Silicon traveling-wave (TW) Mach–Zehnder modulators (MZMs) utilizing carrier-depletion-type phase shifters have been widely integrated as fundamental devices in high-speed advanced modulation format transmitters such as PAM4, QPSK, and QAM for high-capacity optical interconnects [1–4]. Carrier depletion in a reverse-biased $pn$ diode offers a high-speed response due to its small capacitance, but suffers low modulation efficiency [5]. Heterogeneous III-V/Si capacitor modulators show high efficiency [6], while extensive efforts are being made on an optimizing silicon MZM because of its process compatibility, low cost, and monolithic integration. To achieve high modulation efficiency, device optimization has been reported from various aspects, including $pn$ diode designs [7,8], doping [9,10], novel waveguides [11,12], and electrode designs [13–15]. The efficiency improvement usually involves the junction capacitance increase [8,12] or efforts of integrating distributed drivers [14,15]. These optimizations are pre-determined before fabrication, where the performance trade-off usually needs to be delicately designed between modulation efficiency and other properties such as response speed and loss [5,8]. Instead, we are considering an adaptive driving method that allows for post-fabrication achievement of modulation efficiency enhancement. In this Letter, we propose a distributed-bias driving method by exploring the bias nonlinearity of index modulation which originates from the bias dependent capacitance of $pn$ junction and prove this prototype concept viable for efficiency enhancement. Without any diode optimizations, we experimentally demonstrated that this method offered $20\%\sim 30\%$ efficiency enhancement at both 10 and 25 Gbps.

We here explain the principle of the silicon TW-MZM under distributed-bias driving using the driving circuit diagrams in Figs. 1(a) and 1(b) which correspond to the conventional and proposed driving methods, respectively. In the conventional method, the DC bias ($V_f$) and RF signal are input to the front end of the coplanar waveguide (CPW) via a bias-tee and a 50-Ω terminator is connected to the rear end via a DC block. In the proposed method, another DC bias ($V_r$) is input to the rear end with the terminator via another bias-tee. Therefore, the bias voltage ($V_b$) is constant along the CPW in the conventional method, whereas gradually decreased from $V_f$ to $V_r$ in the proposed one, as illustrated in Figs. 1(c) and 1(d), respectively. It is known that the phase modulation efficiency $\mathrm{\Delta }\varphi /\mathrm{\Delta }V$ in a reverse-biased $pn$ junction decreases with bias increasing, which comes from the bias nonlinearity of index change $\mathrm{\Delta }n$.

 

Fig. 1. Driving circuit diagrams of a silicon TW-MZM under (a) conventional constant bias driving and (b) proposed distributed-bias driving. CPW: coplanar waveguide electrode. $V_f$ and $V_b$ are the front and rear biases, respectively. The bias distributions along the CPW shown in (c) and (d) and their efficiency values in (e) and (f) correspond to (a) and (b), respectively.

Download Full Size | PDF

Our discussion here assumes that the overlap between optical mode field and $pn$ junction is kept same. Since the bias is constant along the CPW in the conventional method, as shown in Fig. 1(c), the value of $\mathrm{\Delta }\varphi /\mathrm{\Delta }V$ is equal everywhere and, thus, its reverse when $\mathrm{\Delta }\varphi =\pi$ can be multiplied by the phase shifter length to quantify the modulation efficiency. This multiplication is generally known as $V_{\pi }L$. However, $V_{\pi }L$ is not suitable to describe the modulation efficiency for the distributed-bias driving because the bias is not constant, as shown in Fig. 1(d), i.e., $\mathrm{\Delta }\varphi /\mathrm{\Delta }V$ is position dependent along the CPW. Therefore, we have to consider the position dependent efficiency value $\eta$ ($\mathrm{\Delta }\varphi /\mathrm{\Delta }V$ per unit length) and evaluate the total phase change $\mathrm{\Delta }\mathrm{\varphi }=\int \eta (z)·V_{\mathrm{pp}}(z)\mathrm{d}z$ for efficiency quantification, where $V_{\mathrm{pp}}$ is the peak-to-peak driving voltage. The position dependent efficiency values for the conventional and proposed methods are given in Figs. 1(e) and 1(f), respectively, which are obtained by device simulation using Lumerical DEVICE and MODE [16] with a uniform carrier density $1\times {10}^{18}{\mathrm{cm}}^{-3}$ in $pn$ junction. The simulation method has been outlined in our previous paper [12]. As displayed, the distributed-bias driving method shows a gradually increased efficiency value along the CPW due to the bias decrease. Therefore, the distributed-bias driving is expected to give higher modulation efficiency provided that a lower bias cannot be used throughout under a large input $V_{\mathrm{pp}}$. Note that all biases used in the text denote the reverse bias of $pn$ junction.

Before discussing distributed-bias driving, we explain the fabricated TW-MZM device, measurement system, and its fundamental properties. Figure 2(a) shows the MZM device that was fabricated on a 220 nm photonic SOI wafer with a 3 μm buried oxide at the AIST SCR 300 mm silicon photonic platform. The modulator is an arm-balanced MZM consisting of two 3 dB couplers and two phase shifters. Each arm has one heater on it. The phase shifters are 4 mm long and adopt the rib waveguides with a width of a 600 and $\sim 110\mathrm{nm}$ thick slab. The horizontal $pn$ junctions were embedded at the waveguide center with target doping densities of $\sim 1\times {10}^{18}{\mathrm{cm}}^{-3}$ in both $p$- and $n$-doped regions. The MZM adopts GSGSG-configured TW-electrodes with 10 μm wide signal electrodes that are loaded with the junction capacitors via n-doped regions, and the modulation is based on carrier depletion. The electrode metal is $\sim 1.2\mathrm{\mu m}$ thick AlCu alloy. Except for the phase shifters, we used 430 nm-wide channel waveguides which are connected to the rib waveguides using a low-loss conversion structure.

 

Fig. 2. (a) Photograph of the fabricated silicon TW-MZM. (b) High-frequency measurement system of an MZM under distributed-bias driving. Wg, waveguide; SMA, SMA cable; TLS, tunable laser source; PPG, pulse pattern generator; PM, power meter; EDFA, erbium-doped fiber amplifier; OSC, oscilloscope; Term, 50-Ω terminator; PC, computer; Bias-T, bias-tee; DC, direct-current source.

Download Full Size | PDF

The red arrows in Fig. 2(a) indicate the light input and output ports. Figure 2(b) shows the measurement system for distributed-bias driving. The light ($\lambda =1.55\mathrm{\mu m}$) of TE polarization was coupled into the device through a tapered fiber. The RF signal from a 28 Gbps pulse pattern generator (PPG) and a direct current (DC) bias (DC1) were input to the front end (left) of bottom arm using a bias-tee via a high-speed probe. Similarly, another DC bias (DC2) and a 50-Ω terminator were loaded to the rear end (right). The modulated optical signal was then selectively connected to a power meter or an erbium-doped fiber amplifier (EDFA). After the EDFA, it was sent to a high-speed oscilloscope with a 30 GHz optical plug-in module to convert light signal back to an electrical one for eye pattern measurement. We used single-arm driving instead of push-pull driving and controlled the phase of its top arm to maintain the MZM at the quadrature point. No narrow-band wavelength filter was used after the EDFA to intentionally improve the signal-to-noise ratio.

Measured properties of the phase shifter are summarized in Fig. 3. Figure 3(a) shows the bias dependent efficiency values which were evaluated under the DC condition. (The CPW is under constant bias.) The value has an obvious increase with the decrease of the bias within about 4 V and is nearly constant for $>4\mathrm{V}$. The $\pi$-shift voltage ($V_{\pi }$) was measured at about 7.8 V, and the corresponding $V_{\pi }L$ was about $3.12\mathrm{V}·\mathrm{cm}$. The propagation loss shown in Fig. 3(b) decreases with the bias increase because the bias increase widens the depletion layer. At zero and 4 volts, it is about 11.5 and 8.8 dB/cm, respectively, which means 4.60 and 3.52 dB losses for a 4 mm length. The figure of merit $\alpha V_{\pi }L$ is about $27.5\mathrm{V}·\mathrm{dB}$, similar to those in Refs. [5,13,17]. Figure 3(c) compares the capacitances obtained from the C–V measurement, the analytical calculation using equation (1) [18], and the device simulation:

 

Fig. 3. (a) Bias dependent efficiency values. (b) Propagation loss of the phase shifter versus bias. (c) Capacitance versus bias. (d) Electro-optical response under the conventional constant bias driving. The black fitting lines in (a)–(c) are for eye guidance.

Download Full Size | PDF

In Eq. (1), we used $L$ (phase shifter length) = 4 mm, A (junction cross-section area) = $4\mathrm{mm}\times 220\mathrm{nm}$, the carrier densities $N_A=N_D=1\times {10}^{18}{\mathrm{cm}}^{-3}$, $V_T$ (built-in potential) $=0.75\mathrm{V}$, and ${ϵ}_r=11.7$. The measured capacitance at zero voltage is similar to that in Ref. [5]. Its bias dependence can be roughly approximated by the calculation and simulation, since the actual capacitance may contain other contributions besides the $pn$ junction [18], from which we can clearly notice the above-mentioned bias nonlinearity of $\mathrm{\Delta }C/\mathrm{\Delta }V$. We measured the small signal electro-optical (EO) response using an Agilent N5230C network analyzer which covered the frequency range from 10 MHz to 20 GHz. The RF signal was applied to the MZM, and the modulated optical signal was converted to an electrical signal using an external 40 GHz photodiode (PD), and the RF output of the PD was sent back to the analyzer. Figure 3(d) shows the responses under the constant bias driving and the 3 dB bandwidth increases from about 11–13 GHz, when the bias was tuned from 0 to 5 V, showing similar bandwidths as Ref. [13]. When biased higher than 2 V, this MZM guarantees $>25\mathrm{Gbps}$ operation.

To examine the high-frequency modulation efficiency of a silicon TW-MZM under distributed-bias driving, we intend to measure eye diagrams instead of the static $V_{\pi }L$ due to the above-mentioned nonuniform efficiency distribution along the CPW. The eye diagrams were recorded under a $2^{15}-1$ non-return-to-zero pseudorandom binary sequence signal. The $V_{\mathrm{pp}}$ were set to 3 and 3.5 V for 10 and 25 Gbps, respectively. The biases ($V_f$ and $V_r$) were set by DC1 and DC2, respectively, as shown in Fig. 2(b). Figures 4(a) and 4(b) show the 10 and 25 Gbps eye diagrams, respectively. On each figure, $V_f->V_r$ was indicated. Each row has the same $V_f$, but different $V_r$. $V_f=V_r$ means the constant bias driving, and $V_f>V_r$ means the distributed-bias driving. For each bias condition, we need to scan the heating voltage at the top arm of the MZM to locate the quadrature point. Thus, the left-column figures correspond to the conventional cases where the diagrams exhibit clear eye openings for both 10 and 25 Gbps. It is important to mention that the shape of the eye diagrams at both 10 and 25 Gbps is almost determined by the electrical pulses of our PPG output, as we confirmed with back-to-back eye diagrams of the PPG. The extinction ratios at $V_f=V_r=3V$ in the left-top eye diagrams are about 3.0 and 3.2 dB for 10 and 25 Gbps, respectively. When decreasing $V_r$ by 2 V for each $V_f$ (middle column) and further to 0.5 V (right column), the eye opening is further enlarged, which indicates that the distributed-bias driving enables higher efficiency for a silicon TW-MZM. For quantification, all measured eye amplitudes ($\mathrm{\Delta }A$), including those from Fig. 4, are plotted in Figs. 5(a) and 5(b) in relation to $V_r$. For each $V_f$, $\mathrm{\Delta }A$ is gradually enhanced with the decrease of $V_r$, and it can be increased by $20\sim 30\%$ when $V_r$ is decreased to 0.5 V for both 10 and 25 Gbps compared to the conventional constant bias driving ($V_f=V_b$). This originates from the efficiency increase with the decrease in the bias shown in Fig. 3(a). If converting this improvement ratio to effective $V_{\pi }L$, it suggests that $3\mathrm{V}·\mathrm{cm}$ can be decreased to $2.3\sim 2.5\mathrm{V}·\mathrm{cm}$. Although small, this improvement is not obtained by pre-fabrication optimization and suggests a feasibility of adaptive driving to achieve additional merits.

 

Fig. 4. Eye diagrams at (a) 10 and (b) 25 Gbps under different front (before arrow) $V_f$ and rear (after arrow) $V_r$ biases. $V_f=V_r$ means the constant bias driving. $V_f>V_r$ means the distributed-bias driving. The dotted lines are for guidance.

Download Full Size | PDF

 

Fig. 5. Eye amplitude in relation of the rear bias ($V_r$) under different front biases ($V_f$) at (a) 10 and (b) 25 Gbps. (c) and (d) simulated total phase change ($\mathrm{\Delta }\mathrm{\varphi }$) of the 4 mm phase shifter and the corresponding transmission change ($\mathrm{\Delta }T$) of an MZM under different $V_f$ and $V_r$. At the quadrature point, $\mathrm{\Delta }T=0.25{|e^{-i}\mathrm{\Delta }{\mathrm{\varphi }}^{/2}+e^{-i}{\pi }^{/2}|}^2-0.25{|e^i\mathrm{\Delta }{\mathrm{\varphi }}^{/2}+e^{-i}{\pi }^{/2}|}^2$.

Download Full Size | PDF

We also performed the simulation on an MZM under the distributed-bias driving for confirmation. The simulation procedure is (i) calculate $\mathrm{\Delta }\varphi (V)$ using Lumerical simulators [12,16]; (ii) discretize device by $\mathrm{\Delta }z$ and obtain $V_b(z)$ in terms of $V_f$ and $V_b$; (iii) calculate $V_{\mathrm{pp}}(z)$ at a given RF power attenuation ratio; (iv) get total phase change $\mathrm{\Delta }\mathrm{\varphi }=\int [\mathrm{\Delta }\varphi (V_b+V_{\mathrm{pp}}/2)-\mathrm{\Delta }\varphi (V_b-V_{\mathrm{pp}}/2)]\mathrm{d}z$. We assumed RF power attenuation of 10 and 20 dB for a 4 mm CPW at 10 and 25 GHz, respectively, which were estimated from the measured transmission line properties. The calculated $\mathrm{\Delta }\mathrm{\varphi }$ in radian (rad) is shown in Fig. 5(c). The distributed-bias driving has larger $\mathrm{\Delta }\mathrm{\varphi }$ than the constant bias driving as expected. The MZM equation given in the caption of Fig. 5 should be considered to convert $\mathrm{\Delta }\mathrm{\varphi }$ to the transmission change $\mathrm{\Delta }T$ that can be directly compared to the measured eye amplitude $\mathrm{\Delta }A$. The corresponding $\mathrm{\Delta }T$ is shown in Fig. 5(d). The increase ratio of $\mathrm{\Delta }\mathrm{\varphi }$ in Fig. 5(c) from the point $V_f=V_b$ to the maximum is within $25\%\sim 35\%$, and that of $\mathrm{\Delta }T$ is between $15\%\sim 25\%$, which is 5% lower than the experimental increase ratio. Considering this error, the $\mathrm{\Delta }T$ dependence on the rear bias gives reasonable agreement with the experimental results of $\mathrm{\Delta }A$. The applicable range of this method depends on the input $V_{pp}$ and RF attenuation. For a typical RF attenuation level of silicon modulators [18], a low $V_r(\sim 0.5\mathrm{V})$ is still accessible at $V_{\mathrm{pp}}\sim 3\mathrm{V}$ and 25 GHz for a 4 mm length.

Finally, we also measured the EO responses of the MZM under distributed-bias driving (not shown) for $V_f$ of 3–5 V and did not observe noticeable bandwidth degradation compared to the conventional constant bias driving. The EO responses are almost the same as those in Fig. 2(d). To understand this phenomenon, we estimate the RC bandwidth [$f_{\mathrm{RC}}=1/(2\pi \mathrm{RC})$] using the measured capacitances (C) at both zero and 4 V in Fig. 2(c). At 4 V, $C=0.26\mathrm{fF}/\mathrm{\mu m}$. Given an estimated resistance $R\sim 3\mathrm{\Omega }$, $f_{\mathrm{RC}}$ is estimated to be as high as $\sim 51\mathrm{GHz}$ for the 4 mm long MZM. Even at zero voltage (maximum capacitance case), $C=0.38\mathrm{fF}/\mathrm{\mu m}$ and $f_{\mathrm{RC}}$ is $\sim 35\mathrm{GHz}$, still much higher than the EO bandwidth in Fig. 3(d). Thus, the EO response is mostly determined by impedance and RF-optical velocity matching conditions instead of an RC bandwidth.

This Letter is the proof of concept of adaptive driving, and we did not try to circumvent additional power consumption due to the bias-difference-induced current flow in the electrode. For actual application of this method, we are considering a multi-segmented electrode by inserting the designed impedance-matched capacitors into the CPW, which features one RF and multi-DC inputs. Then the power will remain the same as traditional driving. This consideration is to incorporate the well-established coplanar waveguide-based microwave components [19] into silicon photonics towards performance breakthrough and innovative functions.

In summary, we proposed an adaptive distributed-bias driving method for a silicon TW-MZM and studied its high-frequency modulation performance. This method could enhance the high-frequency modulation efficiency by $20\sim 30\%$ at both 10 and 25 Gbps through utilizing bias nonlinearity of phase modulation. This adaptive concept could give flexibilities in modulator design and performance trade-off.