We present measurements of the nonlinear distortions of a traveling-wave silicon Mach-Zehnder modulator based on the carrier depletion effect. Spurious free dynamic range for second harmonic distortion of 82 dB·Hz1/2 is seen, and 97 dB·Hz2/3 is measured for intermodulation distortion. This measurement represents an improvement of 20 dB over the previous best result in silicon. We also show that the linearity of a silicon traveling wave Mach-Zehnder modulator can be improved by differentially driving it. These results suggest silicon may be a suitable platform for analog optical applications.
©2013 Optical Society of America
Silicon is an attractive medium to fabricate high-speed optical devices due to the capability to share foundry resources with conventional CMOS electronics processes [1,2]. Optical devices fabricated in the silicon material system have shown promise for use in high-speed integrated analog optical links . In particular, traveling wave Mach-Zehnder silicon modulators have been shown as promising candidates for high speed and low drive voltage transmission [4–6].
One important performance metric for an analog optical link is spur-free dynamic range (SFDR) [7–11]. A silicon modulator with a high SFDR allows for its use in analog applications such as SATCOM  or RF-over-fiber communication systems [7,13]. For example, for WLAN systems, an SFDR of 95 dB·Hz2/3 is typically required . However, due to the nature of carrier-depletion modulation, the transfer function contains additional nonlinearities not exhibited in more conventional optical modulation platforms, such as lithium niobate based modulators.
Vacondio et al. have studied the third-order nonlinearity of a Mach-Zehnder Modulator (MZM) and found it to be attractive for certain communications applications with low inter-modulation distortion , but the SFDR was not reported. Recently, Ayazi et al. have characterized the nonlinearities in a silicon ring modulator and found a third-order limited SFDR as high as 84 dB·Hz2/3  and Gutierrez et al. presented a ring-assisted MZM with SFDR of 71.65 dB·Hz2/3 [16,17]. Additionally, Khilo et al. have presented a thorough study of the nonlinearities of a silicon MZM, as well as a biasing and detection scheme to linearize the device . For comparison, the best SFDR reported for a lithium niobate Mach Zehnder modulator are near 120 dB·Hz2/3 [19,20] and up to 128 dB·Hz4/5 for electroabsorption modulators . Here, we demonstrate an SFDRSHD of 82 dB·Hz2/3 and an SFDRIMD of 97 dB·Hz2/3. We note that the SFDRIMD performance is 20 dB greater than the previously presented measurements of a silicon Mach-Zehnder modulator, and it is within 25 dB of what has been demonstrated in lithium niobate. Additionally, we show that the linearity is improved by differential drive. This work demonstrates the viability of silicon as a platform for analog optical applications.
2. Traveling wave Mach-Zehnder modulator fabrication and design
Fabrication occurred at the Institute of Microelectronics (IME)/ASTAR [22,23]. The starting material was an 8” Silicon-on-Insulator wafer from SOITEC, with a Boron-doped top silicon layer of around 10 ohm-cm resistivity and 220 nm thickness, a 2 μm bottom oxide thickness, and a 750 ohm·cm handle silicon wafer, needed for RF performance. A 60 nm anisotropic dry etch was first applied to form the trenches of the grating couplers. Next, the rib waveguides for the modulator were formed using additional etch steps. In all cases 248 nm photolithography was utilized. The p++, p, n++, and n implants for the modulator were performed on the exposed silicon, prior to any oxide fill. This was followed by a rapid thermal anneal at 1030 °C for 5 s for Si dopant activation. It was followed by the formation of contact vias and two levels of aluminum interconnects. Chemical-mechanical planarization was not utilized. The schematic cross-section and device structure is shown in Fig. 1 . Implant recipes were chosen to give peak doping concentrations of approximately 7 x 1017 cm−3 for the p doping regions, 1.7 x 1020 cm−3 for the p++ doping region, 5 x 1017 cm−3 for the n doping concentration, and 5 x 1020 cm−3 for the n++ doping concentration.
The total length of the Mach-Zehnder modulator is 3 mm. Each arm uses co-planar metal strips in a GS configuration and a lateral pn-junction in the waveguide region. Delay loops are placed in the optical path in order to match the RF and optical velocities. The pn-junction is striated to ensure that current flows through the metal transmission lines, rather than in the doped silicon. Additionally, the arms of the modulator are unbalanced by 100 µm to enable biasing by tuning the input wavelength.
3. Spur-free dynamic range
SFDR is defined as the signal to noise ratio of a carrier when the largest spur is at the noise level. To obtain a prediction for SFDR, we will derive an expression for SFDR based on the transfer function of the MZM. When the input signal consists of two tones at frequencies f1 and f2, we are interested in the relative powers in the harmonic terms at 2f1 and 2f2 and intermodulation distortion terms at 2f1-f2 and 2f2-f1. SFDR limited by second harmonic distortion (SHD) refers to the distortion terms at 2f, whereas SFDR limited by intermodulation distortion (IMD) refers to the distortion terms at 2f1-f2 and 2f2-f1. In this section, we examine the second and third order terms of the Taylor expansion of the Mach-Zehnder modulator transfer function to derive expected values for SHD and IMD based on DC measurement data.
The MZM is intentionally unbalanced by 100 µm to allow the device to be biased by tuning the input wavelength. The transfer function for a Mach-Zehnder modulator biased at its quadrature point is
Each arm of the Mach-Zehnder was tested individually. Since the MZM is unbalanced, phase shift may be extracted by examining the shift in the optical spectrum at various bias voltages, as demonstrated in Fig. 2 . Experimental data for the phase shift as a function of voltage is shown in Fig. 3 . This device exhibits a VπL figure of merit of 3.33 V·cm and 4.77 V·cm for the top and bottom arms, respectively.
The DC phase shift vs. voltage data for each arm was fit with a third order polynomial of the form:Table 1 lists the extracted fit parameters for each arm of the MZM. The linear term, b, indicates the small signal performance and a corresponding small-signal VπL figures of merit of 2.3 V·cm and 2.4 V·cm for the top and bottom arms, respectively. Note that the data for the bottom arm phase shift versus reverse bias voltage is negated in order to compare against the performance of the top arm.
Based on the fit of the phase shift versus junction bias at a 0 V bias, we predict a 2nd order limited SFDRSHD of 87 dB·Hz1/2 for a differentially driven MZ and 75 dB·Hz1/2 when driving only a single arm. The gain achieved by differential drive for second harmonic distortion is limited by the relative pn-junction performance of each arm. The difference in phase shift performance between the top and bottom arms, while not known, is assumed to be due to mask misalignment during processing. Since the top and bottom arms exhibit different nonlinearities, biasing the modulator at quadrature does not cancel the second order term as it does for a linear electro-optic effect modulator. This model also predicts an SFDRIMD of 94 dB·Hz2/3 and 98 db·Hz2/3 for the single arm and differential drive cases, respectively. In this case, the third order SFDR is expected to improve by 4 dB not due to cancellation of the third order terms from the pn-junction nonlinearity, but because differential drive effectively increases the output powers of the fundamental and distortion terms by 6 dB.
4. Experimental setup
A tunable laser light source is input into an erbium-doped fiber amplifier and then through a polarization rotator. The polarized light is coupled into the modulator from an optical fiber with a grating coupler holographic lens and routing waveguides. The modulated signal is coupled back into an optical fiber with another grating coupler. Each grating coupler has a known 4.4 ± 0.2 dB loss and the waveguides have 2.2 ± 0.8 dB/cm loss. To achieve quadrature, the wavelength of input light is adjusted to the −3 dB point in the spectrum. The principal limiting factor of this test was the photodetector saturation power of 2 mW. The experimental setup is shown in Fig. 4 .
An arbitrary waveform generator (AWG) and a vector network analyzer (VNA) are used as signal sources. The AWG is capable of producing complementary signals, while the VNA is not. To create a complementary signal, the VNA output is passed through a splitter and recombined after delaying one path with close to three inches of additional rf cabling. The frequency of modulation was adjusted to tune the phase difference and achieve complementary signals. Two signals near 1 GHz were applied to the MZM. In principle, higher bandwidth signals could be used but is limited here by the detection bandwidth of the spectrum analyzer. The detector is a New Focus 1414 photodetector, which has a conversion gain of 15 V/W and responsivity of 0.6 A/W. The bandwidth of the device was measured to be 15.5 GHz, as indicated in Fig. 5 .
A typical RF spectra of intermodulation distortion is presented in Fig. 6 . The nonlinearity of the MZM driven by a single arm is presented in Fig. 7 and the nonlinearity of the differentially driven MZM is shown in Fig. 8 . The EDFA amplified the tunable laser to about 500 mW and 1 mW of light is received at the photodetector. Excess losses due to the implants in the MZM in this process have been reported to be 10 dB/cm , and the total insertion loss of the device biased at quadrature is 6.7 dB. A noise floor of −165 dBm/Hz, limited by optical amplifier noise, was observed and is used to calculate SFDR. A noise figure for the test setup link of 58 dB is measured. This figure could be improved in the future by improving the slope efficiency with a longer device, however, at the cost of a reduced bandwidth.
SFDRSHD and SFDRIMD for the single arm case at 0 V bias are found to be 72 dB·Hz1/2 and 92 dB·Hz2/3, respectively. By differentially driving the modulator the SFDR is found to increase to 82 dB·Hz1/2 and 97 dB·Hz2/3 for SFDRSHD and SFDRIMD, respectively. For both single arm and differential drive operation, these values are within 5 dB of the expected performance from DC measurements of the pn junction nonlinearity. This suggests that the junction is the dominant nonlinearity for this system.
Additionally, since there is a known optical loss after the device, the SFDR of this optical link may be improved in the future. After the output of the MZM, there is 1.2 dB of loss in the routing waveguides, and 6.3 dB of net loss under testing conditions due to the grating coupler. One cannot generally normalize out optical losses from an SFDR calculation, since this neglects the possible power-handling limitations of the devices. But known losses that occur after the device can certainly be removed with improved engineering efforts, without affecting the power that flows through the device. This improvement would be realized in optical links that use photodetectors with higher saturation currents. In fact, a high-speed photodetector fabricated in this platform has previously been demonstrated to exhibit linear behavior for optical powers up to 7.8 mW .
In this case, we note that only about 50 mW of optical power enters the input waveguide of the MZM due to losses from a polarization controller (<1 dB), insertion loss from the fiber array to the on-chip grating coupler (6.3 dB), routing waveguides (1 dB), and y-junction (4 dB). This optical power is well below the power saturation limit of typical silicon photonics devices with these dimensions . Presumably, the SFDR could be further improved by increasing the optical power in the device, through either a more powerful input optical signal, or lower coupling losses. We note that the propagating power in the results described in [19, 20] was on the order of 500 mW and 240 mW, respectively.
In this work, we have presented measurements of the 2nd and 3rd order nonlinearities of a traveling wave carrier depletion-based silicon Mach-Zehnder modulator. We measured an SFDRSHD of 82 dB·Hz1/2 and an SFDRIMD of 97 dB·Hz2/3. These measurements show an improvement in SFDRIMD by 20 dB over what has been previously reported in literature. We also demonstrate that differential drive improves the linearity of the modulator. In addition, future link iterations that reduce the passive coupling losses of the device could potentially further improve SFDR. Based on our results, we believe that silicon-based Mach-Zehnder modulators could become important tools for future analog applications in integrated optics.
The authors would like to thank Gernot Pomrenke, of the Air Force Office of Scientific Research, for his support under the OPSIS and PECASE programs, and would like to thank Mario Panniccia and Justin Rattner, of Intel, for their support of the Institute for Photonic Integration. The authors would also like to thank Mentor Graphics for their support of the OPSIS project. The authors would further like to acknowledge support from the DARPA E-Phi program.
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