2D-3D integration of hexagonal boron nitride and a high-κ dielectric for ultrafast graphene-based electro-absorption modulators

Electro-absorption (EA) waveguide-coupled modulators are essential building blocks for on-chip optical communications. Compared to state-of-the-art silicon (Si) devices, graphene-based EA modulators promise smaller footprints, larger temperature stability, cost-effective integration and high speeds. However, combining high speed and large modulation efficiencies in a single graphene-based device has remained elusive so far. In this work, we overcome this fundamental trade-off by demonstrating the 2D-3D dielectric integration in a high-quality encapsulated graphene device. We integrated hafnium oxide (HfO2) and two-dimensional hexagonal boron nitride (hBN) within the insulating section of a double-layer (DL) graphene EA modulator. This combination of materials allows for a high-quality modulator device with high performances: a ~39 GHz bandwidth (BW) with a three-fold increase in modulation efficiency compared to previously reported high-speed modulators. This 2D-3D dielectric integration paves the way to a plethora of electronic and opto-electronic devices with enhanced performance and stability, while expanding the freedom for new device designs.

B roadband optical modulators with ultra-high-speed, lowdrive voltage, and hysteresis-free operation are key devices for next-generation datacom transceivers 1 . Although Si photonics is nowadays a prime candidate to fulfill these requirements 2,3 , graphene is rapidly becoming a major contender in several optoelectronic applications, such as ultrafast modulators 4,5 and silicon-integrated photodetectors 6,7 . Graphene-based modulators have already proven broadband optical bandwidth 1 , high speed 8,9 , relatively high modulation efficiencies 10 , and temperature stability 8 . These devices are all based on complementary metaloxide-semiconductor (CMOS)-compatible material 7,10-13 , where CMOS design and fabrication techniques can be further leveraged to decrease costs. However, graphene-based modulators are yet to demonstrate all operation requirements at once. More specifically, EA graphene modulators struggle to show high-speed and high modulation efficiencies simultaneously 14 . This bottleneck is mostly due to the weak graphene/dielectric combination and the limited quality of graphene.
Unlike Si technology, where high-κ dielectrics lie at the core of its success, 2D dielectrics are hindering the development of graphene-and other 2D-based electronics and optoelectronic devices 1,13,15 and are clearly outperformed by traditional 3D high-κ dielectrics. This underperforming 2D-dielectric/graphene combination deepens even further the fundamental trade-off between speed and modulation efficiency inherent to the doublelayer (DL) modulators 14 . In the DL architecture, the overlapped top and bottom graphene electrodes act as a capacitor (C). The larger the C, the higher the modulation efficiency. On the other hand, the speed of the modulator defined as f 3dB = 1/(2πRC) is inversely proportional to C (R being the total resistance). In this framework, the quality of graphene appears as a valid turnaround to overcome this fundamental limitation. High electron mobility is expected to minimize the overall resistance and reduce the insertion loss (IL) 1,9 , thus increasing the bandwidth and the extinction ratio (ER). However, the quality of graphene is very sensitive to its environment, e.g., the dielectric to encapsulate it.
In this work, we demonstrate the 2D-3D integration of hBN and HfO 2 within the dielectric section of a DL graphene EA modulator. This dielectric combination enhances the capacitance of the EA modulators without compromising their robustness against high voltages and preserves the high mobility and low doping of intrinsic graphene. As a result, we achieved a static and dynamic (at 40 Gbps) modulation efficiency as high as 2.2 and 1.49 dBV −1 , respectively, a f 3dB bandwidth of~39 GHz, and a device footprint of 60 μm × 0.45 μm ≈ 27 μm 2 (neglecting the metal pads and graphene leads). Moreover, the hBN-HfO 2 -hBNbased devices show a symmetric and nearly hysteresis-free operation. The larger breakdown voltage of this 2D-3D dielectric, even beyond the full transparency regime (i.e., Pauli blocking), increases the ER and reduces the IL of the modulators.

Results
The EA modulators were fabricated on top of a photonic structure 20 formed by two grating couplers 21 feeding light in and out of an optical waveguide (Fig. 1a). The 750-nm-wide waveguide for the device in Fig. 1 was designed to support a single transverse-magnetic (TM) optical mode 20 (see Supplementary Note 3). The presented DL graphene modulators were built, with hBN-encapsulated graphene top and bottom electrodes (Fig. 1d). The hBN-graphene-hBN stacks have been fabricated following state-of-the-art fabrication techniques 22,23 . This ensured low levels of doping and high charge carrier mobilities. We characterized the quality of the resulting modulators (see Supplementary Notes 2 and 6) and extracted a carrier density-independent mobility as high Although hBN-encapsulated graphene devices have allowed for device designs with unprecedented functionalities [24][25][26] and improved performance 23 , such layered dielectric material typically contains impurities and/or crystal defects leading to low breakdown voltages 27,28 . Moreover, the dielectric permittivity of hBN is rather low compared to existing high-κ dielectrics 29 , with a value close to that of SiO 2 (ϵ r~4 ). This low dielectric constant and reduced breakdown voltage (see Supplementary Note 5) compromises not only the power consumption and the ability to reach high modulation efficiencies at reasonably low drive voltages but also limits the IL and the ER of the modulators 1,9 . We thus integrate HfO 2 , a high-κ dielectric material, within the hBNencapsulated graphene electrodes (see the sketch in Fig. 1d).
With such hBN-HfO 2 -hBN dielectric arrangement, graphene remains isolated from HfO 2 , shielded away from any possible out-of-plane dangling bonds of the 3D oxide material (see inset of Fig. 1d for the molecular representation of the 2D-3D dielectric interface). More importantly, the hBN-graphene interfaces remain atomically sharp and clean 22,23,30 . This nanoscale control of the interfaces brings further advantages to real-world EA graphene modulators, like a symmetric and hysteresis-free operation. This is directly visible in the transmission curves as a function of the applied voltage V BT or, alternatively, as a function of the Fermi energy E F at the graphene electrodes (see the bottom and top axis in Fig. 1e and Supplementary Note 9). Both forward and backward voltage sweeps (black and blue traces, respectively) show minor hysteresis and appear symmetric with respect to the charge neutrality point. For comparison, a device fabricated with a HfO 2 -hBN dielectric shows no overlap between the forward and backward sweeps (inset of Fig. 1e). This strong hysteresis is nonetheless expected for this HfO 2 -hBN modulator since, in that case, the top graphene electrode is in direct contact with HfO 2 . The hBN-HfO 2 -hBN modulator device exhibits a modulation efficiency as high as~2.2 dBV −1 within a 0.5 V voltage span (see red linear fit to the data in Fig. 1e). Considering the length of our modulator (~60 μm), we obtain a normalized static modulation efficiency of~0.037 dBV −1 μm −1 , a threefold increase compared to previously reported high-speed graphene EA modulators 9 .
With such a high static modulation efficiency (Fig. 1), one might expect the device speed to be compromised 14 . However, the high mobility of the hBN-encapsulated graphene is expected to increase the bandwidth. This is visible in Fig. 2a, where we calculated the f 3dB bandwidth as a function of the charge carrier-dependent mobility (μ) and contact resistivity (ρ c ) for a graphene modulator with the same geometry and dielectric combination as the device in Fig. 1 (see Supplementary Note 11). As observed, the graphene mobility and the contact resistivity have a major influence on the modulator speed. Considering the mobility μ ≈ 12,000 cm 2 V −1 s −1 (evaluated at V BT = 10.4 V) and the contact resistivity ρ c ≈ 800 Ω μm achieved experimentally (see Supplementary Notes 4 and 11), we expect a bandwidth of f 3dB~4 6 GHz (dashed lines in Fig. 2a). To confirm this value experimentally, we measured the electro-optical (EO) bandwidth of the device in Fig. 1 at a DC voltage V BT = 10.4 V and a peak-to-peak voltage V AC = 200 mV (Fig. 2b). The bandwidth of the measured device attains f 3dB ≈ 39 GHz (without de-embedding, see Supplementary Note 13). This value is close to the capabilities of our setup, limited to 40 GHz by the vector network analyzer and the RF probes (see Supplementary Note 12). Even though the measured f 3dB does not reach the expected f 3dB~4 6 GHz (Fig. 2a), possibly due to an increased contact resistivity of the measuring device (see Supplementary Note 11), this is still the highest f 3dB bandwidth among all graphene-based modulators reported so far 8,9,11,12,31,32 .
The high-speed operation of our modulator device is also supported by non-return-to-zero eye diagram measurements. The data were obtained through an electrical pattern generator (PG) driving the modulator with a 2 31 − 1 pseudo-random binary sequence at 28 and 40 Gbps bit-rate (see Supplementary Note 13). The signal was driven by a 3.5-V peak-to-peak voltage while the DC bias was set to 11 V. The device was terminated with a 50 Ω load to avoid reflections due to the impedance mismatch between the PG electrical output and the modulator (when measured at 40 Gbps). Open eye diagrams at 28 and 40 Gbps are shown in Fig. 2c, with an ER as high as 5. Like the speed of the modulator, the power consumption understood as the switching energy per bit also benefits from the small footprint of the device. Ignoring the parasitic pad capacitance, we obtain for the modulator in Fig. 1 an energy per bit of CðV AC Þ 2 =4 % 160 fJbit À1 , where C = 52 fF is the capacitance between the top and bottom graphene electrodes and V AC = 3.5 V the voltage swing 12 . This value of energy per bit is on par with state-of-the-art SiGe technologies 33,34 .
To directly compare modulators with different dielectrics, it is more convenient to compare the transmission as a function of E F (see the E F axis in Figs. 1e and 3b and c) since E F already considers the thickness and the relative permittivity of the dielectric (see Supplementary Note 7). Operating the modulators at high E F enhances both ER and IL, with the ER (IL) increasing (decreasing) as a function of E F 9 . In the full transparency regime (Pauli blocking, see Supplementary Note 1), the ER is maximized and the IL is expected to become nearly zero for high-quality graphene 1,9 (see Supplementary Note 10). It is thus crucial to determine which dielectric materials facilitate Pauli blocking operation. Figure 3a illustrates the expected maximum E F , as a function of the relative permittivity (ϵ r ) and dielectric strength (E BD ) of any given dielectric. The square boxes in Fig. 3a enclose the expected E max F for the HfO 2 − and hBN-based modulators (in red and green, respectively) and the black star represents the E max These results are confirmed by the transmission traces in Fig. 3b, c. None of the hBN-based modulators were able to withstand Pauli blocking operation (orange-shaded region Fig. 3b), all breaking their hBN dielectric at a similar E max F % 0:4 eV (see vertical dashed lines in Fig. 3b and Supplementary Notes 7 and 8). Even though these hBN-based modulators were too fragile, we obtained modulation efficiencies as high as 0.3, 1.3, and 2 dBV −1 for device lengths L = 12, 24, and 42 μm, respectively. Once normalized by its length, we obtain 0.025, 0.054, and 0.047 dBV −1 μm −1 . These results exceed the state-ofthe-art modulation efficiency of 0.038 dBV −1 μm −110 . Still, the premature hBN breakdown compromises the ER and the IL. Indeed, the measured ER = 0.75, 2.3, and 4.9 dB (data points in Fig. 3b) is far from the simulated ER = 1.8, 4.4, and 7.9 dB (solid traces in Fig. 3b) expected for the 12, 24, and 42 μm-long modulators, respectively (for simulations, refer to Supplementary  Notes 1-3). Likewise, the measured IL = 1, 2.2, and 3.4 dB are higher than IL ≈0 dB expected for high-mobility graphene modulators 1 (see the minimum 0-dB normalized transmission, i.e., neglecting the losses from grating couplers and Si waveguide, achieved by the simulation traces in Fig. 3b and Supplementary Note 10).
On the other hand, the second hBN-HfO 2 -hBN modulator device attains the Pauli blocking regime (Fig. 3c), in agreement with the dielectric characterization of hBN-HfO 2 -hBN ( Fig. 3a and Supplementary Notes 5 and 10), reaching a maximum Fermi energy of E max F % 0:54 eV. The ER and IL improve accordingly, with an ER = 7.8 dB almost twice the value obtained by the hBNbased modulator of comparable length (compare the black and red traces of Fig. 3c, b, respectively) and an IL reaching nearly zero (IL ≈ 0.04 dB in Fig. 3c and Supplementary Note 10). However, being shorter (L = 44 μm) than the device in Fig. 1e  (L = 60 μm), the modulation efficiency is lower (1.3 dBV −1 in a 0.5 V span, see Fig. 3c). We note that the hBN-HfO 2 -hBN device of Fig. 1e has a relatively weak measured ER ≈ 4.4 dB and IL ≈7.8 dB (see Supplementary Note 10) due to an overcautious V BT = 12.1 V applied voltage (or alternatively E F = 0.41 eV). Considering the breakdown capabilities of hBN-HfO 2 -hBN dielectric (black star in Fig. 3a), we evaluated a potential ER ≈ 12 dB and IL ≈ 0.042 dB for this device (see Supplementary Note 10).

Discussion
Although material platforms like lithium niobate 38 Figure 4 shows the dynamic modulation efficiency (extracted from the eye diagrams and normalized by the device length and drive voltage) as a function of the modulation speed (red axis and red data point in Fig. 4) and the static modulation efficiency (measured in DC and normalized by the device length), as a function of the f 3dB bandwidth (black axis and black data point in Fig. 4). To avoid discrepancies due to the different extraction methods, we determine the static modulation efficiency of the compared literature [8][9][10][11][12] using the same method as in Fig. 1e, i.e., by applying a linear fit within a 0.5 V voltage span. The results highlight the trade-offs between speed and modulation efficiency and stress the advantages of an hBN-HfO 2 -hBN dielectric to obtain large static and dynamic modulation efficiencies even at high speed. As observed, the modulation efficiency typically drops for devices with high speed 8,9 , being our device the only modulator able to operate at high speed with a large static and dynamic modulation efficiency (Fig. 4). These results outperform state-ofthe-art graphene and not-yet-commercial silicon-based electroabsorption modulators [43][44][45] (see blue/red and green data clouds, respectively in Fig. 4) when considering the modulation efficiency normalized by the length (i.e., footprint). This figure-of-merit is rather an important one since for many envisaged applications (e.g., chip interconnects), multiple modulator devices are expected to coexist on the same chip.
In this work, we demonstrated the advantages of integrating hBN with a 3D high-κ dielectric for high-quality graphene-based EA modulators. Compared to traditional oxide sputtering or atomic layer deposition (ALD) growth on top of graphene, the integration of HfO 2 in-between hBN prevented any damage to the underlying graphene and allowed clean graphene-hBN interfaces. These clean interfaces yielded a symmetric and nearly hysteresis-free operation. Moreover, this 2D-3D integration enabled full transparency while maintaining the high mobility and low doping of intrinsic graphene. More importantly, the hBN-HfO 2 -hBN-based EA modulators were able to reach high modulation speeds with strong modulation efficiencies, overcoming the fundamental limitations of the DL graphene configuration and outperforming state-of-the-art graphene and Si technologies. The compatibility of this hBN-HfO 2 -hBN dielectric with Si and other 2D materials might allow for considerable scaling improvements and greater device functionality in a broad range of graphene-and 2D-based electronic and optoelectronic applications, even beyond graphene-based modulators.

Methods
Device fabrication. The Si photonic waveguide with a core cross-section of 750 nm × 220 nm was prepared on the IMEC iSiPP25G silicon-on-insulator platform 20 . For the fabrication of the electroabsorption modulator, the graphene and hBN flakes were exfoliated from highly oriented pyrolytic graphite and hBN crystals, respectively. The bottom hBN-graphene-hBN stacks were prepared by the van der Waals assembly technique 22,23 and transferred directly onto the Si waveguide separated by a 10 nm spacer of high-quality thermal SiO 2 . The bottom hBN flake (separating the graphene and the SiO 2 layer) thickness of~5 nm was chosen to enhance the graphene absorption while isolating the graphene from the rough SiO 2 substrate. The top hBN has a thickness of~10 nm. The stack has been etched by reactive ion etching in an oxygen (O 2 ) and trifluoromethane (CHF 3 ) (4:40 sccm) environment to expose the graphene edge. The bottom stack was then contacted by a 3/15/30 nm Cr/Pd/Au metal combination. The 10 nm hafnium oxide film has been deposited at 250°C prior depositions of a 2 nm sputtered SiO 2 seed layer by ALD. Tetrakis-dimethylamido hafnium (TDMAH) (0.4 s purge time) and water vapor (5 s purge time) as precursors have been used in a Savannah G1 system from Cambridge Nanotech. The top hBN-graphene-hBN stack with a 7 nm-and 21 nm-thick bottom and top hBN layers has followed the same fabrication steps as the bottom stack.

Data availability
The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
Received: 11 August 2020; Accepted: 18 December 2020;  Fig. 4 Comparison with other optical modulators. The black and red data points and axis represent the static modulation efficiency as a function of the f 3dB bandwidth and the dynamic modulation efficiency (extracted from eye diagrams) as a function of the modulation speed, respectively. The red, blue, and green data clouds enclose single- 11,12,31,46 and double-layer [8][9][10]32 graphene and silicon [43][44][45] state-of-the-art modulators operating at λ = 1.55 μm. Refer to Supplementary Notes 15 and 16 for a more detailed comparison of graphene-based modulators.