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Abstract
We demonstrate Ge/Si high-power and high-speed distributed traveling wave photodetectors (TWPD) by using the inductive gain peaking technique. Input terminals of TW electrodes are open to enhance RF output efficiencies to output loads. Furthermore, optimized on-chip spiral inductors are incorporated at output terminals of TW electrodes to alleviate bandwidth degradations caused by the absences of matching impedances. A comprehensive equivalent circuit model is developed to calculate the frequency response of this scheme. It is used to optimize the design, and then is validated by measurement results. After inducing on-chip inductors, the bandwidths of 4-stage and 8-stage TWPDs are improved from 32 to 44 GHz and 16 to 24 GHz, respectively. Maximum RF output powers of 4-stage and 8-stage TWPDs with on-chip inductors are measured to be 5.7 dBm and 9.4 dBm at 20 GHz, respectively.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
High-speed and high-power photodetectors (PD) have important applications in a variety of analog optical links, and thus have attracted considerable research attentions for a lone time. Especially, in Radio-over-Fiber (RoF) communication systems [1–3], RF signals are generated at central offices (CO), modulated on optical carriers, and subsequently transmitted to the remote antenna units (RAU). At RAUs, opto-electronic conversions are performed by PDs. Transimpedance amplifiers (TIA) followed by power amplifiers are usually used to amplify RF signals so as to overcome path losses in the wireless channels between the RAUs and the end users [4,5]. However, the use of transimpedance amplifier will extremely increase the cost, complexity and power consumption of the system. An alternative architecture is to amplify the modulated optical signal in optical domain by a high-gain erbium-doped fiber amplifier (EDFA), and then convert the amplified optical signal to a strong RF signal with a high-saturation PD. This scheme eliminates the use of expensive transimpedance amplifiers and thus significantly reduce the RAU complexity and the power consumption [6,7]. However, due to the space charge effect and the thermal failure at high optical power levels, traditional PDs are subjected to a contradiction between the saturation RF output power and the bandwidth [8,9]. In order to address this issue, plenty of high-speed and high-power PDs are demonstrated on III-V material systems by utilizing either the uni-traveling carrier photodetector (UTC-PD) structures [10,11] or the modified UTC-PD structures (MUTC-PD) [12,13]. For instance, the modified UTC-PD flip chip bonded on diamond submount in [12] offers a bandwidth up to 28 GHz and a maximum output RF power of 26.2 dBm at 25 GHz. In Ref. [13], an evanescently-coupled waveguide MUTC-PD is demonstrated with a bandwidth over 105 GHz and a RF output power of 1.3 dBm at this frequency. Despite advanced performances of these III-V PDs, growing research interests are spurred by the consistent progress of silicon photonics to develop high-speed and high-power Ge/Si waveguide PDs on SOI platform [14–16].
There are different approaches to overcome the trade-off between the bandwidth and the saturation power of Ge/Si waveguide PDs. One widely used approach is to manipulate the optical field distribution inside the optical absorption region so as to avoid localized high-density photocarriers [17–19]. In Ref. [19], a Ge-on-Si PD incorporated with double lateral silicon nitride waveguides realize a bandwidth of 60 GHz at -3 V and an internal responsivity of 0.52 A/W at a high input optical power of 25 mW. Another advisable solution is to split the strong incident optical field into multiple independent PD elements. Photocurrents produced by all PD units then can be collected by either lumped electrodes [20] or traveling wave (TW) electrodes [21–23]. Although a well-designed TW electrode is favorable for increasing the bandwidth, it usually needs a matching impedance at its input terminal to avoid the detrimental RF reflection [24,25]. However, the matching impedance shunts half of total photocurrent. The RF power delivered to the load thus would drop by 6 dB. Therefore, it is desired to enhance the RF output efficiency of the silicon TWPD without degrading the bandwidth.
On the other hand, the inductive gain peaking technique has been widely used to increase bandwidths of various Ge/Si waveguide PDs [26–30]. An inductor is able to offset part of the PD’s capacitance effect so that the bandwidth can be elevated to some extent [27]. The inductor can be incorporated in the forms of off-chip bonding wires [26] or on-chip spiral coils [27–30]. For example, the bandwidth of a Ge PD is boosted from 30 GHz to 60 GHz after adding a 360 pF on-chip inductor in [28].
In this paper, we cancel matching impedances at input terminals of silicon TWPDs to enhance their RF output powers. Furthermore, on-chip spiral inductors are integrated to mitigate bandwidth degradations caused by RF reflections at open input terminals. With these measures, silicon TWPDs with high saturation RF output powers and high bandwidths are demonstrated. This paper is organized as follows: In section 2, we build an equivalent circuit model for the TWPD with integrated inductor. The model enables us to calculate the frequency response of the photocurrent and then optimize relevant design parameters. After that, we present measurement results of responsivities, bandwidths and power handling capabilities in section 3. Finally, a conclusion is reached in section 4.
2. Theoretical model and device design
A schematic diagram of the multi-stage TWPD with a peaking inductor is shown in Fig. 1(a). The incident light is coupled into the device by a fiber grating coupler, and then is distributed equally among n PD units by a log2n-stage binary tree made up of 1 × 2 multimode interferometers (MMI). The PD array are evenly spaced with a gap of Δ. Their photocurrents are fed to a coplanar waveguide (CPW) transmission line (TL). In principle, it is necessary to add optical delay lines of proper lengths dn before all PD units so that their RF outputs are synchronized in the CPW electrode. However, since the spacing between adjacent PDs is far shorter than the RF wavelength, the corresponding phase change is insignificant when the RF signal travels between two PD stages [23,31]. As a result, optical delay lines are cancelled in this work, i.e., d1 = d2=…=dn. A detailed discussion about this point will be given in the last paragraph of this section. The input terminal of CPW is open to avoid shunting a half photocurrent produced by the PD array. Therefore, the RF power delivered the load at the output terminal is elevated by 6 dB. However, the penalty is that backwards propagating photocurrents are reflected back at the open input port, and then interfere with forwards propagating photocurrents. The interference would lead to a steep roll-off of the frequency response and eventually degrades the 3dB bandwidth. To mitigate the bandwidth deterioration, a spiral inductor is incorporated at the output terminal of CPW to reduce the roll-off rate at the frequency range of interests.
Fig. 1. (a) Overall schematic diagram of the proposed TWPD with a peaking inductor. (b) Cross-section and equivalent circuit of the PD unit. (c) Cross-section and equivalent circuit of the CPW electrode. (d) Schematic layout and circuit model of the peaking inductor.
In order to optimize relevant design parameters of the device in Fig. 1(a), we at fist build its equivalent circuit model. A cross-sectional view of single Ge/Si waveguide PD unit is shown in Fig. 1(b). Its frequency-response behavior can be modeled by the equivalent circuit developed in [32], which is also plotted in Fig. 1(b). Here, Cj and Rj represent the junction capacitance and resistance, respectively, Rs is the series resistance of the P++ region, Rint and Lint denote the parasitic resistance and inductance of the electrode, respectively. I1 and I2 represent the diffusion and the drift current components, respectively. The response speed and the relative amplitude of I1 are described by a time constant τ1 and a weight factor A1. Similarly, those of I2 are described by τ2 and A2. The sum of A1 and A2 represents the normalized DC photocurrent, i.e., A1 + A2 = 1. In order to extract specific values of all circuit elements, we measure the frequency response of a stand-alone PD unit, and then fit the frequency response predicted by the equivalent circuit in Fig. 1(b) to the measurement result. The fitted and the measured frequency response curves are plotted in Fig. 2, where the 3 dB bandwidth is 50 GHz at -3 V. The inset of Fig. 2 lists the extracted values of all circuit elements. Through the Norton equivalent-circuit analysis, the equivalent circuit of PD can be converted to the parallel connection of a current source iPD and an admittance YPD as shown in Fig. 1(b). Their analytical expressions can be found in [31,33], and thus are not listed here for brevity. Furthermore, the transmission matrix of the single PD unit is given as
Fig. 2. Measured and fitted small-signal frequency responses of the single PD unit. The inset lists the extracted circuit parameters through the curve fitting.
The cross section of the CPW electrode is shown in Fig. 1(c), where W, S, and Wg are the signal electrode width, the ground electrode width, and the gap between the signal and the ground electrodes, respectively. By using the conformal mapping and the partial capacitance methods, we can deduce the equivalent circuit of the CPW, which is also plotted in Fig. 1(c). Analytical expressions of all elements in this circuit can be found in our previous work [31,34]. After introducing the line resistance and the line inductance which reflect the longitudinal current flow in the electrode [34], we can further convert the lumped-element equivalent circuit of CPW into the combination of a series impedance ZCPW and a parallel admittance YCPW as shown in the inset of Fig. 1(c). According to the Telegrapher's equations, the transmission matrix of the CPW between two PD units is calculated as
In order to improve the 3 dB bandwidth through the inductive peaking technique, a two-loop square spiral with an inductance of Lind is added between the GSG pad and the CPW. As shown in Fig. 1(d), its inner loop width, outer loop width and trace width are denoted as din, dout and wind, respectively. By utilizing the 3D electromagnetic simulation tool HFSS, we obtain the S-parameter matrix of the peaking inductor. The transmission matrix Mind of the inductor can be easily deduced from its S-parameter matrix according to Ref. [35].
By joining the specific circuit models of PD unit, passive CPW, and spiral inductor, we obtain a complete circuit model of the device as shown in Fig. 3. The green, yellow and red boxes denote the regions of PD unit, CPW and inductor, respectively. The impedances at the input and the load terminals of the CPW are denoted as Zin and Zload, respectively. According to the transfer-matrix method, the voltage Vi and the current Ii at the i-th current source node satisfy the following iteration relation
To obtain the voltage Vload dropped on the load, we at first assume that V0 and I0 are zero, and then use Eq. (3) iteratively to obtain the voltage Vn and the current In at the n-th node under this assumption. Finally, according to the superposition principle, the relationship between V0 and Vload can be calculated as
Since our scheme utilizes an open input terminal, the value of Zin in Eq. (4) is set to ∞. By solving the two equations listed in Eq. (4), we obtain the voltages at both terminals of the device (i.e., V0 and Vload) which vary with the operation frequency.
We use the model built above to design 4- and 8-stage TWPDs with peaking inductors. The minimal spacing between two adjacent PD units is constrained by the practical footprint of Ge/Si waveguide PD, and thus is selected as Δ=25 µm. As aforementioned, PD units directly utilize the baseline design in the device library provided by the foundry. Therefore, adjustable design parameters are the geometries of the CPW and the spiral inductor. The genetic algorithm is used to optimize the values of W, S, Wg, wind, din and dout with the optimization objective being the 3 dB bandwidth. The optimized results are listed in Table 1. In order to quantify the performance improvement induced by the inductor, reference 4- and 8-stage TWPDs without inductors are also modeled for comparison. Calculated frequency responses of TWPDs with and without inductors are plotted in Fig. 4. The bandwidths of un-peaked 4-stage and 8-stage TWPDs are 27 GHz and 16 GHz, respectively. After integrating inductors, the bandwidths of 4-stage and 8-stage TWPDs are substantially improved to ∼40 GHz and ∼25 GHz, respectively. As the scale of PD array increases, a larger inductor is needed to counteract the enhanced overall capacitance [27]. As a result, the optimized inductors for 4-stage and 8-stage TWPDs are 220 pH and 250 pH at 20 GHz, respectively.
Table 1. The dimensions and simulated bandwidths of optimized TWPDs
We further quantitively analyze the influence of optical delay lines on the bandwidth. Taking the conventional 4-stage TWPD without inductor as an example, we calculate its 3 dB bandwidth as functions of the spacing Δ between adjacent PD units and the step dn-dn-1 of optical delay lines in Fig. 5. When Δ ≥ 85 µm, a proper optical delay step helps to synchronize RF outputs of different PD units, and then improves the 3 dB bandwidth. However, when Δ < 85 µm, the bandwidth improvement by optimizing optical delay lines is imperceptible. The reason is that the spacing Δ is far shorter than the RF wavelength on the order of millimeter [23,31]. As the RF signal generated by one PD propagates to the next stage in the CPW, the accumulated phase change is insignificant. Namely, RF signals originating from different PD units are almost in phase as they propagate in the CPW. As a result, we believe that optical delay lines are not really necessary for our design of which Δ=25 µm.
Fig. 5. Contour map of the calculated 3 dB bandwidth (in GHz) as functions of the spacing Δ between adjacent PD units and the step dn-dn-1 of optical delay lines for the conventional 4-stage TWPD structure.
3. Device fabrication and measure results
Designed TWPDs are fabricated by imec’s silicon photonics platform (iSiPP50G) on a SOI substrate with 220-nm-thick silicon layer and 2-µm-thick buried oxide layer. The thickness and the resistivity of the silicon handling layer are 725 µm and 12 Ω·cm, respectively. As shown in Fig. 1(b), the two metallic layers used to pattern CWP and on-chip inductor have thicknesses of t1 = 0.5 µm and t2 = 0.7 µm, while the spacing between two layers is 0.5 µm. Optical microscope images of fabricated TWPDs are shown in Fig. 6. The footprints of un-peaked 4-stage and 8-stage TWPDs are 490 × 205 µm2 and 585 × 300 µm2, respectively, while those of 4-stage and 8-stage TWPDs integrated with inductors are 490 × 265 µm2 and 585 × 380 µm2 respectively. A conventional 4-stage TWPD with a 50 Ω termination resistor at the input end is also fabricated for comparison. Its size is 490 × 210 µm2.
Fig. 6. Microscope images of (a) the unterminated 4-stage TWPD without inductor, (b) the unterminated peaked 4-stage TWPD with an inductor, (c) the conventional 4-stage TWPD with a 50 Ω termination resistor, (d) the unterminated 8-stage TWPD without inductor, and (e) the unterminated 8-stage TWPD with an inductor.
We firstly test DC characteristics of the fabricated devices. Measured dark currents are shown in Fig. 7(a). The stand-alone PD exhibits a dark current of 0.14 µA at -3 V. Dark currents of the two 4-stage TWPDs with open input teminals are 1.4 µA and 1.2 µA at -3V, while those of the two 8-stage TWPDs are 2.6 µA and 3.1 µA. Because the currents flowing through the matching impedance at the input terminal, the dark current of the 4-stage TWPD with a 50 Ω resistor is 54 mA. Measured DC photocurrents as a function of the on-chip incident optical power are plotted in Fig. 7(b), where the laser wavelength and the bias voltage are 1550 nm and -3 V, respectively. We regard the optical power splitting network as a part of the TWPD. Therefore, the on-chip incident optical power used for the responsivity calculation is defined as the power entering the optical power splitting network, i.e., the output power of the incident fiber minus the coupling loss of the grating coupler. Responsivities of the devices under test (DUT) are extracted through linear fitting. The stand-alone PD offers the highest responsivity of 0.82 A/W. Due to insertion losses of optical power splitting networks, responsivities of 4-stage and 8-stage TWPDs with open input teminals drop slightly to ∼0.78 A/W and ∼0.74 A/W, respectively. The responsivity of 4-stage TWPD with a 50 Ω termination resistor is ∼0.71 A/W.
Fig. 7. (a) Static current-voltage (I-V) characteristics in the dark condition. (b) Measured photocurrents as a function of the on-chip incident optical power at 1550 nm. The bias voltage is -3 V.
Small-signal frequency responses of DUTs are tested by a lightwave component analyzer (Keysight N4373D). The reverse bias provided by a DC source meter (Keithley 2450) is fed to the DUTs through a bias-tee and a GSG probe. The modulated light incident on the fiber grating coupler at 1550 nm has an average power of 0 dBm. Measured frequency responses under -3 V bias are plotted in Fig. 8. The 3 dB bandwidths of un-peaked 4-stage and 8-stage TWPDs without termination resistors are 32 GHz and 16 GHz, respectively. After integrating inductors, resonances between the inductors and the capacitors occur at proper frequencies to enable the gain peaking effect which compensates the high-frequency roll off. The 3 dB bandwidths of 4-stage and 8-stage TWPDs without termination resistors then rises substantially to 44 GHz and 24 GHz, respectively. It is noteworthy that with the aid of the inductor, the bandwidth of unterminated 4-stage TWPD is almost equal to that of the 4-stage TWPD with a 50 Ω termination resistor as shown in Fig. 8(a). In addition, we note that the measurement results in Fig. 8 are basically consistent with the simulation results in Fig. 4. The validity of our theoretical model thus is verified. There are two reasons for evident ripples in measured S21 curves. At first, we haven’t calibrated the response of GSG probe because of the absence of the probe calibration substrate in our lab. Secondly, the input terminal of our CPW electrode is open-circuit. The RF wave reflected by the open input terminal can cause some resonance effects which are associated with the ripples. In Fig. 8(a), the frequency response of the 4-stage TWPD with a 50 Ω resistor at the input terminal is also plotted for comparison. Since the RF reflection is suppressed by the 50 Ω matching impedance, amplitudes of the ripples are weakened to some extent.
Output saturation characteristics of DUTs are measured with an optical heterodyne setup. A detailed description of the setup can be found in [36]. Measured RF output powers of the six DUTs versus the average photocurrent at different frequencies of 1, 5, 10, 20, 30, 40 GHz are plotted in Figs. 9(a)–9(f). The DC bias is fixed at -3 V in these measurements. The maximum RF powers of the conventional 4-stage TWPD structure with a 50 Ω termination resistor are 4.61, 1.83, 0.17, -1.15, -1.85 and -2.89 dBm at the 6 measurement frequencies. After eliminated the terminal resistors at the input terminals, the maximum RF powers of un-peaked/peaked 4-stage TWPDs are boosted to 11/11.2, 7.9/7.6, 6.1/6.5, 4.5/5.7, 3.3/4.8 and 0.6/1.8 dBm, while the corresponding maximum RF powers of un-peaked/peaked 8-stage TWPDs are 14.4/15.6, 12.6/13.2, 10.6/11.4, 8.5/9.4, 6.4/7.1 and 3.1/3.2 dBm. According to the data in Figs. 9(a)–9(f), we systematically compare the maximum RF output powers of the six DUTs in Fig. 10. Taking the 4-stage TWPDs as an example, removing the termination resistor can enhance the maximum RF powers by 6 dB at low frequencies. However, the enhancements of the maximum RF powers are less than 6 dB at high frequencies owing to the bandwidth deteriorations as shown in Fig. 8(a). Furthermore, since the inductor reduces the frequency roll-off as shown in Fig. 8(a), the maximum output powers of the 4-stage TWPD without the termination resistor in Fig. 10 is elevated by ∼ 1 dB after adding the inductor especially at high frequencies. It can also be concluded from Fig. 10 that the RF losses induced by the parasitic resistances of inductors are insignificant. In our measurement, the maximum optical power being coupled into the chip is about 17 dBm. According to the data in [37], the nonlinear loss of silicon waveguide at this power level is insignificant. On the other hand, we have slightly expanded the width of access wavegdue to suppress the potential nonlinear propagation loss.
Fig. 9. RF output powers versus the average photocurrent at different frequencies for (a) the unterminated 4-stage TWPD without inductor, (b) the unterminated 4-stage TWPD with inductor, (c) the unterminated 8-stage TWPD without inductor, (d) the unterminated 8-stage TWPD with inductor, (e) the conventional 4-stage TWPD with a 50 Ω termination resistor, and (f) the single PD unit.
4. Conclusion
In this paper, we demonstrate Ge/Si TWPDs with merits of high RF output efficiency and high bandwidths by leveraging the inductive gain peaking technique. The TW electrodes of our devices are open at input terminals to avoid shunting any photocurrents. In the meanwhile, peaking inductors are integrated with TW electrodes to mitigate bandwidth degradations caused by RF reflections at the open input terminals. An analytical model is built for this TWPD scheme. It enables us to calculate the frequency response and carry out the device optimization. Experimentally, the 4-stage and 8-stage TWPDs with optimized inductors provide 3 dB bandwidths of 44 GHz and 24 GHz, respectively. They show significant bandwidth improvement over the 4-stage and 8-stage TWPDs without inductors whose bandwidths are measured to be 32 GHz and 16 GHz. Besides, the maximum RF output powers of 4- and 8-stage TWPDs with inductors reach 5.7 dBm and 9.4 dBm at 20 GHz, respectively. A comparison between our devices with prior high-power Ge/Si PDs is made in Tab. 2. Thanks to the inductors, our TWPDs show evident advantages in bandwidths. However, the maximum RF power of our 4-stage TWPD is inferior to the 4-stage TWPD in [21]. We note that these two devices are fabricated by different foundries (i.e., imec and IME). The output saturation characteristic of single PD unit is not released in [21]. It is possible that the PD unit used in [21] has a higher saturation output power than our PDK PD unit tested in Fig. 9(f). As a result, our future works include the re-optimization of Ge/Si waveguide PD unit to improve its saturation power [17–19]. Besides, we utilize the MPW service of imec to fabricate the devices in this work. Therefore, many design parameters relevant to the practical processing flow (e.g., thicknesses t1 and t2 of the two metal layers and their vertical positions) are not allowed to change. Our simulation result suggests that if one can optimize these parameters by customizing the processing flow, the performance of Ge/Si TWPD can be further improved.
Table 2. Comparison of the High-Power Ge/Si PDs in Literature and our Work
Funding
Science and Technology Plan Project of Zhejiang (2022C01108); Zhejiang Lab Research Funds (2020LC0AD02); Science and Technology Innovation 2025 Major Project of Ningbo (2020Z021); National Key Research and Development Program of China (2018YFB2200602).
Acknowledgments
The authors would like to thank Dr. Bing Wei, Training Platform of Information and Microelectronic Engineering in Polytechnic Institute of Zhejiang University.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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