Ultra-fast germanium photodiode with 3-dB bandwidth of 265 GHz

in the centre of the waveguide, where the optical intensity is supposed to be highest, leading to the shortest transit times for photocarri-ers. Our approach is based on an initially few-micrometre-wide germanium body with a height of ~400 nm, which is thick enough to ensure sufficiently good crystalline quality. This is a distinctive feature compared to vertical drift field diodes, where the epitaxial growth of thin germanium layers ( < 100 nm) with low defect den-sity is very difficult, and thus the fabrication of photodiodes with reasonably low dark currents is quite challenging 11 .

I ntegrated photonics has enabled the digital communication age, which relies on optical networks at all levels to transport data at very high speed and low cost. Large-scale data centres require highly integrated cost-efficient optical communication solutions, because data-centre interconnects are becoming one of the main cost factors. The technical and economic necessities associated with optical interconnects have fostered the development and rapid maturation of two integrated photonics technology platforms for use in the 1,300-1,600 nm range that is prevalent today. The platforms are conventionally denominated by their material base: (1) silicon photonics and (2) indium phosphide (InP)-based integrated photonics. The importance of the two platforms goes way beyond optoelectronic transceivers and optical communications. Both silicon photonics and InP-based photonics find applications in terahertz generation and sensing, high-speed signal processing and potentially neuromorphic computing. Although silicon photonics enjoys some clear advantages over InP integrated photonics, such as its scalability up to 300-mm wafers and wafer-level co-integration with high-speed electronics, the ultimate and benchmark photodetector performances are achieved with InP 1,2 . InP-based waveguide-coupled photodiodes, even several years ago, had already demonstrated 3-dB bandwidths (f 3-dB ) of 170 GHz and responsivities of 0.27 A W −1 (ref. 3 ). By contrast, germanium photodiodes, which are available on the major silicon photonics platforms, typically show bandwidths in the range of 50-70 GHz (refs. [4][5][6][7]. Beyond these, the demonstration of a germanium photodiode with f 3-dB ≈ 120 GHz and rather high dark current stands out, with some uncertainty regarding the bandwidth due to measurement limitations 8 .
In this Article we demonstrate a genuine silicon photonic photodetector approaching the ultimate performance in terms of optoelectronic bandwidth and responsivity-a silicon waveguide-coupled p-i-n photodiode based on epitaxially grown germanium. Our germanium photodiode shows a bandwidth in excess of 260 GHz at a photocurrent of 1 mA. This device outperforms all other silicon integrated photodetector approaches demonstrated so far by showing a very high bandwidth and substantially high responsivity, while exhibiting low dark current. In terms of the optoelectronic bandwidth only, even the fastest waveguide-coupled III-V photodetectors are outperformed by these germanium photodiodes. Zero-bias 3-dB bandwidths of >65 GHz are achieved, as have already been demonstrated for III-V photodetectors 9 , but not for germanium-based photodiodes until now.
Our work proves that the conventional silicon technology available for standard 200-mm or 300-mm silicon substrates can match or even outperform InP technology in terms of high-speed waveguide-coupled photodetector performance, without the need to resort to more cumbersome III-V material transfer approaches.

Results
Fabrication. In this Article we demonstrate a novel approach that has similarities to the basic fabrication flow described in ref. 10 , in which we demonstrated germanium photodiodes with bandwidths of 110 GHz. However, there are some important differences. With our unique approach, we deviate from the conventional germanium-waveguide integrated design paradigm by developing a novel biconcave germanium fin shape, analogous to the well-known FinFET transistors. This biconcave form of our vertically aligned germanium fin allows the narrowest germanium width to be in the centre of the waveguide, where the optical intensity is supposed to be highest, leading to the shortest transit times for photocarriers. Our approach is based on an initially few-micrometre-wide germanium body with a height of ~400 nm, which is thick enough to ensure sufficiently good crystalline quality. This is a distinctive feature compared to vertical drift field diodes, where the epitaxial growth of thin germanium layers (<100 nm) with low defect density is very difficult, and thus the fabrication of photodiodes with reasonably low dark currents is quite challenging 11 .
We make use of in situ-doped silicon layers, which allows us to entirely waive ion implantation and thus reduce unintended doping of the germanium. This is very beneficial for the high-speed capability of the photodiodes, as the negative impact of minority-carrier diffusion on the high-speed performance of the detectors is efficiently suppressed. Compared to ref. 10 , we have entirely redesigned the process for the in situ n-doped silicon layer, as described in the Methods.
The narrow germanium fin is realized by sequential patterning and is ultimately sandwiched between two complementary in situ-doped silicon layers. Admittedly, this approach depends on the accuracy of the overlaying of lithography masks relative to each other and precise adjustment of the critical dimensions, which are very well controlled and sufficiently sharp. In the present experiments, the overlay and critical dimension accuracies were typically in the range of <10 nm and ~30 nm, respectively. This accuracy was confirmed on several wafers in follow-up lots, so we believe that our approach is potentially suited for the reliable fabrication of germanium-fin photodiodes with feature sizes of 100 nm or less. Fabrication of the novel germanium photodiodes is entirely conducted on IHP's 8-inch BiCMOS pilot line facilities. We utilize 8-inch silicon-on-insulator (SOI) substrate wafers. A schematic of the fabrication flow is presented in Fig. 1a-d.
The in situ-doped silicon layers beside the germanium fin also form laterally oriented offshoots, which, after formation of a silicide layer, enable low-ohmic contacts to access the diode. Tungsten contact plugs are positioned on these silicided silicon offshoots at a safe distance from the optical mode at the same time. Electrical contacting is realized by one layer of AlCu. Additional metal layers that are commonly used have been omitted to save manufacturing time. A cross-sectional image of the device, including the contacts and the first metal layer, is provided in Fig. 1e. We equipped the devices with ground-signal-ground (GSG) pads with pitches of 100 µm and 150 µm to match the different requirements of the respective radiofrequency probes in the lightwave component analyser-and heterodyne measurement set-ups.
Device characterization. Compared to the devices from our previous work 10 or any other state-of-the-art germanium photodetectors 4,7,12-15 , our new photodetectors feature germanium regions with drastically narrowed lateral sizes, as low as ~60 nm. This leads to even higher electric-fields and shorter photocarrier drift times (carrier velocity saturation has long been reached at −2 V for a width of 600 nm or smaller, assuming perfectly vertical sidewalls).
To study the final device dimensions and material quality with high precision and in great detail, scanning transmission electron microscopy (STEM) and energy-dispersive X-ray spectroscopy (EDX) analyses were performed. Cross-sectional images obtained with these techniques are presented in Fig. 1e,f, respectively, based on a lamella created by a focused ion beam. With its biconcave form, the width of the germanium fin at its narrowest point (~60 nm in the centre) is much smaller than at its broadest point (~140 nm at the bottom). We therefore define a nominal device width of 100 nm for the fin, which is the mean of these values.
Compared to the diodes with f 3-dB ≥ 110 GHz described in ref. 10 , this is a reduction in width of ~67%. With both silicon layers on the sides of the germanium fin, the diodes have total lateral widths of a few hundred nanometres. The height of the germanium fin is ~400 nm and the devices presented in this work are 10 µm in length, long enough to ensure sufficient absorption at a wavelength of 1,550 nm. In accordance with the naming scheme already used in ref. 10 , the device with a nominal germanium width of 100 nm and length of 10 µm is termed 'Ge100_10' in the following. To clearly distinguish the different devices from this work and ref. 10 (in which all diodes were 20 µm long), here we also include the device lengths in the labelling. A slightly broader device with nominal width of 150 nm (width of ~110 nm at the narrowest point) is accordingly named Ge150_10.
From the STEM images, it becomes obvious that the vertical sidewalls of the germanium fin are fairly steep, guaranteeing a homogeneous electric field across the light-sensitive germanium, which is important for efficient collection of photogenerated carriers. Sidewall spacers at the vertical sidewalls along the germanium A cut through the structure provides a cross-sectional image for each stage. a, On top of a selectively grown germanium body on an SOI waveguide, on one side, a SiO 2 hard mask is deposited and patterned. b, Dry etch of germanium via the hard mask and subsequent epitaxial deposition of an in situ p-doped silicon layer is followed by overfill with SiO 2 . c, CMP is performed to restore a planar surface and to remove the p-doped Si layer in the outer regions. The hard-mask SiO 2 layer is patterned on the opposite side, followed by a germanium dry etch, in situ n-doped Si epitaxy, plus the planarization steps, as before. d, Finally, an (undoped) germanium fin is realized, which is sandwiched between two complementary in situ-doped silicon layers, such that a lateral Si-Ge-Si p-i-n diode is formed, without the need for ion implantation. More details on the fabrication are provided in the Methods. e, Cross-sectional image, obtained by STEM, of a germanium photodiode (termed Ge100_10) that features in situ-doped (different colours for p-and n-doping) silicon contact regions (f) and an EDX image of the same device. The nominal width is 100 nm, while at the narrowest point the germanium fin is only ~60 nm wide. Both cross-sections are cut perpendicular to the direction of light incidence. Electrical contacts to the photodiode are realized with nickel silicide and a state-of-the-art tungsten contact module (two levels), up to the first metal layer (AlCu). Fig. 1f) prohibit the formation of silicide in close proximity to the germanium, preventing additional optical losses. At the same time, these spacers adjust the distance between the silicide on the lateral silicon offshoots and the germanium fin. The lower parts of the two-stage tungsten plug contact scheme are located on the nickel silicide on top of the lateral silicon offshoots, where the etch process for the plugs has stopped precisely on top of the silicide, which is crucial for low-ohmic contact resistances.

fin (shown in
Optoelectrical high-speed characterization. For estimation of the high-speed optoelectrical properties we used two different set-ups, each with its own individual capabilities and limitations. Calibrated heterodyne measurements up to 325 GHz were performed so the measurement set-up did not limit investigations of the 3-dB bandwidths. On a second set-up, measurements were performed with a 67-GHz lightwave component analyser (LCA). On the heterodyne set-up, characterization of photodiodes is possible at the chip level, whereas measurements are performed separately for the different frequency bands (d.c. to 110 GHz, 110-170 GHz, 140-220 GHz and 220-325 GHz) due to the requirement for specific probes and power meter transitions for each of the radiofrequency bands. Schematic sketches of the heterodyne measurement set-ups are provided in Supplementary Figs. 2 and 3.
After screening various designs on the 67-GHz LCA-based set-up, heterodyne measurements were taken on selected photodiodes up to 350 GHz. The results for these are presented in Fig. 2a,b, which shows the frequency response of two photodiodes with different germanium widths. The germanium Ge100_10 photodetector achieves a 3-dB bandwidth of 265 GHz at a d.c. photocurrent of 1.0 mA, which is an improvement of a factor of ~2.4 compared to ref. 10 .
This device even outperforms the best waveguide-coupled InP photodetectors in terms of their high-speed performance. A photodiode with a slightly broader germanium fin, device Ge150_10, shows a 3-dB bandwidth of 240 GHz at the same d.c. photocurrent of 1.0 mA.
Unlike the heterodyne measurement, with the 67-GHz LCA, wafer-level investigations on a semi-automated wafer probe are possible. Here, the frequency response is determined from optoelectrical S-parameter (scattering parameter) measurements. Limited by the bandwidth of the LCA, a complete assessment of the frequency response and thus the 3-dB bandwidths was not possible for our novel germanium photodiodes. However, this set-up allows for a more extensive investigation, such as the screening of multiple device layouts and various bias and optical power conditions for numerous chips. A schematic sketch of the measurement set-up with the 67-GHz LCA is provided in Supplementary Fig. 4. Figure 2c,d presents normalized frequency response curves under various bias conditions for the Ge150_10 and Ge100_10 photodiodes, respectively. Both devices show only small reverse bias dependencies at d.c. photocurrents of 250-350 µA and yield 3-dB bandwidths that are already certainly higher than 70 GHz at zero bias, which is a notable improvement over the results in ref. 10 . However, for the Ge150_10 photodiode, the frequency response changes are most noticeable between zero bias and −0.25 V, which indicates that the germanium might not be fully depleted at small or zero bias. This could mean that there remains a certain amount of doping in the germanium region. We suspect that there might be a doping gradient near the in situ-doped silicon layer(s), for example, as a result of dopant diffusion, despite the abandonment of ion implantation. Capacitance-voltage characteristics, extracted  from S-parameter measurements, help us to investigate this assertion (Fig. 2e). Series resistances were derived from forward-biased I-V curves measured on three representative chips for both diodes (Fig. 2f). These, together with the capacitances, form the basis for estimation of the cutoff frequency. As shown in Fig. 2e, for the narrowest device, Ge100_10, the capacitance drops from ~9.5 fF at zero bias to ~6.5 fF at −2 V. Under a parasitic capacitance of ~0.6 fF resulting from the protruding vertical silicon offshoots, these values correspond to a change in the depletion widths from ~65 nm to ~90-100 nm (400-nm-high and 10-µm-long germanium), which matches very well the width estimated by STEM. For simplicity we assume perfectly parallel sidewalls, using w D = ε 0 ε r A/C, where w D is the depletion width, ε 0 is the vacuum permittivity, ε r is the relative permittivity, A is the area and C is the extracted capacitance. For the wider device, Ge150_10, the capacitance of ~5.5 fF at −2 V corresponds to a depletion width of ~115-120 nm (we considered a parasitic capacitance of ~0.4 fF). Table 1 summarizes the cutoff frequencies f TT (by transit time, under the assumption of a saturation drift velocity of 0.65 × 10 7 cm s −1 for bulk germanium) and f RC (capacitance C and resistance R, with f RC = 1/(2πRC)). Resistance R includes the series resistance from I-V curves plus the 50-Ω load of the measurement set-up, and capacitance C was extracted from small signal measurements. Finally, considering the photocarrier transit time and RC time constant only, the f 3-dB bandwidths for both diodes were calculated according to ref. 16 . For photodiode Ge100_10, the calculated and measured 3-dB bandwidths match very well. As we solely consider RC and transit time constants in our calculations, we assume that minority-carrier diffusion plays no further role in the high-speed performance, at least not at a bias of −2 V. For the wider photodiode, Ge150_10, there remains some mismatch, probably caused by the relatively low f TT of 220 GHz that we derived from the carrier transit time over a distance of 130 nm. However, we have to consider that the germanium thickness varies in a range of ~10% over the length of the diode, which not only has an impact on the estimated depletion width but also affects the actual width of the germanium fin due to the biconcave form that is created during the etch process. Uncertainties in the range of ~10-20% in the germanium fin width seem thoroughly plausible. For example, a reduction in the width of 10% already leads to ~24-GHz higher f TT and almost a 20-GHz increase in f 3-dB .
At increased optical input power (d.c. photocurrents of ~1.1 mA), a small decrease in the frequency response curves at zero bias can be seen, as shown in Fig. 3a (for Ge100_10 measured on three chips). Under small reverse bias (−0.25 V), this effect is already almost completely compensated as 1-dB bandwidths of 60 GHz or above are restored. Frequency response curves under a reverse bias of 2 V for various optical input power conditions are shown in Fig. 3b,c for the two device types measured at the same chips of one wafer. It can be seen that the 1-dB bandwidths remain above 67 GHz, even for high d.c. photocurrents of 3.2 mA. This robustness against increased photocurrents is a huge improvement compared to our previous results 10 where, with a current of ~3 mA, the 3-dB bandwidth had already dropped to ~60 GHz. Owing to the deployed coupling scheme and the available erbium-doped fibre amplifier (EDFA) on our 67-GHz LCA set-up, investigations with photocurrents larger than 3.2 mA were not possible, but are planned for the future.
Optical performance. Photocurrents and dark currents, measured at various optical input powers (at fibre tip) and bias voltages are shown in Fig. 4a for device Ge150_10. The dark currents (in the range of 100 nA) at room temperature are three to four orders of magnitude lower than the photocurrents (in the range of 0.1-1.2 mA). To estimate the internal responsivity, the losses of the grating coupler and the in-coupling waveguide have to be considered. Transmission spectra of a dedicated test structure (two of the grating couplers with a very short waveguide (2 mm), such that the waveguide propagation losses are negligible) are shown in Fig. 4b. Obviously, the maxima are not perfectly positioned at 1,550 nm, so lower loss can be expected at this wavelength once the grating coupler is fully optimized. At 1,550-nm wavelength, the loss of one single grating coupler is ~3.9 dB (7.8-dB total loss for the test structure), which equals a coupling efficiency of ~40% (more details are provided in the Methods). Plots of the photocurrent versus optical power are provided in Fig.  4c,d, each measured at a bias of −2 V. It is worth noting that no saturation is seen up to high photocurrents of 2.5 mA (at 8 dBm at the fibre tip, equal to 6.3 mW). From the slope of the linear regression of the measured data points, external (at the fibre tip) and internal (at the photodiode) responsivities are determined.
A summary of the internal and external responsivities and quantum efficiencies is available in Table 1. Given the ultra-high bandwidth and this substantially high internal responsivity, photodiode Ge150_10 shows a bandwidth-efficiency product of 86 GHz.

Discussion
Our novel photodetectors combine ultra-high bandwidths of 265 GHz and 240 GHz, determined by heterodyne measurements at a photocurrent of 1.0 mA at −2 V, with low dark currents and substantially high responsivities of 0.3 A W −1 and 0.45 A W −1 . In terms of speed, these devices even outperform the hitherto most sophisticated waveguide-coupled InP-based photodetectors. Zero-bias bandwidths of >65 GHz are achieved for germanium photodetectors, while for InP-based devices, such high zero-bias bandwidth has already been demonstrated 9 . Up to a d.c. photocurrent of 3.2 mA, which is the maximum d.c. photocurrent that could be reached with the available EDFA and the one-dimensional (1D) grating couplers, our novel devices show 1-dB bandwidths of >67 GHz. A current-carrying capacity beyond 3 mA of photocurrent is part of ongoing investigations.

Table 1 | estimation of f 3-dB by taking carrier drift time and RC time constant into account Values at −2 V Ge100_10 Ge150_10
Nominal width (nm) 100 150 Effective width (nm)~80~130 Depletion width, w D (nm)~90-100~115-120 resistance, R (Ω) 59 59 Capacitance, C (fF) 6. Capacitances were extracted from S-parameter measurements. The depletion widths are calculated from the capacitances, under the assumption of perfectly vertical sidewalls and parasitic capacitances from the protruding vertical silicon offshoots. We assume that the biggest fraction of the light would be absorbed nearby and in the centre, where the widths are certainly smaller than the nominal widths, which is why we define an effective width for the estimation of f TT . responsivities have solely been estimated at a wavelength of 1,550-nm. For the bandwidth-efficiency products we refer to the internal responsivities and quantum efficiencies as the external values are mainly dominated by the grating coupler efficiencies and not by the photodiodes themselves.
The room-temperature dark currents are below 200 nA at a bias of −2 V for both Ge100_10 and Ge150_10 diodes, as shown in Fig.  4a for photodiode Ge150_10. At 85 °C, the dark currents increase noticeably, but remain safely below 1 µA, so implementation of our novel ultra-fast germanium photodiodes in actual photonic integrated circuits (for example, in data-centre applications) would certainly be feasible. More details on dark current, including results up to 125 °C, are provided in Supplementary Fig. 2.
Equipping these ultra-fast diodes with inverse tapers could significantly boost their external responsivities. Coupling losses of 1.5 dB, which have already been demonstrated 17 , in combination with device Ge150_10 would yield a bandwidth-efficiency product of ~60 GHz. It is thus feasible that the good external responsivity-based bandwidth-efficiency product of 55 GHz (ref. 18 ) would then be in reach.
Key parameters of the various state-of-the-art waveguide-coupled as well as side-illuminated detectors reported in the literature are compared in Table 2. For fair benchmarking of the photodiode performances independently from the coupling approach, we compare bandwidth-efficiency products based on external (InP) as well as internal (for silicon photonics) responsivities and thus quantum efficiencies. In fact, for InP-based detectors, top illumination , and photocurrents plotted versus optical power for the estimation of internal (at the photodiodes) and external (at the fibre tips) responsivities, each with linear fit, for Ge100_10 (c) and Ge150_10 (d). All measurements were performed on chips from the same wafer. The oval outlines denote common measurements made for different samples. and fibre-to-waveguide coupling by cleaved facets are common, whereas for silicon-based platforms, grating couplers are commonly deployed to couple to nanowaveguides, as in our case. Their coupling efficiencies of typically 50% or even lower accordingly limit external responsivities and quantum efficiencies.
The outstanding enhancement of the 3-dB bandwidth was achieved by a novel construction in which a vertically aligned germanium fin is sandwiched between two complementary in situ-doped silicon regions. Ion implantation can be waived completely, so unintended ion implantation into the light-sensitive germanium is avoided, which is very beneficial for high-speed performance, as minority-carrier diffusion effects are suppressed. The initial fabrication steps for our novel ultra-fast photodiodes are analogous to those of our previous photodetector generation process, which is part of IHP's ePIC (electronic photonic integrated circuit) technology 'SG25H5ePIC' 6,19 . The selective epitaxial growth remains unchanged, including the thickness of the germanium body and the subsequent encapsulation in a thin Si layer. All processes for the separate depositions of the complementary in situ-doped silicon layers were conducted above the thick isolator stack. Accordingly, we do not expect substantial interference with underlying encapsulated devices such as modulators or transistors and believe that the integration into PIC or ePIC processes should be feasible.
Our ultra-fast germanium photodetectors pave the way for silicon photonics-based receivers for applications with symbol rates of 400 GBd or even beyond. Fabrication was entirely conducted on IHP's 8-inch BiCMOS pilot line facilities, so our approach proves that the conventional silicon technology available for standard 200-mm or 300-mm silicon substrates can match or even outperform InP technology in terms of high-speed waveguide-coupled photodetector performance, without the need to resort to more cumbersome III-V material transfer approaches. We demonstrate ultra-high 3-dB bandwidths and internal bandwidth-efficiency products, demonstrating the excellent performance of these germanium photodiodes as advanced waveguide-coupled photodetectors.

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Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/ s41566-021-00893-w.  18 Ref. 20 Ref. 3 Ref. 21 Ref. 22 Ref. 8 Ref. 5 Ref. 15 Ref. 10 this work

Ge150_10 Ge100_10
Material InP  InP  InP  InP  Graphene  Ge  Ge  Ge  Ge  Ge  Ge   3-dB  Compared are the 3-dB bandwidths, internal (int.) and external (ext.) responsivities (resp.) as well as dark currents. All results were determined at C-band/1,550 nm, except for ref. 5 for which only O-band results are available (and are not included here). Values in parentheses indicate the respective bias conditions (NA indicates values that are not available in the original publication). For fair benchmarking of photodiode performances we compare bandwidth-efficiency products based on external (InP) as well as internal (for silicon photonics) responsivities due to the fact that for InP, fibre-to-waveguide coupling is usually performed. By contrast, in silicon-based platforms, grating couplers are most commonly used, whose efficiencies dominate the external quantum efficiency.