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Abstract
We present the design of an adiabatic taper coupled Ge1−xSix electro-absorption modulator, which is based on Franz-Keldysh effect. The device has an active region of 0.8×50 µm2, an extinction ratio of more than 6 dB and an insertion loss less than 3 dB at the wavelength of 1550 nm. The operating bandwidth can be broadened to more than 90 nm by an AlN block assisted heater with only 6.2 mW energy consumption. Moreover, the operating wavelength shift caused by material composition deviation can be compensated to the expected wavelength by thermal tuning. This design may play an important role in next-generation, high-density optical integrations for datacom and high-performance computing.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical interconnection is one of the most promising solutions to break the performance limitations of electrical one as it has wider bandwidth and lower power consumption in data transmission for both long and short range communications [1]. Silicon Photonics (SiP) has emerged as the leading technology platform for optical interconnect due to the possibility of low-cost and high-volume production of Photonic Integrated Circuits (PICs) in Complementary Metal-Oxide-Semiconductor (CMOS) foundries [1–3]. Among various devices, Silicon (Si) electro-optic modulators have become the core of Si photonics integrated systems [4]. Since the first bandwidth SiP modulator with Gigahertz (GHz) modulation frequencies was reported by Intel in 2004 [5], great efforts have been made to improve the modulation efficiency, bandwidth, and insertion loss in the past two decades.
Si Mach-Zehnder Interferometer (MZI) modulators based on free carrier dispersion effect have been widely used in SiP products for their wide optical bandwidth and high-speed performance, and electro-optic (EO) cutoff frequencies in excess of 50 GHz have been reached with the carrier depletion Si modulators [6]. However, in light of applications requiring higher density integration, they suffer from the mm$\def\upmu{\unicode[Times]{x00B5}}^2$-scale size, relatively high energy consumption [7] and requiring complex drivers such as traveling-wave or distributed electrodes [8]. Si ring modulators have compact size and low power consumption but are limited by the narrow optical bandwidth and performance sensitivity arising from process and temperature variations [9]. Alternatively, Electro-Absorption (EA) modulators exploit the Franz-Keldysh (FK) effect [10] or the Quantum-Confined Stark Effect (QCSE) [11] in epitaxially grown GeSi or Germanium (Ge), offering an alternative solution with high potential. The FK effect is known to be a sub-picosecond phenomenon enabling high-speed modulation, and bulk material is relatively easier to grow and fabricate than quantum wells [12]. The FK effect of epitaxial Ge on Si substrates was first reported in 2006 [13]. Afterwards, significant advances have been made regarding the GeSi FK effect optical modulator. The first waveguide-integrated GeSi FK effect modulator with a small active area of 30 $\upmu$m$^2$ was demonstrated in 2008 [14] with an optical modulation speed of 1.2 GHz at a power consumption level of only 50 fJ/bit, and an operating spectrum range of 1539-1553 nm. In 2012, a compact GeSi EA modulator integrated on a 3 $\upmu$m Si waveguide was reported [15], and the 3 dB bandwidth was improved to 40.7 GHz with an operating wavelength range of 35 nm near 1550 nm. And a 56 Gb/s Ge waveguide EA modulator integrated in a 220 nm SOI photonics platform with a total power consumption of 1.84 mW at a CMOS-compatible voltage swing of 2 Vpp was achieved in 2016 [16].
High-speed and energy-efficient modulation is essential for next-generation optical interconnection, especially in applications such as co-package optics for datacom and monolithic optoelectronics integration for high-performance computing [17]. GeSi EA modulators provide unique advantages over many other candidates, offering higher optical bandwidth than Si-based ring modulators, and smaller footprint than the MZI modulators as well as lower power consumption [15]. Still, it’s important to further improve the optical bandwidth for Wavelength Division Multiplexing (WDM), which is achievable for EA modulators considering the influence of temperature on the absorption properties of the GeSi composites with different stoichiometry. Thermally tunable modulators have been intensively studied in SiP platform [18–21], and previous research on thermal effects in EA modulators has focused on the dependence of the device performance with the temperature rather than utilizing it [15,16]. In this paper, for the first time, we analyze the influence of thermal effect on the absorption coefficient of Ge$_{1-x}$Si$_x$ material system. Based on the calculated response of the material and structures, a broadband EA modulator with an optical bandwidth over 90 nm is proposed, and efficient architecture for the microheaters is used to reduce power consumption. This thermal tuning can also play an important role in compensating material composition and manufacturing deviation, and provide a larger fabrication tolerance. When working at the communication wavelength of 1550 nm, it can have an extinction ratio (ER) of more than 6 dB with a 3 V reverse bias applied. In addition, the coupling between the input Si waveguides and the GeSi absorber waveguide is optimized and an insertion loss of less than 3 dB can be achieved.
2. Material absorption response
The physics behind electro-absorption modulator refers to changing of the bulk material bandgap energy ($E_g$) according to the applied electric field, which is called the FK effect. When the proportion of Si in Ge$_{1-x}$Si$_x$ material is less than 2%, the FK effect of the Ge$_{1-x}$Si$_x$ material system can be obtained by linearly interpolating the intrinsic material properties of Ge and Si: $E_{g\_Ge1-xSix} = (1-x)E_{g\_Ge} + xE_{g\_Si}$ [22]. And a generalized theory for calculating the absorption coefficient $\alpha$ can be used [23], where the effects of reverse bias, strain and material composition on the absorption coefficient of Ge$_{1-x}$Si$_x$ system are explained in detail, however, the impact of temperature has not been involved. The absorption properties of this composite semiconductor are affected by temperature in two ways. One is the difference between thermal expansion coefficients of Ge and Si materials, causing strain in Ge$_{1-x}$Si$_x$ system to change with temperature. And the other is the interaction between electrons and phonons, which renormalizes the band energies [24]. Moreover, a very classic formula can be used to calculate the variation of semiconductor bandgap with temperature [25]:
where $E_g(T)$ is the temperature-dependent semiconductor bandgap, $E_0$ is the bandgap of the semiconductor material at 0 K , $T$ is the temperature in Kelvin, and $\alpha$ and $\beta$ are constant coefficients. We list the values of the parameters in Eq. (1) for Si and Ge in Table 1. Note the direct bandgap of Si was not mentioned in [25], we get this value from [26] and curve-fit data in it to obtain the value of $\alpha$ and $\beta$.
Table 1. Values of parameter in Eq. (1) for Ge and Si
The bandgap energy changes in Si and Ge were calculated with Eq. (1), and the results are shown in Fig. 1(a). It is obvious that bandgap decreases with temperature. Also, the direct and indirect bandgap of Ge$_{0.9915}$Si$_{0.0085}$ and Ge$_{0.985}$Si$_{0.015}$ are obtained by the interpolation method as shown in Fig. 1(b). The indirect bandgaps (dotted lines) of two Si composition almost coincide while the direct ones (solid lines) are not convergent. It indicates the composition ratio of Si has a great influence on the direct bandgap.
Fig. 1. (a) Calculated changes in the bandgap energy of Si and Ge. The blue lines represent Si and the red ones represent Ge. (b) Calculated bandgap energy of Ge$_{1-x}$Si$_x$ by interpolation method. The green lines represent Ge$_{0.9915}$Si$_{0.0085}$ the red ones represent Ge$_{0.985}$Si$_{0.015}$. Dotted lines in (a) and (b) are indirect bandgaps and the solid ones are direct bandgap.
In the case of Ge and Ge$_{1-x}$Si$_x$, we only need to focus on the FK effect of the direct gap because its magnitude is about three orders higher than that of the indirect gap [27]. Considering the influence of temperature on the semiconductor band, the absorption coefficient of the direct gap is modeled as Eq. (2), which comes from the Schr$\ddot {o}$dinger equation of electron-hole pairs in the presence of an electric field with Fermi’s Golden Rule applied [23]. For simplicity, a uniform electric field is assumed and only electrons and holes near the band edges of the conduction and valence bands are considered since they contribute the most to the band-to-band transitions.
First, the influence of the different composition ratio of the material on the absorption property at room temperature is calculated on the basis of Eq. (2). The absorption coefficient spectra of Ge$_{0.9915}$Si$_{0.0085}$ is shown in Fig. 2(a). There is a large difference in the absorption coefficient ($\Delta \alpha = \alpha _{off}-\alpha _{on}$) between the OFF status (high electrical field of 70 kV/cm with a reverse bias applied) and ON status (low electrical field of 10 kV/cm caused by built-in potential) at 1550 nm. One of the basic Figures Of Merit (FOM) for an EA modulator is $\Delta \alpha /\alpha _{on}$ as it measures the ratio between the Extinction Ratio (ER) and the Insertion Loss (IL). The inset in Fig. 2(a) shows the FOM as a linear function of the electrical field. It can be seen that FOM increases with the bias value, and the theoretical FOM is about 2.5 when an electric field of 70 kV/cm is applied. So, when this material composition is chosen, the EA modulator can have an ER of 7.5 dB if its IL is 3 dB when an electric field of 70 kV/cm is applied. The FOM as a function of wavelength for different Si compositions is shown in Fig. 2(b), assuming an applied electric field of 70 kV/cm at off status and 10 kV/cm at on status. By increasing the Si composition from 0.85% to 1.5%, the optimal operating wavelength of peak FOM has a blue-shift from 1550 nm to 1500 nm. On the contrary, the optimal operating wavelength redshifts from 1550 nm to 1620 nm when the Si composition reduces from 0.85% to 0% (i.e., pure Ge). It is noteworthy that the magnitude of the peak FOM decreases with the increase of Si content. This is because Ge has a larger absorption coefficient at a shorter wavelength.
Fig. 2. (a) Absorption coefficient spectra of the $\textrm {Ge}_{0.9915}\textrm {Si}_{0.0085}$ with the high and low electric field. Inset: calculated FOM as a linear function of the electric field; (b) and (c) is FOM as a function of wavelength for different Si compositions and different temperature respectively, assuming an applied electric field of 70 kV/cm at off status and 10 kV/cm at on status.
For a fixed composition ratio of $\textrm {Ge}_{1-x}\textrm {Si}_{x}$ (x=0.85%), FOM as a function of wavelength at different temperatures was calculated and shown in Fig. 2(c). When the temperature changes from 300 K to 355 K, according to the FOM response, the wavelength at which FOM has maximum will shift from 1550 nm to a wavelength of 1600 nm. Similarly, a blue-shift is expected by reducing the temperature. Thus, it’s an effective method to broaden the optical bandwidth of the GeSi EA modulator with an appropriately equipped heater. With the thermal tuning approach, the operating wavelength range can be considerably broadened at a cost of 55 K temperature change. Meanwhile, it’s important to figure out an efficient architecture for this method and not to bring large extra power consumption and optical loss to the heat-assisted EA modulator. Considering that the absorption varies with the GeSi composition ratio, it can also be compensated to the expected wavelength by the thermal tuning of the heater.
3. Architecture design of thermal tuning
The traditional heater in silicon photonics is usually a high-resistance material, for example TiN, put directly above the waveguide as illustrated in Fig. 3(a). However, the surrounding SiO$_2$ has a thermal conductivity as small as 1.38 W/m$\cdot$K, leading to low heating efficiency. One method to increase the efficiency of heat transfer is to use a thinner oxide layer, while this solution is not only inefficient but also introduces more optical losses. Until now, various ways have been used to improve thermal efficiency [28,29]. Recently, an AlN-assisted method is proposed for thermal-optics phase shifter, using an AlN block between the heater and the waveguide, which makes the waveguide have a similar temperature as the heater during heating [30]. Still, the efficiency improvement has a limitation due to the heat dissipation by the silicon substrate. It is conceivable that the substrate Si under the device can be removed to isolate the heat [31]. In our design, we employ the structure of the AlN block with a suspended architecture as shown in Fig. 3(b) to build the power-efficient heater for the GeSi EA modulator, which is on a silicon-on-insulator (SOI) platform with ridge waveguides (width=1 $\upmu$m, height=0.22 $\upmu$m, etch depth=0.11 $\upmu$m) on top of 2 $\upmu$m buried oxide (BOX). The size of GeSi waveguide is 0.6$\times$0.35 $\upmu \textrm {m}^{2}$, and the height of AlN block and TiN, whose width is the same as GeSi waveguide, is 1 $\upmu$m and 0.12 $\upmu$m, respectively.
Fig. 3. (a) The traditional structure of a heater; (b) AlN-assisted and substrate removed structure. The EA modulator is designed on an SOI platform with a 1$\times$0.22 $\upmu \textrm {m}^{2}$ ridge waveguide, and the top Si layer is etched to 0.11 $\upmu$m. The width of GeSi waveguide, AlN block and TiN is all 0.6 $\upmu$m for process simplicity, and their height is 0.35 $\upmu$m, 1 $\upmu$m, and 0.12 $\upmu$m, respectively.
We simulated the temperature distribution of both traditional and AlN-assisted structures when a 6.2 mW source power is applied with Lumerical’s 3D Heat Transport Simulator. For the traditional structure, the temperature of the heat source is as high as 352 K as shown in Fig. 4(a), but the temperature of the waveguide is only 314 K according to Fig. 4(c). This can be owing to the small thermal conductivity of SiO$_2$, resulting in the thermal efficiency value low as 26.9%. In our design, the combination of high thermal conductivity of the AlN block and the heat isolation of the suspended structure ensures efficient heat transfer and utilization inside the system. So, the heater temperature can reach 355 K as shown in Fig. 4(b) and the GeSi waveguide temperature is high as 354 K as shown in Fig. 4(d). The thermal efficiency of near 98% is reached with this design. Besides, the heat distribution is uniform enough to obtain good thermal tuning. As AlN has an effective refractive index of 2, it has no impact on the optical mode in waveguide according to our simulations. The influence of TiN on the light propagation is also be negligible because it is 1 $\upmu$m away from the active region.
Fig. 4. Simulated temperature distribution when a 6.2 mW source power is applied. (a) and (b) are traditional and AlN-assisted structure with the substrate removed, respectively. (c) and (d) are the corresponding GeSi waveguide heat distribution, respectively.
4. Modulator design and performance simulation
For the design of bulk material EA modulator, there are several ways to couple GeSi waveguide to Si waveguides [22,23,32]. In our design, the light is coupled from the Si waveguides to GeSi waveguide through adiabatic tapers to reduce the insertion loss. As schematically shown in Fig. 5(a), the light is first input into a Si ridge waveguide, then passes through a Si taper into a wider Si waveguide, and then is coupled into the active region through a GeSi adiabatic taper. And the symmetric design is used in the output side. The Si input and output waveguides are single-mode ridge waveguides with a ridge height of 110 nm, a slab thickness of 110 nm and a width of 400 nm. The Si taper has a length of 10 $\upmu$m, and the width of the intermediate Si waveguide is 1um. For the active part, the GeSi strip waveguide has a length of 50 $\upmu$m, a width of 0.6 $\upmu$m and a thickness of 0.35 $\upmu$m. The design of the GeSi taper, discussed in detail later, is complex because it needs to consider several factors. We use Finite-Different-Time-Domain (FDTD) method to analyze the transmission in the x-z plane of our structure as shown in Fig. 5(b).
Here, we give a detailed discussion on the GeSi taper design. First, the GeSi taper is not suitable to use as the working region because of the small width of the tip, which will build a large electric field in this area and may lead to material breakdown [23]. Therefore, the GeSi taper needs to be designed to be as short as possible to make a compact device and avoid additional loss. On the other hand, a short taper may make the taper nonadiabatic. According to our simulation of the tip width and length of the taper with the FDTD method, when the tip width is 0.15 $\upmu$m and the taper length is 5.7 $\upmu$m, the transmission can reach 0.937 as shown in Fig. 6(a). And the taper is proved to be adiabatic from its transmission spectra from 1530 nm to 1650 nm+ as shown in Fig. 6(b). The decrease of the transmission at short wavelength is due to the absorption of GeSi which is inherently stronger as shown by the red curve in Fig. 6(b). We can see that the transmission is always larger than 0.9 at a longer wavelength than 1530 nm, which means this taper is ensured to be adiabatic. Also, the extra loss caused by the single taper is calculated to be about 0.3 dB at 1550 nm from the black curve in Fig. 6(b). As the taper transmittance is sensitive to the width of the taper tip, it affects the performance of the modulator when it’s bigger than 0.25 $\upmu$m according to Fig. 6(a). Since a narrow width of the taper requires high process accuracy, we choose 0.15 $\upmu$m as a tradeoff.
Fig. 6. (a) Taper transmittance at different tip width and taper length , the marked point stands for which parameters of taper design we use; (b) Taper transmittance from 1500 nm to 1650 nm. The red curve is transmission of GeSi taper and the black one is the extra loss caused by a single taper.
To avoid extra losses caused by electrodes, they are put 1 $\upmu$m away from the waveguide region and have the same length with GeSi strip waveguide as shown in Fig. 7(a). As can be seen from the mode distribution and the electric field distribution of the GeSi waveguide region in Fig. 7(a), light is well confined in the GeSi waveguide, and the electric field distribution of the corresponding region is very uniform. Therefore, the electric field in the waveguide region can be treated as a uniform one. In the simulation, a tilted implant of boron and phosphorus is used to form a horizontal p-i-n junction. The heavily doping carrier concentration is set 2$\times$10$^{19}$ cm$^{-3}$, and doping depth is set as 50 nm for GeSi active region. The light doping region is to reduce the resistance value and improve the RC characteristics of the device, which determines the modulation speed of the EA modulator. We also estimate the 3 dB frequency through a simple RC circuit model, where the resistance R and capacitance C is calculated to be 50.5 $\Omega$ and 9.6 fF when a 3 V reverse bias is applied. Thus, the 3 dB frequency can theoretically reach 165 GHz when we consider an external load resistance of 50 $\Omega$. The energy consumption per bit for dynamic modulation can be estimated by the equation $energy/bit = 1/2(CV_{pp}^2)$ [14], and the dynamic power consumption level is only 43 fJ/bit when the swing voltage is 3 V. For a given 100 Gbps data transmission rate, the total dynamic power consumption of our device is about 105 fJ/bit when consider the extra power consumption from the heater. The built-in potential is about 0.6 eV, and the energy band is tilted when a 3 V reverse is applied as shown in Fig. 7(c). We also get the electric intensity along the y-direction of the intermediate portion of the waveguide in Fig. 7(d). The electric field at 0 V is about 10 kV/cm. With a reverse bias of 3 V, the electric field can reach 70 kV/cm.
Fig. 7. (a) The device with side electrodes. Right top figure and the bottom one is the mode and electric field distribution in GeSi waveguide; (b) Doping profile in simulation; (c) Band energy with 0 V and 3 V reverse bias; (d) electric intensity along y-direction at mid-waveguide height.
In our simulations, the optical transition loss between the GeSi waveguide and the SOI waveguide, and the free-carrier loss in the doped waveguide region are fully considered. For the designed GeSi EA modulator, Ge$_{0.9915}$Si$_{0.0085}$ is used as the active material, and the active region is as small as 0.6$\times$50 $\upmu \textrm {m}^{2}$. Through FDTD simulations, we can see that the designed GeSi EA modulator has a more than 6 dB of ER when a 3 V reverse bias is applied, and less than 3 dB of IL at the communication wavelength of 1550 nm as shown in Fig. 8(a). The corresponding FOM is more than 2.1 as shown by the blue curve in Fig. 8(b). This value is smaller than the material calculation, which is attributed to the additional loss caused by adiabatic taper and free-carrier absorption. Here, we define the Operating Bandwidth (OBW) of EA modulator as the wavelength range of the FOM decreases from the peak value to the 0.707 times, the EA modulator operating bandwidth is about 1530-1580 nm at 300 K as shown in Fig. 8(b). By heating the waveguide to 355 K, we can broaden the OBW to 90 nm or even bigger with a higher temperature as shown by the orange curve in Fig. 8(b). Note that the peak value of FOM will decrease by 0.2 at 355 K due to enhanced absorption of GeSi tapers. Also, as claimed in the material response part, the thermal tuning mechanism can be used to compensate the wavelength shift caused by a larger silicon ingredient in the composition. When Ge$_{0.9915}$Si$_{0.0085}$ material is used, the optimal operating wavelength blue-shifts to 1510 nm as shown by the black curve in Fig. 8(b). But, when the waveguide is heated to 355 K, the operating wavelength return to 1550 nm as shown by the red curve in Fig. 8(b).
Fig. 8. Optical modulation at 1550 nm. (a) the cyan-blue curve and red curve are ER under 3 V reverse bias and IL respectively; (b) FOM of the EA modulator. The blue curve, orange curve, black curve, and red curve is Ge$_{0.9915}$Si$_{0.0085}$ and Ge$_{0.985}$Si$_{0.015}$ at 300K and 350K respectively.
5. Discussion and conclusion
The comparison of the designed EA modulator with the published works is listed in Table 2. In this table, the insertion loss is defined as the on-chip loss, including Si waveguide-to-EA modulator coupling loss, free carrier effect, and Ge absorption. Fiber-to-waveguide coupling loss is excluded. With the highly efficient taper design, an IL of less than 3 dB is achieved. The designed modulator has a comparable ER with the experimental results when similar reverse bias is applied. The operating bandwidth in the references is no more than 35 nm, while a 90 nm OBW is obtained with the AlN-assisted heater in this work. The rate of the band edge shift with temperature is about 0.91 nm/K, as shown in Fig. 8(b), which is larger than 0.76 nm/K in [15] and 0.78 nm/K in [16]. The difference in the rate value might be attributed to the distribution of temperature in the active region and test methods. In addition, we confirm that temperature can be used to compensate for material composition deviation.
Table 2. Comparison between our design and reference ones
In summary, we propose a heater-assisted EA modulator, providing a broadened optical bandwidth from less than 50 nm to 90 nm near 1550 nm, coupled with the ability to compensate the wavelength shift induced by the material composition deviation with a competitive device size, and power consumption when compared with MZI modulators. This device has a great potential prospect in next-generation high-density integration for on-chip interconnect applications.
Funding
Ministry of Science and Technology of the People's Republic of China (2016YFE0130000); National Natural Science Foundation of China (61904185, 61905269); Open Fund of State Key Laboratory of Transient Optics and Photonics; Shanghai Sailing Program (18YF1428200, 19YF1456600).
Disclosures
The authors declare no conflicts of interest.
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