Abstract

We present a study of the influence of high strain on the bandgap and the refractive index of silicon. The results of photoluminescence show that with the strain applied, the silicon bandgap can be adjusted to 0.84 eV and the refractive index of silicon increases significantly. 1.4% change of refractive index of silicon was observed. The strain-induced bandgap shrinkage and absorption coefficient change of silicon are considered as the main cause of the significant refractive index change. The present work indicates that the application of strain is promising to control the refractive index of silicon in devices so that applications such as compensation of thermal effect in optical devices can be achieved.

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2012

C. Schriever, C. Bohley, J. Schilling, and R. B. Wehrspohn, “Strained silicon photonics,” Materials5(12), 889–908 (2012).

2011

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

2010

2009

2008

Y. Amemiya, Y. Tanushi, T. Tokunaga, and S. Yokoyama, “Photoelastic effect in silicon ring resonators,” Jpn. J. Appl. Phys.47(4), 2910–2914 (2008).
[CrossRef]

K.-H. Hong, J. Kim, S.-H. Lee, and J. K. Shin, “Strain-driven electronic band structure modulation of Si nanowires,” Nano Lett.8(5), 1335–1340 (2008).
[CrossRef] [PubMed]

J. Munguía, G. Bremond, J. M. Bluet, J. M. Hartmann, and M. Mermoux, “Strain dependence of indirect band gap for strained silicon on insulator wafers,” Appl. Phys. Lett.93(10), 102101 (2008).
[CrossRef]

2007

2006

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature441(7090), 199–202 (2006).
[CrossRef] [PubMed]

2003

Y. Ishikawa, K. Wada, D. D. Cannon, J. Liu, H.-C. Luan, and L. C. Kimerling, “Strain-induced band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett.82(13), 2044–2046 (2003).
[CrossRef]

Y. Ishikawa, K. Wada, D. D. Cannon, J. Liu, H.-C. Luan, and L. C. Kimerling, “Strain-induced band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett.82(13), 2044–2046 (2003).
[CrossRef]

M. Huang, “Stress effects on the performance of optical waveguides,” Int. J. Solids Struct.40(7), 1615–1632 (2003).
[CrossRef]

1998

A. A. Patrin and M. I. Tarasik, “Optical-absorption spectrum of silicon containing internal elastic stresses,” J. Appl. Spectrosc.65(4), 598–603 (1998).
[CrossRef]

1994

J. Welser, J. L. Hoyt, and J. F. Gibbons, “Electron mobility enhancement in strained-Si n-type metal-oxide- semiconductor field-effect transistors,” IEEE Electron Device Lett.15(3), 100–102 (1994).
[CrossRef]

J. A. McCaulley, V. M. Donnelly, M. Vernon, and I. Taha, “Temperature dependence of the near-infrared refractive index of silicon, gallium arsenide, and indium phosphide,” Phys. Rev. B Condens. Matter49(11), 7408–7417 (1994).
[CrossRef] [PubMed]

K. Bücher, J. Bruns, and H. G. Wagemann, “Absorption coefficient of silicon: An assessment of measurements and the simulation of temperature variation,” J. Appl. Phys.75(2), 1127–1132 (1994).
[CrossRef]

1989

C. G. Van de Walle, “Band lineups and deformation potentials in the model-solid theory,” Phys. Rev. B Condens. Matter39(3), 1871–1883 (1989).
[CrossRef] [PubMed]

Amemiya, Y.

Y. Amemiya, Y. Tanushi, T. Tokunaga, and S. Yokoyama, “Photoelastic effect in silicon ring resonators,” Jpn. J. Appl. Phys.47(4), 2910–2914 (2008).
[CrossRef]

Andersen, K. N.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Baets, R.

Bianco, F.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Bjarklev, A.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Bluet, J. M.

J. Munguía, G. Bremond, J. M. Bluet, J. M. Hartmann, and M. Mermoux, “Strain dependence of indirect band gap for strained silicon on insulator wafers,” Appl. Phys. Lett.93(10), 102101 (2008).
[CrossRef]

Bohley, C.

C. Schriever, C. Bohley, J. Schilling, and R. B. Wehrspohn, “Strained silicon photonics,” Materials5(12), 889–908 (2012).

C. Schriever, C. Bohley, and R. B. Wehrspohn, “Strain dependence of second-harmonic generation in silicon,” Opt. Lett.35(3), 273–275 (2010).
[CrossRef] [PubMed]

Borel, P. I.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Borga, E.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Bose, P.

H. F. Hamann, A. Weger, J. A. Lacey, Z. Hu, P. Bose, E. Cohen, and J. Wakil, “Hotspot-limited microprocessors: direct temperature and power distribution measurements,” IEEE J. Solid-State Circuits42(1), 56–65 (2007).
[CrossRef]

Bremond, G.

J. Munguía, G. Bremond, J. M. Bluet, J. M. Hartmann, and M. Mermoux, “Strain dependence of indirect band gap for strained silicon on insulator wafers,” Appl. Phys. Lett.93(10), 102101 (2008).
[CrossRef]

Bruns, J.

K. Bücher, J. Bruns, and H. G. Wagemann, “Absorption coefficient of silicon: An assessment of measurements and the simulation of temperature variation,” J. Appl. Phys.75(2), 1127–1132 (1994).
[CrossRef]

Bücher, K.

K. Bücher, J. Bruns, and H. G. Wagemann, “Absorption coefficient of silicon: An assessment of measurements and the simulation of temperature variation,” J. Appl. Phys.75(2), 1127–1132 (1994).
[CrossRef]

Cannon, D. D.

Y. Ishikawa, K. Wada, D. D. Cannon, J. Liu, H.-C. Luan, and L. C. Kimerling, “Strain-induced band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett.82(13), 2044–2046 (2003).
[CrossRef]

Y. Ishikawa, K. Wada, D. D. Cannon, J. Liu, H.-C. Luan, and L. C. Kimerling, “Strain-induced band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett.82(13), 2044–2046 (2003).
[CrossRef]

Cazzanelli, M.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Chetrit, Y.

Ciftcioglu, B.

Cohen, E.

H. F. Hamann, A. Weger, J. A. Lacey, Z. Hu, P. Bose, E. Cohen, and J. Wakil, “Hotspot-limited microprocessors: direct temperature and power distribution measurements,” IEEE J. Solid-State Circuits42(1), 56–65 (2007).
[CrossRef]

Degoli, E.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Donnelly, V. M.

J. A. McCaulley, V. M. Donnelly, M. Vernon, and I. Taha, “Temperature dependence of the near-infrared refractive index of silicon, gallium arsenide, and indium phosphide,” Phys. Rev. B Condens. Matter49(11), 7408–7417 (1994).
[CrossRef] [PubMed]

Fage-Pedersen, J.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Frandsen, L. H.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Ghulinyan, M.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Gibbons, J. F.

J. Welser, J. L. Hoyt, and J. F. Gibbons, “Electron mobility enhancement in strained-Si n-type metal-oxide- semiconductor field-effect transistors,” IEEE Electron Device Lett.15(3), 100–102 (1994).
[CrossRef]

Hamann, H. F.

H. F. Hamann, A. Weger, J. A. Lacey, Z. Hu, P. Bose, E. Cohen, and J. Wakil, “Hotspot-limited microprocessors: direct temperature and power distribution measurements,” IEEE J. Solid-State Circuits42(1), 56–65 (2007).
[CrossRef]

Hansen, O.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Hartmann, J. M.

J. Munguía, G. Bremond, J. M. Bluet, J. M. Hartmann, and M. Mermoux, “Strain dependence of indirect band gap for strained silicon on insulator wafers,” Appl. Phys. Lett.93(10), 102101 (2008).
[CrossRef]

Hens, Z.

Hong, K.-H.

K.-H. Hong, J. Kim, S.-H. Lee, and J. K. Shin, “Strain-driven electronic band structure modulation of Si nanowires,” Nano Lett.8(5), 1335–1340 (2008).
[CrossRef] [PubMed]

Hoyt, J. L.

J. Welser, J. L. Hoyt, and J. F. Gibbons, “Electron mobility enhancement in strained-Si n-type metal-oxide- semiconductor field-effect transistors,” IEEE Electron Device Lett.15(3), 100–102 (1994).
[CrossRef]

Hu, Z.

H. F. Hamann, A. Weger, J. A. Lacey, Z. Hu, P. Bose, E. Cohen, and J. Wakil, “Hotspot-limited microprocessors: direct temperature and power distribution measurements,” IEEE J. Solid-State Circuits42(1), 56–65 (2007).
[CrossRef]

Huang, M.

M. Huang, “Stress effects on the performance of optical waveguides,” Int. J. Solids Struct.40(7), 1615–1632 (2003).
[CrossRef]

Ishikawa, Y.

K. Yoshimoto, R. Suzuki, Y. Ishikawa, and K. Wada, “Bandgap control using strained beam structures for Si photonic devices,” Opt. Express18(25), 26492–26498 (2010).
[CrossRef] [PubMed]

P. H. Lim, S. Park, Y. Ishikawa, and K. Wada, “Enhanced direct bandgap emission in germanium by micromechanical strain engineering,” Opt. Express17(18), 16358–16365 (2009).
[CrossRef] [PubMed]

Y. Ishikawa, K. Wada, D. D. Cannon, J. Liu, H.-C. Luan, and L. C. Kimerling, “Strain-induced band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett.82(13), 2044–2046 (2003).
[CrossRef]

Y. Ishikawa, K. Wada, D. D. Cannon, J. Liu, H.-C. Luan, and L. C. Kimerling, “Strain-induced band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett.82(13), 2044–2046 (2003).
[CrossRef]

Izhaky, N.

Jacobsen, R. S.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Kim, J.

K.-H. Hong, J. Kim, S.-H. Lee, and J. K. Shin, “Strain-driven electronic band structure modulation of Si nanowires,” Nano Lett.8(5), 1335–1340 (2008).
[CrossRef] [PubMed]

Kimerling, L. C.

Y. Ishikawa, K. Wada, D. D. Cannon, J. Liu, H.-C. Luan, and L. C. Kimerling, “Strain-induced band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett.82(13), 2044–2046 (2003).
[CrossRef]

Y. Ishikawa, K. Wada, D. D. Cannon, J. Liu, H.-C. Luan, and L. C. Kimerling, “Strain-induced band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett.82(13), 2044–2046 (2003).
[CrossRef]

Kristensen, M.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Lacey, J. A.

H. F. Hamann, A. Weger, J. A. Lacey, Z. Hu, P. Bose, E. Cohen, and J. Wakil, “Hotspot-limited microprocessors: direct temperature and power distribution measurements,” IEEE J. Solid-State Circuits42(1), 56–65 (2007).
[CrossRef]

Lavrinenko, A. V.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Lee, S.-H.

K.-H. Hong, J. Kim, S.-H. Lee, and J. K. Shin, “Strain-driven electronic band structure modulation of Si nanowires,” Nano Lett.8(5), 1335–1340 (2008).
[CrossRef] [PubMed]

Liao, L.

Lim, P. H.

Liu, A.

Liu, J.

Y. Ishikawa, K. Wada, D. D. Cannon, J. Liu, H.-C. Luan, and L. C. Kimerling, “Strain-induced band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett.82(13), 2044–2046 (2003).
[CrossRef]

Y. Ishikawa, K. Wada, D. D. Cannon, J. Liu, H.-C. Luan, and L. C. Kimerling, “Strain-induced band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett.82(13), 2044–2046 (2003).
[CrossRef]

Lommens, P.

Luan, H.-C.

Y. Ishikawa, K. Wada, D. D. Cannon, J. Liu, H.-C. Luan, and L. C. Kimerling, “Strain-induced band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett.82(13), 2044–2046 (2003).
[CrossRef]

Y. Ishikawa, K. Wada, D. D. Cannon, J. Liu, H.-C. Luan, and L. C. Kimerling, “Strain-induced band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett.82(13), 2044–2046 (2003).
[CrossRef]

Luppi, E.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

McCaulley, J. A.

J. A. McCaulley, V. M. Donnelly, M. Vernon, and I. Taha, “Temperature dependence of the near-infrared refractive index of silicon, gallium arsenide, and indium phosphide,” Phys. Rev. B Condens. Matter49(11), 7408–7417 (1994).
[CrossRef] [PubMed]

Mermoux, M.

J. Munguía, G. Bremond, J. M. Bluet, J. M. Hartmann, and M. Mermoux, “Strain dependence of indirect band gap for strained silicon on insulator wafers,” Appl. Phys. Lett.93(10), 102101 (2008).
[CrossRef]

Modotto, D.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Moulin, G.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Munguía, J.

J. Munguía, G. Bremond, J. M. Bluet, J. M. Hartmann, and M. Mermoux, “Strain dependence of indirect band gap for strained silicon on insulator wafers,” Appl. Phys. Lett.93(10), 102101 (2008).
[CrossRef]

Nguyen, H.

Ossicini, S.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Ou, H.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature441(7090), 199–202 (2006).
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Paniccia, M.

Park, S.

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A. A. Patrin and M. I. Tarasik, “Optical-absorption spectrum of silicon containing internal elastic stresses,” J. Appl. Spectrosc.65(4), 598–603 (1998).
[CrossRef]

Pavesi, L.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

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R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature441(7090), 199–202 (2006).
[CrossRef] [PubMed]

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M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
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M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
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C. Schriever, C. Bohley, J. Schilling, and R. B. Wehrspohn, “Strained silicon photonics,” Materials5(12), 889–908 (2012).

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C. Schriever, C. Bohley, J. Schilling, and R. B. Wehrspohn, “Strained silicon photonics,” Materials5(12), 889–908 (2012).

C. Schriever, C. Bohley, and R. B. Wehrspohn, “Strain dependence of second-harmonic generation in silicon,” Opt. Lett.35(3), 273–275 (2010).
[CrossRef] [PubMed]

Sekaric, L.

Shin, J. K.

K.-H. Hong, J. Kim, S.-H. Lee, and J. K. Shin, “Strain-driven electronic band structure modulation of Si nanowires,” Nano Lett.8(5), 1335–1340 (2008).
[CrossRef] [PubMed]

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Taha, I.

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A. A. Patrin and M. I. Tarasik, “Optical-absorption spectrum of silicon containing internal elastic stresses,” J. Appl. Spectrosc.65(4), 598–603 (1998).
[CrossRef]

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Y. Amemiya, Y. Tanushi, T. Tokunaga, and S. Yokoyama, “Photoelastic effect in silicon ring resonators,” Jpn. J. Appl. Phys.47(4), 2910–2914 (2008).
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M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
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J. A. McCaulley, V. M. Donnelly, M. Vernon, and I. Taha, “Temperature dependence of the near-infrared refractive index of silicon, gallium arsenide, and indium phosphide,” Phys. Rev. B Condens. Matter49(11), 7408–7417 (1994).
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M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
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K. Yoshimoto, R. Suzuki, Y. Ishikawa, and K. Wada, “Bandgap control using strained beam structures for Si photonic devices,” Opt. Express18(25), 26492–26498 (2010).
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Y. Ishikawa, K. Wada, D. D. Cannon, J. Liu, H.-C. Luan, and L. C. Kimerling, “Strain-induced band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett.82(13), 2044–2046 (2003).
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Y. Ishikawa, K. Wada, D. D. Cannon, J. Liu, H.-C. Luan, and L. C. Kimerling, “Strain-induced band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett.82(13), 2044–2046 (2003).
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K. Bücher, J. Bruns, and H. G. Wagemann, “Absorption coefficient of silicon: An assessment of measurements and the simulation of temperature variation,” J. Appl. Phys.75(2), 1127–1132 (1994).
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H. F. Hamann, A. Weger, J. A. Lacey, Z. Hu, P. Bose, E. Cohen, and J. Wakil, “Hotspot-limited microprocessors: direct temperature and power distribution measurements,” IEEE J. Solid-State Circuits42(1), 56–65 (2007).
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Weger, A.

H. F. Hamann, A. Weger, J. A. Lacey, Z. Hu, P. Bose, E. Cohen, and J. Wakil, “Hotspot-limited microprocessors: direct temperature and power distribution measurements,” IEEE J. Solid-State Circuits42(1), 56–65 (2007).
[CrossRef]

Wehrspohn, R. B.

C. Schriever, C. Bohley, J. Schilling, and R. B. Wehrspohn, “Strained silicon photonics,” Materials5(12), 889–908 (2012).

C. Schriever, C. Bohley, and R. B. Wehrspohn, “Strain dependence of second-harmonic generation in silicon,” Opt. Lett.35(3), 273–275 (2010).
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Y. Amemiya, Y. Tanushi, T. Tokunaga, and S. Yokoyama, “Photoelastic effect in silicon ring resonators,” Jpn. J. Appl. Phys.47(4), 2910–2914 (2008).
[CrossRef]

Yoshimoto, K.

Zsigri, B.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Appl. Phys. Lett.

Y. Ishikawa, K. Wada, D. D. Cannon, J. Liu, H.-C. Luan, and L. C. Kimerling, “Strain-induced band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett.82(13), 2044–2046 (2003).
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J. Munguía, G. Bremond, J. M. Bluet, J. M. Hartmann, and M. Mermoux, “Strain dependence of indirect band gap for strained silicon on insulator wafers,” Appl. Phys. Lett.93(10), 102101 (2008).
[CrossRef]

Y. Ishikawa, K. Wada, D. D. Cannon, J. Liu, H.-C. Luan, and L. C. Kimerling, “Strain-induced band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett.82(13), 2044–2046 (2003).
[CrossRef]

IEEE Electron Device Lett.

J. Welser, J. L. Hoyt, and J. F. Gibbons, “Electron mobility enhancement in strained-Si n-type metal-oxide- semiconductor field-effect transistors,” IEEE Electron Device Lett.15(3), 100–102 (1994).
[CrossRef]

IEEE J. Solid-State Circuits

H. F. Hamann, A. Weger, J. A. Lacey, Z. Hu, P. Bose, E. Cohen, and J. Wakil, “Hotspot-limited microprocessors: direct temperature and power distribution measurements,” IEEE J. Solid-State Circuits42(1), 56–65 (2007).
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M. Huang, “Stress effects on the performance of optical waveguides,” Int. J. Solids Struct.40(7), 1615–1632 (2003).
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K. Bücher, J. Bruns, and H. G. Wagemann, “Absorption coefficient of silicon: An assessment of measurements and the simulation of temperature variation,” J. Appl. Phys.75(2), 1127–1132 (1994).
[CrossRef]

J. Appl. Spectrosc.

A. A. Patrin and M. I. Tarasik, “Optical-absorption spectrum of silicon containing internal elastic stresses,” J. Appl. Spectrosc.65(4), 598–603 (1998).
[CrossRef]

Jpn. J. Appl. Phys.

Y. Amemiya, Y. Tanushi, T. Tokunaga, and S. Yokoyama, “Photoelastic effect in silicon ring resonators,” Jpn. J. Appl. Phys.47(4), 2910–2914 (2008).
[CrossRef]

Materials

C. Schriever, C. Bohley, J. Schilling, and R. B. Wehrspohn, “Strained silicon photonics,” Materials5(12), 889–908 (2012).

Nano Lett.

K.-H. Hong, J. Kim, S.-H. Lee, and J. K. Shin, “Strain-driven electronic band structure modulation of Si nanowires,” Nano Lett.8(5), 1335–1340 (2008).
[CrossRef] [PubMed]

Nat. Mater.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Nature

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. B Condens. Matter

C. G. Van de Walle, “Band lineups and deformation potentials in the model-solid theory,” Phys. Rev. B Condens. Matter39(3), 1871–1883 (1989).
[CrossRef] [PubMed]

J. A. McCaulley, V. M. Donnelly, M. Vernon, and I. Taha, “Temperature dependence of the near-infrared refractive index of silicon, gallium arsenide, and indium phosphide,” Phys. Rev. B Condens. Matter49(11), 7408–7417 (1994).
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L. Pavesi and D. Lockwood, Silicon Photonics (Springer-Verlag, 2004).

V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, Kramers–Kronig Relations in Optical Materials Research (Springer-Verlag, 2005).

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H. Nakamura, “Strain effects on the band structure for Si nanowires,” in Proceedings of IEEE Conference on Nanotechnology (IEEE NANO Organizers, 2009), pp. 555–558.

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Figures (5)

Fig. 1
Fig. 1

(a) The shape of the designed Si cantilever beam. (b), (c) the schematic cross-section image showing how the beam bends by the operation of probe. The undercut region was generated while removing the BOX by wet etching. (b): Bending Method One, directly pushing down the beam; (c): Bending Method Two, pushing the beam down and forward so that the beam is more bent.

Fig. 2
Fig. 2

(a) The modeled structure of the silicon cantilever beam for simulation. (b) Typical strain distribution obtained by the simulator using Method Two.

Fig. 3
Fig. 3

Typical PL spectra of Si cantilever beam under different strain conditions. The photos in the right side were taken during each operation. The numbers are the TM mode numbers for the Febry-Perot resonator.

Fig. 4
Fig. 4

Cross sectional view of the strain distribution and the corresponding changes of refractive indices of different locations in the bent silicon cantilever beam that has 1.535% tensile strain at eh top surface.

Fig. 5
Fig. 5

The estimation of refractive index change (dashed line) according to the calculation from the fitting results shown in inset, and the refractive index change calculated from experimental data (scattered points). Inset: the estimation of silicon refractive index change by considering the effect of bandgap shift. The black dotted data points are obtained from reference [25].

Tables (1)

Tables Icon

Table 1 Typical peak shifts of free and strained silicon beams

Equations (2)

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mλ=2nL.
Δλ λ = Δn n .

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