## Low-energy MOS depletion modulators in silicon-on-insulator micro-donut resonators coupled to bus waveguides |

Optics Express, Vol. 19, Issue 19, pp. 18122-18134 (2011)

http://dx.doi.org/10.1364/OE.19.018122

Acrobat PDF (1183 KB)

### Abstract

Electrical, optical and electro-optical simulations are presented for a waveguided, resonant, bus-coupled, *p*-doped Si micro-donut MOS depletion modulator operating at the 1.55 μm wavelength. To minimize the switching voltage and energy, a high-K dielectric film of HfO_{2} or ZrO_{2} is chosen as the gate dielectric, while a narrow ring-shaped layer of *p*-doped poly-silicon is selected for the gate electrode, rather than metal, to minimize plasmonic loss loading of the fundamental TE mode. In a 6-μm-diam high-Q resonator, an infrared intensity extinction ratio of 6 dB is predicted for a modulation voltage of 2 V and a switching energy of 4 fJ/bit. A speed-of-response around 1 ps is anticipated. For a modulator scaled to operate at 1.3 μm, the estimated switching energy is 2.5 fJ/bit.

© 2011 OSA

## 1. Introduction

1. S. P. Anderson and P. M. Fauchet, “Ultra-low power modulators using MOS depletion in a high-Q SiO₂-clad silicon 2-D photonic crystal resonator,” Opt. Express **18**(18), 19129–19140 (2010). [CrossRef] [PubMed]

## 2. Design discussion

*λ*that is inversely proportional to Q. Depletion of carriers within the cavity increases the real index of the Si resonator material by an amount Δ

_{q}*n*which in turn changes the effective index of the resonant mode

*n*by an amount Δ

_{eff}*n*. Then Δ

_{eff}*n*produces a shift Δ

_{eff}*λ*of the mode's initial resonance wavelength

*λ*

_{0}. For successful modulation the Q must be high enough and Δ

*n*large enough so that Δ

_{eff}*λ*is comparable to Δ

*λ*. High Q comes from low propagation loss in the waveguided resonator. There are several loss factors such as wall roughness loss, material loss, and waveguide bend loss. The principal loss here arises from gate-electrode loading since the optical mode-tail tunnels through the gate oxide and touches the electrode. In early simulations, we quickly found that a metal gate electrode was not acceptable because of its very high plasmonic loss. The solution to that problem is to employ doped polysilicon as the gate electrode (as is done in the CMOS industry) because the poly-Si loss is orders-of-magnitude smaller than that of metal. The silicon body of the resonator is uniformly doped

_{q}*p*-type or n-type and there is material loss associated with free carrier absorption, although early studies show [2

2. R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. **23**(1), 123–129 (1987). [CrossRef]

^{−1}at the 1.55 μm communications wavelength by restricting the doping concentration to be less than 10

^{17}cm

^{−3}.

3. Z. Xia, A. A. Eftekhar, M. Soltani, B. Momeni, Q. Li, M. Chamanzar, S. Yegnanarayanan, and A. Adibi, “High resolution on-chip spectroscopy based on miniaturized microdonut resonators,” Opt. Express **19**(13), 12356–12364 (2011). [CrossRef] [PubMed]

*n*arises from the free-carrier electro-refraction effect, where Δ

*n*nearly proportional to the change in free carrier concentration Δ

*N*. From ionized impurities in the doped waveguide, there is an initial concentration

*N*of free carriers that exists at zero bias. Carriers are swept out of the active region (rapidly) by the applied field, a removal of Δ

*N = N*at full depletion. Thus a large

*N*seems desireable to yield large Δ

*n*. However, at large

*N*it becomes difficult to deplete the waveguide body since the depletion layer thickness depends upon

*N*

^{–0.5}. Thus a compromise value of

*N*such as 10

^{16}-10

^{17}cm

^{−3}must be chosen in order to deplete “most” of the donut height

*h*—but this ceiling-on-N constrains Δ

*n*. The choice of electrons or holes as the free carriers plays a key role in attaining large Δ

*n*. Early studies [2

2. R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. **23**(1), 123–129 (1987). [CrossRef]

*n*when sweeping out carrier densities of 10

^{16}-10

^{17}cm

^{−3}. That prediction has been verified experimentally over the years; thus, we elected

*p*-type doping of the resonator as discussed below.

*V*applied to the external terminals of the MOS capacitor resonator is divided internally between the Si waveguide region and the gate dielectric region—thus the terminal voltage is higher than the “useful voltage” that depletes the

*p*-Si. This voltage division is governed by the low-frequency dielectric constant

*K*of the gate dielectric with respect to the silicon

*K.*By proper choice of gate dielectric material, the great majority of

*V*will appear across the silicon as desired for minimum-energy switching. This freedom to choose the best dielectric is a valuable aspect of the MOS device. In its design, the MOS modulator has two more degrees-of-freedom than the

*pn*-junction depletion device because the MOS device offers choices for the gate electrode and gate dielectric materials as well as the waveguide core-and-cladding materials. We have exploited this design freedom by selecting the high-

*K*gate dielectric to be either Hafnium dioxide (HfO

_{2}) or Zirconium dioxide (ZrO

_{2}) instead of the conventional low-

*K*gate of silicon dioxide. Hafnium dioxide has had great success in the modern MOSFET industry, and both HfO

_{2}and ZrO

_{2}have

*K*~25. As detailed below, when this thin high-

*K*layer becomes gate material in the micro-donut, the resulting combination of low capacitance and low gate voltage enables ultralow-energy photonic switching.

## 3. Proposed designs

## 4. Electrical simulations

*V*is the threshold voltage

*V*that begins to produce unwanted charge inversion (after depletion) at the gate/Si interface. The “off” and “on” states correspond to situations in which the silicon underneath the gate oxide is either in its original doped state or in its partially depleted state. It is well known that at zero bias a built-in field is sometimes induced in an MOS structure, resulting in a tilted energy band for the silicon near the oxide-silicon interface. In order to restore the flat band condition for silicon, a small flat-band voltage

_{th}*V*needs to be applied for the “off” statewhere

_{fb}*ϕ*is the work function difference between the polycrystalline silicon gate and the silicon,

_{ms}*Q*is the oxide effective charge per unit area at the oxide-silicon interface,

_{ox}*C*is the gate-oxide capacitance per unit areaHere

_{ox}*ε*

_{0}is the permittivity of vacuum,

*K*is the dielectric constant of the oxide, and

_{ox}*t*is the thickness of the oxide layer between the gate electrode and the silicon.

_{ox}*V*is the part of the gate voltage that is actually dropped across the silicon. To prevent the MOS structure from reaching strong inversion at the oxide-silicon interface, we must limitwhere

_{s}*q*is the electron charge,

*k*is the Boltzmann constant, and

_{B}*N*is the intrinsic carrier concentration at the temperature

_{i}*T*. The gate voltage

*V*for the “on” state should thus be limited by the threshold voltage

_{on}*V*of the MOS structureUsing Eq. (5), our early simulations showed that an SiO

_{th}_{2}gate with

*K*= 3.9 required modulation voltages of 10 to 15 volts. We then examined a higher-

*K*silicon-nitride gate dielectric. The Si

_{3}N

_{4}offered lower-voltage control but was still not an optimum dielectric. As a solution to the “10-volt problem”, we turned to the high-

*K*materials discussed above. Utilizing Eqs. (1)–(5), the “off” and “on” state voltages are shown in Figs. 4(a) and 4(b), respectively, for the effects of gate dielectric thickness in the range 100 nm <

*t*< 300 nm and the Si doping concentration for 6 × 10

_{ox}^{16}cm

^{−3}<

*N*< 1 × 10

_{p}^{17}cm

^{−3}. We have used

*Q*= 10

_{ox}^{10}cm

^{–2}for the flat band voltage Eq. (1).

*r*and

_{1}*r*are the outer and inner radii of the poly-Si electrode ring, respectively, and

_{2}*r*

_{0}is the donut’s inner radius. The flat band capacitance for the “off” state can be calculated aswhere the Debye length in silicon isand the “on” state capacitance iswhere the depletion depth in Si isSince the percentage of the silicon body height that can be depleted of charge depends upon the initial doping density

*N*, we have calculated with Eq. (9) the silicon height that could be fully depleted versus a given doping

_{p}*N*and the result is shown in Fig. 5 . We then took the single-mode waveguide height to be 230 nm at

_{p}*λ*= 1550 nm as in the Georgia Tech experiments [3

3. Z. Xia, A. A. Eftekhar, M. Soltani, B. Momeni, Q. Li, M. Chamanzar, S. Yegnanarayanan, and A. Adibi, “High resolution on-chip spectroscopy based on miniaturized microdonut resonators,” Opt. Express **19**(13), 12356–12364 (2011). [CrossRef] [PubMed]

^{16}cm

^{−3}doping, Fig. 5 indicates that 50% of the silicon waveguide can be depleted at the 2.2 V gate voltage, and this prediction is used in the mode overlap calculation of section 5 below.

*h*= 230 nm,

*r*

_{1}= 3.0 μm,

*r*

_{2}= 2.6 μm,

*r*

_{0}= 2.2 μm and

*K*= 25 for HfO

_{2}. The results obtained for “off” and “on” state capacitance using Eqs. (6)–(8) are shown in Figs. 6(a) and 6(b), respectively.

*E*of the MOS modulator can therefore be calculatedand the result is shown in Fig. 7 . Often, in practice, the applied modulation voltage V is a digital voltage that employs a return-to-zero line code in which the signal drops to zero within each clock period—implying that the bit’s energy occupies 50% of the time slot. For that reason, we shall assume that the modulator’s switching energy

_{s}*per bit*is approximately one-half of

*E*.

_{s}*V*of 1.5 to 3.1 V is transistor-compatible (here

_{on}*V*) and the

_{on}= V_{th}*V*of 0.097 to 0.125 V is quite small, while

_{off}*C*of 4 to 12 fF is generally larger than

_{off}*C*of 2.7 to 4.7 fF. The

_{off}*E*of 4 to 14 fJ is generally low. What are the “best”

_{s}*t*and

_{ox}*N*parameters? We have selected from these graphs the values

_{p}*t*= 200 nm and

_{ox}*N*= 8 × 10

_{p}^{16}cm

^{−3}as being optimum because they give a good solution to the minimum-versus-maximum problem of

*E*-vs-Δ

_{s}*λ*. Then

*V*= 2.2 volts,

_{on}= V_{th}*V*= 0.11 volts,

_{off}*C*= 3.6 fF, and

_{on}*C*= 6.9 fF. Assuming that the infrared extinction of the modulator is adequate at this gate voltage,

_{off}*E*= 8.5 fJ and the energy per bit is 4.3 fJ/bit. The MOS field effect modulator is inherently very fast and its modulation speeds are probably limited in practice by the device’s RC time constant, of the order of 1 ps.

_{s}## 5. Optical simulations

_{0}mode as the optimum modulation choice. This mode could be readily found when the donut’s outer radius

*r*

_{1}was 3 μm but we had difficulty in finding stable TE modes for

*r*

_{1}< 3 μm. However, at least for ungated donuts, smaller r

_{1}are feasible because experiments [3

3. Z. Xia, A. A. Eftekhar, M. Soltani, B. Momeni, Q. Li, M. Chamanzar, S. Yegnanarayanan, and A. Adibi, “High resolution on-chip spectroscopy based on miniaturized microdonut resonators,” Opt. Express **19**(13), 12356–12364 (2011). [CrossRef] [PubMed]

_{0}mode at

*r*

_{1}= 1.95 μm for a SiO

_{2}-clad Si donut on 1 μm of buried oxide, with

*h*= 230 nm. In those experiments, the unloaded Q was 80,000 and a loaded Q of 30,000 was found when their micro-donut was side coupled across a 240 nm air gap to a Si strip waveguide.

_{2}thickness. At

*λ*

_{0}= 1558.92 nm, the following parameters were used in the electromagnetic simulations; a refractive index of 1.87 for HfO

_{2}[7

7. M. Jerman, Z. Qiao, and D. Mergel, “Refractive index of thin films of SiO_{2}, ZrO_{2}, and HfO_{2} as a function of the films’ mass density,” Appl. Opt. **44**(15), 3006–3012 (2005). [CrossRef] [PubMed]

_{2}. The inner radius r

_{o}of the Si donut was 2.2 μm while the outer radius was 3.0 μm, with a Si height of 230 nm. For both the ring-shaped gate dielectric and gate electrode, the inner radius was 2.6 μm with a 3.0 μm outer radius so that the 400-nm radial width

*r*

_{1}–

*r*

_{2}matched the mode width. We used thicknesses of

*t*= 200 nm,

_{ox}*t*= 200 nm, with a gate electrode

_{e}*p*-doping of 1 × 10

^{19}cm

^{−3}which produces an optical intensity attenuation factor of 80 cm

^{−1}while the Si waveguide

*p*-doping was 8 × 10

^{16}cm

^{−3}which gives a loss factor of 0.3 cm

^{−1}.

*t*, with the result presented in Fig. 8 . At the optimum

_{ox}*t*= 200 nm discussed earlier, we see that the unloaded Q is 23,120 where we found

_{ox}*λ*

_{0}of 1558.92 nm and an effective mode index of 2.564. Figure 9 illustrates the spatial intensity distribution of this high-Q TE

_{0}mode. When coupled to a bus channel waveguide for modulation use, the resonator Q decreases by an amount that depends upon the strength of evanescent-wave side coupling. We have chosen the critical-coupling condition as being useful for electro-modulation applications. For this choice, the loaded Q is 50% of the unloaded value; namely 11,560. This is equivalent to a mode propagation loss of about 39 dB per “cm of circumference” in the cavity.

## 6. Electro-optical response

2. R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. **23**(1), 123–129 (1987). [CrossRef]

**23**(1), 123–129 (1987). [CrossRef]

*n*= 8.5 × 10

^{–18}(Δ

*N*)

_{p}^{0.8}with the hole depletion Δ

*N*expressed in cm

_{p}^{−3}. We shall determine the Δ

*n*that occurs when the resonator is partially depleted at

_{eff}*V*=

*V*. Our goal is to calculate the wavelength dependence of the bus waveguide’s output power in the

_{on}*V*and

_{off}*V*states so as to determine the extinction ratio. Using the electromagnetic software, we first calculate the spectral dependence of bus intensity transmittance for the loaded-Q (11,540) device at

_{on}*V*. Then we examine the spectral shift (the translation on the wavelength scale) of that curve.

_{off}*λ*using the approximations: Δ

*λ/λ*

_{0}= Δ

*n*/

_{eff}*n*(which may underestimate the actual Δ

_{eff}*λ*). Further, we say that Δ

*n*is given by the spatial overlap integral of the on-state E

_{eff}^{2}mode-intensity profile with the depleted region of the resonator. In the depleted volume of the Si waveguide Δ

*N*= 8 × 10

_{p}^{16}cm

^{−3}and from the above hole-depletion formula we get Δ

*n*= 4.5 × 10

^{–4}in the upper half of the donut. Thus we use Δ

*n*=

_{eff}*M*Δ

*n*, where

*M*is the normalized overlap factor. To find

*M*, we used the Gaussian mode profile shown in Fig. 10 where

*t*= 0.5

_{d}*h*. This gives

*M*= 0.35 which implies that Δ

*n*= 1.6 × 10

_{eff}^{–4}. Using that, we then found Δ

*λ*= (Δ

*n*/

_{eff}*n*)

_{eff}*λ*= 0.097 nm when

_{0}*n*= 2.564. It is interesting to compare this shift to the FWHM linewidth Δ

_{eff}*λ*= 0.135 nm of the loaded-Q modulator, namely Δ

_{q}*λ*=0.72Δ

*λ*. Also our Δ

_{q}*λ*compares to Δ

*λ*= 0.044 nm in Fig. 9 of [1

1. S. P. Anderson and P. M. Fauchet, “Ultra-low power modulators using MOS depletion in a high-Q SiO₂-clad silicon 2-D photonic crystal resonator,” Opt. Express **18**(18), 19129–19140 (2010). [CrossRef] [PubMed]

*λ/*Δ

*λ*ratios generally make it easy to attain a large depth of modulation. Let us define

_{q}*T*as the off-state transmittance,

_{off}*T*as the on-state transmittance, and

_{on}*T*/

_{on}*T*as the extinction ration ER. We are going to operate the modulator in the “light-to-dark” mode. Thus, in Fig. 11 we have two choices of the operation-wavelength indicated by the vertical dashed lines; one approach gives the lowest insertion loss

_{off}*T*for which ER ≥ 6 dB, the other wavelength selection gives the highest ER irrespective of

_{off}*T*. For the first case, we estimate at

_{off}*λ*= 1559.05 nm that

*T*= −1.1 dB,

_{off}*T*= - 7.1 dB and ER = 6.0 dB, while the second approach at the

_{on}*T*valley where

_{on}*λ*= 1550.02 nm, gives

*T*= - 1.8 dB,

_{off}*T*= - 25.5 dB and ER = 23.7 dB. Because Δ

_{on}*λ*scales with

*V*, there is a tradeoff between gate voltage magnitude and ER. For example, if we reduced the gate voltage

_{on}*V*to 1 volt, the 6 dB extinction would decrease to something like 2.7 dB.

_{on}**19**(13), 12356–12364 (2011). [CrossRef] [PubMed]

## 7. Wavelength dependence of modulator performance

*t*/

_{d}*h*, the same Δ

*λ*and the same ER found at 1.55 μm. This means (for a fixed HfO

_{2}gate thickness) that we shall have to scale the p-type doping densities of both the waveguide body and the polysilicon gate electrode. For a given level of hole concentration in Si or poly-Si, we note that the free-carrier optical absorption loss of each region (parameters that enter into the mode Q calculation) is proportional to wavelength-squared [8], while at a given wavelength the optical intensity-attenuation factor of each material is roughly proportional to its individual free-hole concentration. Because of these scaling laws, it is necessary to reduce the doping levels of both regions as

*λ*is increased beyond 1.55 μm in order to maintain the 1.55 μm performance. So the two

*p*-dopings scale as 1/

*λ*

^{2}. We have found that this doping adjustment gives acceptable modulator performance over the 1.3 to 4.0 μm range. However, for

*λ*> 4 μm, the

*p*-doping of the gate electrode falls below 10

^{18}cm

^{−3}, increasing the series resistance R of the device to a high value that is probably not acceptable.

*E*as a function of wavelength. The principle here is that

_{s}*E*is proportional to the fundamental mode volume of the donut. In order to attain single-TE

_{s}_{0}-mode operation over 1.3 <

*λ*< 5.0 μm, we scaled

*r*

_{0,}

*r*

_{1,}

*r*

_{2}, and

*h*in proportion to

*λ*. This implies that the resonant-mode volume of our donut is scaling as

*λ*

^{3}. For that reason, we estimate—taking the best-case 1.55 μm result

*E*= 8.5 fJ as a reference—that

_{s}*E*= 5.0 fJ at

_{s}*λ*= 1.3 μm (2.5 fJ/bit), with

*E*increasing to 146 fJ at

_{s}*λ*= 4 μm. Clearly, we expect a low-energy technology at 1.3 μm.

*E*will as the smallest

_{s,min}*E*that gives 6 dB of extinction. At a fixed gate-electrode doping,

_{s}*E*will depends upon the choice of

_{s,min}*N*,

_{p}*V*, and

_{on}*t*. As seen in Fig. 11 of their paper, Anderson and Fauchet [1

_{ox}1. S. P. Anderson and P. M. Fauchet, “Ultra-low power modulators using MOS depletion in a high-Q SiO₂-clad silicon 2-D photonic crystal resonator,” Opt. Express **18**(18), 19129–19140 (2010). [CrossRef] [PubMed]

*N*and

_{p}*V*at a fixed

_{on}*t*to minimize

_{ox}*E*. They then repeated the procedure at other values of

_{s}*t*, thereby constructing a plot of

_{ox}*E*

_{s,min}*vs*

*t*. By analogy to their Fig. 11, we anticipate that our 1.55 μm

_{ox}*E*will be less than 10 fJ over a range of

_{s,min}*t*centered at 200 nm.

_{ox}## 8. Discussion and conclusion

_{2}-gated microdonut MOS-depletion electro-optical modulator with a

*p*-doped poly Si gate electrode and a

*p*-doped Si resonator body side-coupled through an evanescent-wave air-gap to one or two Si nanowire bus waveguides. At

*λ*= 1.55 μm, useful depths of optical intensity modulation at the bus output are predicted and 2 × 2 electro-optical switching looks equally feasible. The modulator is anticipated to work well over the 1.3 to 4.0 μm wavelength range.

_{0}mode in a 6-μm-diam Si donut having a 8 × 10

^{16}cm

^{−3}

*p*-type doping of the waveguide body, 230 nm waveguide height, 200 nm gate dielectric thickness, and 200 nm gate electrode thickness comprised of poly-Si doped

*p*-type at 1 × 10

^{19}cm

^{−3}. Electromagnetic mode modeling shows an unloaded Q of 23,120 with the side-loaded Q taken to be 11,560 giving a 0.135 nm FWHM linewidth. Then, with 2.2 volts applied to the gate, about half of the waveguide height is depleted of holes, resulting in a mode/charge overlap factor of 0.35 and a change in mode effective index of 1.6 × 10

^{−4}which shifts the initial resonance by 0.097 nm, thereby yielding a modulation extinction ratio on the bus of at least 6 dB. The on- and off-state capacitances of the device are 3.6 and 6.9 fF, respectively, and the switching energy is estimated to be 8.5 fJ or 4.3 fJ/bit with a modulation response time of about 1 ps as limited by the RC time constant. For a modulator scaled to operate at the 1.3 μm wavelength, the switching energy is estimated to be 2.5 fJ/bit.

9. J. Hendrickson, R. Gibson, M. Gehl, J. D. Olitzky, S. Zandbergen, H. M. Gibbs, G. Khitrova, T. Alasaarela, A. Saynatjoki, S. Honkanen, A. Homyk, and A. Scherer, “One-dimensional photonic crystal nanobeam cavities,” Chapter in *Quantum Optics with Semiconductor Nanostructures*, F. Jahnke ed., (Woodhead Publishing), to be published (2011).

11. B. Cluzel, K. Foubert, L. Lalouat, E. Picard, J. Dellinger, D. Peyrade, F. de Fornel, and E. Hadji, “Optical field molding within near-field coupled twinned nanobeam cavities,” paper IWB3 in OSA Advanced Photonics Conference, *Integrated Photonics Research, Silicon, and Nanophotonics,* Toronto, Canada (12–15 June 2011).

_{2}-gated nanobeam. Specifically, if the nanobeam has cross-section dimensions of 230 nm × 400 nm for TE

_{0}guiding at

*λ*= 1.55 μm, then the same

*p*-dopings and the same gate dielectric-and-electrode layer thicknesses derived here for the micro-donut would be used in the nanobeam over an 8 μm active length. Our MOS structure also applies to the inline Fabry Perot cavity in Fig. 1(a) of [12

12. B. Schmidt, Q. Xu, J. Shakya, S. Manipatruni, and M. Lipson, “Compact electro-optic modulator on silicon-on-insulator substrates using cavities with ultra-small modal volumes,” Opt. Express **15**(6), 3140–3148 (2007). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | S. P. Anderson and P. M. Fauchet, “Ultra-low power modulators using MOS depletion in a high-Q SiO₂-clad silicon 2-D photonic crystal resonator,” Opt. Express |

2. | R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. |

3. | Z. Xia, A. A. Eftekhar, M. Soltani, B. Momeni, Q. Li, M. Chamanzar, S. Yegnanarayanan, and A. Adibi, “High resolution on-chip spectroscopy based on miniaturized microdonut resonators,” Opt. Express |

4. | W. A. Zortman, M. R. Watts, D. C. Trotter, R. W. Young, and A. L. Lentine, “Low-power high-speed silicon microdisk modulators,” paper CThJ4, Conference on Lasers and Electro-Optics, San Jose, CA (2010). |

5. | M. R. Watts, D. C. Trotter, and R. W. Young, “Maximally confined high-speed second-order silicon microdisk switches,” paper PDP14, OFC/NFOEC, San Diego, CA (2008). |

6. | S. J. Emelett and R. A. Soref, “Analysis of dual-microring-resonator cross-connect switches and modulators,” Opt. Express |

7. | M. Jerman, Z. Qiao, and D. Mergel, “Refractive index of thin films of SiO |

8. | M. Nedeljkovic, R. Soref, and G. Mashanovich, “Free-carrier electro-refraction and electro-absorption modulation predictions for silicon over the 1 – 14 μm infrared range,” submitted to Opt. Mater. Express (June 2011). |

9. | J. Hendrickson, R. Gibson, M. Gehl, J. D. Olitzky, S. Zandbergen, H. M. Gibbs, G. Khitrova, T. Alasaarela, A. Saynatjoki, S. Honkanen, A. Homyk, and A. Scherer, “One-dimensional photonic crystal nanobeam cavities,” Chapter in |

10. | H.-C. Liu, C. Santis, and A. Yariv, “Coupled-resonator optical waveguide (CROWs) based on grating resonators with modulated bandgap,” paper SLTuB2 in OSA Advanced Photonics Conference, |

11. | B. Cluzel, K. Foubert, L. Lalouat, E. Picard, J. Dellinger, D. Peyrade, F. de Fornel, and E. Hadji, “Optical field molding within near-field coupled twinned nanobeam cavities,” paper IWB3 in OSA Advanced Photonics Conference, |

12. | B. Schmidt, Q. Xu, J. Shakya, S. Manipatruni, and M. Lipson, “Compact electro-optic modulator on silicon-on-insulator substrates using cavities with ultra-small modal volumes,” Opt. Express |

**OCIS Codes**

(130.3120) Integrated optics : Integrated optics devices

(130.4110) Integrated optics : Modulators

**ToC Category:**

Integrated Optics

**History**

Original Manuscript: July 6, 2011

Manuscript Accepted: August 24, 2011

Published: August 31, 2011

**Citation**

Richard Soref, Junpeng Guo, and Greg Sun, "Low-energy MOS depletion modulators in silicon-on-insulator micro-donut resonators coupled to bus waveguides," Opt. Express **19**, 18122-18134 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-19-18122

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### References

- S. P. Anderson and P. M. Fauchet, “Ultra-low power modulators using MOS depletion in a high-Q SiO₂-clad silicon 2-D photonic crystal resonator,” Opt. Express18(18), 19129–19140 (2010). [CrossRef] [PubMed]
- R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron.23(1), 123–129 (1987). [CrossRef]
- Z. Xia, A. A. Eftekhar, M. Soltani, B. Momeni, Q. Li, M. Chamanzar, S. Yegnanarayanan, and A. Adibi, “High resolution on-chip spectroscopy based on miniaturized microdonut resonators,” Opt. Express19(13), 12356–12364 (2011). [CrossRef] [PubMed]
- W. A. Zortman, M. R. Watts, D. C. Trotter, R. W. Young, and A. L. Lentine, “Low-power high-speed silicon microdisk modulators,” paper CThJ4, Conference on Lasers and Electro-Optics, San Jose, CA (2010).
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