1. Introduction

Silicon photonics [1–26] has been extensively studied over the past decades. It is widely considered as a promising technique to provide high-performance and low-cost solutions to optical interconnects, optical communications, microwave photonics and so on [2,3]. Among its applications, silicon photonic interconnects have attracted the most attention. Great efforts have been made to develop the necessary devices, including silicon-based lasers [4,5], modulators [6–11], multiplexers and demultiplexers [12,13], routers [14,15] and detectors [16–18]. The characteristics which help silicon photonic interconnects win the competition with electrical interconnects and other solutions are broad bandwidth, low cost, low latency, low power consumption and so on. Among them, low power consumption may be the most important factor [19,20]. Modulators have occupied a large part of the optical link’s power budget. A lot of work has been done to lower the power consumption of modulators [21–26], but the carrier-depletion Mach-Zehnder silicon optical modulator still needs a high driving voltage and a large power consumption, which is not compatible with the current CMOS process. Using differential driving voltage in a push-pull configuration is an efficient method to lower the driving voltage and power consumption [26]. In this paper, the modulation efficiency is improved by optimizing the doping parameters, which makes the modulator possible to operate with a small differential driving voltage of 0.5 V. An 80 nm intrinsic silicon gap between the n and p doped regions is adopted to reduce the junction capacitance of the diode, and the unopened diode works faster under a small differential driving voltage without DC power consumption. Finally, the modulator operates at a speed of 26 Gbit/s by a power consumption of 3.79 mW. The corresponding power efficiency is 146 fJ/bit.

2. Device design and fabrication

Silicon Mach-Zehnder optical Modulators, using the carrier depletion effect, usually have low modulation efficiency. To shift the spectra by a free spectral range, a relative large voltage of more than 6V is needed for a 4-mm phase shifter [8–11]. And the power consumption is high. In order to reduce the driving voltage, the figure of merit ${\text{V}}_{\pi }L$ should be reduced. We use the abrupt junction model to concisely analyze the relationship between the doping parameters and the refractive index change $\Delta \text{n}$. Normally, a mid-level doping concentration (1 × 10¹⁷~2 × 10¹⁸ /cm³) is adopted [8–11,21–23], which does not cause a large absorption loss. In this doping concentration range, the p-doping plays a dominant role in changing the refractive index [1]. For a lateral abrupt PN junction, the depletion width in the p-type doped region [27] is expressed by

where ${\epsilon }_s$, $V$, $e$, $N_d$ and $N_a$ represent the permittivity constant of silicon, the reverse voltage, the electrical quantity of a single electron, the n-doping concentration and the p-doping concentration respectively. If a low reverse voltage of around 1 V is applied, the p-type depletion region is only several tens of nanometers in width. So it is reasonable to assume that the overlap of the optical field with the p-type depletion region is constant [28]. It is indicated that the refractive index change in the p-type doped region is proportional to $N_a{}^{0.8}$ [1]. The total refractive index change $\Delta \text{n}$can be written as

after considering the coupling of the optical field with the p-type depletion region. According to Eq. (2), for a constant $V$and $N_d$, $\Delta \text{n}$ has a maximum value, when the following condition is satisfied:

This conclusion is different from the previous works [11,21], in which the p-doping concentration is designed to be lower than the n-doping concentration. Therefore a wider p-type depletion region and a better mode overlapping efficiency are expected to be achieved. However, the lower doping concentration reduces the modulation efficiency per unit width and the total modulation efficiency is not good for a small driving voltage.

Traditionally, carrier-depletion silicon modulators need a reverse bias to make the carriers in the diode move by the drift effect. A travelling wave electrode design needs a termination to absorb the electrical wave at the end. Normally the termination on the chip is a resistor. So there is always DC power consumption on the chip. Although a DC block test can be done by using another probe to absorb the electrical wave off the chip [11,29], a DC block termination is hard to be integrated on the chip because it needs a large capacitor. In order to eliminate the DC power consumption, the diode is inevitably designed to work under a forward voltage. Traditionally, the modulator working with a forward voltage has a slow speed. But if the forward voltage is less than the threshold voltage, the diode will not work in a large injection mode. It is possible for the modulator to work in a fast speed, because the corresponding capacitor under a small forward voltage is still low.

Figure 1 illustrates the cross section of the phase shifter and the optical microscope image. The multi-mode interference (MMI) splitter and combiner are utilized. To achieve a better confinement of the optical field in the depletion region, the waveguide is 400 nm in width, 220 nm in height, and 70 nm in the slab thickness. The p-type doped region is to the right of the middle of the core with an offset of 50 nm. The p-type depletion region is designed to overlay the core part of the optical field. To increase the threshold voltage of the diode, an intrinsic silicon gap of 80 nm between the n-type and p-type doped regions is adopted. The conclusion expressed by Eq. (3) is based on an ideal abrupt PN junction model. Considering the doping profile and the intrinsic silicon gap, we have optimized the doping concentration relationship. According to the numerical simulation, the p-doping concentration of 1 × 10¹⁸/cm³ and the n-doping concentration of 8 × 10¹⁷/cm³ are used. There is a heavily doping concentration of 5.5 × 10²⁰/cm³ for both the p-type and n-type heavily doped regions to form a good ohmic contact. Both the P++ and N++ regions are 1 μm away from the side of the ridge to minimize the optical absorption loss.

 

Fig. 1 (a) Schematic of the cross section of the modulation region. (b) Optical microscope image of the modulator with a CPW electrode and termination resistors.

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Two coplanar waveguide (CPW) electrodes are used as the electrical transmission line. In order to lower the driving voltage, a push-pull driving configuration is adopted. A probe with GSGSG pattern, which supports differential signal transmission, is used to couple the electrical signal into the device. The electrodes are designed in combination with the doping parameters. We have used the commercial software package HFSS to simulate the CPW electrode with a diode embedded below. The optical and electrical signal velocities are simulated to be 0.26 c and 0.28 c (c is the light speed in vacuum). Electrical transmission loss along the phase shifter is reduced as less as possible [30]. After the satisfaction of the above two conditions, the characteristic impedance can only be designed to be 33 Ω. Two termination resistors made of TiN are integrated in the chip to absorb the electrical wave at the other end of the electrode. The resistance of the terminators is 33 Ω.

3. Experimental result and discussion

In order to measure the modulation efficiency accurately, we have fabricated devices with no termination resistors, eliminating the possible thermal effect of the resistors. Figure 2 shows the normalized transmission spectra of a 4-mm-long device under a differential voltage of 1.6 V with 0.8 V reverse bias on both arms. It is obviously that the spectrum shifts half a free spectral range. The changed phase difference between two arms is π. So the device exhibits a high modulation efficiency of 1.28 V·cm. This result supports our analysis on the modulation efficiency.

 

Fig. 2 Response spectra of a device with a 4-mm-long phase shifter under a differential voltage of 1.6 V with a reverse bias of 0.8 V on both arms.

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Normally, a modulator with 4-mm-long phase shifter is too large to be integrated in CMOS chips. A 2-mm-long phase shifter may be acceptable [29]. Figure 3 shows the response spectra of a 2-mm-long device under different voltages. The differential 0.5 V does not have a reverse bias and the voltage varies from −0.25 V to 0.25 V. Differential 1 V and 2 V have reverse bias of 0.5 V and 1 V respectively. The spectrum has obviously shifted although it does not shift by half a free spectral range. The insertion loss is 12.5 dB, which includes 8 dB of two MMIs and 4.5 dB of 2-mm-long phase shifter.

 

Fig. 3 Response spectra of a device with a 2-mm-long phase shifter under different differential voltages.

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The data transmission experiment is performed. Monochromatic light from a tunable laser is amplified by an erbium-doped fiber amplifier and then coupled into the input port of the device through a lensed fiber. A signal quality analyzer (Anritsu MP1800A) is used to provide a 26 Gbit/s data stream. The modulated optical signal is fed into a digital communication analyzer (Agilent 86100A) with a 20 GHz optical head for eye diagram observation.

A 2-mm-long device with the termination resistors is used to perform the dynamic data transmission experiment. A voltage swing of 0.5 V with no bias is used to drive the modulator. On each arm, the driving voltage varies from 0.25 V to −0.25 V. One arm was driven with data and the other arm was driven with $\overline{\text{data}}$. The data rate is 26 Gbit/s. Figure 4(a) indicates the variation of the static and dynamic extinction ratios with the working wavelength. The wavelength does not drift at all because of the thermal balance between two arms. The little difference of extinction ratios is mainly caused by the small mismatch between the characteristic impedance of the device and that of the probe and the propagation loss of electrical wave. The dynamic extinction ratio increases as the working wavelength approaches to the destructive interference wavelength, but the extra insertion loss becomes larger at the same time. Figures 4(b), 4(c) and 4(d) are the eye diagrams at the wavelengths of 1553.25 nm, 1552.75 nm and 1552.3 nm. The extinction ratios are 1.37 dB, 3.25 dB and 9.03 dB respectively, and the corresponding extra losses are 1.5 dB, 4 dB and 10 dB. Although the eye diagrams at low extra loss exhibit low extinction ratios, they are clearly opened. The fast response of the modulator with no reverse bias means that the improvement successfully prevents the diode from working in a slow large-injection mode. There is an unsuitable wavelength range from 1552.04 nm to 1552.30 nm for the modulator. If the modulator works at any wavelength in this range, the optical output does not change monotonically with the applied voltage. For example, when the modulator works at 1552.1 nm and the applied electrical voltage increases, the output optical signal will decrease first, and then increase. The fidelity of the modulator output is not sufficient for data transmission in the designated range near the null point of the modulator transfer function. As a result of the elimination of DC power consumption and low driving voltage, the maximum power consumption can be reduced to 3.79 mW ($P=2\times (\frac{1}{4}\cdot \frac{V_{pp}{}^2}{R}),$$V_{pp}\text{=0}\text{.5 }V,$$R=33\Omega$), when the modulator transmits a continuous data 1 or 0. The corresponding power efficiency is 146 fJ/bit. According to the International Technology Roadmap for Semiconductors (ITRS), CMOS transistor supply voltage will continue to drop to 0.71 V in 2019. Recent work [26,31,32] indicates that a lower voltage than what predicted by ITRS is needed for exascale computing. For example, logic gates run with 0.35 V are demonstrated [33]. Therefore, the low driving voltage makes the modulator possible to be directly driven by a CMOS digital integrated circuit at next-generation 22 nm technology node, where the photonic interconnect starts to play a dominant role in chip-multiprocessors [34].

 

Fig. 4 (a) Static and dynamic extinction ratios versus working wavelength. 26 Gbit/s eye diagrams at the working wavelengths of 1553.25 nm (b), 1552.75 nm (c), and 1552.3 nm (d). All data are achieved with the differential driving voltage of 0.5 V with no bias.

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We can use a larger voltage to improve the extinction ratio at a low cost of small extra loss. For the same 2-mm-long device, the extinction ratio is 14.61 dB under 2 V differential driving voltage swing with 1 V reverse bias when the modulator is operated at −3 dB under quadrature (Fig. 5 ).

 

Fig. 5 26 Gbit/s eye diagram at the wavelength of 1551.6 nm and 3 dB under quadrature.

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4. Conclusion

We have optimized the modulation efficiency and the figure of merit ${\text{V}}_{\pi }L$ is reduced to 1.28 V·cm. We have reduced the capacitance of the diode under a small forward bias. A fast response is achieved, and the DC power consumption is eliminated at the same time. When the modulator is operated at the minimum of the modulation transfer function, the device exhibits an extinction ratio of 9 dB, under a differential driving voltage of 0.5 V with no DC bias. The maximum power consumption is 3.8 mW and the corresponding power efficiency is 146 fJ/bit.