2D-3D integration of hBN 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 first 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 novel combination of materials allows for a high-quality modulator device with record high performances: a ∼39GHz bandwidth (BW) with a three-fold increase in modulation efficiency compared to previously reported high speed modulators. This first demonstration of 2D-3D 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.

high-speed 8,9 , relatively high modulation efficiencies 10 and temperature stability 8 . These devices are all based on CMOS compatible materials 7,10-13 , where CMOS design and fabrication techniques can be further leveraged to decrease costs. However, graphene-based modulators have 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 the 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 under-performing 2D-dielectric/graphene combination deepens even further the fundamental trade-off between speed and modulation efficiency inherent to the 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. A 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. Indeed, no graphene/dielectric combination has been able to ensure high charge carrier mobilities and low levels of residual doping in existing graphene waveguide-coupled modulators 16 . The growth of non-layered (i.e. 3D) dielectrics , e.g. aluminum oxide (Al 2 O 3 ), silicon nitride (SiN) or HfO 2 directly on top of graphene leads to low electronic mobility [16][17][18] and/or inhomogeneous doping 19 .  FIG. 1. Device geometry and static characterization. a, Optical image of a photonic device consisting of two grating couplers (GC), a silicon optical waveguide (Si WG) and a hBN-HfO 2 -hBN based graphene EA modulator on top (see zoom-in optical and scanning electron microscope (SEM) images for details). The metal contacts are yellow/brown and the bottom and top graphene electrodes violet and light blue, respectively. The core of the waveguide is highlighted by the green dashed lines. b, Electrical connections and schematic cross-section of a EA modulator with a hBN-HfO 2 -hBN dielectric. The top and bottom graphene electrodes are fully encapsulated by hBN (in green) protecting both graphene electrodes from the out-of-plane dangling bonds typical of 3D oxide materials, e.g. HfO 2 (in red). See inset for a molecular representation. c, Transmission curves as a function of the voltage between the bottom and top graphene electrodes (V BT -axis, bottom) and the Fermi energy at the graphene electrodes (E F -axis, top) for the EA modulator in panel a with a hBN-HfO 2 -hBN dielectric (see sketch). The 1550 nm excitation power was set to 0 dBm. The forward and backward voltage sweeps (black and blue, respectively) show no major hysteresis compared to a modulator with a hBN-HfO 2 dielectric (see inset). The red line is a linear fit to the forward voltage sweep within a 0.5 V voltage span (extracted slope: 2.2 dB/V).
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 its 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 dB/V and 1.49 dB/V, respectively, a f 3dB bandwidth of ∼ 39 GHz and a device footprint of 60 µm x 0.45 µm ≈ 27µm 2 (neglecting the metal pads and graphene leads). Moreover, the hBN-HfO 2 -hBN based 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.

I. RESULTS AND DISCUSSIONS
The EA modulators were fabricated on top of a photonic structure 20 formed by two gratings 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 sections III in SI). The presented DL graphene modulators were built, for the very first time, with hBN-encapsulated graphene top and bottom electrodes (Fig. 1b). 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 (sections II and VI in SI) and extracted a carrier density-independent mobility as high as 30,000 cm 2 /(Vs) at room temperature 23 (section II in SI).
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 section V in SI) 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 hBN-encapsulated graphene electrodes (see the sketch in Fig. 1b).
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 . c, 2 31 -1 pseudo-random binary sequence non-return-to-zero eye diagram at 28 Gbps and 40 Gbps. The EA modulator is d.c. biased at V BT = 11 V and driven by a V AC = 3.5 V peak-to-peak RF signal. The eye diagram measured at 40 Gbps has a 5.2 dB ER and a 2.28 dB signal-to-noise ratio (SNR). The green arrows indicate the 0 W baseline.
tation 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 hysteresisfree 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 bottom and top axis in Fig. 1c and section IX in SI). 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. 1c). 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 dB/V within a 0.5 V voltage span (see red linear fit to the data in Fig. 1c).
Considering the length of our modulator (∼ 60 µm), we obtain a normalized static modulation efficiency of ∼ 0.037 dB/Vµm, a three-fold 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 (section XI in SI). 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 /(Vs) (evaluated at V BT = 10.4 V) and the contact resistivity ρ c ≈ 800 Ω·µm achieved experimentally (sections IV and XI in SI), we expect a bandwidth of f 3dB ∼ 46 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 deembedding, section XIII in SI). This value is close to the capabilities of our setup, limited to 40 GHz by the vector network analyzer (VNA) and the RF probes (section XII in SI). Even tough the measured f 3dB does not reach the expected f 3dB ∼ 46 GHz (Fig. 2a), possibly due to an increased contact resistivity of the measured device (section XI in SI), this is still the highest f 3dB bandwidth among all graphene-based modulators reported so far 8,9,11,12,34,35 .
The high-speed operation of our modulator device is also supported by non-return to zero (NRZ) 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 (PRBS)  at 28 and 40 Gbps bit-rate (section XII in SI). 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 Gbps and 40 Gbps are shown in Fig. 2c, with an ER as high as 5.2 dB and a signal-to-noise ratio (SNR) of 2.28 dB for the latter (see section XIV in SI for an eye-diagram at 10Gbps). These results confirm the large modulation efficiency of our hBN-HfO 2 -hBN-based modulator device, even at high speeds, with a record-high dynamic modulation efficiency of 1.49 dB/V at 40 Gbps 9 .
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 C(V AC ) 2 /4 ≈ 160 fJ/bit, 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 36,37 .
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 Fig. 1c and Fig. 3b and c) since E F already considers the thickness and the relative permittivity of the dielectric (section VII in SI). 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 section I in SI), the ER is maximized and the IL is expected to become nearly zero for highquality graphene 1,9 (section X in SI). It is thus crucial to determine which dielectric materials facilitate Pauli blocking operation. Fig. 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 2and hBN-based modulators (in red and green, respectively) and the black star represents the E max F = 0.57 eV expected for the hBN-HfO 2 -hBN modulator of Fig. 1c (section X in SI). The boundaries of the boxes are taken from literature 28,31-33 (marked with dots) and from our dielectric characterization (marked with stars, sections V and X in SI). All dielectric materials fulfilling E max F > 0.5 eV (see white fringe in Fig. 3a) allow full transparency, i.e. Pauli blocking. The comparison in Fig. 3a highlights the advantages of the hBN-HfO 2 -hBN dielectric (black star), achieving higher E F values than the hBN Comparison graph. 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-11,12,34,38 and double-layer [8][9][10]35 graphene and silicon-39-41 state-of-the-art modulators operating at λ = 1.55 µm. Refer to sections XV and XVI in SI for a more detailed comparison of graphene-based modulators.
dielectric while equally preserving the intrinsic qualities of graphene.
These results are confirmed by the transmission traces in Fig. 3b and 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 section VII and VIII in SI). Even though these hBN-based modulators were too fragile, we obtained modulation efficiencies as a high as 0.3, 1.3 and 2 dB/V for device lengths L = 12, 24 and 42 µm, respectively. Once normalized by its length, we obtain 0.025, 0.054 and 0.047 dB/(Vµm). These results exceed the state-of-the-art modulation efficiency of 0.038 dB/(Vµm) 10 . 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) are 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 sections I-III in SI). Likewise, the measured IL=1, 2.2 and 3.4 dB are higher than the 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 section X in SI).
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 sections V and X in SI), 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 hBN-based modulator of comparable length (compare the black and red traces of Fig. 3c and b, respectively) and a IL reaching nearly zero (IL ≈ 0.04 dB in Fig. 3c and section X in SI). However, being shorter (L= 44 µm) than the device in Fig. 1c (L= 60 µm), the modulation efficiency is lower (1.3 dB/V in a 0.5 V span, see Fig. 3c). We note that the hBN-HfO 2 -hBN device of Fig. 1c has a relatively weak measured ER ≈ 4.4 dB and IL ≈ 7.8 dB (section X in SI) due to an over-cautious 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 (section X in SI).  44,46 . Nowadays, Si and graphene are envisaged as the most scalable, cost-effective and CMOS compatible materials for amplitude modulator applications 1 . To compare our results with state-of-the-art graphene and Si amplitude modulators, both EA and Mach-Zehnder interferometer configurations included, we summarize our results in Fig. 4 and in sections XV and XVI of SI. Fig. 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 8-12 using the same method as in Fig. 1c, i.e. by applying a linear fit within a 0.5 V voltage span. Results highlight the trade-offs between speed and modulation efficiency and stresses the advantages of a 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-of-the-art graphene and not yet commercial silicon-based electro-absorption modulators [39][40][41] (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.

II. CONCLUSION
With this work, we demonstrated the advantages of integrating hBN with a 3D high-κ dielectric for highquality graphene-based EA modulators. Compared to traditional oxide sputtering or ALD-growth on top of graphene, the integration of HfO 2 in between hBN prevented any damage of 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-ofthe-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.