Abstract

Experimental results for refractive index variation induced by depletion in a silicon structure integrated in a PIN diode are reported. Thermal effect has been dissociated from the electrical contribution due to carrier density variation induced by a reverse bias voltage. A figure of merit VπLπ of 3.1 V.cm has been obtained at 1.55μm. Numerical simulations show a good agreement between experimental and theoretical index variations.

© 2006 Optical Society of America

1. Introduction

Silicon microphotonics has generated an increasing interest in the recent years. Integrating optics and electronics on a same chip would allow the enhancement of integrated circuit (IC) performances, whereas telecommunications could benefit of the development of low cost solutions for high-speed optoelectronic devices and systems. One of the key elements for the development of silicon microphotonics is the realization of active devices in particular high bandwidth integrated optical modulators [1].

Although several ways have been investigated for high speed optical modulation in Si or Si based device, such as the use of Pockels effect in strained silicon [2] or in SiGe superlattices [3], the quantum-confined Stark effect in silicon-germanium/germanium quantum well structures [4], most studies are based on free carrier concentration variations, which are responsible for local refractive index variations and then phase modulation of a guided wave traveling through the active region [5–10].

To obtain carrier concentration variation, injection in PIN diodes has been widely used, but this solution generally leads to limited bandwidth due to carrier recombination time. Operation close to 1Gbit/s has been recently demonstrated with a ring resonator based modulator, with rise and fall times of 200 and 150 ps, respectively [5]. Carrier accumulation near the gate dielectric of a MOS capacitor permits to overcome this limitation. Data transmission at 10 Gbit/s has been demonstrated [6]. Another way to achieve high frequency operation is to use carrier depletion in a reverse biased PIN diode. A SiGe/Si Modulation-Doped Multiple Quantum Well (MD-MQW) structure has been proposed. Phase modulation has been experimentally demonstrated [7], and the intrinsic frequency response theoretically investigated [8]. The device speed mainly depends on the time needed for carriers to escape from and to be captured into the quantum wells (QWs). Rise time and fall time smaller than 10 ps have been estimated.

In this paper an original all-silicon device for phase modulation is described. It is based on a doped layer inserted in a PIN diode. Like in the SiGe/Si MD-MQW structure, carrier depletion is used, but in the all-silicon device, carriers do not encounter any barrier and ultra short response times, lower than 2 ps have been estimated [9]. Experimental evidence for phase modulation in such a structure is here reported.

2. Device design

The active region of the structure is schematically shown in Fig. 1.

 

Fig. 1. Device structure: a highly doped P+ layer is inserted in a silicon PIN diode.

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It is based on a doped P+ silicon layer introduced as source of free holes in the core of a non-intentionally doped (nid) Si region (~1016cm-3). This structure is placed between P+ and N+ regions which form the N and P parts of the PIN diode. This stack is epitaxially grown on a silicon-on-insulator (SOI) substrate to constitute a planar waveguide created by the refractive index difference between silicon and silicon oxide.

At equilibrium, holes are electrostatically localized in the P+ layer. When a reverse bias voltage is applied to the diode, the space-charge expands through the device. Holes are swept out from the active region thanks to the electrical field. Carrier density variations are responsible for refractive index variations, and thus for a phase shift of the optical guided mode propagating through the device.

In the device under consideration, the active region has been epitaxially grown by Reduced-Pressure Chemical Vapor Deposition (RP-CVD) on a full silicon-on-insulator (SOI) wafer. The P+ layer in the middle of the structure is about 150 nm thick, with a doping level > 5.1018 cm-3. The P and N par of the PIN diode are 50 nm thick, with a doping concentration of 1018 cm-3.

The overall sample thickness is 500 nm, which is closely compatible with the integration in a rib SOI microwaveguide. The layer stack is locally etched down to the N+ layer, to get the bottom electrical contact. The device is covered by a silicon oxide layer in which apertures are etched for the electrical contacts. Good optical quality facets are obtained by cleavage and lead to setting up a Fabry-Perot cavity. The sample length is 2.01 mm.

Classical technological processes have been used, i.e. optical lithography, etching, metal deposition and lift-off, to realize the whole device with contact metallization. To simplify the device fabrication, the metal was deposited above the waveguide in this test device, although this is not favorable for low optical losses. For the modulator integration in a single mode microwaveguide, the metal has to be placed not above but close to the waveguide, while electrical continuity can be ensured by a thin P+ layer, as described in [10] for a SiGe/Si modulator that presents a similar tradeoff between low losses and high RC-due cutoff frequency.

3. Experiment

The phase modulation measurement relies on the shift of Fabry-Perot (FP) fringes when a bias voltage is applied on the diode. The FP cavity is formed by the optical waveguide between the cleaved facets of the sample. The resonance condition gives the wavelength at each maximum of the transmission spectrum as a function of the device length and of the effective index of the guided mode (Eq. (1)).

2neff(λ)L=

A first order approximation then gives the relation between the effective index variation of the guided mode and the induced shift of a resonance wavelength Δλ, which is experimentally determined for different values of the bias voltage:

Δneff(λ)=Δλλng(λ)

ng is the group index which is determined according to Eq. (3), where Δλp is the experimental wavelength difference between two successive resonance peaks, and L is the device length.

ng(λp)=λp22LΔλp

The experimental set-up uses a tunable laser in the 1550 nm range. A linearly polarized light beam is coupled into the waveguide using a polarization maintaining lensed-fiber. The output light is collected by an objective and is measured with a IR detector. Electrical probes are used to bias the diode.

As a typical example, two transmission spectra of the device recorded for wavelengths close to 1.55μm and for bias voltages of 0 and -4V respectively are reported in Fig. 2. The resonance wavelength shift is clearly visible. About 20 periods are taken into account in the experimental determination, to minimize experimental unreliability. Furthermore it can be noticed that the fringe contrast increases with the reverse bias, which is due to the free-carrier absorption decrease when holes are swept out of the active region.

 

Fig. 2. Example of experimental transmission spectra of the device recorded for 0V and - 4V.

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The effective index variation with bias voltage ranging from 0 to -6V is deduced using Eq. (2), and the experimental results are plotted in Fig 3. The effective index variation increases as the reverse bias voltage increases. An index variation of 1.7.10-4 is obtained between 0 and -6V.

 

Fig. 3. Experimental effective index variation versus PIN bias voltage: measured effective index variation, electrical (due to hole depletion) and thermal contributions.

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This index variation may have two contributions: the first one from hole depletion in the structure and the second one from thermal effect related to the electrical power dissipated in the device which becomes more important as the reverse bias increases. Indeed, the recorded current/voltage characteristic shows a slight increase of the electrical current before avalanche breakdown (Fig. 4).

 

Fig. 4. Experimental current/voltage characteristic of the diode.

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To realize a high speed modulator, thermal contribution cannot be used, and it acts as a parasitic effect. Those two contributions have been dissociated using the method presented in Ref. [4], and results are reported in Fig. 3. It can be seen that there is no thermal contribution to the measured index variation from 0 to -2V, and it still represents a minor part up to -6V. Electrical contribution to the index variation due to carrier depletion in the diode reaches 1.10-4 at -4V. To evaluate the modulation phase efficiency a figure of merit is usually defined as the product VπLπ, where Vπ and Lπ are respectively the applied voltage and the length required to obtain a π phase shift of the guided wave. Neglecting dispersion effect, Lπ can be determined by the following Eq.:

Lπ=λ2Δneff

The lower the VπLπ product, the more efficient the phase shifter.

The electrical contribution to the index variation of 1.10-4 at -4V leads to VπLπ=3.1 V.cm. This is only slightly lower than the experimental index variation measured in a SiGe-Si Modulation-Doped Multiple Quantum Well (MD-MQW) structure which was 1.4.10-4 at -4V, leading to a VπLπ value of 2.2V.cm [7] and compares favourably with published values for the MOS capacitor based modulator (VπLπ = 3.3V.cm [6]).

The result presented here forms the first experimental evidence for index modulation by carrier depletion in all silicon structure. The effective index variation in such a phase shifter could be improved by optimization of the structure, which requires numerical simulations. In a first step comparison between experiments and effective index variation modeling has been performed.

4. Structure modeling

Calculation of the hole distributions have been performed using a physical device simulation package (DESSIS-ISE [11]). This software performs numerical resolution of Poisson, carrier density continuity, and drift-diffusion equations. In these simulations, Fermi-Dirac statistic is used. Temperature and doping-dependent models are employed for carrier mobility, taking into account high field saturation. Auger and Shockley-Read-Hall (SRH) recombination mechanisms are included. The refractive index variation and the absorption losses in silicon at λ=1.55 μm due to free carriers are deduced from hole density distribution using the following formula [12]:

Δn=8,8.1022ΔN8,5.1018ΔP0,8
Δα=8,5.1018ΔN+6,0.1018ΔP

where ΔN and ΔP are the electron and hole concentration variations (cm-3) respectively.

The local refractive index variations determined from the calculated hole density profiles using Eq. (5) have been introduced in a mode solver [13] in order to determine the effective index variation of the optical mode propagating through to the multilayer stack.

The structure properties are given for TE light polarization and at 1.55 μm wavelength. For the optical calculations, the refractive indices of Si and SiO2 have been taken equal to 3.475 and 1.45 respectively.

The theoretical effective index change due to hole depletion has been evaluated and is plotted in Fig. 5.

 

Fig. 5. Theoretical effective index variation versus PIN bias voltage.

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The general behavior of the experimental and modeling effective index variations with PIN bias are very similar. Theoretical index variation is a bit greater, but the difference between the results can be explained by the deviation of the real sample parameters from those used for modeling. An effective index variation of 1.8 10-4 is expected at -4V.

5. Conclusion

A new kind of all-silicon phase shifter, based on carrier depletion in a doped layer inserted inside a PIN diode has been made. Experimental evidence of efficient phase shift has been obtained with such a structure. Thermal effects are negligible for bias voltages of a few volts. The contribution arising from hole depletion in the structure yields a figure of merit VπLπ equal to 3.1 V.cm. Process and design optimizations will be performed to further increase this phase shifter efficiency. The integration of the modulator in a single mode microwaveguide requires careful precaution to obtain both low losses and high frequency operation. The tradeoff between optical losses and RC cutoff frequency has been studied for a SiGe/Si modulator with similar tradeoff [7].

Such a phase shifter structure is well suited for the realization of integrated high speed modulators.

Acknowledgments

The authors would like to thank Daniel Bouchier from IEF and Joaquin Torres and Patrick Cogez from ST Microelectronics for fruitful discussions. The authors are very grateful to the staff of the IEF/CTU and CEA-LETI clean rooms. This work is supported by the French RMNT project CAURICO.

References and links

1. G.T. Reed and C.E. Jason Png, “Silicon optical modulators,” Materials Todays 40–50, (2005). [CrossRef]  

2. R.S. Jacobsen, K.N. Andersen, P.I. Borel, J. Page-Pedersen, L.H. Frandsen, O. Hansen, M. Kristensen, A.V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsidri, and A. Bjarklev, “Strained silicon as a new electro-optical material,” Nature 441, 199–202 (2006). [CrossRef]   [PubMed]  

3. P. Yu, J. Wu, and B. Zhu “Enhanced quantum-confined Pockels effect in SiGe superlattices,” Phys. Rev. B 73,235328 (2006). [CrossRef]  

4. Y. Kuo, Y. Lee, Y. Ge, S. Ren, J. Roth, T. Kamins, D. Miller, and J. Harris “Strong quantum-confined Stark effect in germanium quantum well structures on silicon,” Nature 437, 1334–1336 (2005). [CrossRef]   [PubMed]  

5. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometer-scale silicon electro-optic modulator,” Nature 435, 325–327 (2005). [CrossRef]   [PubMed]  

6. 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). [CrossRef]   [PubMed]  

7. A. Lupu, D. Marris, D. Pascal, J.-L. Cercus, A. Cordat, V. L. Thanh, and S. Laval, “Experimental evidence for index modulation by carrier depletion in SiGe/Si multiple quantum well structures,” App. Phys. Lett. 85, 887–889, (2004). [CrossRef]  

8. D. Marris, E. Cassan, and L. Vivien, “Time response analysis of SiGe/Si modulation-doped multiple quantum well structures for optical modulation,” J. Appl. Phys. 96, 6109–6112, (2004). [CrossRef]  

9. D. Marris-Morini, X. Le Roux, D. Pascal, L. Vivien, E. Cassan, J.M. Fédéli, J.F. Damlencourt, D. Bouville, J. Palomo, and S. Laval, “High speed all-silicon modulation-doped optical modulator,” presented at the EMRS-spring meeting, Nice, 29 mai-2 june 2006.

10. S. Maine, D. Marris-Morini, L. Vivien, D. Pascal, E. Cassan, and S. Laval, “Design optimisation of SiGe/Si:modulation-doped multiple quantum well modulator for high speed operation,” in Proc SPIE 6183 (2006), 618360D1-6. [CrossRef]  

11. ISE software, http://www.ise.com/.

12. R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. QE-23123–129 (1987). [CrossRef]  

13. PhotonDesign software, http://www.photond.com.

References

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  1. G. T. Reed, and C. E. J. Png, "Silicon optical modulators," Materials Todays 40-50, (2005).
    [CrossRef]
  2. R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Page-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsidri, and A. Bjarklev, "Strained silicon as a new electro-optical material," Nature 441, 199-202 (2006).
    [CrossRef] [PubMed]
  3. P. Yu, J. Wu, and B. Zhu "Enhanced quantum-confined Pockels effect in SiGe superlattices," Phys. Rev. B 73, 235328 (2006).
    [CrossRef]
  4. Y. Kuo, Y. Lee, Y. Ge, S. Ren, J. Roth, T. Kamins, D. Miller, and J. Harris "Strong quantum-confined Stark effect in germanium quantum well structures on silicon," Nature 437, 1334-1336 (2005).
    [CrossRef] [PubMed]
  5. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometer-scale silicon electro-optic modulator," Nature 435, 325-327 (2005).
    [CrossRef] [PubMed]
  6. 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).
    [CrossRef] [PubMed]
  7. A. Lupu, D. Marris, D. Pascal, J.-L. Cercus, A. Cordat, V. L. Thanh, and S. Laval, "Experimental evidence for index modulation by carrier depletion in SiGe/Si multiple quantum well structures," Appl. Phys. Lett. 85, 887-889, (2004).
    [CrossRef]
  8. D. Marris, E. Cassan, and L. Vivien, "Time response analysis of SiGe/Si modulation-doped multiple quantum well structures for optical modulation," J. Appl. Phys. 96, 6109-6112, (2004).
    [CrossRef]
  9. D. Marris-Morini, X. Le Roux, D. Pascal, L. Vivien, E. Cassan, J. M. Fédéli, J. F. Damlencourt, D. Bouville, J. Palomo, and S. Laval, "High speed all-silicon modulation-doped optical modulator," presented at the EMRS-spring meeting, Nice, 29 mai-2 june 2006.
  10. S. Maine, D. Marris-Morini, L. Vivien, D. Pascal, E. Cassan, and S. Laval, "Design optimisation of SiGe/Si:modulation-doped multiple quantum well modulator for high speed operation," in Integrated Optics, Silicon Photonics, and Photonic Integrated Circuits, G. C. Righini, ed., Proc SPIE 6183 (2006), 618360D1-6.
    [CrossRef]
  11. ISE software, http://www.ise.com/.
  12. R. Soref, and B. Bennett, "Electrooptical effects in silicon," IEEE J. Quantum Electron. QE-23123-129 (1987).
    [CrossRef]
  13. PhotonDesign software, http://www.photond.com.

2006 (2)

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Page-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsidri, and A. Bjarklev, "Strained silicon as a new electro-optical material," Nature 441, 199-202 (2006).
[CrossRef] [PubMed]

P. Yu, J. Wu, and B. Zhu "Enhanced quantum-confined Pockels effect in SiGe superlattices," Phys. Rev. B 73, 235328 (2006).
[CrossRef]

2005 (3)

Y. Kuo, Y. Lee, Y. Ge, S. Ren, J. Roth, T. Kamins, D. Miller, and J. Harris "Strong quantum-confined Stark effect in germanium quantum well structures on silicon," Nature 437, 1334-1336 (2005).
[CrossRef] [PubMed]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometer-scale silicon electro-optic modulator," Nature 435, 325-327 (2005).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

2004 (2)

A. Lupu, D. Marris, D. Pascal, J.-L. Cercus, A. Cordat, V. L. Thanh, and S. Laval, "Experimental evidence for index modulation by carrier depletion in SiGe/Si multiple quantum well structures," Appl. Phys. Lett. 85, 887-889, (2004).
[CrossRef]

D. Marris, E. Cassan, and L. Vivien, "Time response analysis of SiGe/Si modulation-doped multiple quantum well structures for optical modulation," J. Appl. Phys. 96, 6109-6112, (2004).
[CrossRef]

1987 (1)

R. Soref, and B. Bennett, "Electrooptical effects in silicon," IEEE J. Quantum Electron. QE-23123-129 (1987).
[CrossRef]

Andersen, K. N.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Page-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsidri, and A. Bjarklev, "Strained silicon as a new electro-optical material," Nature 441, 199-202 (2006).
[CrossRef] [PubMed]

Bennett, B.

R. Soref, and B. Bennett, "Electrooptical effects in silicon," IEEE J. Quantum Electron. QE-23123-129 (1987).
[CrossRef]

Bjarklev, A.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Page-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsidri, and A. Bjarklev, "Strained silicon as a new electro-optical material," Nature 441, 199-202 (2006).
[CrossRef] [PubMed]

Borel, P. I.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Page-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsidri, and A. Bjarklev, "Strained silicon as a new electro-optical material," Nature 441, 199-202 (2006).
[CrossRef] [PubMed]

Cassan, E.

D. Marris, E. Cassan, and L. Vivien, "Time response analysis of SiGe/Si modulation-doped multiple quantum well structures for optical modulation," J. Appl. Phys. 96, 6109-6112, (2004).
[CrossRef]

Cercus, J.-L.

A. Lupu, D. Marris, D. Pascal, J.-L. Cercus, A. Cordat, V. L. Thanh, and S. Laval, "Experimental evidence for index modulation by carrier depletion in SiGe/Si multiple quantum well structures," Appl. Phys. Lett. 85, 887-889, (2004).
[CrossRef]

Cordat, A.

A. Lupu, D. Marris, D. Pascal, J.-L. Cercus, A. Cordat, V. L. Thanh, and S. Laval, "Experimental evidence for index modulation by carrier depletion in SiGe/Si multiple quantum well structures," Appl. Phys. Lett. 85, 887-889, (2004).
[CrossRef]

Franck, T.

Frandsen, L. H.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Page-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsidri, and A. Bjarklev, "Strained silicon as a new electro-optical material," Nature 441, 199-202 (2006).
[CrossRef] [PubMed]

Ge, Y.

Y. Kuo, Y. Lee, Y. Ge, S. Ren, J. Roth, T. Kamins, D. Miller, and J. Harris "Strong quantum-confined Stark effect in germanium quantum well structures on silicon," Nature 437, 1334-1336 (2005).
[CrossRef] [PubMed]

Hansen, O.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Page-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsidri, and A. Bjarklev, "Strained silicon as a new electro-optical material," Nature 441, 199-202 (2006).
[CrossRef] [PubMed]

Harris, J.

Y. Kuo, Y. Lee, Y. Ge, S. Ren, J. Roth, T. Kamins, D. Miller, and J. Harris "Strong quantum-confined Stark effect in germanium quantum well structures on silicon," Nature 437, 1334-1336 (2005).
[CrossRef] [PubMed]

Hodge, D.

Jacobsen, R. S.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Page-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsidri, and A. Bjarklev, "Strained silicon as a new electro-optical material," Nature 441, 199-202 (2006).
[CrossRef] [PubMed]

Kamins, T.

Y. Kuo, Y. Lee, Y. Ge, S. Ren, J. Roth, T. Kamins, D. Miller, and J. Harris "Strong quantum-confined Stark effect in germanium quantum well structures on silicon," Nature 437, 1334-1336 (2005).
[CrossRef] [PubMed]

Keil, U. D.

Kristensen, M.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Page-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsidri, and A. Bjarklev, "Strained silicon as a new electro-optical material," Nature 441, 199-202 (2006).
[CrossRef] [PubMed]

Kuo, Y.

Y. Kuo, Y. Lee, Y. Ge, S. Ren, J. Roth, T. Kamins, D. Miller, and J. Harris "Strong quantum-confined Stark effect in germanium quantum well structures on silicon," Nature 437, 1334-1336 (2005).
[CrossRef] [PubMed]

Laval, S.

A. Lupu, D. Marris, D. Pascal, J.-L. Cercus, A. Cordat, V. L. Thanh, and S. Laval, "Experimental evidence for index modulation by carrier depletion in SiGe/Si multiple quantum well structures," Appl. Phys. Lett. 85, 887-889, (2004).
[CrossRef]

Lavrinenko, A. V.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Page-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsidri, and A. Bjarklev, "Strained silicon as a new electro-optical material," Nature 441, 199-202 (2006).
[CrossRef] [PubMed]

Lee, Y.

Y. Kuo, Y. Lee, Y. Ge, S. Ren, J. Roth, T. Kamins, D. Miller, and J. Harris "Strong quantum-confined Stark effect in germanium quantum well structures on silicon," Nature 437, 1334-1336 (2005).
[CrossRef] [PubMed]

Liao, L.

Lipson, M.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometer-scale silicon electro-optic modulator," Nature 435, 325-327 (2005).
[CrossRef] [PubMed]

Liu, A.

Lupu, A.

A. Lupu, D. Marris, D. Pascal, J.-L. Cercus, A. Cordat, V. L. Thanh, and S. Laval, "Experimental evidence for index modulation by carrier depletion in SiGe/Si multiple quantum well structures," Appl. Phys. Lett. 85, 887-889, (2004).
[CrossRef]

Marris, D.

A. Lupu, D. Marris, D. Pascal, J.-L. Cercus, A. Cordat, V. L. Thanh, and S. Laval, "Experimental evidence for index modulation by carrier depletion in SiGe/Si multiple quantum well structures," Appl. Phys. Lett. 85, 887-889, (2004).
[CrossRef]

D. Marris, E. Cassan, and L. Vivien, "Time response analysis of SiGe/Si modulation-doped multiple quantum well structures for optical modulation," J. Appl. Phys. 96, 6109-6112, (2004).
[CrossRef]

Miller, D.

Y. Kuo, Y. Lee, Y. Ge, S. Ren, J. Roth, T. Kamins, D. Miller, and J. Harris "Strong quantum-confined Stark effect in germanium quantum well structures on silicon," Nature 437, 1334-1336 (2005).
[CrossRef] [PubMed]

Morse, M.

Moulin, G.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Page-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsidri, and A. Bjarklev, "Strained silicon as a new electro-optical material," Nature 441, 199-202 (2006).
[CrossRef] [PubMed]

Ou, H.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Page-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsidri, and A. Bjarklev, "Strained silicon as a new electro-optical material," Nature 441, 199-202 (2006).
[CrossRef] [PubMed]

Page-Pedersen, J.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Page-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsidri, and A. Bjarklev, "Strained silicon as a new electro-optical material," Nature 441, 199-202 (2006).
[CrossRef] [PubMed]

Pascal, D.

A. Lupu, D. Marris, D. Pascal, J.-L. Cercus, A. Cordat, V. L. Thanh, and S. Laval, "Experimental evidence for index modulation by carrier depletion in SiGe/Si multiple quantum well structures," Appl. Phys. Lett. 85, 887-889, (2004).
[CrossRef]

Peucheret, C.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Page-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsidri, and A. Bjarklev, "Strained silicon as a new electro-optical material," Nature 441, 199-202 (2006).
[CrossRef] [PubMed]

Pradhan, S.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometer-scale silicon electro-optic modulator," Nature 435, 325-327 (2005).
[CrossRef] [PubMed]

Ren, S.

Y. Kuo, Y. Lee, Y. Ge, S. Ren, J. Roth, T. Kamins, D. Miller, and J. Harris "Strong quantum-confined Stark effect in germanium quantum well structures on silicon," Nature 437, 1334-1336 (2005).
[CrossRef] [PubMed]

Roth, J.

Y. Kuo, Y. Lee, Y. Ge, S. Ren, J. Roth, T. Kamins, D. Miller, and J. Harris "Strong quantum-confined Stark effect in germanium quantum well structures on silicon," Nature 437, 1334-1336 (2005).
[CrossRef] [PubMed]

Rubin, D.

Samara-Rubio, D.

Schmidt, B.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometer-scale silicon electro-optic modulator," Nature 435, 325-327 (2005).
[CrossRef] [PubMed]

Soref, R.

R. Soref, and B. Bennett, "Electrooptical effects in silicon," IEEE J. Quantum Electron. QE-23123-129 (1987).
[CrossRef]

Thanh, V. L.

A. Lupu, D. Marris, D. Pascal, J.-L. Cercus, A. Cordat, V. L. Thanh, and S. Laval, "Experimental evidence for index modulation by carrier depletion in SiGe/Si multiple quantum well structures," Appl. Phys. Lett. 85, 887-889, (2004).
[CrossRef]

Vivien, L.

D. Marris, E. Cassan, and L. Vivien, "Time response analysis of SiGe/Si modulation-doped multiple quantum well structures for optical modulation," J. Appl. Phys. 96, 6109-6112, (2004).
[CrossRef]

Wu, J.

P. Yu, J. Wu, and B. Zhu "Enhanced quantum-confined Pockels effect in SiGe superlattices," Phys. Rev. B 73, 235328 (2006).
[CrossRef]

Xu, Q.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometer-scale silicon electro-optic modulator," Nature 435, 325-327 (2005).
[CrossRef] [PubMed]

Yu, P.

P. Yu, J. Wu, and B. Zhu "Enhanced quantum-confined Pockels effect in SiGe superlattices," Phys. Rev. B 73, 235328 (2006).
[CrossRef]

Zhu, B.

P. Yu, J. Wu, and B. Zhu "Enhanced quantum-confined Pockels effect in SiGe superlattices," Phys. Rev. B 73, 235328 (2006).
[CrossRef]

Zsidri, B.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Page-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsidri, and A. Bjarklev, "Strained silicon as a new electro-optical material," Nature 441, 199-202 (2006).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

A. Lupu, D. Marris, D. Pascal, J.-L. Cercus, A. Cordat, V. L. Thanh, and S. Laval, "Experimental evidence for index modulation by carrier depletion in SiGe/Si multiple quantum well structures," Appl. Phys. Lett. 85, 887-889, (2004).
[CrossRef]

IEEE J. Quantum Electron. (1)

R. Soref, and B. Bennett, "Electrooptical effects in silicon," IEEE J. Quantum Electron. QE-23123-129 (1987).
[CrossRef]

J. Appl. Phys. (1)

D. Marris, E. Cassan, and L. Vivien, "Time response analysis of SiGe/Si modulation-doped multiple quantum well structures for optical modulation," J. Appl. Phys. 96, 6109-6112, (2004).
[CrossRef]

Nature (3)

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Page-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsidri, and A. Bjarklev, "Strained silicon as a new electro-optical material," Nature 441, 199-202 (2006).
[CrossRef] [PubMed]

Y. Kuo, Y. Lee, Y. Ge, S. Ren, J. Roth, T. Kamins, D. Miller, and J. Harris "Strong quantum-confined Stark effect in germanium quantum well structures on silicon," Nature 437, 1334-1336 (2005).
[CrossRef] [PubMed]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometer-scale silicon electro-optic modulator," Nature 435, 325-327 (2005).
[CrossRef] [PubMed]

Opt. Express (1)

Phys. Rev. B (1)

P. Yu, J. Wu, and B. Zhu "Enhanced quantum-confined Pockels effect in SiGe superlattices," Phys. Rev. B 73, 235328 (2006).
[CrossRef]

Other (5)

D. Marris-Morini, X. Le Roux, D. Pascal, L. Vivien, E. Cassan, J. M. Fédéli, J. F. Damlencourt, D. Bouville, J. Palomo, and S. Laval, "High speed all-silicon modulation-doped optical modulator," presented at the EMRS-spring meeting, Nice, 29 mai-2 june 2006.

S. Maine, D. Marris-Morini, L. Vivien, D. Pascal, E. Cassan, and S. Laval, "Design optimisation of SiGe/Si:modulation-doped multiple quantum well modulator for high speed operation," in Integrated Optics, Silicon Photonics, and Photonic Integrated Circuits, G. C. Righini, ed., Proc SPIE 6183 (2006), 618360D1-6.
[CrossRef]

ISE software, http://www.ise.com/.

PhotonDesign software, http://www.photond.com.

G. T. Reed, and C. E. J. Png, "Silicon optical modulators," Materials Todays 40-50, (2005).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Device structure: a highly doped P+ layer is inserted in a silicon PIN diode.

Fig. 2.
Fig. 2.

Example of experimental transmission spectra of the device recorded for 0V and - 4V.

Fig. 3.
Fig. 3.

Experimental effective index variation versus PIN bias voltage: measured effective index variation, electrical (due to hole depletion) and thermal contributions.

Fig. 4.
Fig. 4.

Experimental current/voltage characteristic of the diode.

Fig. 5.
Fig. 5.

Theoretical effective index variation versus PIN bias voltage.

Equations (6)

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

2 n eff ( λ ) L =
Δ n eff ( λ ) = Δ λ λ n g ( λ )
n g ( λ p ) = λ p 2 2 L Δ λ p
L π = λ 2 Δ n eff
Δ n = 8,8 . 10 22 Δ N 8,5 . 10 18 Δ P 0,8
Δ α = 8,5 . 10 18 Δ N + 6,0 . 10 18 Δ P

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