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Abstract
In this paper, we analyze a compact silicon photonic phase modulator at 1.55 μm using epsilon-near-zero transparent conducting oxide (TCO) films. The operating principle of the non-resonant phase modulator is field-effect carrier density modulation in a thin TCO film deposited on top of a passive silicon waveguide with a CMOS-compatible fabrication process. We compare phase modulator performance using both indium oxide (In2O3) and cadmium oxide (CdO) TCO materials. Our findings show that practical phase modulation can be achieved only when using high-mobility (i.e. low-loss) epsilon-near-zero materials such as CdO. The CdO-based phase modulator has a figure of merit of 17.1°/dB in a compact 5 μm length. This figure of merit can be increased further through the proper selection of high-mobility TCOs, opening a path for device miniaturization and increased phase shifts.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical communication systems employ both amplitude and phase modulators for signal processing. These modulators should satisfy stringent requirements of low power consumption, high bandwidth, small footprint, and a fabrication process that is CMOS compatible. Silicon-based electro-optic modulators have shown much promise in recent years due to the large material index, high modal confinement, low absorption losses at short-infrared telecommunications wavelengths, and compatibility with CMOS fabrication processes [1–4].
Despite these advantages, a fundamental tradeoff exists between efficiency and bandwidth due to the weak light matter interaction in silicon [5]. For example, non-resonant silicon Mach-Zehnder modulators can achieve wide optical bandwidths at the expense of millimeter-scale device lengths [6]. Recently, this size/bandwidth tradeoff has been broken using plasmonic [7, 8] and epsilon-near-zero (ENZ) effects [9] in hybrid silicon modulators [10–18]. ENZ effects occur near a point where the real part of a material’s permittivity crosses zero, transitioning from a low-loss dielectric to a lossy metal. At frequencies near this transition point, light-matter interaction can be greatly enhanced by confining light into sub-wavelength geometries [19–26]. Transparent conducting oxides (TCO) such as indium tin oxide (ITO), indium oxide (In2O3), and cadmium oxide (CdO) are useful materials for ENZ-based devices since they have a permittivity that can be tuned either electrically or optically; furthermore, their ENZ crossing points are in the near-infrared wavelength range, making them well suited for telecommunication applications [27, 28].
To date, most modeling and experimental efforts have focused on amplitude modulation rather than phase modulation. In this paper, we present the design of a compact ENZ phase modulator based on a gate-tunable TCO layer that is integrated on top of a passive silicon waveguide for the first time. The impact of the TCO’s carrier density and mobility on the phase change properties of the phase modulator are investigated through two-dimensional (2D) finite-difference-time-domain (FDTD) simulations. In particular, our numerical analysis shows that with this device geometry significant levels of phase modulation can only be achieved by employing high mobility TCO materials such as CdO. To establish an optimum operating point for the phase modulator, a phase modulation figure of merit (FOM) is defined as
which results in a FOM of 17.1°/dB in a 5 µm long modulator with high-mobility CdO. This FOM is a ~4x improvement over the same device geometry when lower-mobility In2O3 is used as the TCO film. In addition, the 5 µm long In2O3 based modulator only reaches a peak phase shift of –24.3° which is insufficient for most phase modulator applications. These results open a path for an experimental demonstration of compact and optically broadband phase modulators in an integrated optics platform.The paper is organized as follows: Section 2 details the device geometry, providing a generic description of the operating principles of the TCO-based ENZ phase modulator. In Section 3 we investigate the phase modulator performance versus accumulation layer carrier concentration using In2O3, since this material has been used successfully in ENZ amplitude modulators [15]. Because In2O3 provides limited phase change properties, in Section 4 we explore phase modulation in a device with the same geometry in which the In2O3 has been replaced with a TCO with an order of magnitude higher mobility, CdO. Finally, in Section 5 we investigate the phase performance of TCO-based device as a function of carrier mobility.
2. TCO gate-tunable ENZ phase modulator
The proposed phase modulator shown schematically in Fig. 1 utilizes plasmonic effects and ENZ confinement in a stable inorganic TCO film that has a gate-tunable charge carrier density. The phase modulator is comprised of a silicon waveguide with a height of 340 nm that is fabricated on a silicon-on-insulator substrate. A 10 nm-thick tunable TCO layer is integrated on top of the waveguide with a connection to a metal pad that forms the base electrical contact for the metal-oxide-semiconductor like device. A gate dielectric with a thickness of 10 nm is sandwiched between the TCO layer and a 200 nm thick top gate metal contact. This device topology has a fabrication process that is CMOS compatible and can support phase modulation of both transverse-electric (TE) and transverse-magnetic (TM) modes.
Fig. 1 (a) 3D view of the TCO ENZ modulator, and (b) associated 2D cross-section. In panel (a), the phase of the TM mode dominant field Ey is explicitly marked.
The dielectric permittivity of the thin-film TCO can be described using the Drude model
where is the high frequency limit of the permittivity, is the plasma frequency, and is the damping factor. The plasma frequency is given bywhere is the carrier concentration, is the electron charge, is the absolute permittivity of vacuum, and is the effective mass. The damping factor is given bywhereis the material mobility.Figure 2 shows the real and imaginary parts of the permittivity for a general TCO material under biased and unbiased conditions. In the unbiased state, the TCO has a uniform background carrier concentration throughout the film, resulting in a material that behaves like a low-loss dielectric for wavelengths shorter than the ENZ wavelength. In practice, this can be achieved by controlling the carrier concentration in the film during deposition [15]. When a voltage is placed across the device, the carriers accumulate at the TCO/gate dielectric interface which creates an accumulation layer with increased carrier concentration [10]. This accumulation layer is modeled as a 1-nm-thick layer with carrier concentration in the range of 1020 cm−3, which was previously shown to provide good agreement with experimental In2O3 ENZ photonic modulators results [15]. This increased carrier concentration results in a blueshift of the ENZ wavelength and transition to a material with metallic behavior with increased imaginary permittivity and loss at the unbiased ENZ wavelength. It should be noted that the 9 nm-thick TCO region below the accumulation layer is modeled with a constant unbiased carrier concentration and only the accumulation layer has a varying carrier concentration with applied voltage.
Fig. 2 Real (solid) and imaginary (dashed) parts of a general TCO permittivity versus wavelength for both biased (green) and unbiased (black) states. By applying a voltage across the device, the ENZ point can be moved across the infrared region of the spectrum.
For device operation, we aim to increase carrier accumulation such that the ENZ wavelength blueshifts to near the optical carrier wavelength of 1.55 µm. As the ENZ wavelength approaches the device operating wavelength there is a strong enhancement in modal confinement in the accumulation layer [14, 19] which results in both phase and amplitude modulation in the propagating signal. A phase delay is generated relative to the unbiased state by confining the mode to the low-index ENZ layer. As the ENZ point approaches the operating wavelength, confinement within the accumulation layer increases while the mode effective index decreases; both of these effects increase the phase delay through the active region of the modulator. Initially, In2O3 is investigated in Sec. 3 for its phase modulation performance using the device geometry in Fig. 1.
3. Indium oxide phase modulator
Two-dimensional FDTD simulations of the phase modulator shown in Fig. 1 were performed using Lumerical FDTD [29] with In2O3 as the TCO material, a high-k hafnia (HfO2) gate dielectric, and gold (Au) top and bottom metal contacts. It should be noted both two-dimensional and three-dimensional FDTD simulations of this device geometry have yielded similar results [19], so two-dimensional FDTD simulations were utilized in order to reduce the computational time. The silicon waveguide is excited under TM mode excitation (dominant field component in the y-direction) with a 5 μm long phase modulator section.
The In2O3 Drude model parameters for several carrier concentration levels are listed in Table 1, with the resulting dielectric permittivities shown in Fig. 3(a). The parameters in Table 1 were chosen to place the device wavelength in the near to mid-infrared region and are consistent with experimentally achievable results [14, 15]. Given that the exact mobility at each carrier concentration/gate voltage between the unbiased and biased states is not known, a conservative estimate of the lowest biased state mobility from [19] was assumed for all carrier concentrations except in the unbiased condition.
Table 1. Drude model parameters for In2O3 as a function of carrier concentration.
Fig. 3 (a) Real (solid) and imaginary (dashed) parts of the permittivity of In2O3 versus wavelength for several accumulation layer carrier concentration levels listed in Table 1 including N = 3.24 × 1019 cm−3 (black, unbiased state) and N = 3.53 × 1020 cm−3 (green, biased state). (b) Numerical results for the average Ey phase difference and integrated propagating power at a wavelength of 1.55 μm with the active region of the ENZ phase modulator spanning from x = 0 μm to x = 5 μm (highlighted with the grey shaded region) and with N = 2.5 × 1020 cm−3. (c) Phase modulator figure of merit (FOM) versus accumulation layer carrier concentration level referenced 7.5 μm from the modulator output.
Figure 3(b) shows the average (through the thickness of the 340 nm silicon waveguide) Ey phase difference at λ = 1.55 μm, relative to the unbiased phase condition with a carrier concentration of 2.5 × 1020 cm−3 in the In2O3 accumulation layer. This carrier concentration was selected for Fig. 3(b) because it results in the largest phase shift for the In2O3 phase modulator. The average phase difference is negative since the reduced mode effective index in the biased state results in less phase change relative to the unbiased case. The average phase shift (referenced 7.5 μm from the modulator output) is –24.3° through the 5 µm long modulator. The power propagating along the waveguide integrated in the y-direction for N = 2.5 × 1020 cm−3 is also shown in Fig. 3(b), which results in a loss of –5.7 dB. The loss in the unbiased state with N = 3.24 × 1019 cm−3 is –2.5 dB. The ripple in both the amplitude and phase response in Fig. 3(b) is due to the presence of a standing wave within the modulator.
The FOM is plotted in Fig. 3(c) versus carrier concentration level (referenced 7.5 μm from the modulator output) and shows a peak of 4.46°/dB with N = 2.25 × 1020 cm−3 for the 5 μm modulator. From this peak FOM, we calculate that a In2O3-based device requiring a 180° phase delay would result in a length of 46.3 μm and optical attenuation of more than 40 dB, which is far too much loss for practical devices. Next, we investigate in Sec. 4 replacing the In2O3 with a TCO with higher mobility.
4. High-mobility cadmium oxide phase modulator
The TCO mobility has been shown to impact the associated field level within the accumulation layer [19], with higher mobilities and lower losses resulting in larger peak field levels. In this section, we study the phase response in these high mobility films versus accumulation layer carrier concentration. Table 2 lists the Drude model parameters for CdO that were used in the FDTD phase modulator simulations. The unbiased and biased model parameters are consistent with data reported by Sachet et al. in [30]. Since the exact mobility at each carrier concentration/gate voltage between the unbiased and biased states is not known, a conservative estimate of the lowest biased state mobility from [30] was assumed for all carrier concentrations except in the unbiased condition.
Table 2. Drude model parameters for the CdO as a function of carrier concentration.
Figure 4 shows the CdO permittivity versus wavelength for the cases listed in Table 2. The unbiased static carrier concentration of the CdO material is 9.94 × 1019 cm−3 which places the ENZ crossing in the near-infrared range at a wavelength of 3.6 μm. Therefore, in the unbiased case, CdO behaves as a dielectric at the working wavelength of 1.55 μm. As listed in Table 2, the CdO ENZ point crosses at a wavelength of 1.55 μm for a biased carrier concentration of 5.4 × 1020 cm−3 but, as will be discussed later, phase shifts required for most practical applications (2π rad) occur at lower carrier concentration levels.
Fig. 4 Real (solid) and imaginary (dashed) parts of the permittivity of CdO versus wavelength for several accumulation layer carrier concentration levels.
Two-dimensional FDTD simulations of the phase modulator were performed versus CdO accumulation layer carrier concentration for a 5 μm long modulator under TM mode excitation into the silicon waveguide. Figure 5(a) shows the average (through the thickness of the 340 nm silicon waveguide) Ey phase difference relative to the unbiased phase condition at λ = 1.55 μm for varying carrier concentrations. As with the In2O3 phase modulator, the phase in the biased case lags the unbiased case. As the carrier concentrations increase, so does the phase difference with a flat response outside of the ENZ modulator. The 5 μm long modulator yields phase shifts of –92.9° and –178.1° (referenced 7.5 μm away from the modulator output) for carrier concentrations of 4.9 × 1020 cm−3 and 5.2 × 1020 cm−3, respectively. It should be noted that in Fig. 5(a), the phase ripple outside of the modulator is due to the subtraction of the biased and unbiased phase signals and the raw phase of the is smooth outside of the phase modulator for the carrier concentrations here shown.
Fig. 5 (a) Numerical results for the average Ey phase difference, and (b) the integrated propagating power at a wavelength of 1.55 μm and with the active region of the ENZ phase modulator spanning from x = 0 μm to x = 5 μm (highlighted with the grey shaded region). The results are plotted along the waveguide for various carrier concentrations N in cm−3, indicated in panel (a) for each curve.
Figure 5(b) shows the power propagating along the waveguide integrated in the y-direction for the various carrier concentrations shown in Fig. 5(a). A loss of –5.58 dB is incurred for a phase shift of –92.9° (N = 4.9 × 1020 cm−3) with the loss increasing to –16.0 dB with a phase shift of –178.1° (N = 5.2 × 1020 cm−3). Figure 6(a) shows the corresponding average phase difference at λ = 1.55 μm versus accumulation layer carrier densities between 3.2 and 5.3 × 1020 cm−3 with resulting phase shifts of –13.9° to –229.8° across this range (referenced 7.5 μm from the output of the phase modulator). While the phase shift response exhibits a linear dependence at lower doping concentration levels, as the ENZ crossing point approaches the operating wavelength the phase shift rapidly changes. Since most phase shifter applications require low loss and less than ~2π rad or ~360° of phase shift [31, 32], the phase modulator would be operated at a carrier concentration smaller than that required to move the TCO ENZ point to the operating wavelength.
Fig. 6 (a) Numerical results for the average Ey phase difference and (b) figure of merit (FOM) for the phase modulator for the 5 μm long modulator versus CdO accumulation layer carrier concentration.
The FOM is plotted versus carrier density in Fig. 6(b), and shows a peak of 17.1°/dB at N = 4.8 × 1020 cm−3. Simulations were performed of a 10 μm long modulator which showed the same FOM peak value in Fig. 6(b) since both the phase-shift and loss scale linearly. For TCO carrier concentrations approaching the ENZ crossing point, the loss of the phase modulator increases rapidly, causing a drop in the FOM despite the larger levels of phase shift. From this peak FOM, we calculate that a CdO-based device requiring a 180° phase delay would result in an optical attenuation of 10.52 dB and length of 11.52 μm, which is significantly less loss and size compared to the In2O3-based device from the previous section.
Thus far the FOM has been defined for a 5 μm long phase modulator, however, in order to better compare to other phase modulator technologies with varying sizes we will normalize the FOM by length. Watts et al. in [1] reported a silicon-based Mach-Zehnder phase modulator that experimentally achieved 1.53 rad of phase shift for a 1 mm long modulator biased at 5 V with a corresponding loss of 3 dB at λ = 1.55 μm. This yields a FOM of 29.2°/dB for the 1 mm long device. If we normalize the FOM by length, then for the silicon Mach-Zehnder device in [1] we obtain 0.029°/(dB∙μm) which is two orders of magnitude lower than the normalized FOM achieved in this work of 3.42°/(dB∙μm). For a 180° phase shift, the CdO-based ENZ phase modulator achieves a size reduction of 178x, while incurring 1.7x more loss compared to the Mach-Zehnder device in [1].
We use CdO here as an exemplar high mobility TCO material since its ENZ crossing is in the near to mid-infrared range [14, 19, 30]. However, in general, other suitable high-mobility ENZ materials with mobility larger than or equal to ~200 cm2/(Vs) would lead to results similar to those shown in this paper.
5. Dependence of the phase change and figure of merit on the CdO mobility
Based on Sec. 3 and Sec. 4, it is evident that the proposed phase modulator topology requires a TCO material with high mobility to achieve practical levels of phase shift while reducing excess loss. In this section, modulator phase shift, loss, and FOM are investigated versus CdO mobility with a fixed accumulation carrier density of N = 4.8 × 1020 cm−3, which is chosen from the apex of the FOM curve in Fig. 6(b) and results in a ENZ wavelength of 1.64 µm. While there are practical limitations to achievable TCO mobilities, it is still important to understand the phase modulator performance versus mobility with the likelihood of future material developments and improvements.
Figure 7(a) shows both the average Ey phase-shift through the 340 nm thick waveguide and the loss integrated in the y-direction of the phase modulator versus accumulation layer mobility ranging from 25 to 675 cm2/(Vs). A low mobility of 25 cm2/(Vs) results in only –11.5° of average phase shift with the phase change improving to –76.1° with μ = 200 cm2/(Vs). The lower mobility results in smaller field concentrations in the accumulation layer and less modal confinement, as shown in Fig. 8(a), which results in smaller phase changes. Note that in Fig. 8(a) the magnitude of Ey is normalized by the Ey field magnitude maximum at the input of the phase modulator (x = –0.1 μm). In addition, the higher TCO mobilities result in a magnitude of the permittivity which is closer to zero at λ = 1.64 μm as shown in Fig. 8(c). In Fig. 7(a) the phase response flattens out for mobilities above 200 cm2/(Vs) with –81.3° of phase change achieved for μ = 675 cm2/(Vs). The phase modulator loss generally decreases with higher mobilities, since we are operating at a dielectric permittivity point below the ENZ crossing with a minimal loss of –2.85 dB for 675 cm2/(Vs). The FOM improves with higher levels of CdO mobility as shown in Fig. 7(b), with a mobility of 675 cm2/(Vs) resulting in an FOM of 28.6 °/dB. From this FOM, we calculate that a device requiring a 180° phase delay would result in an optical attenuation of 6.31 dB, with an overall length of 11.06 μm. It should be noted that the higher mobility materials must still follow a Drude model response in the wavelength region of interest.
Fig. 7 (a) Numerical results for the average Ey phase difference and the integrated power at λ = 1.55 μm versus TCO mobility with N = 4.8 × 1020 cm−3. (b) Phase modulator FOM versus TCO mobility with N = 4.8 × 1020 cm−3.
Fig. 8 (a) FDTD simulations of |Ey| (normalized to the Ey field magnitude maximum at the input to the phase modulator at x = –0.1 μm) halfway along the 5 μm phase modulator plotted through the thickness of the device in the y-direction at z = 0 μm for three different TCO mobilities (25, 250, and 675 cm2/(Vs)) with N = 4.8 × 1020 cm−3. Note that the 1 nm-thick TCO accumulation layer is positioned between 0.349 and 0.35 μm, in correspondence of the field peak, better visible in the inset. (b) Phase modulator device cross-section; the dashed black line indicates the location of the field in panel (a). Magnitude of the TCO permittivity versus wavelength for mobilities of 25, 250, and 675 cm2/(Vs) with N = 4.8 × 1020 cm−3 (c).
A simple parallel plate capacitor model can be used to estimate the drive voltage required to achieve a certain carrier concentration in the accumulation layer of the TCO. The bias voltage is given by
where ΔN is the difference in carrier concentration in the accumulation layer between the biased and unbiased states (in units of Coloumb/m3), tacc is the thickness of the accumulation layer, dox is the thickness of the oxide layer, is the absolute permittivity of free space, and is the DC relative permittivity of the oxide layer. Using a HfO2 DC relative permittivity of 16, , , and ΔN = 3.81 × 1020 cm−3, which corresponds to the peak FOM carrier concentration difference, the predicted bias voltage is 4.3 V (note this value would be smaller if either a thinner oxide layer or less conservative oxide permittivity is used). This results in an estimated VπLπ of only 0.005 V∙cm given a modulator length of 11.52 μm and a TCO mobility of 250 cm2/(Vs) in the accumulation layer.6. Conclusion
We have shown numerical analyses of a compact phase modulator based on epsilon-near-zero confinement in stable inorganic TCO materials. Modulators based on ENZ confinement have demonstrated ultra-compact footprints and wide bandwidths. Our results demonstrate that high-mobility (i.e. low-loss) ENZ materials are pivotal to achieve phase modulations usable in device applications for this phase modulator topology. We achieved a figure of merit of 17.1°/dB through a 5 μm long modulator based on CdO and a VπLπ of only 0.005 V∙cm using a conservative mobility of 250 cm2/(Vs). Materials with even larger mobility can increase the figure of merit further, opening a path for additional device miniaturization and increased modulation depth and phase shifts.
Funding
Laboratory Directed Research and Development (LDRD), Sandia National Laboratories; U.S. Department of Energy (DE-NA0003525).
Acknowledgment
This work was supported by the Laboratory Directed Research and Development Program at Sandia National Laboratories. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.
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