission from SiV centres in diamond produced by ion implantation,” J. Phys. B39(1), 37–41 (2006).
[CrossRef]

Wang, C. F.

C. F. Wang, Y.-S. Choi, J. C. Lee, E. L. Hu, J. Yang, and J. E. Butler, “Observation of whispering gallery modes in nanocrystalline diamond microdisks,” Appl. Phys. Lett.90(8), 081110 (2007).
[CrossRef]

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, “Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond,” Appl. Phys. Lett.91(20), 201112 (2007).
[CrossRef]

Wang, K.-M.

F. Chen, L. Wang, Y. Jiang, X.-L. Wang, K.-M. Wang, G. Fu, Q.-M. Lu, C. E. Rüter, and D. Kip, “Optical channel waveguides in Nd: YVO4 crystal produced by O+ ion implantation,” Appl. Phys. Lett.88(7), 071123 (2006).
[CrossRef]

Wang, L.

F. Chen, L. Wang, Y. Jiang, X.-L. Wang, K.-M. Wang, G. Fu, Q.-M. Lu, C. E. Rüter, and D. Kip, “Optical channel waveguides in Nd: YVO4 crystal produced by O+ ion implantation,” Appl. Phys. Lett.88(7), 071123 (2006).
[CrossRef]

Wang, X.-L.

F. Chen, L. Wang, Y. Jiang, X.-L. Wang, K.-M. Wang, G. Fu, Q.-M. Lu, C. E. Rüter, and D. Kip, “Optical channel waveguides in Nd: YVO4 crystal produced by O+ ion implantation,” Appl. Phys. Lett.88(7), 071123 (2006).
[CrossRef]

Watson, I. M.

E. Gu, H. W. Choi, C. Liu, C. Griffin, J. M. Girkin, I. M. Watson, M. D. Dawson, G. McConnell, and A. M. Gurney, “Reflection/transmission confocal microscopy characterization of single-crystal diamond microlens arrays,” Appl. Phys. Lett.84(15), 2754–2756 (2004).
[CrossRef]

Watt, F.

A. A. Bettiol, S. V. Rao, E. J. Teo, J. A. van Kan, and F. Watt, “Fabrication of buried channel waveguides in photosensitive glass using proton beam writing,” Appl. Phys. Lett.88(17), 171106 (2006).
[CrossRef]

Weber, H. P.

S. Gloor, V. Romano, W. Lüthy, H. P. Weber, V. V. Kononenko, S. M. Pimenov, V. I. Konov, and A. V. Khomich, “Antireflection structures written by excimer laser on CVD diamond,” Appl. Phys., A Mater. Sci. Process.70(5), 547–550 (2000).
[CrossRef]

Wei, D. T. Y.

D. T. Y. Wei, W. W. Lee, and L. R. Bloom, “Large refractive index change induced by ion implantation in lithium niobate,” Appl. Phys. Lett.25(6), 329–331 (1974).
[CrossRef]

Weinfurter, H.

C. Wang, C. Kurtsiefer, H. Weinfurter, and B. Burchard, “Single photon emission from SiV centres in diamond produced by ion implantation,” J. Phys. B39(1), 37–41 (2006).
[CrossRef]

Wilson, J. I. B.

M. G. Jubber, M. Liehr, J. L. McGrath, J. I. B. Wilson, I. C. Drummond, P. John, D. K. Milne, R. W. McCullough, J. Geddes, D. P. Higgins, and M. Schlapp, “Atom beam treatment of diamond films,” Diamond Related Materials4(4), 445–450 (1995).
[CrossRef]

Wu, W.

W. Wu and S. Fahy, “Molecular-dynamics study of single-atom radiation damage in diamond,” Phys. Rev. B Condens. Matter49(5), 3030–3035 (1994).
[CrossRef] [PubMed]

Yang, J.

C. F. Wang, Y.-S. Choi, J. C. Lee, E. L. Hu, J. Yang, and J. E. Butler, “Observation of whispering gallery modes in nanocrystalline diamond microdisks,” Appl. Phys. Lett.90(8), 081110 (2007).
[CrossRef]

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, “Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond,” Appl. Phys. Lett.91(20), 201112 (2007).
[CrossRef]

Zavedeev, E. V.

A. V. Khomich, V. I. Kovalev, E. V. Zavedeev, R. A. Khmelnitskiy, and A. A. Gippius, “Spectroscopic ellipsometry study of buried graphitized layers in the ion-implanted diamond,” Vacuum78(2-4), 583–587 (2005).
[CrossRef]

Zhou, C.

I. Aharonovich, C. Zhou, A. Stacey, J. Orwa, S. Castelletto, D. Simpson, A. D. Greentree, F. Treussart, J.-F. Roch, and S. Prawer, “Enhanced single-photon emission in the near infrared from a diamond color center,” Phys. Rev. B79(23), 235316 (2009).
[CrossRef]

Ziegler, J. F.

J. F. Ziegler, M. D. Ziegler, and J. P. Biersack, “SRIM – The stopping and range of ions in matter (2010),” Nucl. Instrum. Methods Phys. Res. B268(11-12), 1818–1823 (2010).
[CrossRef]

Ziegler, M. D.

J. F. Ziegler, M. D. Ziegler, and J. P. Biersack, “SRIM – The stopping and range of ions in matter (2010),” Nucl. Instrum. Methods Phys. Res. B268(11-12), 1818–1823 (2010).
[CrossRef]

Adv. Mater. (Deerfield Beach Fla.) (1)

B. A. Fairchild, P. Olivero, S. Rubanov, A. D. Greentree, F. Waldermann, R. A. Taylor, I. Walmsley, J. M. Smith, S. Huntington, B. C. Gibson, D. N. Jamieson, and S. Prawer, “Fabrication of Ultrathin Single-Crystal Diamond Membranes,” Adv. Mater. (Deerfield Beach Fla.)20(24), 4793–4798 (2008).
[CrossRef]

Anal. Bioanal. Chem. (1)

L. Giuntini, “A review of external microbeams for ion beam analyses,” Anal. Bioanal. Chem.401(3), 785–793 (2011).
[CrossRef] [PubMed]

Appl. Phys. Lett. (8)

D. T. Y. Wei, W. W. Lee, and L. R. Bloom, “Large refractive index change induced by ion implantation in lithium niobate,” Appl. Phys. Lett.25(6), 329–331 (1974).
[CrossRef]

E. W. Maby, C. W. Magee, and J. H. Morewood, “Volume expansion of ion-implanted diamond,” Appl. Phys. Lett.39(2), 157–158 (1981).
[CrossRef]

C. Uzan-Saguy, C. Cytermann, R. Brener, V. Richter, M. Shaanan, and R. Kalish, “Damage threshold for ion-beam induced graphitization of diamond,” Appl. Phys. Lett.67(9), 1194–1196 (1995).
[CrossRef]

C. F. Wang, Y.-S. Choi, J. C. Lee, E. L. Hu, J. Yang, and J. E. Butler, “Observation of whispering gallery modes in nanocrystalline diamond microdisks,” Appl. Phys. Lett.90(8), 081110 (2007).
[CrossRef]

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, “Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond,” Appl. Phys. Lett.91(20), 201112 (2007).
[CrossRef]

E. Gu, H. W. Choi, C. Liu, C. Griffin, J. M. Girkin, I. M. Watson, M. D. Dawson, G. McConnell, and A. M. Gurney, “Reflection/transmission confocal microscopy characterization of single-crystal diamond microlens arrays,” Appl. Phys. Lett.84(15), 2754–2756 (2004).
[CrossRef]

A. A. Bettiol, S. V. Rao, E. J. Teo, J. A. van Kan, and F. Watt, “Fabrication of buried channel waveguides in photosensitive glass using proton beam writing,” Appl. Phys. Lett.88(17), 171106 (2006).
[CrossRef]

F. Chen, L. Wang, Y. Jiang, X.-L. Wang, K.-M. Wang, G. Fu, Q.-M. Lu, C. E. Rüter, and D. Kip, “Optical channel waveguides in Nd: YVO4 crystal produced by O+ ion implantation,” Appl. Phys. Lett.88(7), 071123 (2006).
[CrossRef]

Appl. Phys., A Mater. Sci. Process. (1)

S. Gloor, V. Romano, W. Lüthy, H. P. Weber, V. V. Kononenko, S. M. Pimenov, V. I. Konov, and A. V. Khomich, “Antireflection structures written by excimer laser on CVD diamond,” Appl. Phys., A Mater. Sci. Process.70(5), 547–550 (2000).
[CrossRef]

Chin. Opt. Lett. (1)

Diamond Related Materials (5)

P. Olivero, S. Rubanov, P. Reichart, B. C. Gibson, S. T. Huntington, J. R. Rabeau, A. D. Greentree, J. Salzman, D. Moore, D. N. Jamieson, and S. Prawer, “Characterization of three-dimensional microstructures in single-crystal diamond,” Diamond Related Materials15(10), 1614–1621 (2006).
[CrossRef]

D. P. Hickey, K. S. Jones, and R. G. Elliman, “Amorphization and graphitization of single-crystal diamond – a transmission electron microscopy study,” Diamond Related Materials18(11), 1353–1359 (2009).
[CrossRef]

M. P. Hiscocks, C. J. Kaalund, F. Ladouceur, S. T. Huntington, B. C. Gibson, S. Trpkovski, D. Simpson, E. Ampem-Lassen, S. Prawer, and J. E. Butler, “Reactive ion etching of waveguide structures in diamond,” Diamond Related Materials17(11), 1831–1834 (2008).
[CrossRef]

M. G. Jubber, M. Liehr, J. L. McGrath, J. I. B. Wilson, I. C. Drummond, P. John, D. K. Milne, R. W. McCullough, J. Geddes, D. P. Higgins, and M. Schlapp, “Atom beam treatment of diamond films,” Diamond Related Materials4(4), 445–450 (1995).
[CrossRef]

P. Olivero, S. Calusi, L. Giuntini, S. Lagomarsino, A. Lo Giudice, M. Massi, S. Sciortino, M. Vannoni, and E. Vittone, “Controlled variation of the refractive index in ion-damaged diamond,” Diamond Related Materials19(5-6), 428–431 (2010).
[CrossRef]

J. Phys. B (1)

C. Wang, C. Kurtsiefer, H. Weinfurter, and B. Burchard, “Single photon emission from SiV centres in diamond produced by ion implantation,” J. Phys. B39(1), 37–41 (2006).
[CrossRef]

Nature (1)

P. Kok and B. W. Lovett, “Materials science: Qubits in the pink,” Nature444(7115), 49–49 (2006).
[CrossRef] [PubMed]

Nucl. Instrum. Methods Phys. Res. A (1)

L. Giuntini, M. Massi, and S. Calusi, “The external scanning proton microprobe of Firenze: a comprehensive description,” Nucl. Instrum. Methods Phys. Res. A576(2-3), 266–273 (2007).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. B (8)

M. Massi, L. Giuntini, M. Chiari, N. Gelli, and P. A. Mandò, “The external beam microprobe facility in Florence: set-up and performance,” Nucl. Instrum. Methods Phys. Res. B190(1-4), 276–282 (2002).
[CrossRef]

S. Calusi, E. Colombo, L. Giuntini, A. L. Giudice, C. Manfredotti, M. Massi, G. Pratesi, and E. Vittone, “The ionoluminescence apparatus at the LABEC external microbeam facility,” Nucl. Instrum. Methods Phys. Res. B2662306–2310 (2008).
[CrossRef]

P. A. Mandò, “Advantages and limitations of external beams in applications to arts & archeology, geology and environmental problems,” Nucl. Instrum. Methods Phys. Res. B85(1-4), 815–823 (1994).
[CrossRef]

T. Calligaro, J.-C. Dran, E. Ioannidou, B. Moignard, L. Pichon, and J. Salomon, “Development of an external beam nuclear microprobe on the Aglae facility of the Louvre museum,” Nucl. Instrum. Methods Phys. Res. B161–163, 328–333 (2000).
[CrossRef]

P. A. Mandò, “Measurement of low currents in an external beam set-up,” Nucl. Instrum. Methods Phys. Res. B85, 815 (1994).

M. Chiari, A. Migliori, and P. A. Mandò, “Measurement of low currents in an external beam set-up,” Nucl. Instrum. Methods Phys. Res. B188, 162–165 (2002).
[CrossRef]

J. F. Ziegler, M. D. Ziegler, and J. P. Biersack, “SRIM – The stopping and range of ions in matter (2010),” Nucl. Instrum. Methods Phys. Res. B268(11-12), 1818–1823 (2010).
[CrossRef]

L. Babsail, N. Hamelin, and P. D. Townsend, “Helium-ion implanted waveguides in zircon,” Nucl. Instrum. Methods Phys. Res. B59–60, 1219–1222 (1991).
[CrossRef]

Opt. Eng. (1)

Y. Fu and B. K. A. Ngoi, “Investigation of diffractive optical element fabricated on diamond film by use of focused ion beam direct milling,” Opt. Eng.42(8), 2214–2217 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. (2)

R. L. Hines, “Radiation Damage of Diamond by 20-keV Carbon Ions,” Phys. Rev.138(6A), A1747–A1751 (1965).
[CrossRef]

R. L. Hines and R. Arndt, “Radiation effects of bombardment of quartz and vitreous silica by 7.5-kev to 59-kev positive ions,” Phys. Rev.119(2), 623–633 (1960).
[CrossRef]

Phys. Rev. B (2)

I. Aharonovich, C. Zhou, A. Stacey, J. Orwa, S. Castelletto, D. Simpson, A. D. Greentree, F. Treussart, J.-F. Roch, and S. Prawer, “Enhanced single-photon emission in the near infrared from a diamond color center,” Phys. Rev. B79(23), 235316 (2009).
[CrossRef]

I. Aharonovich, S. Castelletto, B. C. Johnson, J. C. McCallum, D. A. Simpson, A. D. Greentree, and S. Prawer, “Chromium single-photon emitters in diamond fabricated by ion implantation,” Phys. Rev. B81(12), 121201 (2010).
[CrossRef]

Phys. Rev. B Condens. Matter (2)

J. F. Prins, T. E. Derry, and J. P. Sellschop, “Volume expansion of diamond during ion implantation,” Phys. Rev. B Condens. Matter34(12), 8870–8874 (1986).
[CrossRef] [PubMed]

W. Wu and S. Fahy, “Molecular-dynamics study of single-atom radiation damage in diamond,” Phys. Rev. B Condens. Matter49(5), 3030–3035 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J.-P. Poizat, and P. Grangier, “Single photon quantum cryptography,” Phys. Rev. Lett.89(18), 187901 (2002).
[CrossRef] [PubMed]

S. Lagomarsino, P. Olivero, F. Bosia, M. Vannoni, S. Calusi, L. Giuntini, and M. Massi, “Evidence of Light Guiding in Ion-Implanted Diamond,” Phys. Rev. Lett.105(23), 233903 (2010).
[CrossRef] [PubMed]

Proc. SPIE (1)

M. Vannoni, G. Molesini, S. Sciortino, S. Lagomarsino, P. Olivero, and E. Vittone, “Interferometric characterization of mono-and polycrystalline CVD diamond,” Proc. SPIE7389, 738931, 738931-6 (2009).
[CrossRef]

Science (1)

S. Prawer and A. D. Greentree, “Applied physics. Diamond for quantum computing,” Science320(5883), 1601–1602 (2008).
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Sens. Actuators (1)

H. Björkman, P. Rangsten, and K. Hjort, “Diamond microstructures for optical micro electromechanical systems,” Sens. Actuators78(1), 41–47 (1999).
[CrossRef]

Thin Solid Films (1)

K. L. Bhatia, S. Fabian, S. Kalbitzer, C. Klatt, W. Krätschmer, R. Stoll, and J. F. P. Sellschop, “Optical effects in carbon-ion irradiated diamond,” Thin Solid Films324(1-2), 11–18 (1998).
[CrossRef]

Vacuum (1)

A. V. Khomich, V. I. Kovalev, E. V. Zavedeev, R. A. Khmelnitskiy, and A. A. Gippius, “Spectroscopic ellipsometry study of buried graphitized layers in the ion-implanted diamond,” Vacuum78(2-4), 583–587 (2005).
[CrossRef]

Other (3)

K. Creath, “Phase-shifting interferometry techniques,” in Progress in Optics (Elsevier, 1988).

J. H. Bruning, “Fringe Scanning Interferometers,” in Optical Shop Testing (Wiley, 1978).

J. F. Ziegler, J. P. Biersack, and U. Littmark, The Stopping and Range of Ions in Solids (Pergamon, 1985)

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Figures (7)

Fig. 1
Fig. 1

Exit nozzle of the ion microbeam line: (1) detectors for Ion Beam Analysis (not used in this application) (2) X-ray detector for beam charge measurement, (3) vista camera and micro camera; the arrow indicates the ion beam direction. Inset: Details of the system for beam charge measurement.

Fig. 2
Fig. 2

Transmission optical image of several 125 × 125 μm2 implanted areas. Progressive darkening of the implantation regions with increasing total fluence, along with fading of induced ion-luminescence [48], allows a qualitative control of the implantation progress.

Fig. 3
Fig. 3

Schematics of the experimental principle of the Zygo interferometric microscope.

Fig. 4
Fig. 4

Schematics a) Map of the OPD profile of an area implanted with 3 MeV protons at a fluency of 7.5·1016 cm−2; b) map of the swelling profile of the same implantation. The two profiles have opposite signs because swelling gives a shorter optical path in reflection, while damage produces a longer optical path in transmission measurements.

Fig. 5
Fig. 5

Behaviour of the ratio OP D E ( ϕ )/ I E as a function of the fluency. In the inset, particular of the points representing eight different impantations at a same nominal fluency but with different values of the instantaneous current (a factor 5 of variation).

Fig. 6
Fig. 6

Behaviour of the ratio AL D E ( ϕ )/ I E as a function of the fluence.

Fig. 7
Fig. 7

Functions p ( E ) ( z ) for implantations of protons with energies of 2 and 3 MeV.

Tables (1)

Tables Icon

Table 1 Values of the Coefficient c Resulting from the Linear Fitting of the Data Relevant to 2 MeV and 3 MeV Proton Implantations

Equations (7)

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

ALD= λ HeNe 4π ln( T 0 T ).
OPD=OP D m ( n 0 1 )h , ALD=OP D m k 0 h,
n ^ ( z )= n ^ 0 + c ^ ν( z ).
COPD= 0 + [ n ^ ( z ) n ^ 0 ] dz,
COP D ( E ) ( ϕ )=c I ( E ) ϕ with I ( E ) = 0 + p ( E ) ( z ) dz,
n ^ =2.41+[ (4.34±0.05)+i(2.86±0.04) ] 10 23 cm 3 ν
Δn n = ( n 2 1 )( n 2 +2 ) 6 n 2 [ ΔV V + Δα α +F ]

Metrics