1. Introduction

In order to monolithically integrate photonic links in a CMOS chip, silicon-based laser diodes [1, 2], optical modulators [3, 4], multiplexers/de-multiplexers [5, 6], optical routers [7, 8] and optical detectors [9–11] have been widely studied, among which optical modulator behaves as the interface between the electronic domain and its optical counterpart [12-13]. In 2004 and 2005, Intel Corporation [3] and Cornell University [4] developed two kinds of silicon optical modulators with the modulation frequency approaching to 1 GHz by the carrier dispersion effect [14]. It was first found that it is possible to integrate a fast silicon optical modulator in a CMOS chip. Since Liu et al. [15] demonstrated a high-speed carrier-depletion Mach-Zehnder Interferometer (MZI) silicon optical modulator, a lot of works [16–18] have been done to reduce the insertion loss and improve the extinction ratio and the polarization performance. But the driving voltage is still around 5 V, which is not compatible with the microelectronic integrated circuits since it is very difficult for CMOS chips to supply such a high voltage at a high frequency. Nowadays, reducing the core voltage of CMOS chips is a trend. In the same conditions, low voltage means low power consumption and less heat dissipation problems. In order to reduce the driving voltage, we design a coplanar waveguide electrode with low transmission loss. Our simulation result indicates that the loaded electrode containing a 2-mm-long phase shifter has a transmission loss of less than 3 dB when the frequency is below 16 GHz. 12.5 Gbit/s data transmission experiment is performed. An extinction ratio of 12.78 dB is achieved when the applied voltage swing is 2 V. The voltage swing can be even reduced to 1 V with a reverse bias voltage of 0.5 V, while the device still has an extinction ratio of 7.67 dB with a reverse bias voltage of 0.8 V.

2. Device design and fabrication

As a result of the relatively low modulation efficiency, the phase shifter of the carrier-depletion MZI silicon optical modulator is always long. For a high-speed modulator, a simple lumped circuit model cannot be used any more. Supposing the mode refractive index of the coplanar waveguide (CPW) electrode is 4, the wavelength of the electrical wave with the frequency of 20 GHz is 3.75 mm, which is comparable to the length of the phase-shifter. So, we should use a distributed circuit model to analyze the modulator. There are three points to be considered for designing a phase shifter with a CPW electrode. Firstly, the characteristic impedance of the phase shifter should be 50 Ω in order to avoid the reflection of the electrical signal from the probe. At the same time, the termination resistor should have the same value with the characteristic impedance of the phase shifter. Otherwise, the reflection at the termination resistor will deteriorate the modulated optical signal. Secondly, the velocities of the electrical and optical signals should be matched well. Otherwise, the modulation efficiency will decrease and the intersymbol interference will occur. Finally, the transmission loss of the CPW electrode should be as small as possible. Otherwise, dynamic modulation depth will be much less than the static extinction ratio. An equivalent circuit model is used to analyze the electrical properties of the phase shifter and reduce its electrical transmission loss.

Figure 1 illustrates the equivalent circuit model of the diode alone. $C_D$ and $R_S$ represent the depletion capacitance and series resistance per unit length, respectively. is the angular frequency. To achieve a fast response, inequality (1) should be satisfied. This condition guarantees that most of the voltage can be applied to the capacitor which is the modulation part. In other words, the modulated optical signal will have a short rise time.

 

Fig. 1 (a) Cross section of the diode and (b) its equivalent circuit model.

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Figure 2 is the distributed circuit model of the modulator’s CPW electrode with a diode embedded below. $L_E$, $R_E$ and $C_E$ represent the inductance, resistance and capacitance of the metal electrode with unit length. $\Delta \text{Z}$ represents a small distance along the electrode. We can use this model to create a differential equation to describe the electrical properties of the phase shifter.

 

Fig. 2 Distributed circuit model of the CPW electrode with a diode embedded below.

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The distributed circuit model can be further transformed to a model shown in Fig. 3 and the classic transmission line theory of microwave engineering [19] can be used. The transformed parallel and are expressed by

 

Fig. 3 Transformed circuit model of the CPW electrode with a diode embedded below.

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Then we can calculate the complex propagation constant and the characteristic impedance Z as

In order to demonstrate the mechanism qualitatively and clearly, a first-order approximation is adopted and Eq. (4) is simplified to the follow equations:

Considering the inequality (1), and can be simplified:

Finally, we can write the expressions of the real and imaginary parts of the propagation constant in Eq. (3) as

A commercial software package HFSS based on the finite-element method is used to check the theoretical analysis and get the optimized parameters quantitatively. Because the software cannot simulate the active region, the depletion region is replaced by a passive parallel capacitor. Figure 4(a) illustrates that the attenuation constant $\alpha$ decreases linearly with an increase in the signal track width. This means that the electrical loss decreases linearly as the electrode resistance ${\text{R}}_{\text{E}}$ decreases, as predicted by Eq. (6). Moreover, the attenuation constant $\alpha$ changes with the signal and ground metal gap, which is consistent with the relationship between the attenuation constant $\alpha$ and the electrode capacitance $C_{\text{E}}$ in Eq. (6). Figure 4(b) shows that the attenuation constant $\alpha$ decreases linearly as the series resistance ${\text{R}}_{\text{s}}$ decreases, which also can be predicted by Eq. (6). Figures 4(c), 4(d) and 4(e) show the dependence of the propagation constant $\beta$, the characteristic impedance Z and the attenuation constant $\alpha$ on the frequency respectively. Figures 4(e) and 4(f) show the dependence of the attenuation constant $\alpha$ on the frequency for R_s = 18 Ω·mm and R_s = 4.5 Ω·mm. Note that all the other parameters are same for two figures. According to Eq. (6), the attenuation constant increases quadratically with the frequency and diode capacitance, as shown in Fig. 4(f). Note that Eq. (6) is valid on condition that inequality (1) is satisfied. If a large series resistance of 18 Ω·mm is adopted and the frequency is larger than 15 GHz, the quadratic relationship of the attenuation constant with the frequency will not be valid, as shown in Fig. 4(e). Although the theoretical equations cannot accurately predict the characteristics of the device at a high frequency, they can still show us a correct direction to optimize the device. According to the simulation results, the optical and electrical velocities can be matched by changing the geometrical parameters of the phase shifter. Reducing the series resistance is very important. Firstly, larger diode capacitor should be adopted to achieve higher modulation efficiency for the carrier-depletion Mach-Zehnder modulator. In order to keep the device working at the same speed, the series resistor should be lower. Secondly, the device with lower series resistance could have lower electrical transmission loss. Higher doped silicon can reduce the series resistance, but a larger optical loss will be induced at the same time. Although the device with a series resistance of 4.5 Ω·mm has a better electrical performance, it is estimated that the doping concentration should be larger than 5 × 10¹⁸/cm³, which will cause a massive optical loss. As a compromise, the series resistance is designed to be 14 Ω·mm. Adopting the material with higher electron and hole mobilities may be a promising method to further improve the device performance.

 

Fig. 4 Simulation results with commercial software package HFSS. (a) Attenuation constant $\alpha$ versus track width and signal and ground metal gap, when series resistance ${\text{R}}_{\text{s}}$, diode capacitance $C_D$and frequency $f$are 4.5 Ω·mm, 100 pF/mm and 10 GHz, respectively. (b) Attenuation constant $\alpha$ versus track width and series resistance ${\text{R}}_{\text{s}}$, when signal and ground metal gap, diode capacitance $C_D$and frequency $f$are 5.5 mm, 100 pF/mm and 10 GHz, respectively. (c) Propagation constant $\beta$ versus frequency and diode capacitance $C_D$, when series resistance ${\text{R}}_{\text{s}}$, track width and signal and ground metal gap are 4.5 Ω·mm, 28 um and 5.5 μm, respectively. (d) Characteristic impedance ${\rm Z}$ versus frequency and diode capacitance $C_D$, when series resistance ${\text{R}}_{\text{s}}$, track width and signal and ground metal gap are 4.5 Ω·mm, 28 μm and 5.5 μm. (e) Attenuation constant $\alpha$ versus frequency and diode capacitance $C_D$, when series resistance ${\text{R}}_{\text{s}}$, track width and signal and ground metal gap are 18 Ω·mm, 28 μm and 5.5 μm, respectively. (f) Attenuation constant $\alpha$ versus frequency and diode capacitance $C_D$, when series resistance ${\text{R}}_{\text{s}}$, track width and signal and ground metal gap are 4.5 Ω·mm, 28 μm and 5.5 μm, respectively.

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Actually, it is very hard to make all the three targets perfect simultaneously. A tradeoff has to be done. In the on-chip application environment, the characteristic impedance of the modulator should be matched to the output impedance of the driving circuit, which is not always 50 Ω and can be adjusted by electrical circuit design. So the electrical and optical velocities should be matched first. And then the electrical transmission loss should be reduced as small as possible. Finally the characteristic impedance of the device should be an acceptable value. The characteristic impedance of our device is designed to be 33 Ω.

The optical structure of the device is based on a MZI design. There is a built-in arm length difference of 120 μm. A multimode interference (MMI) structure is adopted as the optical splitter and combiner. The silicon ridge waveguide is 600 nm in width, 220 nm in height and 70 nm in the slab thickness. Both arms of the device are doped to balance the transmission loss. Figure 5(a) illustrates the schematic cross section of the modulation region. The p-doping concentration is 1×10¹⁸/cm³, and the n-doping concentration is 8×10¹⁷/cm³. The p-n junction locates 100 nm right of the middle of the ridge, because the hole is more efficient to change the refractive index than the electron [11]. The p-type doped region is designed to have an efficient overlap with the strongest optical mode in the middle of the waveguide. The P++ and N++ doped regions are 1 μm away from the side of the ridge. In order to reduce the capacitance of the diode, a 40 nm-wide gap between p-type and n-type doped regions is adopted [20].

 

Fig. 5 (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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Figure 5(b) is the optical microscope image of the device. A CPW electrode is used as the electrical transmission line. A probe with GSG pattern is used to couple the electrical signal into the device. The metal thickness is 1.5 μm. the signal track width is 28 μm and the signal and ground metal gap is 5.5 μm. A termination resistor made of TiN is integrated in the chip to absorb the electrical wave at the other end of the electrode and avoid the reflection, which can deteriorate the performance of the device. The resistance of the terminator is 33 Ω.

3. Experimental result and discussion

Figure 6 shows the normalized spectra of the device under different applied voltages. Obviously, the spectrum shifts to the longer wavelength with an increase in the driving voltage. The insertion loss is about 19 dB, which includes 6 dB coupling loss between the device and the lensed fibers, 9 dB propagation loss originating from the two MMIs and 4 dB propagation loss induced by the doped regions. The on-off extinction ratio is about 27 dB when the driving voltage increases from 0 V to 2 V. For a device with a 3-mm phase shifter, the spectrum could shift by half a free spectral range under a reverse voltage of 5.5 V, which indicates a modulation efficiency of 1.65 V·cm

 

Fig. 6 Response spectra of the device with different driving voltages.

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The data transmission experiment is performed with the following setup (see Fig. 7 ). Monochromatic light with the wavelength of 1551.66 nm from a tunable laser is amplified by an erbium-doped fiber amplifier (EDFA) 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 12.5 Gbit/s data stream. The electrical signal is directly coupled into the device by a probe without any amplification. The output light is amplified by another EDFA and then passes through a tunable bandpass optical filter. The modulated optical signal is fed into a digital communication analyzer (Agilent 86100A) with a 20 GHz optical head for eye diagram observation. The device is reversely biased at 0.8 V. When the driving voltage swing is 2 V, the device exhibits an extinction ratio of 12.79 dB with a reverse bias of 0.8 V. There is even an extinction ratio of 7.67 dB when the driving voltage swing is 1 V with a reverse bias voltage of 0.5 V. The maximum power consumptions of the modulator are 98 mW and 30 mW when the driving voltage swings are 2 V and 1 V, respectively. The corresponding energy efficiency is 7.8 pJ/bit and 2.4 pJ/bit. The maximum power consumption happens when the modulator is DC biased to transmit a data of continuous “1”. However, they will dramatically decrease to 20 mW and 5 mW, if a DC block termination is adopted and the DC power consumption is eliminated [21]. Then the maximum power consumption will happen when the modulator transmits “1” and “0” repeatedly. Finally the energy efficiency could be reduced to 400 fJ/bit. Such a design is in process and the discussion is left for future.

 

Fig. 7 Experimental setup of the data transmission experiment.

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Although the dynamic extinction ratio is high, it is much less than the static one. The reason can be explained as follows. Because of the MMIs’ relatively large insertion loss and the low output power of the laser diode, we use an EDFA to amplify the modulated light signal. So the detected extinction ratio is related to the EDFA’s power response. We measure the EDFA’s power response (see Fig. 9 ) with the same experimental setup as in the data transmission experiments. We find that the amplification is not linear in the large input power range. The original data “1” and “0” are not amplified by the same times. Even in the linear range of a logarithmic coordinate, the slope ratio is only 0.7, which means that there is also a deterioration of the extinction ratio. In order to know the original extinction ratio of the modulated optical data, we calculate the power of the amplified data “1” and “0”, which can be observed from the eye diagrams on the digital communication analyzer. Then we reversely deduce the original extinction ratio according to the EDFA’s power response shown in Fig. 8 . When the driving voltage swing is 2 V, the deduced original dynamic extinction ratio is 23 dB. Considering the characteristic impedance of the device is 33 Ω, only 80% of the input voltage is coupled into the device. So the voltage applied to the device is 1.6 V when the voltage from the data source is 2 V. The corresponding static extinction ratio is 25 dB. The small difference is caused by the device’s low electrical transmission loss and the tiny mismatch among the probe, the cables and the electrical connectors. Anyway it is within the experiment tolerance. So is the occasion when the driving voltage swing is 1 V.

 

Fig. 9 Power response of the EDFA

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Fig. 8 (a) Eye diagram of 12.5 Gbit/s data measured with a driving voltage swing of 2 V and the reverse bias of 0.8 V. (b) Eye diagram of 12.5 Gbit/s data measured with a driving voltage swing of 1 V and the reverse bias of 0.5 V.

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4. Conclusion

We use the equivalent distributed circuit model to analyze the electrical properties of the phase shifter with a CPW electrode and optimize its performance. We have successfully reduced the driving voltage swing of the carrier-depletion Mach-Zehnder silicon optical modulator to an acceptable value for CMOS-compatible integration. As a result of the low electrical transmission loss of a 2-mm-long phase shifter, 2 V driving voltage swing leads to an extinction ratio of about 13 dB even with the deterioration effect of the EDFA. The device can even work with the driving voltage swing of 1 V to achieve an extinction ratio of about 7.67 dB. The energy efficiency is 7.8 pJ/bit and 2.4 pJ/bit for 2 V and 1 V driving voltage. This could be reduced to only 400 fJ/bit with the help of a DC block termination.