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Abstract
In this paper, a carrier-injection electro-absorption modulator (EAM) at 2 µm is demonstrated on Ge-on-Si platform. The EAM shows a compact size and high modulation efficiency due to the strong free-carrier electroabsorption (FCEA) effect in Ge. A modulation depth of 40 dB can be obtained under the injection current of only 420 mA. Small-signal frequency response measurement is performed and a small-signal equivalent circuit model is proposed. Based on reflection coefficients and equivalent circuit, the frequency response of carrier-injection EAM is discussed in detail. The 500 Mbps open eye diagram verifies the data-processing capacity of our EAM at 2 µm wavelength for its application in biological, chemical molecular detection, and infrared imaging systems.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Silicon-based photonics has attracted considerable attention in the near-infrared (NIR) band, especially at 1310 nm and 1550 nm, due to its application in optical interconnects and communications system. However, the NIR fiber-optic telecommunication system is gradually approaching its capacity limit because of the exponential growth of internet data transmission, and "capacity crunch" of the optical communication system may happen in the future [1]. With the emergence of low-loss hollow-core photonic band-gap fiber (HC-PBGF), the 2 $\mu m$ waveband is extended as a promising waveband due to its prospects in applications, from spatial division multiplexing to gas sensing, and potentially of particular interest for next generation telecoms infrastructure [2]. Fundamental components for 2 $\mu m$ have been developed, such as GeSn photodetectors [3], lasers [4], and arrayed waveguide grating [5] etc. Among them, electro-optic modulator at 2 $\mu m$, as the key part of optical module, still has a long way to go. Si-based modulators, mainly based on free-carrier plasma effects [6], can be classified as carrier-depletion, carrier-accumulation, and carrier-injection types. Among these types, carrier-injection modulator has the advantages of both compact size and power efficiency. Since carrier injection is a microsecond process, carrier-injection modulators are mainly designed for applications such as biological, chemical molecular detection and infrared imaging systems [7–9].
Carrier-injection modulators based on Mach-Zehnder interferomer (MZI) and micro-ring resonator (MRR) have been demostrated for NIR and 2 $\mu m$ waveband [10–13], utilizing the free-carrier electrorefraction effect in Si. In 2013, Suguru Akiyama reveals the bandwidth limiting factor of carrier-injection modulators based on MZI and the possibility of achieving high speed performance of carrier-injection modulators [14]. However, MZI modulator suffer from its large footprint of the order of $mm^2$ and MRR modulator is with a compact size at the sacrifice of optical bandwidth, thermal tolerance, and fabrication tolerance, which is not a good choice for practical application. Electro-absorption modulator (EAM) based on Franz-Keldysh (FK) effect in Ge has been demonstrated with compact size and high-speed characteristics [15]. However, the operating wavelength of FK effect is close to the wavelength corresponding to the band gap and cannot be applied in 2 $\mu m$. It is necessary to utilize some other mechanisms to design compact modulators for the special application purpose of the 2 $\mu m$ waveband and above.
Ge becoming increasingly important and attractive, especially for its uses in mid-infrared (MIR) photonics, due to its transparency over a wide wavelength range from 2 $\mu m$ to 16.7 $\mu m$ [16]. It is also with a high carrier mobility and a high refractive index (about 4$\sim$4.1 for wavelength of 2$\sim$20 $\mu m$) [17] and compatible with Si process. The first Ge-on-Si waveguide is demonstrated in 2012, followed by the realization of passive devices such as low loss multimode interferometers, grating couplers, arrayed waveguide grating and polarization rotators and active devices such as thermo-optic phase shifters and photodetectors based on Ge-on-Si platform [18–25]. In 2015, the free carrier plasma effects in Ge has been revealed by Nedeljkovic et al. [26], showing a stronger free-carrier effect than Si, especially the free-carrier electroabsorption (FCEA) effect (more than 1000 times stronger). However, there has been little progress in the study of carrier-injection Ge modulators for the 2 $\mu m$ wavelength. Therefore, it is desirable and possible to realize a modulator with high modulation depth and efficiency on Ge-on-Si platform by using the FCEA effect.
In this paper, we design, model, and demonstrate a compact high-modulation-depth and high-modulation-efficiency EAM at 2 $\mu m$ on Ge-on-Si platform. Working at PIN forward-biased state, the EAMs show a minimum modulation region length as short as 70 $\mu m$ and a modulation depth of 40 dB under the injection current of only 420 mA. To characterize and analyze the high-frequency behavior of the Ge-on-Si carrier-injection EAM, small-signal frequency response measurement is performed and a comprehensive small-signal equivalent circuit model is proposed. The equivalent circuit-calculated frequency response matches exactly well with the measured result, revealing the influencing factors of small-signal characteristics for EAMs. 500 Mbps open eye diagram is obtained, which verifies the data-processing capacity of our EAM at 2 $\mu m$ wavelength for its application in biological, chemical molecular detection, and infrared imaging systems.
2. Device designs and fabrications
Not-to-scale cross-section and top-view of EAM are depicted in Fig. 1(a). The EAM investigated in this work is fabricated on a Ge-on-Si platform with a Ge layer of 1 $\mu m$. Ge waveguide is obtained utilizing deep ultraviolet (DUV) lithography and inductively coupled plasma (ICP) etching, with an etch depth of 400 nm. As can be seen in Fig. 1(b), 1.2 $\mu m$-wide Ge rib waveguide is formed with a steep and smooth sidewall. Subsequently, heavily doped active region, used to form ohmic contact and inject carriers into the Ge waveguide, is realized by implanting $BF^{2+}$ and $P^{2-}$ into Ge slab. EAMs with different active region lengths (70, 100, 130, 160, 190, 220 $\mu m$, respectively) are fabricated and the optical microscope image of EAM with an active region length of 190 $\mu m$ (EAM-190) is shown in Fig. 1(c).
Fig. 1. (a) Not-to-scale cross section and top view of the fabricated EAM. (b) Scanning electron microscope (SEM) image of the Ge waveguide. (c) Optical microscope image of the EAM with an active region length of 190 $\mu m$.
The forward-biased carrier-injection EAM utilizes the free-carrier dispersion effect. By injecting carriers into the rib region, the absorption coefficient $\alpha$ of the material can be changed. The change of the absorption coefficient will directly lead to the change of the output optical power of the EAM and realize optical intensity modulation. The prediction of free-carrier electroabsorption (FCEA) effect in Ge [26] for 2 $\mu m$ is given in Eq. (1):
The separation S between the Ge waveguide and the heavily doped region is optimized by simulating the active-region waveguide loss under different S. The simulation results are plotted in Fig. 2(a). With the increase of S, the waveguide loss gradually decreases and approaches constant when S becomes over 2 $\mu m$. However, it is not suggested to design too much separation between the waveguide and the heavily doped region, since the modulation efficiency decreases with the separation, and the series resistance also increases. To consider both the modulation efficiency and loss with a balance view, a separation is chosen to be 2 $\mu m$ to make the trade-off. The inset in Fig. 2(a) shows the mode profile of the Ge waveguide, which exhibits good single-mode characteristics. To maximize the I/O coupling efficiency of waveguide on Ge-on-Si platform, the edge coupler is optimized. Forward tapered spot size converter (SSC) is used in this work for edge coupling, as is shown in Fig. 2(b). The width of the SSC ($W_{SSC}$) should be optimized to maximize the overlap of the mode field between the tapered fiber and edge coupler. Besides, the length of the SSC ($L_{SSC}$) should be optimized to achieve adiabatic transmission and reduce mode transmission loss. It can be seen from Fig. 2(c) that when $W_{SSC}$ is 8 $\mu m$, the coupling efficiency with fiber is the maximum. The inset of Fig. 2(c) shows the SEM image of the cross section of the coupler with a $W_{SSC}$ of 8 $\mu m$. Then, the influence of $L_{SSC}$ on the insertion loss (IL) is studied. As is shown in Fig. 2(d), the IL does not change along with $L_{SSC}$ when $L_{SSC}$ is more than 100 $\mu m$. To increase the fabrication tolerance of the subsequent deep etching process and keep the core device away from the chip edge, we take $L_{SSC}$ as 200 $\mu m$. The inset of Fig. 2(d) shows the optical field distribution along the optical transmission direction of SSC coupler with a $L_{SSC}$ of 200 $\mu m$.
Fig. 2. (a) Simulated active-region waveguide loss under different separation S. (b) Schematic diagram of forward taper SSC. (c) Simulated coupling efficiency under different $W_{SSC}$. (d) Simulated forward taper SSC loss under different $L_{SSC}$.
3. DC and AC characteristics
The current-voltage (I-V) characteristics of the EAMs is obtained by using a high-precision digital source meter (Keithley 2611A) at room temperature. Figure 3(a) shows the I-V curves of the EAMs from -1 V to 4 V, which exhibit typical PIN junction behaviors. The DC response of the modulator is further measured. A thulium-doped fiber laser (Thorlabs LFL2000) with an output wavelength of 2000 nm is employed as the light source. A polarization controller and a lensed fiber are used to ensure polarization alignment and focus the light into the Ge waveguide by an edge coupler. After passing through the active region of the Ge waveguide, the output light from the chip is measured by a commercial optical power meter. DC voltage from Keithley 2611A is applied onto the electrode pad via a ground-signal-ground (GSG) probe to inject carriers into the Ge rib waveguide. The normalized modulation depth of the EAMs as a function of injection current is depicted in Fig. 3(b). A same injection current represents a same amount of injected carriers. Figure 3(b) shows the influence trend of the amount of injected carriers on the modulation depth. Due to the strong FCEA effect of Ge at the 2 $\mu m$ band, an extinction depth of more than 40 dB can be achieved. When continue to increase the injected current beyond those 40 dB points, a higher modulation depth will be realized, but is too weak to be measured by the power sensor due to its minimum power measuring range. For EAM-70, an extinction depth of 40 dB can be obtained with only an injection current of 420 mA. To compare the extinction ability of EAMs with different active region lengths, the modulation depths at 1, 2 and 3 V is extracted. As can be seen in Fig. 4, a longer EAM has a higher modulation depth at the same applied voltage, which may lead to a better big-signal dynamic performance under a same $V_{PP}$. This is because a longer EAM has a smaller series resistance but a larger current cross-sectional area, so different lengths of EAM have the same current density under the same bias. That is, they are with the same carrier density, resulting the same absorption coefficient according to Eq. (1). It should be mentioned that a longer EAM would have a lower series resistance, which may lead to a higher Joule heat and power consumption at the same applied voltage. The appropriate length of EAM should be chose based on the actual requirements. The measurement result of the DC response indicates the forward-biased Ge-on-Si EAM with a potential of achieving ultra-high modulation depth, which is pivotal for its application in biological and chemical molecular detection, infrared imaging systems, and other fields.
Fig. 3. (a) Measured I-V curves for EAMs with different active region lengths. (b) Modulation depth of EAMs as a function of injection current.
Small-signal frequency response measurement is performed at a forward-biased DC voltage of 0.5 V to characterize the RF modulation characteristics. The electro-optic bandwidth of the EAMs is obtained, using a Keysight vector network analyzer (N5247B), a 10 GHz commercial photodetector, and a 50 $\Omega$-terminated GSG RF probe. As depicted in Fig. 5, there is little difference in frequency response characteristics among EAMs with different active region lengths, showing an average 3-dB bandwidth ($f_{3dB}$) of about 212 MHz.
4. Small-signal equivalent circuit model for carrier-injection EAM
To further investigate the factors influencing the frequency response characteristics of the forward-biased carrier-injection Ge EAM, a small-signal equivalent circuit model is proposed. The equivalent circuit is shown in Fig. 6(a), in which $R_{para}$, $L_{para}$ and $C_{para}$ represent the parasitic resistances, inductances and capacitance from the metal interconnects, respectively. $C_{Ge}$, $C_{Si}$ and $G_{Ge}$, $G_{Si}$ in blue color represent the capacitor and conductance in the intrinsic region of Si and Ge. For Ge-on-Si EAM, $C_{Si}$ and $G_{Si}$ cannot be ignored because of the non-negligible current leakage in Si.
Fig. 6. (a) Comprehensive Equivalent circuit model for Ge-on-Si carrier-injection EAM. (b) Equivalent circuit model for Ge-on-Si carrier-injection EAM in the PIN reverse-biased state. (c) Equivalent circuit model for Ge-on-Si carrier-injection EAM in the PIN forward-biased state.
In order to extract $R_{para}$, $L_{para}$ , $C_{para}$ and $C_{sub}$ which do not change with voltage, a reverse bias voltage of 3 V is applied to the EAMs and their reflection coefficients (i.e., $S_{11}$) are measured from 10 MHz to 40 GHz using the VNA. In the reverse bias state of PIN, there is almost no conductance in Ge and Si. The equivalent circuit model in depleted state can be simplified as shown in Fig. 6(b), where $C_{j,Ge}$ and $C_{j,Si}$ are the depletion capacitance in Ge and Si. By fitting the measured reflection coefficient to the simulated reflection coefficient based on the circuit parameters until the exact match, the value of each parameter in the circuit can be obtained. The measured and simulated reflection coefficients for EAM-70 and EAM-220 at -3 V are depicted in Fig. 7, showing good agreement. The extracted parameters values are given in Table 1.
Fig. 7. Measured and simulated reflection coefficients for EAM-70 and EAM-220 from 10 MHz to 40 GHz at -3 V.
Table 1. Extracted $R_{para}$, $L_{para}$, $C_{para}$ and $C_{sub}$ for EAM-70 and EAM-220.
The carrier-injection Ge-on-Si EAM works in forward-biased mode and the equivalent circuit model can be simplified as shown in Fig. 6(c), where $G_D$, $G_D$ and $R_S$ are the total conductance, diffusion capacitance and series resistance in Si and Ge, respectively. According to [28], $G_D$ and $C_D$ are functions of frequency and can be expressed as:
where $G_0$ is the DC conductance, which can be get from the measured I-V curves, and $\tau$ is the effective carrier lifetime. The carrier lifetime $\tau$ varies with the doping concentration as empirically described in Eq. (4) according to [6]: According to the study of E. Gaubas et al. [29], effective carrier lifetime $\tau$ of 1.0 ns is taken in our equivalent circuit model. For the EAM based on the free carrier absorption effect, the output light amplitude varies with the absorption coefficient $\alpha$, while $\alpha$ is proportional to the stored charge $Q_D$. Therefore, the modulator frequency response of this forward-biased Ge-on-Si EAM can be calculated by calculate the charge $Q_D$ stored by the diffusion capacitor $C_D$ and be expressed as the stored charge $Q_D$ normalized to its low-frequency ($\omega _0$) value:Fig. 8. Measured and simulated modulator frequency response from 10 MHz to 10 GHz for EAM-70 and EAM-220.
$(R_{Load}+R_S)C_D$ and $R_D C_D$ are defined as circuit time constant and carrier recombination time. If $(R_{Load}+R_S) \ll R_D$, $\tau \approx (R_{Load}+R_S)C_D$. In this case, $(R_{Load}+R_S) \ll R_D$ holds, due to the intrinsic layer between N, P heavily doped regions. So, the carrier lifetime is more circuit time constant ($R_S$) dependent and less carrier recombination time ($R_D$) dependent. In future work, methods can be adopted such as adding a lightly doped region as the transition region and replacing the contact metal Al by Pt or Ni to optimize the ohmic contact, which reduces the series resistance to further improves the bandwidth.
5. Large-signal characterization
The data-handling capacity of the EAMs is verified by measuring the eye-diagram large-signal acquisitions at different data rate. 300 Mbps, 500 Mbps, 800 Mbps and 1 Gbps pseudorandom bit sequence (PRBS) electrical signals of $2^{31}-1$ are generated by an arbitrary waveform generator (AWG, Agilent 80C10B). The electrical signals are amplified to the peak-to-peak voltage ($V_{pp}$) of 4 V by an RF amplifier and applied to EAMs via a bias-tee and a 50 $\Omega$-terminated GSG probe and simultaneously, a DC bias of 0.5 V is applied to the device by bias-tee. The 2000 nm-wavelength light emitted by the laser is amplified by TDFA and then coupled into the EAM. The optical signal modulated by EAM enters the commercial 10 GHz photodetector and is converted into an electrical signal and finally input into the oscilloscope subsequently. For EAMs with different active region lengths, a longer EAM should have a better big-signal dynamic performance according to Fig. 4. Measured 300 Mbps, 500 Mbps, 800 Mbps and 1 Gbps eye diagrams for EAM-220 at 2000 nm is shown in Fig. 9. 500 Mbps open eye diagram is obtained, with a dynamic extinction ratio (ER) of 4.54 dB.
6. Conclusion
In conclusion, a compact carrier-injection electro-absorption modulator based on a Ge-on-Si platform at 2 $\mu m$ wavelength is demonstrated, characterized, and analyzed. Due to the strong free-carrier electroabsorption effect in Ge, the fabricated EAM shows high modulation depth and high modulation efficiency. Small-signal frequency response measurement is performed, showing an average $f_{3dB}$ of about 212 MHz. A small-signal equivalent circuit model is proposed to explore the influencing factors of frequency response characteristics of small signals and the parasitic parameters is extracted by fitting the measured reflection coefficient. Good agreement is realized between the tested and calculated results. The 500 Mbps open eye diagram verifies the data-processing capacity of our EAM at 2 $\mu m$ wavelength. The compact size, high modulation efficiency, and manufacturing simplicity of this Ge-on-Si EAM will enable its application advantage in MIR photonics, especially in field such as gas sensing, molecular detection, and infrared imaging systems.
Funding
National Key Research and Development Program of China (2020YFB2206103); National Natural Science Foundation of China (61975196); China Computer Interconnect Technology Alliance (CCITA) funding (20220102); .
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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