Silicon photonics is a fascinating technology to realize large-scale electronics-photonics integration on a chip with low cost, high bandwidth, large volume, high energy efficiency, and complementary metal-oxide semiconductor (CMOS) compatibility [1–5]. Silicon photonics has been proving its great worth in data centers, long-haul telecommunication, integrated quantum communication, integrated microwave photonics, artificial intelligence (AI), and high-performance computers [2,4–8].

One of the key building blocks of silicon photonics is photodetectors (PDs) that convert high-speed optical signals to electrical signals [9,10]. However, the intrinsic properties of silicon (Si), an indirect band-gap semiconductor with a band-gap energy of 1.1 eV which is transparent in the near-IR wavelength band (1.3–1.55 μm), make it challenging to realize photodetection [10]. As an option, germanium (Ge), which possesses great linear absorption up to 1550 nm and can be extended up to 2000 nm by exploiting tensile-strained germanium-on-silicon (Ge-on-Si) bandgap shrinkage, has appeared as a prime choice for photodetection [11–14]. The measured absorption coefficients of Ge material are about ${10}^4{\mathrm{cm}}^{-1}$ at 1310 nm and $5\times {10}^3{\mathrm{cm}}^{-1}$ at 1550 nm [15,16]. The chief drawback of the 4.2% lattice mismatch between Ge and Si, which will result in a high misfit dislocation density and make it difficult to achieve the high-quality epitaxial growth of thick Ge on Si, has been alleviated by employing the technique of two-step Ge epitaxial deposition and continuous or cyclic thermal treatment [10,11,13,17–19]. In recent years, with different approaches developed to realize high-quality epitaxial growth Ge on Si, a variety of Ge-on-Si PDs have been designed and demonstrated, mainly focusing on p-i-n (PIN) [20] and metal-semiconductor-metal (MSM) devices [21].

Compared to a Si waveguide, the ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguide features a large band gap and absence of two-photon or free-carrier absorption in the telecom band, ultralow propagation loss ($<1\text{dB/}\mathrm{m}$), as well as low nonlinearity and a wide-band transparency window (0.4–4.5 μm) [35–38]. Additionally, several major foundries, such as AIM Photonics, CompoundTek, ST Microelectronics, and CEA-Leti, have pronounced their silicon photonic platforms integrated with at least one ${\mathrm{Si}}_3{\mathrm{N}}_4$ layer. However, the combining of Ge-on-Si PD with ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguides has not been explored much. Especially, to the best of the authors’ knowledge, a Ge-on-Si PD with a double lateral coupling scheme has not been proposed and demonstrated.

In this paper, we report the first concept of a Ge-on-Si PD with double lateral ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguides, which can serve as a novel waveguide-integrated coupling configuration as shown in Fig. 1. The double lateral coupling ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguides will decouple the light propagation from the Ge absorption and Si slab waveguide. They allow for independent optimization of quantum efficiency, operation speed, and power handling. The Ge-on-Si PD based on lateral coupling ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguides has several distinctive advantages. (1) The lateral ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguides can be designed relatively free. This might be very beneficial to manipulating the optical field in the Ge absorption region to attain uniform photocarrier distribution, which will be helpful to improve quantum efficiency and operation speed. (2) The light propagation in the double lateral ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguides will avoid the optical loss caused by bottom doped silicon slab waveguide. The doping density of the silicon slab waveguide can be appropriately adjusted to achieve higher operation speed again. (3) As the ${\chi }^{(3)}$ of ${\mathrm{Si}}_3{\mathrm{N}}_4$ is about 20 times lower than that of Si in the telecommunication wavelength range, the light propagation in the double lateral ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguides possesses lower nonlinearity [35]. Therefore, the ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguide can sustain higher optical power density than the Si waveguide and evade two-photon absorption, which means wide-input-power dynamic range. (4) The combination of high-speed Ge-on-Si PD with a ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguide could be a novel active ${\mathrm{Si}}_3{\mathrm{N}}_4$ platform that could achieve the integration of coherent receivers at 1 μm and the visible light band.

We design and fabricate the Ge-on-Si PD with double lateral coupling ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguides based on a commercial standard silicon-on-insulator (SOI) platform. To comprehensively characterize the proposed lateral coupling Ge-on-Si PD, first, the static current-voltage (I-V) characteristic and responsivity are measured. Then equivalent circuit model and theoretical 3 dB OE bandwidth investigation are implemented. Second, the small-signal (S21, S11) radio-frequency (RF) measurements for the ${\mathrm{Si}}_3{\mathrm{N}}_4$-based lateral coupling PD are executed. Finally, the high-speed and high-power large-signal measurements, including non-return-to-zero (NRZ) on-off-keying (OOK) and four-level pulse amplitude modulation (PAM-4) eye diagrams are attained.

For regular butt-coupling and evanescent-coupling (bottom) schemes, the light is injected into Ge region all at once with nonuniform optical field distribution in the absorber, which will cause a large electron–hole pair density at the Ge-Si waveguide interface [13,25]. The high density of photogenerated electron–hole pairs generates relatively strong gradient of charge, which will induce a large electric field opposing to the applied external voltage. This phenomenon is called carrier screening [39,40], which will drastically degrade the 3 dB OE bandwidth. Therefore, the uniform optical field distribution in the Ge region will be helpful to generate homogeneous electron–hole pair density, and consequently, it is beneficial to improving the operation speed. Figure 2(d) shows the cross-sectional view of field distribution of the ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguide with 800 nm and 450 nm width and the side view of field distribution of the Ge absorption region. The light propagates along the $x$ axis. Compared with butt coupling and evanescent coupling (bottom), it is obvious that the light spreads more uniformly in the whole Ge absorption region by using double lateral ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguides.

To profoundly analyze the high-frequency response of the fabricated Ge-on-Si PD with double lateral ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguides, first, the theoretical calculation of the 3 dB OE bandwidth is presented. Then the small-signal measurements for the Ge-on-Si PD are implemented. It is well known that the RF response of a Ge-on-Si PD is largely controlled by carrier transit-time-limited bandwidth ($f_{\mathrm{tr}}$) and resistor-capacitor (RC)-limited bandwidth ($f_{\mathrm{RC}}$) in the active PIN regions [27,41]. The carrier transit frequency $f_{\mathrm{tr}}$ can be written as $$f_{\mathrm{tr}}=\frac{0.45{\upsilon }_b}{d},$$(1)where ${\upsilon }_b$ is the carrier saturation drift velocity (Ge: ${\upsilon }_b=6\times {10}^6\mathrm{cm}/\mathrm{s}$) and $d$ is the thickness of the intrinsic Ge zone. For the proposed Ge-on-Si PD with double lateral ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguides, the intrinsic Ge (i-Ge) region is about 0.3 μm. Therefore, the theoretical $f_{\mathrm{tr}}$ is estimated to be 90 GHz. The limit of the RC bandwidth can be calculated by [27,41] $$f_{\mathrm{RC}}=\frac{1}{2\pi RC},$$(2)where $R$ is the total resistance, which includes the series resistance $R_s$ and the load resistance $R_{\mathrm{load}}$, and $C$ is the capacitance, including the junction capacitance $C_j$ and the parasitic capacitance $C_p$. Based on the extracted parameters ($R$ and $C$) from the S11 measurement, the $f_{\mathrm{RC}}$ is evaluated to be approximately 82.4 GHz.

The total 3 dB frequency response, determined by $f_{\mathrm{tr}}$ and $f_{\mathrm{RC}}$, can be calculated by [41,42] $$f_{3\mathrm{dB}}=\frac{1}{\sqrt{f_{\mathrm{RC}}^{-2}+f_{\mathrm{tr}}^{-2}}}.$$(3)Therefore, the theoretical 3 dB OE bandwidth $f_{3\mathrm{dB}}$ of a Ge-on-Si PD with lateral ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguides is evaluated to be approximately 60.8 GHz.

Compared to the butt-coupling scheme, the possible freely chosen parameters of an evanescent-coupling configuration based on double lateral ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguides include waveguide thickness, gap width, and waveguide shape (strip or rib or tapered waveguide and so on). One difference between the coupling configuration of the ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguide on top and on the double lateral sides of the absorber is the way to adjust the gap width between the ${\mathrm{Si}}_3{\mathrm{N}}_4$ and the absorber. For the ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguide on top of the absorber, in order to change the gap width, the thickness of the silica (${\mathrm{SiO}}_2$) layer has to be adjusted during the fabrication processes. Nevertheless, for the ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguide on the double lateral sides of the absorber, the variation of gap width can be realized just by designing the layout. It is very easy and accessible. Another difference is the light evanescent coupling from one side and both sides. For high input optical power, it is well known that the capability to manipulate the optical field in the absorption region to attain uniform photocarrier distribution is very beneficial to improving quantum efficiency and operation speed [34,39,42,43]. The evanescent coupling from both sides has the advantage of manipulating the optical field in the absorber. Although the lateral ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguides can be designed relatively free, in order to achieve high coupling efficiency, there are still trade-offs between Ge absorber thickness, gap width, and ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguide thickness [33].

In our proposed structure, the silicon-based $1\times 2$ MMI splitter and the two Si to ${\mathrm{Si}}_3{\mathrm{N}}_4$ inter-layer transitions are integral parts of the proposed Ge-on-Si PD. The losses of the silicon-based $1\times 2$ MMI splitter and Si to ${\mathrm{Si}}_3{\mathrm{N}}_4$ inter-layer transition are about 0.3 dB and 0.2 dB, respectively. The responsivity of the Ge-on-Si PD is about 0.36 A/W without correcting for the losses of these components (0.5 dB). In future designed structures, the silicon-based $1\times 2$ MMI splitter and Si to ${\mathrm{Si}}_3{\mathrm{N}}_4$ inter-layer transitions can be replaced by a ${\mathrm{Si}}_3{\mathrm{N}}_4$-based $1\times 2$ MMI splitter, which might further decrease the losses and improve the internal responsivity. The evanescent coupling from both sides will lead to a standing wave pattern in the absorber as shown in Fig. 2(d). This phenomenon is similar to the Ge-on-Si PD with four-directional light input [42], but its effect on optical signal reception can be nearly ignored.

In summary, as a proof-of-concept demonstration, we have proposed a novel light coupling scheme of waveguide-integrated Ge-on-Si PD: lateral coupling by employing double lateral ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguides. It features uniform optical field distribution in the Ge absorption region and allows for independent optimization of quantum efficiency, operation speed, and power handling. The maximum responsivity is estimated to be approximately 0.52 A/W with 25 mW input power at 1550 nm, which can be further enhanced by decreasing the gap between the ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguide and the 220 nm Si slab and increasing the gap between the ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguide and the metal copper. Based on the equivalent circuit model and extracted parameters, the Ge-on-Si PDs with double lateral ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguides have reached theoretical 3 dB OE bandwidths of up to 60.8 GHz, which is well matched to the experimentally demonstrated 60 GHz under 4 mA photocurrent at DC bias voltage $-3\mathrm{V}$. Under 1 mA photocurrent, the 70, 80, 90, and 100 Gbit/s NRZ and 100, 120, 140, and 150 Gbit/s PAM-4 clear openings of the eye diagrams are obtained without utilizing any offline DSP at the RX side. The clear open electrical eye diagrams of 60 Gbit/s NRZ under 5, 10, 15, and 20 mA photocurrent at the DC bias voltage of $-3\mathrm{V}$ are also attained, which exhibits the detection capability of high-speed and high-power signal. We are currently making great efforts to improve the quantum efficiency and further explore the high-speed and high-power handling ability of Ge-on-Si PD with double lateral ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguides. Overall, the proposed lateral ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguide structure is flexibly extendable to the light coupling scheme, which shows favorable performances. It is believed that our proposed Ge-on-Si PD has the great potential to achieve low-complexity and low-cost $>100\mathrm{Gbit}/\mathrm{s}$ data reception per lane for future 400/800 GbE transceivers, which can be utilized in data centers, long-haul telecommunication, and high-performance computers. The characteristic of high-speed and wide-input-power dynamic range makes it attractive to integrated microwave photonics application, such as ultra-broadband wireless communication.