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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 10 — May. 20, 2013
  • pp: 12699–12712
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Theoretical investigation of ultracompact and athermal Si electro-optic modulator based on Cu-TiO2-Si hybrid plasmonic donut resonator

Shiyang Zhu, G. Q. Lo, and D. L. Kwong  »View Author Affiliations


Optics Express, Vol. 21, Issue 10, pp. 12699-12712 (2013)
http://dx.doi.org/10.1364/OE.21.012699


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Abstract

An ultracompact silicon electro-optic modulator operating at 1550-nm telecom wavelengths is proposed and analyzed theoretically, which consists of a Cu-TiO2-Si hybrid plasmonic donut resonator evanescently coupled with a conventional Si channel waveguide. Owing to a negative thermo-optic coefficient of TiO2 (~-1.8 × 10−4 K−1), the real part of effective modal index of the curved Cu-TiO2-Si hybrid waveguide can be temperature-independent (i.e., athermal) if the TiO2 interlayer and the beneath Si core have a certain thickness ratio. A voltage applied between the ring-shaped Cu cap and a cylinder metal electrode positioned at the center of the donut, − which makes Ohmic contact to Si, induces a ~1-nm-thick free-electron accumulation layer at the TiO2/Si interface. The optical field intensity in this thin accumulation layer is significantly enhanced if the accumulation concentration is sufficiently large (i.e., > ~6 × 1020 cm−3), which in turn modulates both the resonance wavelengths and the extinction ratio of the donut resonator simultaneously. For a modulator with the total footprint inclusive electrodes of ~8.6 μm2, 50-nm-thick TiO2, and 160-nm-thick Si core, FDTD simulation predicts that it has an insertion loss of ~2 dB, a modulation depth of ~8 dB at a voltage swing of ~6 V, a speed-of-response of ~35 GHz, and a switching energy of ~0.45 pJ/bit, and it is athermal around room temperature. The modulator’s performances can be further improved by optimization of the coupling strength between the bus waveguide and the donut resonator.

© 2013 OSA

1. Introduction

A CMOS compatible integrated Si electro-optical (EO) modulator is a key component in Si electronic photonic integrated circuits (EPICs) [1

1. A. Chen and E. J. Murphy, Broadband optical modulators: science, technology, and applications, (CRC Press, Taylor & Francis Group, 2011).

]. Many kinds of Si EO modulators have been reported recently [2

2. D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. L. Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE 97(7), 1199–1215 (2009). [CrossRef]

,3

3. K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsug, T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4, 518–526 (2010).

], mostly relying on the free-carrier dispersion effect of Si to modulate the Si refractive index based on a MOS capacitor [4

4. A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427(6975), 615–618 (2004). [CrossRef] [PubMed]

, 5

5. R. Soref, J. Guo, and G. Sun, “Low-energy MOS depletion modulators in silicon-on-insulator micro-donut resonators coupled to bus waveguides,” Opt. Express 19(19), 18122–18134 (2011). [CrossRef] [PubMed]

], a PIN diode [6

6. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005). [CrossRef] [PubMed]

], or a PN junction [7

7. A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15(2), 660–668 (2007). [CrossRef] [PubMed]

]. Either a Mach-Zehnder interferometer (MZI) [4

4. A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427(6975), 615–618 (2004). [CrossRef] [PubMed]

,7

7. A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15(2), 660–668 (2007). [CrossRef] [PubMed]

] or a waveguide-ring resonator (WRR) [5

5. R. Soref, J. Guo, and G. Sun, “Low-energy MOS depletion modulators in silicon-on-insulator micro-donut resonators coupled to bus waveguides,” Opt. Express 19(19), 18122–18134 (2011). [CrossRef] [PubMed]

,6

6. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005). [CrossRef] [PubMed]

] is utilized to convert the phase variation into the intensity modulation. The WRR modulators offer smaller footprints than the MZI modulators but at the price of narrower optical bandwidth, higher temperature sensitivity due to the relatively large thermo-optic (TO) coefficient of Si (~1.8 × 10−4 K−1), and limited modulation speed due to the long photon lifetime in the resonator if the resonator has a very high quality factor (Q value).

One approach to suppress the temperature sensitivity of Si resonators is by overlaying a polymer coating with a negative TO coefficient [8

8. J. M. Lee, D. J. Kim, H. Ahn, S. H. Park, and G. Kim, “Temperature dependence of silicon nanophotonic ring resonator with a polymeric overlayer,” J. Lightwave Technol. 25(8), 2236–2243 (2007). [CrossRef]

], but polymers are currently not compatible with CMOS process. Another approach is by overcoupling the ring resonator to a balanced MZI [9

9. B. Guha, B. B. C. Kyotoku, and M. Lipson, “CMOS-compatible athermal silicon microring resonators,” Opt. Express 18(4), 3487–3493 (2010). [CrossRef] [PubMed]

], but it requires complex design and sacrifices the footprint. Moreover, due to the fundamental diffraction limit of light propagation along Si waveguides, the WRR modulators are still quite large as compared with the nanoscale electronic devices. The minimum bending radius is ~1.5 μm for Si single-mode channel waveguides [10

10. Q. Xu, D. Fattal, and R. G. Beausoleil, “Silicon microring resonators with 1.5-μm radius,” Opt. Express 16(6), 4309–4315 (2008). [CrossRef]

] and is usually larger than ~5 μm for Si rib waveguides in which the EO modulators are implemented. The total footprint of Si WRR modulators inclusive of the electrodes is usually larger than ~200 μm2.

A technology emerging recently which can scale down the dimension of optical devices far beyond the diffraction limit is plasmonics, which deals with surface plasmon polariton (SPP) signal propagating along the metal-dielectric interfaces [11

11. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010). [CrossRef]

]. Several ultracompact plasmonic EO modulators have been proposed and/or demonstrated [12

12. K. F. MacDonald and N. I. Zheludev, “Active plasmonics: current status,” Laser Photon. Rev. 4(4), 562–567 (2010). [CrossRef]

,13

13. J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett. 9(2), 897–902 (2009). [CrossRef] [PubMed]

]. However, they mostly rely on active materials other than Si and/or require non-standard CMOS techniques for fabrication. For ease of implementation into the exiting Si EPICs, it is preferred to use Si as the active material and the modulator is waveguide-based. A horizontal Cu-insulator-Si-insulator-Cu nanoplasmonic waveguide is a plasmonic waveguide enabling to realize plasmonic modulator [14

14. S. Y. Zhu, T. Y. Liow, G. Q. Lo, and D. L. Kwong, “Silicon-based horizontal nanoplasmonic slot waveguides for on-chip integration,” Opt. Express 19(9), 8888–8902 (2011). [CrossRef] [PubMed]

], which has a MOS capacitor structure and the Si core can be used as the active material. Electro-absorption (EA) and phase modulations have been experimentally demonstrated based on this plasmonic waveguide [15

15. S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Electro-absorption modulation in horizontal metal-insulator-silicon-insulator-metal nanoplasmonic slot waveguides,” Appl. Phys. Lett. 99(15), 151114 (2011). [CrossRef]

,16

16. S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Phase modulation in horizontal metal-insulator-silicon-insulator-metal plasmonic waveguides,” Opt. Express 21(7), 8320–8330 (2013). [CrossRef]

], but a relatively large driving voltage is required to reach 3-dB modulation in the EA modulators or π-phase shift in the MZI modulators. Another feasible plasmonic waveguide is a vertical Cu-insulator-Si hybrid plasmonic waveguide (HPW) [17

17. M. Z. Alam, J. Meier, J. S. Aitchison, and M. Mojahedi, “Super mode propagation in low index medium,” in Conf. on Lasers and Electro-Optics, Maryland, art. JThD (2007).

,18

18. S. Zhu, G. Q. Lo, and D. L. Kwong, “Experimental demonstration of vertical Cu/SiO2/Si hybrid plasmonic waveguide components on an SOI platform,” IEEE Photon. Technol. Lett. 24(14), 1224–1226 (2012). [CrossRef]

]. WRRs with radius of ~1-2 μm and Q-value of ~200-300 have been experimentally demonstrated based on the Cu-SiO2-Si HPW [19

19. S. Zhu, G. Q. Lo, and D. L. Kwong, “Performance of ultracompact copper-capped silicon hybrid plasmonic waveguide-ring resonators at telecom wavelengths,” Opt. Express 20(14), 15232–15246 (2012). [CrossRef] [PubMed]

]. Theoretically, the radius of such plasmonic WRRs can be reduced to submicron (e.g., ~0.8 μm) [20

20. D. Dai, Y. Shi, S. He, L. Wosinski, and L. Thylen, “Silicon hybrid plasmonic submicron-donut resonator with pure dielectric access waveguides,” Opt. Express 19(24), 23671–23682 (2011). [CrossRef] [PubMed]

]. Moreover, if TiO2, – which has a negative TO coefficient of ~-1.8 × 10−4 K−1 and is transparent at near-infrared wavelengths [21

21. G. Gulsen and M. N. Inci, “Thermal optical properties of TiO2 films,” Opt. Mater. 18(4), 373–381 (2002). [CrossRef]

], is used as the insulator between the Cu-cap and the Si core, the plasmonic WRRs can be athermal. TiO2 is also used as a gate dielectric in MOS electronics, whose dielectric constant ranges from 4 to 86 depending on the detailed fabrication processes [22

22. R. Paily, A. DasGupta, N. DasGupta, P. Bhattacharya, P. Misra, T. Ganguli, L. M. Kukreja, A. K. Balamurugan, S. Rajagopalan, and A. K. Tyagi, “Pulsed laser deposition of TiO2 for MOS gate dielectric,” Appl. Surf. Sci. 187(3-4), 297–304 (2002). [CrossRef]

]. The Cu-TiO2-Si HPW is also a MOS capacitor, thus enabling a voltage to be applied between the Cu cap and the Si core to modulate its propagation property. It is expected that the WRR modulators based on this hybrid plasmonic WRR may overcome the abovementioned two critical issues of the conventional WRR modulators, i.e., footprint miniaturization and temperature-sensitivity suppression. This paper presents a systematical investigation on ultracompact WRR modulators based on the Cu-TiO2-Si HPW.

2. Device structure

The structure of the proposed modular is shown in Fig. 1
Fig. 1 (a) Top view, and (b) cross-sectional view of the proposed Si plasmonic resonator modulator, the bus waveguide is a conventional single-mode Si channel waveguide and the resonator is a Cu-TiO2-Si hybrid plasmonic donut with two electrodes located at the Cu cap and center-donut, respectively. The structural parameters are also indicated.
schematically. It consists of a Cu-TiO2-Si hybrid plasmonic donut resonator and a bus waveguide. The modulator can be seamlessly inserted in a dense Si channel waveguide-based photonic circuit. To reduce the insertion loss, the bus waveguide is a conventional Si channel waveguide. To reduce the overall footprint, a donut rather than a ring is used, thus the electrode for Si Ohmic contact can be positioned at the center of the donut and the donut forms a standard MOS capacitor (the other electrode is the Cu cap).

The cylindrical electrode for Si Ohmic contact has radius of r0. The outer radius of the Si donut is R and the inner radius is (R – WP), where WP is the width of Si core of the curved hybrid plasmonic waveguide. The separation between the resonator and the bus waveguide is “gap”. The Si height is H, the slab thickness in the Si donut is tslab, and the TiO2 thickness is tox. The Cu-cap thickness is set to be much larger than the penetration depth of the SPP mode in the metal (~26 nm). Because the plasmonic mode can only be excited by the electric field of optical mode perpendicular to the metal/dielectric interface, the proposed modulator is valid only for the transverse magnetic (TM)-polarized light.

The modulators are fabricated on silicon-on-insulator wafers. The Si pattern of the bus and donut waveguides are defined by partially dry etching of Si down to tslab using a thin SiO2 layer as the etching mask, following by dry etching of the remaining Si down to the buried SiO2 using both SiO2 and photo-resistor as the etching mask. Using this etching method, there is no misalignment issue between the inner and outer rings of the donut. After Si patterning, a thick SiO2 is deposited and a ring-shaped window is opened to expose the surface of the Si core. There exists possible misalignment between the SiO2 window and the beneath Si core due to fabrication imperfection. Here, the SiO2 window (hence the width of the TiO2/Cu cap, Wox) is intentionally designed to be larger than the beneath Si core by ΔWP in each side, thus Wox = WP + 2ΔWP. TiO2 is then deposited on the Si core through the windows, followed by Cu deposition and Cu chemical mechanical polishing (CMP) to remove TiO2 and Cu outside the windows. The structural parameters are initially chosen based on our experience [23

23. S. Zhu, G. Q. Lo, and D. L. Kwong, “Toward athermal plasmonic ring resonators based on Cu-TiO2-Si hybrid plasmonic waveguide,” in Optical Fiber Communication Conf. (OFC 2013) (California USA, 2013), art. OW3F.1.

], as listed in Table 1

Table 1. The initial parameter setting of the plasmonic EO modulator

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. Then, one of these parameters is varied while the others keep the same to investigate its effect on the whole performance.

The refractive indices of Si, SiO2, TiO2, and Cu depend both on wavelength and temperature. For simplification, the indices as well as the TO coefficients at 1550-nm wavelength and room temperature (RT) are used here, as listed in Table 2

Table 2. Optical parameters of Si, SiO2, TiO2, and Cu at 1550-nm and RT

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. The validity of these optical parameters has been verified as the calculated propagation losses of plasmonic waveguides agree well with the experimental results measured at 1550-nm wavelength and RT [23

23. S. Zhu, G. Q. Lo, and D. L. Kwong, “Toward athermal plasmonic ring resonators based on Cu-TiO2-Si hybrid plasmonic waveguide,” in Optical Fiber Communication Conf. (OFC 2013) (California USA, 2013), art. OW3F.1.

]. Be noted that the quantitative results in this paper are accurate only near 1550-nm wavelengths and room temperature.

3. Thermo-optic simulations

Figure 3
Fig. 3 The dneff/dT value of curved Cu-TiO2-Si HPW as a function of the TiO2 thickness for (a) HPWs with H = 220 nm and WP of 100, 200, and 300 nm respectively, and (b) HPWs with WP = 200 nm and H of 340, 280, 220, and 160 nm respectively. The other structural parameters are as listed in Table 1. The athermal point is defined when dneff/dT = 0.
plots dneff/dT versus tox for curved Cu-TiO2-Si HPWs. As expected, dneff/dT decreases monotonically with tox increasing because the ratio of optical intensity in the TiO2 layer increases. However, the slope of the dneff/dT~tox curves decreases with tox increasing. This observation can be explained by the fact that the hybrid mode shown in Fig. 2(a) is a superposition of a pure SPP mode located at the Cu/TiO2 interface (i.e., waveguide without the Si core) and a pure optical mode located at the Si core (i.e., waveguide without the metal). The hybrid mode becomes more optical-like when tox increasing [27

27. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008). [CrossRef]

]. In the extreme case when tox is sufficiently larger (e.g., > ~200 nm), it behaves as a pure optical mode as the conventional Si waveguide with TiO2 behaving as a cladding layer, thus dneff/dT will be independent on tox. One sees from Fig. 3 that the dneff/dT~tox curve depends on the Si core width WP weakly, while depends on the Si height H strongly. The critical tox at which dneff/dT = 0 (i.e., athermal point) depends on WP weakly, while increases with H increasing. Electrically, a thin gate dielectric is preferred to reduce the driving voltage. Optically, the height of the Si waveguide should be thick enough for vertical optical confinement. To balance the electric and optical requirements, our modulator is set to be H = 160 nm and tox = 50 nm. It is athermal as read from Fig. 3(b).

4. Electrical simulations

A semiconductor device simulation software MEDICI is used to obtain the two-dimensional (2D) dynamic free carrier distribution in the MOS capacitor at different biases, as in the case of conventional Si MOS modulators [28

28. C. T. Shin, Z. W. Zeng, and S. Chao, “Design and analysis of MOS-capacitor microring optical modulator with SPC poly-silicon gate,” J. Lightwave Technol. 27, 3861–3873 (2009). [CrossRef]

]. The dielectric constant of TiO2 is set to 80, which is reachable for a high-quality TiO2 film [22

22. R. Paily, A. DasGupta, N. DasGupta, P. Bhattacharya, P. Misra, T. Ganguli, L. M. Kukreja, A. K. Balamurugan, S. Rajagopalan, and A. K. Tyagi, “Pulsed laser deposition of TiO2 for MOS gate dielectric,” Appl. Surf. Sci. 187(3-4), 297–304 (2002). [CrossRef]

]. The Si core of the resonator is n-type doped with concentration (ND) of 5 × 1018 cm−3 in the rib and slab region and 2 × 1020 cm−3 in the contact region for good Ohmic contact. Auger recombination, Shockley-Hall-Read recombination, surface recombination, Fermi-Dirac statics, and the Modified Local Density Approximation (MLDA) method in the MEDICI are included to account for the heavy doping and the quantum confinement effect on the carrier concentration near the TiO2/Si interface [29

29. J. Sune, P. Olivo, and B. Ricco, “Quantum-mechanical modeling of accumulation layers in MOS structure,” IEEE Trans. Electron. Dev. 39(7), 1732–1739 (1992). [CrossRef]

]. The 2D free carrier distribution in the MOS capacitor under 5-V bias is shown in Fig. 4(a)
Fig. 4 (a) Two-dimensional electron distribution of Cu-TiO2-Si MOS capacitor under 5-V bias. Free electrons are accumulated near the TiO2/Si interface. (b) Electron concentration contour near the TiO2/Si interface, different color represents different concentration. (c) One-dimensional electron distribution along y-axis of Cu-TiO2-Si capacitor as shown schematically in the inset under different biases. The depletion width Wdep and the accumulation layer thickness tAcL are also indicated.
. The accumulated electrons are located near the TiO2/Si interface. To see the 2D distribution more clearly, the figure near the interface is enlarged, as shown in Fig. 4(b). We can see that the electron concentration contours are almost in parallel with the TiO2/Si interface. Therefore, the 2D distribution of free electron distribution N(x,y) can be simplified by a one-dimensional (1D) distribution N(y). Figure 4(c) plots 1D electron distributions along y-axis for the Cu-TiO2-Si MOS capacitor under different biases ranging from −1 V to 8 V. At the −1 V bias, the electrons are depleted from the interface. The depletion width Wdep (ND0.5) is ~16.3 nm when ND = 5 × 1018 cm−3. With the gate voltage increasing, the electrons are accumulated at the interface, maximizing at a short distance (~0.3-0.5 nm) away from the interface due to the quantum mechanical effect and then decreasing to ND quickly with the distance from the interface increasing. The free-electron distribution approaches to the interface more closely when V increases. These results agree well with the experimental observation [30

30. A. Tardella and J. N. Chazalviel, “Highly accumulated electron layer at a semiconductor/electrolyte interface,” Phys. Rev. B Condens. Matter 32(4), 2439–2448 (1985). [CrossRef] [PubMed]

]. As a first approximation, the electron distribution is approximated by a step function to define an accumulation layer (AcL) which has width of tAcL and average concentration of NAcL as:
NAcL=ε0εdetoxtAcL(VVFB)=ε0εdetAcLEd.
(1)
where ε0 is the vacuum permittivity, εd is the dielectric constant of the gate dielectric, e is electronic charge, VFB is the flat-band voltage, and Ed is the electric field in the gate dielectric. Here, we simply assume tAcL = 1nm. At large V, tAcL will be smaller than 1 nm and NAcL will be larger than that predicted from Eq. (1). The achievable NAcL depends on the breakdown field of the gate dielectric, and it can be larger than 1020 cm−3 for modern CMOS devices.

For transient state simulations, the gate voltage V is increased from 0 to 8 V with the ramp time of the gate voltage of 10 fs. The free electron concentration in the 1-nm AcL is plotted in Fig. 5
Fig. 5 (a) The transient response of the electron concentration in the 1-nm-thick AcL of the Cu-TiO2-Si MOS capacitor at the gate voltage variation between 0 and 8 V. Rise and fall time are defined as 10% to 90% time period. The solid curve is for a MOS capacitor with n+-contact just below the electrode as shown in Fig. 4(a) and the dash curve is for a MOS capacitor with the n+-contact extended to the Si rib.
as a function of time. Rise time (tr) of the electron concentration is defined as the time for the electron concentration to increase from 10% to 90%, and fall time (tf) is defined as the time for the electron concentration to drop from 90% to 10%. In the case of Si n+-contact just below the electrode, as shown in Fig. 4(a), the sum of these times s = tr + tf) is ~29 ps. The modulation speed estimated from the inverse of τs is ~34 GHz. The speed can be improved by shortening the distance between the accumulation layer and the n+ contact. In the case that the n+ contact in the Si slab is extended to the Si rib, both tr and tf decrease, as shown by the dash curve in Fig. 5. τs is read to ~9.3 ps for this MOS capacitor, which corresponds to a ~107-GHz modulation speed. However, the propagation loss of the curved HPW will increase from 0.27 dB/μm to 0.31 dB/μm when the doping level in the Si slab is increased from 5 × 1018 cm−3 to 2 × 1020 cm−3 (while keeping the doping level in the Si rib to be 5 × 1018 cm−3). To balance the propagation loss and the speed, the n+ doping may be extended to a certain location between the Si rib and the electrode.

The proposed EO modulator is a MOS capacitor working between the depletion and accumulation states. The switching energy Es per bit of the MOS modulator can be roughly estimated as:
Es=12CdepVdep2+12CaccuVaccu2.
(2)
where Cdep and Caccu are capacitances under the depletion and accumulation states respectively. Because Cdep is smaller than Caccu and Vdep is smaller than Vaccu, Es is mainly determined by the second term of Eq. (2), namely the accumulation state. Caccu can be approximated to the gate oxide capacitance as CaccuAtoxε0εd, where A is the active area. For the modulator with structural parameters as listed in Table 1, A is 1.76 μm2 and Caccu is ~25 fF. If the driving voltage is 6 V, Es is estimated to be ~0.45 pJ.

5. Electro-optic simulations

The modification of Si reflective index (nSi + ikSi) at 1550 nm depends on the free carrier concentration (ΔNe for electrons and ΔNh for holes) almost linearly as:

Δn=[8.8×1022ΔNe+8.5×1018(ΔNh)0.8],Δα=8.5×1018ΔNe+6×1018ΔNh.
(3)

The simple calculation based on Eq. (5) represents an ideal condition of WRRs in which many effects are ignored. To verify the results observed in Fig. 8, three-dimensional (3D) full-difference time-domain (FDTD) simulation is performed. To enhance the coupling between the bus waveguide and the resonator, a race-track shaped resonator is used. The gap between the bus waveguide and the resonator is set to 10 nm and the directional coupling length is set to be 500 nm. The total footprint of the modulator inclusive electrodes is ~8.6 μm2, and the active area A is ~1.96 μm2. To minimize the simulation error during simulation in different states, only the Si complex index in the 1-nm-thick AcL is changed as read from Fig. 6(b), while all other settings including the grid size keep the same. Figure 9(a)
Fig. 9 (a) Transmission spectra of the plasmonic modulator under accumulation with NAcL of 1 × 1020 cm−3 and 6 × 1020 cm−3, obtained from FDTD simulation; (b) Media 1 the optical power density in the modulator with 1 × 1020 cm−3 NAcL at λ = 1546 nm, and (c) The optical power distribution in the modulator with NAcL = 6 × 1020 cm−3 at λ = 1546 nm. The output power is modulated from ~-10 dB to ~-2 dB at this wavelength.
plots the transmission spectra for the modulator under accumulation states with NAcL = 1 × 1020 cm−3 or 6 × 1020 cm−3, which corresponds to a bias of 1.1 V or 6.8 V, respectively, according to Eq. (1). In the case of NAcL = 1 × 1020 cm−3, ER is ~9 dB near 1550 nm, which corresponds to α = ~0.74 and |t| = ~0.85. When NAcL increases to 6 × 1020 cm−3, the resonant waveguides are blue-shifted by ~13.5 nm and ER is reduced to be ~2.5 dB because of the reduction of α to ~0.67. At 1546 nm wavelength, the output power is modified from ~-10 dB to ~-2 dB by increasing NAcL from 1 × 1020 to 6 × 1020 cm−3. The optical power distributions in the modulator with NAcL of 1 × 1020 and 6 × 1020 cm−3 are shown in Figs. 9(b) and 9(c) respectively, and dynamic light propagation through the modulator is shown by the attached movie (Media 1). One sees that in the case of NAcL = 1 × 1020 cm−3, the modulator is almost in on-resonance as α being close to |t|, which results in optical trap in the resonator and small output power of ~-10 dB. In the case of NAcL = 6 × 1020 cm−3, the modulator is in off-resonator as α being larger than |t|, which results in large output power of ~-2 dB. Thus this modulator operating at 1546 nm has modulation depth of ~8.0 dB and insertion loss of ~2 dB. The relatively low insertion loss (as compared with other plasmonic modulators [15

15. S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Electro-absorption modulation in horizontal metal-insulator-silicon-insulator-metal nanoplasmonic slot waveguides,” Appl. Phys. Lett. 99(15), 151114 (2011). [CrossRef]

,16

16. S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Phase modulation in horizontal metal-insulator-silicon-insulator-metal plasmonic waveguides,” Opt. Express 21(7), 8320–8330 (2013). [CrossRef]

]) is benefited from the conventional Si channel bus waveguide. As the abovementioned, both the modulation depth and the insertion loss can be further improved by adjusting the coupling between the bus waveguide and the resonator.

6. Conclusions

Appendix

In this appendix, we discuss the further miniaturization of the ring radius and the fabrication tolerance.

Acknowledgment

This work was supported by the Science and Engineering Research Council of A*STAR (Agency for Science, Technology and Research), Singapore Grant 092-154-0098.

References and links

1.

A. Chen and E. J. Murphy, Broadband optical modulators: science, technology, and applications, (CRC Press, Taylor & Francis Group, 2011).

2.

D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. L. Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE 97(7), 1199–1215 (2009). [CrossRef]

3.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsug, T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4, 518–526 (2010).

4.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427(6975), 615–618 (2004). [CrossRef] [PubMed]

5.

R. Soref, J. Guo, and G. Sun, “Low-energy MOS depletion modulators in silicon-on-insulator micro-donut resonators coupled to bus waveguides,” Opt. Express 19(19), 18122–18134 (2011). [CrossRef] [PubMed]

6.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005). [CrossRef] [PubMed]

7.

A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15(2), 660–668 (2007). [CrossRef] [PubMed]

8.

J. M. Lee, D. J. Kim, H. Ahn, S. H. Park, and G. Kim, “Temperature dependence of silicon nanophotonic ring resonator with a polymeric overlayer,” J. Lightwave Technol. 25(8), 2236–2243 (2007). [CrossRef]

9.

B. Guha, B. B. C. Kyotoku, and M. Lipson, “CMOS-compatible athermal silicon microring resonators,” Opt. Express 18(4), 3487–3493 (2010). [CrossRef] [PubMed]

10.

Q. Xu, D. Fattal, and R. G. Beausoleil, “Silicon microring resonators with 1.5-μm radius,” Opt. Express 16(6), 4309–4315 (2008). [CrossRef]

11.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010). [CrossRef]

12.

K. F. MacDonald and N. I. Zheludev, “Active plasmonics: current status,” Laser Photon. Rev. 4(4), 562–567 (2010). [CrossRef]

13.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett. 9(2), 897–902 (2009). [CrossRef] [PubMed]

14.

S. Y. Zhu, T. Y. Liow, G. Q. Lo, and D. L. Kwong, “Silicon-based horizontal nanoplasmonic slot waveguides for on-chip integration,” Opt. Express 19(9), 8888–8902 (2011). [CrossRef] [PubMed]

15.

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Electro-absorption modulation in horizontal metal-insulator-silicon-insulator-metal nanoplasmonic slot waveguides,” Appl. Phys. Lett. 99(15), 151114 (2011). [CrossRef]

16.

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Phase modulation in horizontal metal-insulator-silicon-insulator-metal plasmonic waveguides,” Opt. Express 21(7), 8320–8330 (2013). [CrossRef]

17.

M. Z. Alam, J. Meier, J. S. Aitchison, and M. Mojahedi, “Super mode propagation in low index medium,” in Conf. on Lasers and Electro-Optics, Maryland, art. JThD (2007).

18.

S. Zhu, G. Q. Lo, and D. L. Kwong, “Experimental demonstration of vertical Cu/SiO2/Si hybrid plasmonic waveguide components on an SOI platform,” IEEE Photon. Technol. Lett. 24(14), 1224–1226 (2012). [CrossRef]

19.

S. Zhu, G. Q. Lo, and D. L. Kwong, “Performance of ultracompact copper-capped silicon hybrid plasmonic waveguide-ring resonators at telecom wavelengths,” Opt. Express 20(14), 15232–15246 (2012). [CrossRef] [PubMed]

20.

D. Dai, Y. Shi, S. He, L. Wosinski, and L. Thylen, “Silicon hybrid plasmonic submicron-donut resonator with pure dielectric access waveguides,” Opt. Express 19(24), 23671–23682 (2011). [CrossRef] [PubMed]

21.

G. Gulsen and M. N. Inci, “Thermal optical properties of TiO2 films,” Opt. Mater. 18(4), 373–381 (2002). [CrossRef]

22.

R. Paily, A. DasGupta, N. DasGupta, P. Bhattacharya, P. Misra, T. Ganguli, L. M. Kukreja, A. K. Balamurugan, S. Rajagopalan, and A. K. Tyagi, “Pulsed laser deposition of TiO2 for MOS gate dielectric,” Appl. Surf. Sci. 187(3-4), 297–304 (2002). [CrossRef]

23.

S. Zhu, G. Q. Lo, and D. L. Kwong, “Toward athermal plasmonic ring resonators based on Cu-TiO2-Si hybrid plasmonic waveguide,” in Optical Fiber Communication Conf. (OFC 2013) (California USA, 2013), art. OW3F.1.

24.

S. Roberts, “Optical properties of copper,” Phys. Rev. 118(6), 1509–1518 (1960). [CrossRef]

25.

http://www.lumerical.com.

26.

W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6(1), 47–73 (2012). [CrossRef]

27.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008). [CrossRef]

28.

C. T. Shin, Z. W. Zeng, and S. Chao, “Design and analysis of MOS-capacitor microring optical modulator with SPC poly-silicon gate,” J. Lightwave Technol. 27, 3861–3873 (2009). [CrossRef]

29.

J. Sune, P. Olivo, and B. Ricco, “Quantum-mechanical modeling of accumulation layers in MOS structure,” IEEE Trans. Electron. Dev. 39(7), 1732–1739 (1992). [CrossRef]

30.

A. Tardella and J. N. Chazalviel, “Highly accumulated electron layer at a semiconductor/electrolyte interface,” Phys. Rev. B Condens. Matter 32(4), 2439–2448 (1985). [CrossRef] [PubMed]

31.

R. Soref, R. E. Peale, and W. Buchwald, “Longwave plasmonics on doped silicon and silicides,” Opt. Express 16(9), 6507–6514 (2008). [CrossRef] [PubMed]

32.

M. Wu, Z. Han, and V. Van, “Conductor-gap-silicon plasmonic waveguides and passive components at subwavelength scale,” Opt. Express 18(11), 11728–11736 (2010). [CrossRef] [PubMed]

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(240.6680) Optics at surfaces : Surface plasmons
(250.7360) Optoelectronics : Waveguide modulators
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Integrated Optics

History
Original Manuscript: January 29, 2013
Revised Manuscript: April 5, 2013
Manuscript Accepted: April 5, 2013
Published: May 16, 2013

Citation
Shiyang Zhu, G. Q. Lo, and D. L. Kwong, "Theoretical investigation of ultracompact and athermal Si electro-optic modulator based on Cu-TiO2-Si hybrid plasmonic donut resonator," Opt. Express 21, 12699-12712 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-10-12699


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References

  1. A. Chen and E. J. Murphy, Broadband optical modulators: science, technology, and applications, (CRC Press, Taylor & Francis Group, 2011).
  2. D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. L. Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE97(7), 1199–1215 (2009). [CrossRef]
  3. K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsug, T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).
  4. A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature427(6975), 615–618 (2004). [CrossRef] [PubMed]
  5. R. Soref, J. Guo, and G. Sun, “Low-energy MOS depletion modulators in silicon-on-insulator micro-donut resonators coupled to bus waveguides,” Opt. Express19(19), 18122–18134 (2011). [CrossRef] [PubMed]
  6. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature435(7040), 325–327 (2005). [CrossRef] [PubMed]
  7. A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express15(2), 660–668 (2007). [CrossRef] [PubMed]
  8. J. M. Lee, D. J. Kim, H. Ahn, S. H. Park, and G. Kim, “Temperature dependence of silicon nanophotonic ring resonator with a polymeric overlayer,” J. Lightwave Technol.25(8), 2236–2243 (2007). [CrossRef]
  9. B. Guha, B. B. C. Kyotoku, and M. Lipson, “CMOS-compatible athermal silicon microring resonators,” Opt. Express18(4), 3487–3493 (2010). [CrossRef] [PubMed]
  10. Q. Xu, D. Fattal, and R. G. Beausoleil, “Silicon microring resonators with 1.5-μm radius,” Opt. Express16(6), 4309–4315 (2008). [CrossRef]
  11. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010). [CrossRef]
  12. K. F. MacDonald and N. I. Zheludev, “Active plasmonics: current status,” Laser Photon. Rev.4(4), 562–567 (2010). [CrossRef]
  13. J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett.9(2), 897–902 (2009). [CrossRef] [PubMed]
  14. S. Y. Zhu, T. Y. Liow, G. Q. Lo, and D. L. Kwong, “Silicon-based horizontal nanoplasmonic slot waveguides for on-chip integration,” Opt. Express19(9), 8888–8902 (2011). [CrossRef] [PubMed]
  15. S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Electro-absorption modulation in horizontal metal-insulator-silicon-insulator-metal nanoplasmonic slot waveguides,” Appl. Phys. Lett.99(15), 151114 (2011). [CrossRef]
  16. S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Phase modulation in horizontal metal-insulator-silicon-insulator-metal plasmonic waveguides,” Opt. Express21(7), 8320–8330 (2013). [CrossRef]
  17. M. Z. Alam, J. Meier, J. S. Aitchison, and M. Mojahedi, “Super mode propagation in low index medium,” in Conf. on Lasers and Electro-Optics, Maryland, art. JThD (2007).
  18. S. Zhu, G. Q. Lo, and D. L. Kwong, “Experimental demonstration of vertical Cu/SiO2/Si hybrid plasmonic waveguide components on an SOI platform,” IEEE Photon. Technol. Lett.24(14), 1224–1226 (2012). [CrossRef]
  19. S. Zhu, G. Q. Lo, and D. L. Kwong, “Performance of ultracompact copper-capped silicon hybrid plasmonic waveguide-ring resonators at telecom wavelengths,” Opt. Express20(14), 15232–15246 (2012). [CrossRef] [PubMed]
  20. D. Dai, Y. Shi, S. He, L. Wosinski, and L. Thylen, “Silicon hybrid plasmonic submicron-donut resonator with pure dielectric access waveguides,” Opt. Express19(24), 23671–23682 (2011). [CrossRef] [PubMed]
  21. G. Gulsen and M. N. Inci, “Thermal optical properties of TiO2 films,” Opt. Mater.18(4), 373–381 (2002). [CrossRef]
  22. R. Paily, A. DasGupta, N. DasGupta, P. Bhattacharya, P. Misra, T. Ganguli, L. M. Kukreja, A. K. Balamurugan, S. Rajagopalan, and A. K. Tyagi, “Pulsed laser deposition of TiO2 for MOS gate dielectric,” Appl. Surf. Sci.187(3-4), 297–304 (2002). [CrossRef]
  23. S. Zhu, G. Q. Lo, and D. L. Kwong, “Toward athermal plasmonic ring resonators based on Cu-TiO2-Si hybrid plasmonic waveguide,” in Optical Fiber Communication Conf. (OFC 2013) (California USA, 2013), art. OW3F.1.
  24. S. Roberts, “Optical properties of copper,” Phys. Rev.118(6), 1509–1518 (1960). [CrossRef]
  25. http://www.lumerical.com .
  26. W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev.6(1), 47–73 (2012). [CrossRef]
  27. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008). [CrossRef]
  28. C. T. Shin, Z. W. Zeng, and S. Chao, “Design and analysis of MOS-capacitor microring optical modulator with SPC poly-silicon gate,” J. Lightwave Technol.27, 3861–3873 (2009). [CrossRef]
  29. J. Sune, P. Olivo, and B. Ricco, “Quantum-mechanical modeling of accumulation layers in MOS structure,” IEEE Trans. Electron. Dev.39(7), 1732–1739 (1992). [CrossRef]
  30. A. Tardella and J. N. Chazalviel, “Highly accumulated electron layer at a semiconductor/electrolyte interface,” Phys. Rev. B Condens. Matter32(4), 2439–2448 (1985). [CrossRef] [PubMed]
  31. R. Soref, R. E. Peale, and W. Buchwald, “Longwave plasmonics on doped silicon and silicides,” Opt. Express16(9), 6507–6514 (2008). [CrossRef] [PubMed]
  32. M. Wu, Z. Han, and V. Van, “Conductor-gap-silicon plasmonic waveguides and passive components at subwavelength scale,” Opt. Express18(11), 11728–11736 (2010). [CrossRef] [PubMed]

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