Abstract

Digital holographic microscopy (DHM) is an interferometric technique that allows real-time imaging of the entire complex optical wave-front (amplitude and phase) reflected by or transmitted through a sample. To our knowledge, only the quantitative phase is exploited to measure topography, assuming homogeneous material sample and a single reflection on the surface of the sample. In this paper, dual-wavelength DHM measurements are interpreted using a model of reflected wave propagation through a three-interfaces specimen (2 layers deposited on a semi-infinite layer), to measure simultaneously topography, layer thicknesses and refractive indices of micro-structures. We demonstrate this DHM reflectometry technique by comparing DHM and profilometer measurement of home-made SiO2/Si targets and Secondary Ion Mass Spectrometry (SIMS) sputter craters on specimen including different multiple layers.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef]

2009 (1)

P. Pereyra and A. Robledo-Martinez, "On the equivalence of the summation and transfer-matrix methods in wave propagation through multilayers of lossless and lossy media," Eur. J. Phys. 30, 393-401 (2009).
[CrossRef]

2008 (4)

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. Magistretti, and P. Marquet, "Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer," Cytometry Part A 73a, 895-903 (2008).
[CrossRef]

C. Yelleswarapu, S.-R. Kothapalli, and D. Rao, "Optical Fourier techniques for medical image processing and phase contrast imaging," Opt. Commun. 281, 1876-1888 (2008).
[CrossRef] [PubMed]

P. Hlubina, J. Lunacek, D. Ciprian, and R. Chlebus, "Spectral interferometry and reflectometry used to measure thin films," Applied Physics B: Lasers and Optics 92, 203-207 (2008).
[CrossRef]

J. Kühn, F. Charrière, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, "Axial sub-nanometer accuracy in digital holographic microscopy," Meas. Sci. Technol. 19, 074007 (2008).
[CrossRef]

2006 (1)

D. S. McPhail, "Applications of Secondary Ion Mass Spectrometry (SIMS) in Materials Science," J. Mater. Sci. 41, 873-903 (2006).
[CrossRef]

2005 (1)

2004 (1)

S. de Nicola, P. Ferraro, A. Finizio, S. Grilli, G. Coppola, M. Iodice, P. De Natale, and M. Chiarini, "Surface topography of microstructures in lithium niobate by digital holographic microscopy," Meas. Sci. Technol. 15, 961-968 (2004).
[CrossRef]

2003 (1)

Y. Yamamura and M. Ishida, "Simulation of oxide sputtering and SIMS depth profiling of delta-doped layer," Applied Surface Science 203-204, 62-68 (2003).
[CrossRef]

2000 (1)

Y. Wang and E. A. Irene, "Consistent refractive index parameters for ultrathin SiO2 films," J. Vac. Sci. Technol. B 18, 279-282 (2000).
[CrossRef]

1999 (1)

C. Moore, "Optical reflectometry elucidates layer thicknesses," III-Vs Review 12, 34-37 (1999).
[CrossRef]

1990 (1)

A. Kalnitsky, S. P. Tay, J. P. Ellul, S. Chongsawangvirod, J. W. Andrews, and E. A. Irene, "Measurements and modeling of thin silicon dioxide films on silicon," J. Electrochem. Soc. 1, 234-238 (1990).
[CrossRef]

1985 (1)

C. Cobianu, C. Pavelescu, and A. Paunescu, "The effect of deposition conditions on the refractive index of LTCVD SiO2 films," Journal of Materials Science Letters 4, 1419-1420 (1985).
[CrossRef]

Andrews, J. W.

A. Kalnitsky, S. P. Tay, J. P. Ellul, S. Chongsawangvirod, J. W. Andrews, and E. A. Irene, "Measurements and modeling of thin silicon dioxide films on silicon," J. Electrochem. Soc. 1, 234-238 (1990).
[CrossRef]

Barbul, A.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. Magistretti, and P. Marquet, "Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer," Cytometry Part A 73a, 895-903 (2008).
[CrossRef]

Charrière, F.

J. Kühn, F. Charrière, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, "Axial sub-nanometer accuracy in digital holographic microscopy," Meas. Sci. Technol. 19, 074007 (2008).
[CrossRef]

Chiarini, M.

S. de Nicola, P. Ferraro, A. Finizio, S. Grilli, G. Coppola, M. Iodice, P. De Natale, and M. Chiarini, "Surface topography of microstructures in lithium niobate by digital holographic microscopy," Meas. Sci. Technol. 15, 961-968 (2004).
[CrossRef]

Chlebus, R.

P. Hlubina, J. Lunacek, D. Ciprian, and R. Chlebus, "Spectral interferometry and reflectometry used to measure thin films," Applied Physics B: Lasers and Optics 92, 203-207 (2008).
[CrossRef]

Chongsawangvirod, S.

A. Kalnitsky, S. P. Tay, J. P. Ellul, S. Chongsawangvirod, J. W. Andrews, and E. A. Irene, "Measurements and modeling of thin silicon dioxide films on silicon," J. Electrochem. Soc. 1, 234-238 (1990).
[CrossRef]

Ciprian, D.

P. Hlubina, J. Lunacek, D. Ciprian, and R. Chlebus, "Spectral interferometry and reflectometry used to measure thin films," Applied Physics B: Lasers and Optics 92, 203-207 (2008).
[CrossRef]

Cobianu, C.

C. Cobianu, C. Pavelescu, and A. Paunescu, "The effect of deposition conditions on the refractive index of LTCVD SiO2 films," Journal of Materials Science Letters 4, 1419-1420 (1985).
[CrossRef]

Colomb, T.

J. Kühn, F. Charrière, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, "Axial sub-nanometer accuracy in digital holographic microscopy," Meas. Sci. Technol. 19, 074007 (2008).
[CrossRef]

Coppola, G.

S. de Nicola, P. Ferraro, A. Finizio, S. Grilli, G. Coppola, M. Iodice, P. De Natale, and M. Chiarini, "Surface topography of microstructures in lithium niobate by digital holographic microscopy," Meas. Sci. Technol. 15, 961-968 (2004).
[CrossRef]

Cuche, E.

J. Kühn, F. Charrière, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, "Axial sub-nanometer accuracy in digital holographic microscopy," Meas. Sci. Technol. 19, 074007 (2008).
[CrossRef]

Dasari, R.

De Natale, P.

S. de Nicola, P. Ferraro, A. Finizio, S. Grilli, G. Coppola, M. Iodice, P. De Natale, and M. Chiarini, "Surface topography of microstructures in lithium niobate by digital holographic microscopy," Meas. Sci. Technol. 15, 961-968 (2004).
[CrossRef]

de Nicola, S.

S. de Nicola, P. Ferraro, A. Finizio, S. Grilli, G. Coppola, M. Iodice, P. De Natale, and M. Chiarini, "Surface topography of microstructures in lithium niobate by digital holographic microscopy," Meas. Sci. Technol. 15, 961-968 (2004).
[CrossRef]

Depeursinge, C.

J. Kühn, F. Charrière, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, "Axial sub-nanometer accuracy in digital holographic microscopy," Meas. Sci. Technol. 19, 074007 (2008).
[CrossRef]

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. Magistretti, and P. Marquet, "Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer," Cytometry Part A 73a, 895-903 (2008).
[CrossRef]

Ellul, J. P.

A. Kalnitsky, S. P. Tay, J. P. Ellul, S. Chongsawangvirod, J. W. Andrews, and E. A. Irene, "Measurements and modeling of thin silicon dioxide films on silicon," J. Electrochem. Soc. 1, 234-238 (1990).
[CrossRef]

Emery, Y.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. Magistretti, and P. Marquet, "Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer," Cytometry Part A 73a, 895-903 (2008).
[CrossRef]

J. Kühn, F. Charrière, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, "Axial sub-nanometer accuracy in digital holographic microscopy," Meas. Sci. Technol. 19, 074007 (2008).
[CrossRef]

Feld, M.

Ferraro, P.

S. de Nicola, P. Ferraro, A. Finizio, S. Grilli, G. Coppola, M. Iodice, P. De Natale, and M. Chiarini, "Surface topography of microstructures in lithium niobate by digital holographic microscopy," Meas. Sci. Technol. 15, 961-968 (2004).
[CrossRef]

Finizio, A.

S. de Nicola, P. Ferraro, A. Finizio, S. Grilli, G. Coppola, M. Iodice, P. De Natale, and M. Chiarini, "Surface topography of microstructures in lithium niobate by digital holographic microscopy," Meas. Sci. Technol. 15, 961-968 (2004).
[CrossRef]

Grilli, S.

S. de Nicola, P. Ferraro, A. Finizio, S. Grilli, G. Coppola, M. Iodice, P. De Natale, and M. Chiarini, "Surface topography of microstructures in lithium niobate by digital holographic microscopy," Meas. Sci. Technol. 15, 961-968 (2004).
[CrossRef]

Hlubina, P.

P. Hlubina, J. Lunacek, D. Ciprian, and R. Chlebus, "Spectral interferometry and reflectometry used to measure thin films," Applied Physics B: Lasers and Optics 92, 203-207 (2008).
[CrossRef]

Ikeda, T.

Iodice, M.

S. de Nicola, P. Ferraro, A. Finizio, S. Grilli, G. Coppola, M. Iodice, P. De Natale, and M. Chiarini, "Surface topography of microstructures in lithium niobate by digital holographic microscopy," Meas. Sci. Technol. 15, 961-968 (2004).
[CrossRef]

Irene, E. A.

Y. Wang and E. A. Irene, "Consistent refractive index parameters for ultrathin SiO2 films," J. Vac. Sci. Technol. B 18, 279-282 (2000).
[CrossRef]

A. Kalnitsky, S. P. Tay, J. P. Ellul, S. Chongsawangvirod, J. W. Andrews, and E. A. Irene, "Measurements and modeling of thin silicon dioxide films on silicon," J. Electrochem. Soc. 1, 234-238 (1990).
[CrossRef]

Ishida, M.

Y. Yamamura and M. Ishida, "Simulation of oxide sputtering and SIMS depth profiling of delta-doped layer," Applied Surface Science 203-204, 62-68 (2003).
[CrossRef]

Kalnitsky, A.

A. Kalnitsky, S. P. Tay, J. P. Ellul, S. Chongsawangvirod, J. W. Andrews, and E. A. Irene, "Measurements and modeling of thin silicon dioxide films on silicon," J. Electrochem. Soc. 1, 234-238 (1990).
[CrossRef]

Korenstein, R.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. Magistretti, and P. Marquet, "Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer," Cytometry Part A 73a, 895-903 (2008).
[CrossRef]

Kothapalli, S.-R.

C. Yelleswarapu, S.-R. Kothapalli, and D. Rao, "Optical Fourier techniques for medical image processing and phase contrast imaging," Opt. Commun. 281, 1876-1888 (2008).
[CrossRef] [PubMed]

Kühn, J.

J. Kühn, F. Charrière, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, "Axial sub-nanometer accuracy in digital holographic microscopy," Meas. Sci. Technol. 19, 074007 (2008).
[CrossRef]

Lunacek, J.

P. Hlubina, J. Lunacek, D. Ciprian, and R. Chlebus, "Spectral interferometry and reflectometry used to measure thin films," Applied Physics B: Lasers and Optics 92, 203-207 (2008).
[CrossRef]

Magistretti, P.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. Magistretti, and P. Marquet, "Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer," Cytometry Part A 73a, 895-903 (2008).
[CrossRef]

Marquet, P.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. Magistretti, and P. Marquet, "Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer," Cytometry Part A 73a, 895-903 (2008).
[CrossRef]

J. Kühn, F. Charrière, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, "Axial sub-nanometer accuracy in digital holographic microscopy," Meas. Sci. Technol. 19, 074007 (2008).
[CrossRef]

McPhail, D. S.

D. S. McPhail, "Applications of Secondary Ion Mass Spectrometry (SIMS) in Materials Science," J. Mater. Sci. 41, 873-903 (2006).
[CrossRef]

Montfort, F.

J. Kühn, F. Charrière, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, "Axial sub-nanometer accuracy in digital holographic microscopy," Meas. Sci. Technol. 19, 074007 (2008).
[CrossRef]

Moore, C.

C. Moore, "Optical reflectometry elucidates layer thicknesses," III-Vs Review 12, 34-37 (1999).
[CrossRef]

Paunescu, A.

C. Cobianu, C. Pavelescu, and A. Paunescu, "The effect of deposition conditions on the refractive index of LTCVD SiO2 films," Journal of Materials Science Letters 4, 1419-1420 (1985).
[CrossRef]

Pavelescu, C.

C. Cobianu, C. Pavelescu, and A. Paunescu, "The effect of deposition conditions on the refractive index of LTCVD SiO2 films," Journal of Materials Science Letters 4, 1419-1420 (1985).
[CrossRef]

Pereyra, P.

P. Pereyra and A. Robledo-Martinez, "On the equivalence of the summation and transfer-matrix methods in wave propagation through multilayers of lossless and lossy media," Eur. J. Phys. 30, 393-401 (2009).
[CrossRef]

Popescu, G.

Rao, D.

C. Yelleswarapu, S.-R. Kothapalli, and D. Rao, "Optical Fourier techniques for medical image processing and phase contrast imaging," Opt. Commun. 281, 1876-1888 (2008).
[CrossRef] [PubMed]

Rappaz, B.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. Magistretti, and P. Marquet, "Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer," Cytometry Part A 73a, 895-903 (2008).
[CrossRef]

Robledo-Martinez, A.

P. Pereyra and A. Robledo-Martinez, "On the equivalence of the summation and transfer-matrix methods in wave propagation through multilayers of lossless and lossy media," Eur. J. Phys. 30, 393-401 (2009).
[CrossRef]

Tay, S. P.

A. Kalnitsky, S. P. Tay, J. P. Ellul, S. Chongsawangvirod, J. W. Andrews, and E. A. Irene, "Measurements and modeling of thin silicon dioxide films on silicon," J. Electrochem. Soc. 1, 234-238 (1990).
[CrossRef]

Wang, Y.

Y. Wang and E. A. Irene, "Consistent refractive index parameters for ultrathin SiO2 films," J. Vac. Sci. Technol. B 18, 279-282 (2000).
[CrossRef]

Yamamura, Y.

Y. Yamamura and M. Ishida, "Simulation of oxide sputtering and SIMS depth profiling of delta-doped layer," Applied Surface Science 203-204, 62-68 (2003).
[CrossRef]

Yelleswarapu, C.

C. Yelleswarapu, S.-R. Kothapalli, and D. Rao, "Optical Fourier techniques for medical image processing and phase contrast imaging," Opt. Commun. 281, 1876-1888 (2008).
[CrossRef] [PubMed]

Applied Physics B: Lasers and Optics (1)

P. Hlubina, J. Lunacek, D. Ciprian, and R. Chlebus, "Spectral interferometry and reflectometry used to measure thin films," Applied Physics B: Lasers and Optics 92, 203-207 (2008).
[CrossRef]

Applied Surface Science (1)

Y. Yamamura and M. Ishida, "Simulation of oxide sputtering and SIMS depth profiling of delta-doped layer," Applied Surface Science 203-204, 62-68 (2003).
[CrossRef]

Cytometry Part A (1)

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. Magistretti, and P. Marquet, "Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer," Cytometry Part A 73a, 895-903 (2008).
[CrossRef]

Eur. J. Phys. (1)

P. Pereyra and A. Robledo-Martinez, "On the equivalence of the summation and transfer-matrix methods in wave propagation through multilayers of lossless and lossy media," Eur. J. Phys. 30, 393-401 (2009).
[CrossRef]

III-Vs Review (1)

C. Moore, "Optical reflectometry elucidates layer thicknesses," III-Vs Review 12, 34-37 (1999).
[CrossRef]

J. Electrochem. Soc. (1)

A. Kalnitsky, S. P. Tay, J. P. Ellul, S. Chongsawangvirod, J. W. Andrews, and E. A. Irene, "Measurements and modeling of thin silicon dioxide films on silicon," J. Electrochem. Soc. 1, 234-238 (1990).
[CrossRef]

J. Mater. Sci. (1)

D. S. McPhail, "Applications of Secondary Ion Mass Spectrometry (SIMS) in Materials Science," J. Mater. Sci. 41, 873-903 (2006).
[CrossRef]

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

Y. Wang and E. A. Irene, "Consistent refractive index parameters for ultrathin SiO2 films," J. Vac. Sci. Technol. B 18, 279-282 (2000).
[CrossRef]

Journal of Materials Science Letters (1)

C. Cobianu, C. Pavelescu, and A. Paunescu, "The effect of deposition conditions on the refractive index of LTCVD SiO2 films," Journal of Materials Science Letters 4, 1419-1420 (1985).
[CrossRef]

Meas. Sci. Technol. (2)

S. de Nicola, P. Ferraro, A. Finizio, S. Grilli, G. Coppola, M. Iodice, P. De Natale, and M. Chiarini, "Surface topography of microstructures in lithium niobate by digital holographic microscopy," Meas. Sci. Technol. 15, 961-968 (2004).
[CrossRef]

J. Kühn, F. Charrière, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, "Axial sub-nanometer accuracy in digital holographic microscopy," Meas. Sci. Technol. 19, 074007 (2008).
[CrossRef]

Opt. Commun. (1)

C. Yelleswarapu, S.-R. Kothapalli, and D. Rao, "Optical Fourier techniques for medical image processing and phase contrast imaging," Opt. Commun. 281, 1876-1888 (2008).
[CrossRef] [PubMed]

Opt. Lett. (1)

Other (12)

E. Cuche, P. Marquet, and C. Depeursinge, "Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms," Appl. Opt. 38, 6994-7001 (1999). URL http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-38-34-6994.
[CrossRef]

P. Marquet, B. Rappaz, P. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, "Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy," Opt. Lett. 30, 468-470 (2005). URL http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-30-5-468.
[CrossRef] [PubMed]

B. Rappaz, F. Charrière, C. Depeursinge, P. Magistretti, and P. Marquet, "Simultaneous cell morphometry and refractive index measurement with dual-wavelength digital holographic microscopy and dye-enhanced dispersion of perfusion medium," Opt. Lett. 33, 744-746 (2008). URL http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-33-7-744.
[CrossRef] [PubMed]

H. Wahba and T. Kreis, "Characterization of graded index optical fibers by digital holographic interferometry," Appl. Opt. 48, 1573-1582 (2009). URL http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-48-8-1573.
[CrossRef] [PubMed]

URL http://refractiveindex.info/.

S. Debnath, M. Kothiyal, J. Schmit, and P. Hariharan, "Spectrally resolved white-light phase-shifting interference microscopy for thickness-profile measurements of transparent thin film layers on patterned substrates," Opt. Express 14, 4662 (2006). URL http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-11-4662.
[CrossRef] [PubMed]

S. K. Debnath, J. Kothiyal, Mahendra P. Schmit, and P. Hariharan, "Spectrally resolved phase-shifting interferometry of transparent thin films: sensitivity of thickness measurements," Appl. Opt. 45, 8636-8640 (2006). URL http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-45-34-8636.
[CrossRef] [PubMed]

J. Kühn, T. Colomb, F. Montfort, F. Charrière, Y. Emery, E. Cuche, P. Marquet, and C. Depeursinge, "Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition," Opt. Express 15, 7231-7242 (2007). URL http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-12-7231.
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C. Mann, L. Yu, C.-M. Lo, and M. Kim, "High-resolution quantitative phase contrast microscopy by digital holography," Opt. Express 13, 8693-8698 (2005). URL http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-22-8693.
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E. Cuche, P. Marquet, and C. Depeursinge, "Spatial filtering for zero-order and twin image elimination in digital off-axis holography," Appl. Opt. 39, 4070-4075 (2000). URL http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-39-23-4070.
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T. Colomb, J. Kühn, F. Charrière, C. Depeursinge, P. Marquet, and N. Aspert, "Total aberrations compensation in digital holographic microscopy with a reference conjugated hologram," Opt. Express 14, 4300-4306 (2006). URL http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-10-4300.
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T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, and C. Depeursinge, "Numerical parametric lens for shifting, magnification and complete aberration compensation in digital holographic microscopy," J. Opt. Soc. Am. A 23, 3177-3190 (2006). URL http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-12-3177.
[CrossRef] [PubMed]

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Figures (10)

Fig. 1.
Fig. 1.

DHM R1100® setup. Two lasers sources can be alternatively switched on. The object wave Oi passes through a condenser CL and a microscope objective MO to illuminate the sample with a collimated beam. The reflected wave interferes with the reference wave Ri , whose optical path length can be adjusted with the optical path retarder OPR.

Fig. 2.
Fig. 2.

Multilayer schematic. ψ ill is the illumination wave, (experimentally α = 0), and ψ r (r=0,…) are the multiple reflections of order r. x 0 is the position that corresponds to the Gaussian center of the degree of coherence function g(OPL,OPR).

Fig. 3.
Fig. 3.

Model for structures of height h(x,y) and RI nd deposited on a semi-infinite wafer (d 2 = ∞) with RI nw . The multiple layers function (Eq. 11) is defined from the respective origin 0, 0’ and so on, for each step.

Fig. 4.
Fig. 4.

Etching dug in 3-layers wafer model. The maximum coherence position is x 0 = 0. The etching is delimited by 5 different areas (I,V: outside crater; II and IV crater edges; and III maximum depth). The layers are defined by the RIs nk and thicknesses dk .

Fig. 5.
Fig. 5.

Test target reconstructed wavefronts (a,c) amplitude and (b,d) phase images for λ 1 (a,b) and λ 2 (c,d). Steps are manufactured to be nominally 375, 525, 975, 1200 and 1275 nm high. The rectangles in (a) correspond to the ROIs used for the spatial averaging of complex data for RIs determination, the dashed rectangle in (b) defines the ROI used for the phase normalization.

Fig. 6.
Fig. 6.

Topography of (a) low, and (c) high resolution test targets; (b, d) respective profiles comparison between DHM [8 pixels average profile along red line in (a,c)] and Tencor Alphastep 200 profilometer. The standard deviations between the vertical lines are used to define the uncertainty in Table 1.

Fig. 7.
Fig. 7.

3-layers (Au/SiO2/Si) SIMS sample reconstructed wavefronts (a,c) amplitude and (b,d) phase images for λ 1 (a,b) and λ 2 (c,d). The dashed rectangle in (a) delineates the ROI used for phase normalization.

Fig. 8.
Fig. 8.

(a) Topographic image of SIMS crater sputtered in three layers of 40 nm Au, 100 nm SiO2 and Si; (b) profile comparison between DHM [8 pixels average profile along red line] and Tencor Alphastep 200 profilometer.

Fig. 9.
Fig. 9.

SIMS sample reconstructed wavefronts (a,c) amplitude and (b,d) phase images for λ 1. The SiO2 layer thicknesses are assumed to be respectively (a,b) 100 nm and (c,d) 35 nm. The dashed rectangles delineate the ROI used for the spatial averaging for the phase normalization and the plain line rectangles define the ROI for bottom crater average values.

Fig. 10.
Fig. 10.

(a,c) Topographic images of SIMS crater sputtered in two layers of (a) 100 nnm and (c) 35 nm SiO2 and Si; (b,d) profiles comparison between DHM [8 pixels average profile along red line] and Tencor Alphastep 200 profilometer.

Tables (1)

Tables Icon

Table 1. Comparison between theoretical step height and their measurement with DHM reflectometry and stylus profilometer

Equations (21)

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I Hi = R i 2 + O i 2 + R i O i * + R i * O i ,
Γ H = 1 R i O i , ref * exp ( i ϕ i , ref ) ,
ψ i , H = Γ H R i O i , ref * = O i O i , ref exp [ i ( ϕ i ϕ i , ref ) ] .
ψ i , H = g ( OPL , OPR ) R i O i * ,
g ( OPL , OPR ) = exp [ - ( OPL OPR ) 2 2 σ 2 ] ,
L c = 2 σ ( 2 In 2 ) 1 2 .
r kl = ( n k n l ) ( n k + n l ) ,
t kl = 2 n k ( n k + n l ) .
ψ 0 = r 01 g ( 0 , OPR ) , ψ 1 = t 01 r 12 t 10 exp ( i 2 π λ 2 d 1 n 1 ) g [ ( 2 d 1 n 1 ) , OPR ] = Tg ( X ) , ψ 2 = t 01 r 12 t 10 r 12 t 10 exp ( i 2 π λ 4 d 1 n 1 ) g [ ( 4 d 1 n 1 ) , OPR ] + t 01 r 12 t 23 r 21 t 10 exp [ i 2 π λ ( 2 d 1 n 1 + 2 d 2 n 2 ) ] g [ ( 2 d 1 n 1 + 2 d 2 n 2 ) , OPR ] = ATg ( 2 X ) + BTg ( X + Y ) , ψ 3 = t 01 r 12 t 10 r 12 t 10 r 12 t 10 exp ( i 2 π λ 6 d 1 n 1 ) g [ ( 6 d 1 n 1 ) , OPR ] + t 01 r 12 r 10 t 12 r 23 t 21 t 10 exp [ i 2 π λ ( 4 d 1 n 1 + 2 d 2 n 2 ) ] g [ ( 4 d 1 n 1 + 2 d 2 n 2 ) , OPR ] + t 01 t 12 r 23 t 21 r 10 r 12 t 10 exp [ i 2 π λ ( 4 d 1 n 1 + 2 d 2 n 2 ) ] g [ ( 4 d 1 n 1 + 2 d 2 n 2 ) , OPR ] + t 01 t 12 r 23 r 21 r 23 t 21 t 10 exp [ i 2 π λ ( 2 d 1 n 1 + 4 d 2 n 2 ) ] g [ ( 2 d 1 n 1 + 4 d 2 n 2 ) , OPR ] = A 2 Tg ( 3 X ) + ABTg ( 2 X + Y ) + BCTg ( 2 X + Y ) + BDTg ( X + 2 Y ) ,
ψ r ψ r + 1 ATg ( m X + nY ) { AATg [ ( m + 1 ) X + nY ] ABTg [ mX + ( n + 1 ) Y ] BTg ( mX + nY ) { BCTg [ ( m + 1 ) X + nY ] BDTg [ mX + ( n + 1 ) Y ] CTg ( mX + nY ) { CATg [ ( m + 1 ) X + nY ] CBTg [ mX + ( n + 1 ) Y ] DTg ( mX + nY ) { DCTg [ ( m + 1 ) X + nY ] DDTg [ mX + ( n + 1 ) Y ]
ψ ( d , n , x 0 ) = [ r = 0 N ψ r exp ( i 2 π λ 2 x 0 n 0 ) ] * = r = 0 N ψ r * exp ( i 2 π λ 2 x 0 n 0 )
ψ ( x , y ) = ψ [ d ( x , y ) , n ( x , y ) , x 0 ( x , y ) ]
d ( x , y ) = [ h ( x , y ) , ]
n ( x , y ) = { [ n 0 , n w , 0,0 ] if h ( x , y ) = 0 [ n 0 , n d , n w , 0 ] if h ( x , y ) > 0
x 0 ( x , y ) = h ( x , y ) .
d ( x , y ) = { [ d 1 + h ( x , y ) , d 2 ] if h ( x , y ) < d 1 [ d 1 + d 2 + h ( x , y ) , ] if d 1 < h ( x , y ) < d 1 + d 2 [ , ] if d 1 + d 2 < h ( x , y )
n ( x , y ) = { [ n 0 , n 1 , n 2 , n 3 ] if h ( x , y ) < d 1 [ n 0 , n 2 , n 3 , n 3 ] if d 1 < h ( x , y ) < d 1 + d 2 [ n 0 , n 3 , n 3 , n 3 ] if d 1 + d 2 < h ( x , y )
x 0 ( x , y ) = h ( x , y )
ψ ̄ exp ( x , y ) = ψ exp ( x , y ) exp [ i ϕ exp ( h = 0 ) ] ,
ψ ̄ ( x , y ) = ψ ( x , y ) ψ ( h = 0 ) .
MSE = i = 1 2 j = 1 S ψ ̄ ij ψ ̄ ij , exp d n ,

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