Abstract

We provide detailed analysis of a four terminal p + pnn + optical modulator integrated into a silicon-on-insulator (SOI) rib waveguide. The proposed depletion device has been designed to approach birefringence free operation. The modulation mechanism is the carrier depletion effect in a pn junction; carrier losses induced are minimised in our design and because we use a depletion device, the device is insensitive to carrier lifetime. The rise time and fall time of the proposed device have both been calculated to be 7 ps for a reverse bias of only 5 volts. A maximum excess loss of 2 dB is predicted for TE and TM due to the presence of p type and n type carriers in the waveguide.

© 2005 Optical Society of America

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  1. C. Cocorullo , M. Iodice , I. Rendina , and P.M. Sarro , “ Silicon thermo-optical micro-modulator with 700 khz 3db bandwidth ,” IEEE Photonics Technol. Lett.   7 , 363 – 365 ( 1995 ).
    [Crossref]
  2. R. A. Soref and B.R Bennett , “ Electrooptical effects in silicon ,” IEEE J. Quantum Electron.   23 , 123 – 129 ( 198 ).
    [Crossref]
  3. C. E. Png , G. T. Reed , R. M. Atta , G. J. Ensell , and A. G. R. Evans , “ Development of small silicon modulators in silicon-on-insulator (SOI) ,” Proc. SPIE   4997 , 190 – 197 ( 2003 ).
    [Crossref]
  4. A. Liu , R. Jones , L. Liao , D. S. Rubio , D. Rubin , O. Cohen , R. Nicolaescu , and M. Paniccia , “ High-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor ,” Nature (London)   427 , 615 – 618 ( 2004 ).
    [Crossref]
  5. L. Liao , D. Samara-Rubio , M. Morse , A. Liu , D. Hodge , D. Rubin , U. D. Keil , and T. Franck , “ High speed silicon mach-zehnder modulator ,” Opt. Express   13 , 3129 – 3135 ( 2005 ). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-3129 .
    [Crossref] [PubMed]
  6. Q. Xu , B. Shmidt , S. Pradhan , and M. Lipson , “ Micrometre-scale silicon electro-optic modulator ,” Nature (London)   435 , 325 – 327 ( 2005 ).
    [Crossref]
  7. F. Gan and F. X. Kartner , “ High-speed silicon electrooptic Modulator design ,” IEEE Photonics Technol. Lett.   17 , 1007 – 1009 ( 2005 ).
    [Crossref]
  8. http://www.rsoftinc.com .
  9. R. A. Soref and B. R. Bennett , “ Kramers-Kronig analysis of E-O switching in silicon ,” SPIE Integrated Opt. Circuit Eng   704 , 32 – 37 ( 1986 ).
  10. Silvaco Internationnal, 4701 Patrick Henry drive,Bldg 1, Santa Clara, CA 94054, http://www.silvaco.com .
  11. 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/SiO 2 waveguide:experiments and model ,” Appl. Phys. Lett.   77 , 1617 – 1619 ( 2000 ).
    [Crossref]

2005 (3)

L. Liao , D. Samara-Rubio , M. Morse , A. Liu , D. Hodge , D. Rubin , U. D. Keil , and T. Franck , “ High speed silicon mach-zehnder modulator ,” Opt. Express   13 , 3129 – 3135 ( 2005 ). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-3129 .
[Crossref] [PubMed]

Q. Xu , B. Shmidt , S. Pradhan , and M. Lipson , “ Micrometre-scale silicon electro-optic modulator ,” Nature (London)   435 , 325 – 327 ( 2005 ).
[Crossref]

F. Gan and F. X. Kartner , “ High-speed silicon electrooptic Modulator design ,” IEEE Photonics Technol. Lett.   17 , 1007 – 1009 ( 2005 ).
[Crossref]

2004 (1)

A. Liu , R. Jones , L. Liao , D. S. Rubio , D. Rubin , O. Cohen , R. Nicolaescu , and M. Paniccia , “ High-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor ,” Nature (London)   427 , 615 – 618 ( 2004 ).
[Crossref]

2003 (1)

C. E. Png , G. T. Reed , R. M. Atta , G. J. Ensell , and A. G. R. Evans , “ Development of small silicon modulators in silicon-on-insulator (SOI) ,” Proc. SPIE   4997 , 190 – 197 ( 2003 ).
[Crossref]

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/SiO 2 waveguide:experiments and model ,” Appl. Phys. Lett.   77 , 1617 – 1619 ( 2000 ).
[Crossref]

1995 (1)

C. Cocorullo , M. Iodice , I. Rendina , and P.M. Sarro , “ Silicon thermo-optical micro-modulator with 700 khz 3db bandwidth ,” IEEE Photonics Technol. Lett.   7 , 363 – 365 ( 1995 ).
[Crossref]

1986 (1)

R. A. Soref and B. R. Bennett , “ Kramers-Kronig analysis of E-O switching in silicon ,” SPIE Integrated Opt. Circuit Eng   704 , 32 – 37 ( 1986 ).

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/SiO 2 waveguide:experiments and model ,” Appl. Phys. Lett.   77 , 1617 – 1619 ( 2000 ).
[Crossref]

Atta, R. M.

C. E. Png , G. T. Reed , R. M. Atta , G. J. Ensell , and A. G. R. Evans , “ Development of small silicon modulators in silicon-on-insulator (SOI) ,” Proc. SPIE   4997 , 190 – 197 ( 2003 ).
[Crossref]

Bennett, B. R.

R. A. Soref and B. R. Bennett , “ Kramers-Kronig analysis of E-O switching in silicon ,” SPIE Integrated Opt. Circuit Eng   704 , 32 – 37 ( 1986 ).

Bennett, B.R

R. A. Soref and B.R Bennett , “ Electrooptical effects in silicon ,” IEEE J. Quantum Electron.   23 , 123 – 129 ( 198 ).
[Crossref]

Cocorullo, C.

C. Cocorullo , M. Iodice , I. Rendina , and P.M. Sarro , “ Silicon thermo-optical micro-modulator with 700 khz 3db bandwidth ,” IEEE Photonics Technol. Lett.   7 , 363 – 365 ( 1995 ).
[Crossref]

Cohen, O.

A. Liu , R. Jones , L. Liao , D. S. Rubio , D. Rubin , O. Cohen , R. Nicolaescu , and M. Paniccia , “ High-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor ,” Nature (London)   427 , 615 – 618 ( 2004 ).
[Crossref]

Ensell, G. J.

C. E. Png , G. T. Reed , R. M. Atta , G. J. Ensell , and A. G. R. Evans , “ Development of small silicon modulators in silicon-on-insulator (SOI) ,” Proc. SPIE   4997 , 190 – 197 ( 2003 ).
[Crossref]

Evans, A. G. R.

C. E. Png , G. T. Reed , R. M. Atta , G. J. Ensell , and A. G. R. Evans , “ Development of small silicon modulators in silicon-on-insulator (SOI) ,” Proc. SPIE   4997 , 190 – 197 ( 2003 ).
[Crossref]

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/SiO 2 waveguide:experiments and model ,” Appl. Phys. Lett.   77 , 1617 – 1619 ( 2000 ).
[Crossref]

Franck, T.

Gan, F.

F. Gan and F. X. Kartner , “ High-speed silicon electrooptic Modulator design ,” IEEE Photonics Technol. Lett.   17 , 1007 – 1009 ( 2005 ).
[Crossref]

Hodge, D.

Iodice, M.

C. Cocorullo , M. Iodice , I. Rendina , and P.M. Sarro , “ Silicon thermo-optical micro-modulator with 700 khz 3db bandwidth ,” IEEE Photonics Technol. Lett.   7 , 363 – 365 ( 1995 ).
[Crossref]

Jones, R.

A. Liu , R. Jones , L. Liao , D. S. Rubio , D. Rubin , O. Cohen , R. Nicolaescu , and M. Paniccia , “ High-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor ,” Nature (London)   427 , 615 – 618 ( 2004 ).
[Crossref]

Kartner, F. X.

F. Gan and F. X. Kartner , “ High-speed silicon electrooptic Modulator design ,” IEEE Photonics Technol. Lett.   17 , 1007 – 1009 ( 2005 ).
[Crossref]

Keil, U. D.

Kimerling, L. 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/SiO 2 waveguide:experiments and model ,” Appl. Phys. Lett.   77 , 1617 – 1619 ( 2000 ).
[Crossref]

Lee, K. K.

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/SiO 2 waveguide:experiments and model ,” Appl. Phys. Lett.   77 , 1617 – 1619 ( 2000 ).
[Crossref]

Liao, L.

L. Liao , D. Samara-Rubio , M. Morse , A. Liu , D. Hodge , D. Rubin , U. D. Keil , and T. Franck , “ High speed silicon mach-zehnder modulator ,” Opt. Express   13 , 3129 – 3135 ( 2005 ). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-3129 .
[Crossref] [PubMed]

A. Liu , R. Jones , L. Liao , D. S. Rubio , D. Rubin , O. Cohen , R. Nicolaescu , and M. Paniccia , “ High-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor ,” Nature (London)   427 , 615 – 618 ( 2004 ).
[Crossref]

Lim, D. R.

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/SiO 2 waveguide:experiments and model ,” Appl. Phys. Lett.   77 , 1617 – 1619 ( 2000 ).
[Crossref]

Lipson, M.

Q. Xu , B. Shmidt , S. Pradhan , and M. Lipson , “ Micrometre-scale silicon electro-optic modulator ,” Nature (London)   435 , 325 – 327 ( 2005 ).
[Crossref]

Liu, A.

L. Liao , D. Samara-Rubio , M. Morse , A. Liu , D. Hodge , D. Rubin , U. D. Keil , and T. Franck , “ High speed silicon mach-zehnder modulator ,” Opt. Express   13 , 3129 – 3135 ( 2005 ). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-3129 .
[Crossref] [PubMed]

A. Liu , R. Jones , L. Liao , D. S. Rubio , D. Rubin , O. Cohen , R. Nicolaescu , and M. Paniccia , “ High-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor ,” Nature (London)   427 , 615 – 618 ( 2004 ).
[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/SiO 2 waveguide:experiments and model ,” Appl. Phys. Lett.   77 , 1617 – 1619 ( 2000 ).
[Crossref]

Morse, M.

Nicolaescu, R.

A. Liu , R. Jones , L. Liao , D. S. Rubio , D. Rubin , O. Cohen , R. Nicolaescu , and M. Paniccia , “ High-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor ,” Nature (London)   427 , 615 – 618 ( 2004 ).
[Crossref]

Paniccia, M.

A. Liu , R. Jones , L. Liao , D. S. Rubio , D. Rubin , O. Cohen , R. Nicolaescu , and M. Paniccia , “ High-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor ,” Nature (London)   427 , 615 – 618 ( 2004 ).
[Crossref]

Png, C. E.

C. E. Png , G. T. Reed , R. M. Atta , G. J. Ensell , and A. G. R. Evans , “ Development of small silicon modulators in silicon-on-insulator (SOI) ,” Proc. SPIE   4997 , 190 – 197 ( 2003 ).
[Crossref]

Pradhan, S.

Q. Xu , B. Shmidt , S. Pradhan , and M. Lipson , “ Micrometre-scale silicon electro-optic modulator ,” Nature (London)   435 , 325 – 327 ( 2005 ).
[Crossref]

Reed, G. T.

C. E. Png , G. T. Reed , R. M. Atta , G. J. Ensell , and A. G. R. Evans , “ Development of small silicon modulators in silicon-on-insulator (SOI) ,” Proc. SPIE   4997 , 190 – 197 ( 2003 ).
[Crossref]

Rendina, I.

C. Cocorullo , M. Iodice , I. Rendina , and P.M. Sarro , “ Silicon thermo-optical micro-modulator with 700 khz 3db bandwidth ,” IEEE Photonics Technol. Lett.   7 , 363 – 365 ( 1995 ).
[Crossref]

Rubin, D.

L. Liao , D. Samara-Rubio , M. Morse , A. Liu , D. Hodge , D. Rubin , U. D. Keil , and T. Franck , “ High speed silicon mach-zehnder modulator ,” Opt. Express   13 , 3129 – 3135 ( 2005 ). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-3129 .
[Crossref] [PubMed]

A. Liu , R. Jones , L. Liao , D. S. Rubio , D. Rubin , O. Cohen , R. Nicolaescu , and M. Paniccia , “ High-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor ,” Nature (London)   427 , 615 – 618 ( 2004 ).
[Crossref]

Rubio, D. S.

A. Liu , R. Jones , L. Liao , D. S. Rubio , D. Rubin , O. Cohen , R. Nicolaescu , and M. Paniccia , “ High-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor ,” Nature (London)   427 , 615 – 618 ( 2004 ).
[Crossref]

Samara-Rubio, D.

Sarro, P.M.

C. Cocorullo , M. Iodice , I. Rendina , and P.M. Sarro , “ Silicon thermo-optical micro-modulator with 700 khz 3db bandwidth ,” IEEE Photonics Technol. Lett.   7 , 363 – 365 ( 1995 ).
[Crossref]

Shmidt, B.

Q. Xu , B. Shmidt , S. Pradhan , and M. Lipson , “ Micrometre-scale silicon electro-optic modulator ,” Nature (London)   435 , 325 – 327 ( 2005 ).
[Crossref]

Soref, R. A.

R. A. Soref and B. R. Bennett , “ Kramers-Kronig analysis of E-O switching in silicon ,” SPIE Integrated Opt. Circuit Eng   704 , 32 – 37 ( 1986 ).

R. A. Soref and B.R Bennett , “ Electrooptical effects in silicon ,” IEEE J. Quantum Electron.   23 , 123 – 129 ( 198 ).
[Crossref]

Xu, Q.

Q. Xu , B. Shmidt , S. Pradhan , and M. Lipson , “ Micrometre-scale silicon electro-optic modulator ,” Nature (London)   435 , 325 – 327 ( 2005 ).
[Crossref]

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/SiO 2 waveguide:experiments and model ,” Appl. Phys. Lett.   77 , 1617 – 1619 ( 2000 ).
[Crossref]

IEEE J. Quantum Electron. (1)

R. A. Soref and B.R Bennett , “ Electrooptical effects in silicon ,” IEEE J. Quantum Electron.   23 , 123 – 129 ( 198 ).
[Crossref]

IEEE Photonics Technol. Lett. (2)

C. Cocorullo , M. Iodice , I. Rendina , and P.M. Sarro , “ Silicon thermo-optical micro-modulator with 700 khz 3db bandwidth ,” IEEE Photonics Technol. Lett.   7 , 363 – 365 ( 1995 ).
[Crossref]

F. Gan and F. X. Kartner , “ High-speed silicon electrooptic Modulator design ,” IEEE Photonics Technol. Lett.   17 , 1007 – 1009 ( 2005 ).
[Crossref]

Nature (London) (2)

Q. Xu , B. Shmidt , S. Pradhan , and M. Lipson , “ Micrometre-scale silicon electro-optic modulator ,” Nature (London)   435 , 325 – 327 ( 2005 ).
[Crossref]

A. Liu , R. Jones , L. Liao , D. S. Rubio , D. Rubin , O. Cohen , R. Nicolaescu , and M. Paniccia , “ High-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor ,” Nature (London)   427 , 615 – 618 ( 2004 ).
[Crossref]

Opt. Express (1)

Proc. SPIE (1)

C. E. Png , G. T. Reed , R. M. Atta , G. J. Ensell , and A. G. R. Evans , “ Development of small silicon modulators in silicon-on-insulator (SOI) ,” Proc. SPIE   4997 , 190 – 197 ( 2003 ).
[Crossref]

SPIE Integrated Opt. Circuit Eng (1)

R. A. Soref and B. R. Bennett , “ Kramers-Kronig analysis of E-O switching in silicon ,” SPIE Integrated Opt. Circuit Eng   704 , 32 – 37 ( 1986 ).

Other (2)

Silvaco Internationnal, 4701 Patrick Henry drive,Bldg 1, Santa Clara, CA 94054, http://www.silvaco.com .

http://www.rsoftinc.com .

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Figures (9)

Fig. 1.
Fig. 1.

Schematic cross-section of SOI strip waveguide for 1.55 μm wavelength with an integrated three terminal p-n diode for plasma dispersion modulation.

Fig. 2.
Fig. 2.

Change in absorption coefficient in the rib region for different reverse bias voltages.

Fig. 3.
Fig. 3.

Losses induced by one phase shifter of 2.5 mm for different voltages.

Fig. 4.
Fig. 4.

Refractive index change in the ridge for different voltages.

Fig. 5.
Fig. 5.

Phase shift induced by the modulator for a length L=2.5 mm.

Fig. 6.
Fig. 6.

Current against transient time when switching from 5 to 10 volts and from 5 to 0 volts for a voltage rise time of 5 ps.

Fig. 7.
Fig. 7.

Current against transient time for different square wave voltage functions rise time.

Fig. 8.
Fig. 8.

”Turn On” Phase shift induced by the MZI against transient time.

Fig. 9.
Fig. 9.

”Turn Off” Phase shift induced by the MZI against transient time.

Tables (3)

Tables Icon

Table 1. Silicon plasma dispersion modulators recently reported in the literature ((*) Fabricated device).

Tables Icon

Table 2. Optical simulation parameters.

Tables Icon

Table 3. Electrical simulation parameters.

Equations (4)

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Δn eff = λ 2 L π
Δn = Δn e + Δn h = [ 8.8 × 10 22 × Δ N e + 8.5 × 10 22 × ΔN h 0.8 ]
Δ α = Δ α e + Δ α h = 8.5 × 10 18 × Δ N e + 6 × 10 18 × Δ N h
C J = A S N A N D 2 ( N A + N D ) × ( ϕ B + V D )

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