Abstract

A major issue in the fabrication of integrated Bragg grating filters in highly confined waveguides is the average effective index fluctuations caused by waveguide dimension variations. Lateral variations are caused by the sidewall roughness created during the etching process while vertical variations are coming from the wafer silicon layer thickness non-uniformity. Grating spectral distortions are known to result solely from the low spatial frequency components of these variations. As a result, in this work, we present an experimental method to quantify such relevant spatial components by stitching a hundred high-resolution scanning electron microscope images. Additionally, we propose two techniques to reduce, in the design, the phase noise impact on integrated Bragg gratings without relying on fabrication process improvements. More specifically, we show that the use of hybrid multimode/singlemode waveguides reduce by more than one order of magnitude the effect of sidewall roughness on integrated Bragg gratings while we show that the fabrication of ultra-compact gratings in spiral waveguides mitigate the impact of the silicon layer thickness variations.

© 2013 OSA

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2013 (1)

2012 (4)

2011 (1)

2010 (1)

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness Induced Backscattering in Optical Silicon Waveguides,” Phys. Rev. Lett.104(3), 033902 (2010).
[CrossRef] [PubMed]

2009 (1)

2008 (1)

S. Sardo, F. Giacometti, S. Doneda, U. Colombo, M. D. Muri, A. Donghi, R. Morson, G. Mutinati, A. Nottola, M. Gentili, and M. C. Ubaldi, “Line edge roughness (LER) reduction strategy for SOI waveguides fabrication,” Microelectron. Eng.85(5–6), 1210–1213 (2008).
[CrossRef]

2005 (2)

2003 (4)

T. Barwicz and H. I. Smith, “Evolution of line-edge roughness during fabrication of high-index-contrast microphotonic devices,” J. Vac. Sci. Technol. B21(6), 2892–2896 (2003).
[CrossRef]

A. Rosenthal and M. Horowitz, “Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings,” IEEE J. Quantum Electron.39(8), 1018–1026 (2003).
[CrossRef]

G. P. Patsis, V. Constantoudis, A. Tserepi, E. Gogolides, and G. Grozev, “Quantification of line-edge roughness of photoresists. I. A comparison between off-line and on-line analysis of top-down scanning electron microscopy images,” J. Vac. Sci. Technol. B21(3), 1008–1018 (2003).
[CrossRef]

V. Constantoudis, G. P. Patsis, A. Tserepi, and E. Gogolides, “Quantification of line-edge roughness of photoresists. II. Scaling and fractal analysis and the best roughness descriptors,” J. Vac. Sci. Technol. B21(3), 1019–1026 (2003).
[CrossRef]

2001 (1)

2000 (1)

K. K. Lee, D. R. Lim, H.-C. Luan, A. Agarwal, J. Foresi, and L. C. Kimerling, “Effect of size and roughness on light transmission in a Si/SiO2 waveguide: Experiments and model,” Appl. Phys. Lett.77(11), 1617 (2000).
[CrossRef]

1992 (1)

F. Ladouceur, J. D. Love, and T. J. Senden, “Measurement of surface roughness in buried channel waveguides,” Electron. Lett.28(14), 1321–1322 (1992).
[CrossRef]

1988 (1)

V. Eswaran and S. B. Pope, “Direct numerical simulations of the turbulent mixing of a passive scalar,” Phys. Fluids31(3), 506–520 (1988).
[CrossRef]

Agarwal, A.

K. K. Lee, D. R. Lim, H.-C. Luan, A. Agarwal, J. Foresi, and L. C. Kimerling, “Effect of size and roughness on light transmission in a Si/SiO2 waveguide: Experiments and model,” Appl. Phys. Lett.77(11), 1617 (2000).
[CrossRef]

Ayazi, A.

Ayotte, N.

Baehr-Jones, T.

Barwicz, T.

T. Barwicz and H. A. Haus, “Three-Dimensional Analysis of Scattering Losses Due to Sidewall Roughness in Microphotonic Waveguides,” J. Lightwave Technol.23(9), 2719–2732 (2005).
[CrossRef]

T. Barwicz and H. I. Smith, “Evolution of line-edge roughness during fabrication of high-index-contrast microphotonic devices,” J. Vac. Sci. Technol. B21(6), 2892–2896 (2003).
[CrossRef]

Bedard, S.

Belhadj, N.

A. D. Simard, N. Belhadj, Y. Painchaud, and S. LaRochelle, “Apodized Silicon-on-Insulator Bragg Gratings,” IEEE Photon. Technol. Lett.24(12), 1033–1035 (2012).
[CrossRef]

Canciamilla, A.

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness Induced Backscattering in Optical Silicon Waveguides,” Phys. Rev. Lett.104(3), 033902 (2010).
[CrossRef] [PubMed]

Cerrina, F.

Chrostowski, L.

Colombo, U.

S. Sardo, F. Giacometti, S. Doneda, U. Colombo, M. D. Muri, A. Donghi, R. Morson, G. Mutinati, A. Nottola, M. Gentili, and M. C. Ubaldi, “Line edge roughness (LER) reduction strategy for SOI waveguides fabrication,” Microelectron. Eng.85(5–6), 1210–1213 (2008).
[CrossRef]

Constantoudis, V.

G. P. Patsis, V. Constantoudis, A. Tserepi, E. Gogolides, and G. Grozev, “Quantification of line-edge roughness of photoresists. I. A comparison between off-line and on-line analysis of top-down scanning electron microscopy images,” J. Vac. Sci. Technol. B21(3), 1008–1018 (2003).
[CrossRef]

V. Constantoudis, G. P. Patsis, A. Tserepi, and E. Gogolides, “Quantification of line-edge roughness of photoresists. II. Scaling and fractal analysis and the best roughness descriptors,” J. Vac. Sci. Technol. B21(3), 1019–1026 (2003).
[CrossRef]

Delage, A.

Ding, R.

Doneda, S.

S. Sardo, F. Giacometti, S. Doneda, U. Colombo, M. D. Muri, A. Donghi, R. Morson, G. Mutinati, A. Nottola, M. Gentili, and M. C. Ubaldi, “Line edge roughness (LER) reduction strategy for SOI waveguides fabrication,” Microelectron. Eng.85(5–6), 1210–1213 (2008).
[CrossRef]

Donghi, A.

S. Sardo, F. Giacometti, S. Doneda, U. Colombo, M. D. Muri, A. Donghi, R. Morson, G. Mutinati, A. Nottola, M. Gentili, and M. C. Ubaldi, “Line edge roughness (LER) reduction strategy for SOI waveguides fabrication,” Microelectron. Eng.85(5–6), 1210–1213 (2008).
[CrossRef]

Eswaran, V.

V. Eswaran and S. B. Pope, “Direct numerical simulations of the turbulent mixing of a passive scalar,” Phys. Fluids31(3), 506–520 (1988).
[CrossRef]

Ferrari, C.

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness Induced Backscattering in Optical Silicon Waveguides,” Phys. Rev. Lett.104(3), 033902 (2010).
[CrossRef] [PubMed]

Foresi, J.

K. K. Lee, D. R. Lim, H.-C. Luan, A. Agarwal, J. Foresi, and L. C. Kimerling, “Effect of size and roughness on light transmission in a Si/SiO2 waveguide: Experiments and model,” Appl. Phys. Lett.77(11), 1617 (2000).
[CrossRef]

Gentili, M.

S. Sardo, F. Giacometti, S. Doneda, U. Colombo, M. D. Muri, A. Donghi, R. Morson, G. Mutinati, A. Nottola, M. Gentili, and M. C. Ubaldi, “Line edge roughness (LER) reduction strategy for SOI waveguides fabrication,” Microelectron. Eng.85(5–6), 1210–1213 (2008).
[CrossRef]

Giacometti, F.

S. Sardo, F. Giacometti, S. Doneda, U. Colombo, M. D. Muri, A. Donghi, R. Morson, G. Mutinati, A. Nottola, M. Gentili, and M. C. Ubaldi, “Line edge roughness (LER) reduction strategy for SOI waveguides fabrication,” Microelectron. Eng.85(5–6), 1210–1213 (2008).
[CrossRef]

Gogolides, E.

G. P. Patsis, V. Constantoudis, A. Tserepi, E. Gogolides, and G. Grozev, “Quantification of line-edge roughness of photoresists. I. A comparison between off-line and on-line analysis of top-down scanning electron microscopy images,” J. Vac. Sci. Technol. B21(3), 1008–1018 (2003).
[CrossRef]

V. Constantoudis, G. P. Patsis, A. Tserepi, and E. Gogolides, “Quantification of line-edge roughness of photoresists. II. Scaling and fractal analysis and the best roughness descriptors,” J. Vac. Sci. Technol. B21(3), 1019–1026 (2003).
[CrossRef]

Grist, S.

Grozev, G.

G. P. Patsis, V. Constantoudis, A. Tserepi, E. Gogolides, and G. Grozev, “Quantification of line-edge roughness of photoresists. I. A comparison between off-line and on-line analysis of top-down scanning electron microscopy images,” J. Vac. Sci. Technol. B21(3), 1008–1018 (2003).
[CrossRef]

Harris, N. C.

Haus, H. A.

Hochberg, M.

Horowitz, M.

A. Rosenthal and M. Horowitz, “Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings,” IEEE J. Quantum Electron.39(8), 1018–1026 (2003).
[CrossRef]

Jaeger, N. A. F.

Janz, S.

Kimerling, L. C.

Ladouceur, F.

F. Ladouceur, J. D. Love, and T. J. Senden, “Measurement of surface roughness in buried channel waveguides,” Electron. Lett.28(14), 1321–1322 (1992).
[CrossRef]

Lamontagne, B.

Lapointe, J.

LaRochelle, S.

Lee, K. K.

K. K. Lee, D. R. Lim, L. C. Kimerling, J. Shin, and F. Cerrina, “Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction,” Opt. Lett.26(23), 1888–1890 (2001).
[CrossRef] [PubMed]

K. K. Lee, D. R. Lim, H.-C. Luan, A. Agarwal, J. Foresi, and L. C. Kimerling, “Effect of size and roughness on light transmission in a Si/SiO2 waveguide: Experiments and model,” Appl. Phys. Lett.77(11), 1617 (2000).
[CrossRef]

Lee, P.

Lim, A. E.-J.

Lim, D. R.

K. K. Lee, D. R. Lim, L. C. Kimerling, J. Shin, and F. Cerrina, “Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction,” Opt. Lett.26(23), 1888–1890 (2001).
[CrossRef] [PubMed]

K. K. Lee, D. R. Lim, H.-C. Luan, A. Agarwal, J. Foresi, and L. C. Kimerling, “Effect of size and roughness on light transmission in a Si/SiO2 waveguide: Experiments and model,” Appl. Phys. Lett.77(11), 1617 (2000).
[CrossRef]

Liow, T.-Y.

Liu, Y.

Lo, G.-Q.

Love, J. D.

F. Ladouceur, J. D. Love, and T. J. Senden, “Measurement of surface roughness in buried channel waveguides,” Electron. Lett.28(14), 1321–1322 (1992).
[CrossRef]

Luan, H.-C.

K. K. Lee, D. R. Lim, H.-C. Luan, A. Agarwal, J. Foresi, and L. C. Kimerling, “Effect of size and roughness on light transmission in a Si/SiO2 waveguide: Experiments and model,” Appl. Phys. Lett.77(11), 1617 (2000).
[CrossRef]

Martinelli, M.

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness Induced Backscattering in Optical Silicon Waveguides,” Phys. Rev. Lett.104(3), 033902 (2010).
[CrossRef] [PubMed]

Melloni, A.

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness Induced Backscattering in Optical Silicon Waveguides,” Phys. Rev. Lett.104(3), 033902 (2010).
[CrossRef] [PubMed]

Mookherjea, S.

M. A. Schneider and S. Mookherjea, “Modeling Transmission Time of Silicon Nanophotonic Waveguides,” IEEE Photon. Technol. Lett.24(16), 1418–1420 (2012).
[CrossRef]

Morichetti, F.

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness Induced Backscattering in Optical Silicon Waveguides,” Phys. Rev. Lett.104(3), 033902 (2010).
[CrossRef] [PubMed]

Morson, R.

S. Sardo, F. Giacometti, S. Doneda, U. Colombo, M. D. Muri, A. Donghi, R. Morson, G. Mutinati, A. Nottola, M. Gentili, and M. C. Ubaldi, “Line edge roughness (LER) reduction strategy for SOI waveguides fabrication,” Microelectron. Eng.85(5–6), 1210–1213 (2008).
[CrossRef]

Muri, M. D.

S. Sardo, F. Giacometti, S. Doneda, U. Colombo, M. D. Muri, A. Donghi, R. Morson, G. Mutinati, A. Nottola, M. Gentili, and M. C. Ubaldi, “Line edge roughness (LER) reduction strategy for SOI waveguides fabrication,” Microelectron. Eng.85(5–6), 1210–1213 (2008).
[CrossRef]

Mutinati, G.

S. Sardo, F. Giacometti, S. Doneda, U. Colombo, M. D. Muri, A. Donghi, R. Morson, G. Mutinati, A. Nottola, M. Gentili, and M. C. Ubaldi, “Line edge roughness (LER) reduction strategy for SOI waveguides fabrication,” Microelectron. Eng.85(5–6), 1210–1213 (2008).
[CrossRef]

Nottola, A.

S. Sardo, F. Giacometti, S. Doneda, U. Colombo, M. D. Muri, A. Donghi, R. Morson, G. Mutinati, A. Nottola, M. Gentili, and M. C. Ubaldi, “Line edge roughness (LER) reduction strategy for SOI waveguides fabrication,” Microelectron. Eng.85(5–6), 1210–1213 (2008).
[CrossRef]

Painchaud, Y.

Patsis, G. P.

V. Constantoudis, G. P. Patsis, A. Tserepi, and E. Gogolides, “Quantification of line-edge roughness of photoresists. II. Scaling and fractal analysis and the best roughness descriptors,” J. Vac. Sci. Technol. B21(3), 1019–1026 (2003).
[CrossRef]

G. P. Patsis, V. Constantoudis, A. Tserepi, E. Gogolides, and G. Grozev, “Quantification of line-edge roughness of photoresists. I. A comparison between off-line and on-line analysis of top-down scanning electron microscopy images,” J. Vac. Sci. Technol. B21(3), 1008–1018 (2003).
[CrossRef]

Pinguet, T.

Pope, S. B.

V. Eswaran and S. B. Pope, “Direct numerical simulations of the turbulent mixing of a passive scalar,” Phys. Fluids31(3), 506–520 (1988).
[CrossRef]

Rosenthal, A.

A. Rosenthal and M. Horowitz, “Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings,” IEEE J. Quantum Electron.39(8), 1018–1026 (2003).
[CrossRef]

Sardo, S.

S. Sardo, F. Giacometti, S. Doneda, U. Colombo, M. D. Muri, A. Donghi, R. Morson, G. Mutinati, A. Nottola, M. Gentili, and M. C. Ubaldi, “Line edge roughness (LER) reduction strategy for SOI waveguides fabrication,” Microelectron. Eng.85(5–6), 1210–1213 (2008).
[CrossRef]

Schmid, J. H.

Schneider, M. A.

M. A. Schneider and S. Mookherjea, “Modeling Transmission Time of Silicon Nanophotonic Waveguides,” IEEE Photon. Technol. Lett.24(16), 1418–1420 (2012).
[CrossRef]

Senden, T. J.

F. Ladouceur, J. D. Love, and T. J. Senden, “Measurement of surface roughness in buried channel waveguides,” Electron. Lett.28(14), 1321–1322 (1992).
[CrossRef]

Shi, W.

Shin, J.

Simard, A. D.

Smith, H. I.

T. Barwicz and H. I. Smith, “Evolution of line-edge roughness during fabrication of high-index-contrast microphotonic devices,” J. Vac. Sci. Technol. B21(6), 2892–2896 (2003).
[CrossRef]

Sparacin, D. K.

Spector, S. J.

Streshinsky, M.

Syrett, B. A.

Teo, S. H.-G.

Torregiani, M.

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness Induced Backscattering in Optical Silicon Waveguides,” Phys. Rev. Lett.104(3), 033902 (2010).
[CrossRef] [PubMed]

Tserepi, A.

V. Constantoudis, G. P. Patsis, A. Tserepi, and E. Gogolides, “Quantification of line-edge roughness of photoresists. II. Scaling and fractal analysis and the best roughness descriptors,” J. Vac. Sci. Technol. B21(3), 1019–1026 (2003).
[CrossRef]

G. P. Patsis, V. Constantoudis, A. Tserepi, E. Gogolides, and G. Grozev, “Quantification of line-edge roughness of photoresists. I. A comparison between off-line and on-line analysis of top-down scanning electron microscopy images,” J. Vac. Sci. Technol. B21(3), 1008–1018 (2003).
[CrossRef]

Ubaldi, M. C.

S. Sardo, F. Giacometti, S. Doneda, U. Colombo, M. D. Muri, A. Donghi, R. Morson, G. Mutinati, A. Nottola, M. Gentili, and M. C. Ubaldi, “Line edge roughness (LER) reduction strategy for SOI waveguides fabrication,” Microelectron. Eng.85(5–6), 1210–1213 (2008).
[CrossRef]

Waldron, P.

Wang, X.

Yap, K. P.

Yun, H.

Zhang, Y.

Appl. Phys. Lett. (1)

K. K. Lee, D. R. Lim, H.-C. Luan, A. Agarwal, J. Foresi, and L. C. Kimerling, “Effect of size and roughness on light transmission in a Si/SiO2 waveguide: Experiments and model,” Appl. Phys. Lett.77(11), 1617 (2000).
[CrossRef]

Electron. Lett. (1)

F. Ladouceur, J. D. Love, and T. J. Senden, “Measurement of surface roughness in buried channel waveguides,” Electron. Lett.28(14), 1321–1322 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Rosenthal and M. Horowitz, “Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings,” IEEE J. Quantum Electron.39(8), 1018–1026 (2003).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

A. D. Simard, N. Belhadj, Y. Painchaud, and S. LaRochelle, “Apodized Silicon-on-Insulator Bragg Gratings,” IEEE Photon. Technol. Lett.24(12), 1033–1035 (2012).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

(a) Typical top-down SEM image of a photonic wire. (b) Typical intensity profile of a pixel column (taken at the position of the red line in (a)). (c) Typical top-down SEM image converted into a binary image with the threshold shown by the black line in (b). The red lines are the outer waveguide sidewalls. (d) Typical superposition of the waveguide width fluctuation from every image of a set of measurement. The thick blue line is the linear regression of the average waveguide width fluctuation per pixel (black curve).

Fig. 2
Fig. 2

(a) Waveguide width fluctuation obtained from top-down SEM taken at the same location with different working distance. (b) Dependency of the average waveguide width caused by a variation of the working distance.

Fig. 3
Fig. 3

(a) Typical overlap of the waveguide width fluctuation between three consecutive images (red, blue and green). The black curve is the averaged waveguide width as a function of position. (b) Typical waveguide width fluctuation profile as a function of position. The black line is the raw data (corresponding to the black line of (a)) while the blue line is a filtered version of the waveguide width profile. (c) Autocorrelation function of the waveguide width fluctuation of the filtered (blue) and unfiltered (black) curve of (b). The red curve is the decaying exponential autocorrelation fit. (d) Probability density functions of the sidewall roughness. The red curve is a Gaussian function.

Fig. 4
Fig. 4

Schematic of the IBGs.

Fig. 5
Fig. 5

(a) Comparison of the experimental reflection spectrum of a typical straight grating on a 1200 nm wide waveguide (in red) with the reconstructed reflection spectrum (in black). Retrieved (b) λB and (c) Δn profiles, which are used to calculate the black curve of (a).

Fig. 6
Fig. 6

(a) Bragg wavelength standard deviation as a function of the waveguide width. The black curve contains both the impact of the sidewall roughness and the wafer height fluctuations, while the blue and red curve takes those to effect independently. The cyan lines are the optical measurement of 2 mm-long IBGs while the purple line is the optical measurement for spiral IBGs. (b) Schematic of spiral IBGs.

Fig. 7
Fig. 7

Typical spectral response of 2 mm-long (a) straight grating on a 800 nm wide waveguide, (b) straight grating on a 1200 nm wide waveguide and (c) spiral grating on a 1200 nm wide waveguide. The blue curves are the designs while the black curves are the experimental results.

Fig. 8
Fig. 8

Superposition of every Bragg wavelength fluctuation measurements for (a) 800 nm straight waveguide, (b) 1200 nm straight waveguide and (c) 1200 nm spiral waveguide.

Equations (11)

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R SWR ( Δz )= lim L 1 L L/2 L/2 Δx(z)Δx(z+Δz)dz R WHF ( Δz )= lim L 1 L L/2 L/2 Δy(z)Δy(z+Δz)dz
R SWR ( Δz )= σ SWR 2 exp( | Δz | L c,SWR ) R WHF ( Δz )= σ WHF 2 exp( | Δz | L c,WHF )
G SWR ( f z )= 2 σ SWR 2 L c,SWR 1+4 π 2 L c,SWR 2 f z 2 G WHF ( f z )= 2 σ WHF 2 L c,WHF 1+4 π 2 L c,WHF 2 f z 2
σ λ B =2Λ σ n
σ n = 2 C SWR 2 σ SWR 2 + C WHF 2 σ WHF 2
f c = 2 n g λ B ( λ B Δλ 1 ) 2 n g Δλ λ B 2 ,
σ ˜ 2 = f c f c G Δx ( f z )d f z = 4 σ 2 L c f c 4 π 2 L c 2 f c 2 +1 .
σ ˜ SWR 2 8 n g L c Δλ λ B 2 σ SWR 2 σ ˜ WHF 2 8 n g L c Δλ λ B 2 σ WHF 2
σ ˜ λ B =2Λ σ ˜ n =2Λ 2 C SWR 2 σ ˜ SWR 2 + C WHF 2 σ ˜ WHF 2
σ ˜ λ B = 8Λ n g Δλ λ B ( C SWR 2 L c,SWR σ SWR 2 + 1 2 C WHF 2 L c,WHF σ WHF 2 )
σ ˜ λ B,WHF 8Λ C WHF σ WHF λ B n g Δλ L c,WHF 2

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