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## Creator

Hitesh Agarwal, Bernat Terrés, Lorenzo Orsini, Alberto Montanaro, Vito Sorianello, Marianna Pantouvaki, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Dries Van Thourhout, Marco Romagnoli, Frank H. L. Koppens

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[2D-3D integration of hexagonal boron nitride and a high-κ dielectric for ultrafast graphene-based electro-absorption modulators](https://mdr.nims.go.jp/datasets/575cb377-8a19-4f75-bff8-e0ba1703b28b)

## Fulltext

2D-3D integration of hexagonal boron nitride and a high-κ dielectric for ultrafast graphene-based electro-absorption modulatorsARTICLE2D-3D integration of hexagonal boron nitride and ahigh-κ dielectric for ultrafast graphene-basedelectro-absorption modulatorsHitesh Agarwal 1,9, Bernat Terrés1,9✉, Lorenzo Orsini1,2, Alberto Montanaro3, Vito Sorianello3,Marianna Pantouvaki4, Kenji Watanabe 5, Takashi Taniguchi 6, Dries Van Thourhout 7,Marco Romagnoli 3 & Frank H. L. Koppens 1,8✉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-effectiveintegration and high speeds. However, combining high speed and large modulation effi-ciencies in a single graphene-based device has remained elusive so far. In this work, weovercome this fundamental trade-off by demonstrating the 2D-3D dielectric integration in ahigh-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 mod-ulator device with high performances: a ~39 GHz bandwidth (BW) with a three-fold increasein modulation efficiency compared to previously reported high-speed modulators. This 2D-3Ddielectric integration paves the way to a plethora of electronic and opto-electronic deviceswith enhanced performance and stability, while expanding the freedom for new devicedesigns.https://doi.org/10.1038/s41467-021-20926-w OPEN1 ICFO—Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona) 08860, Spain. 2 Dipartimento di Fisica“E. Fermi”, Università di Pisa, Pisa 56127, Italy. 3 Consorzio Nazionale per le Telecomunicazioni (CNIT), Photonic Networks and Technologies NationalLaboratory, Pisa 56124, Italy. 4 Department of 3D and Silicon photonics systems, Imec, Leuven 3001, Belgium. 5 Research Center for Functional Materials,National Institute for Materials Science, Tuskuba 305-0044, Japan. 6 International Center for Materials Nanoarchitectonics, National Institute for MaterialsScience, Tsukuba 305-0044, Japan. 7 Photonics Research Group, Department of Information Technology, Ghent University-IMEC, Gent 9000, Belgium.8 ICREA—Institució Catalana de Recerca i Estudis Avançats, Barcelona 08010, Spain. 9These authors contributed equally: Hitesh Agarwal, Bernat Terrés.✉email: bernat.terres@icfo.eu; frank.koppens@icfo.euNATURE COMMUNICATIONS |         (2021) 12:1070 | https://doi.org/10.1038/s41467-021-20926-w |www.nature.com/naturecommunications 11234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-021-20926-w&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-021-20926-w&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-021-20926-w&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-021-20926-w&domain=pdfhttp://orcid.org/0000-0002-9418-7966http://orcid.org/0000-0002-9418-7966http://orcid.org/0000-0002-9418-7966http://orcid.org/0000-0002-9418-7966http://orcid.org/0000-0002-9418-7966http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0003-0111-431Xhttp://orcid.org/0000-0003-0111-431Xhttp://orcid.org/0000-0003-0111-431Xhttp://orcid.org/0000-0003-0111-431Xhttp://orcid.org/0000-0003-0111-431Xhttp://orcid.org/0000-0002-4274-5620http://orcid.org/0000-0002-4274-5620http://orcid.org/0000-0002-4274-5620http://orcid.org/0000-0002-4274-5620http://orcid.org/0000-0002-4274-5620http://orcid.org/0000-0001-9764-6120http://orcid.org/0000-0001-9764-6120http://orcid.org/0000-0001-9764-6120http://orcid.org/0000-0001-9764-6120http://orcid.org/0000-0001-9764-6120mailto:bernat.terres@icfo.eumailto:frank.koppens@icfo.euwww.nature.com/naturecommunicationswww.nature.com/naturecommunicationsBroadband optical modulators with ultra-high-speed, low-drive voltage, and hysteresis-free operation are key devicesfor next-generation datacom transceivers1. Although Siphotonics is nowadays a prime candidate to fulfill theserequirements2,3, graphene is rapidly becoming a major contender inseveral optoelectronic applications, such as ultrafast modulators4,5and silicon-integrated photodetectors6,7. Graphene-based mod-ulators have already proven broadband optical bandwidth1, highspeed8,9, relatively high modulation efficiencies10, and temperaturestability8. These devices are all based on complementary metal–oxide–semiconductor (CMOS)-compatible material7,10–13, whereCMOS design and fabrication techniques can be further leveraged todecrease costs. However, graphene-based modulators are yet todemonstrate all operation requirements at once. More specifically,EA graphene modulators struggle to show high-speed and highmodulation efficiencies simultaneously14. This bottleneck is mostlydue to the weak graphene/dielectric combination and the limitedquality of graphene.Unlike Si technology, where high-κ dielectrics lie at the core ofits success, 2D dielectrics are hindering the development of gra-phene- and other 2D-based electronics and optoelectronicdevices1,13,15 and are clearly outperformed by traditional 3Dhigh-κ dielectrics. This underperforming 2D-dielectric/graphenecombination deepens even further the fundamental trade-offbetween speed and modulation efficiency inherent to the double-layer (DL) modulators14. In the DL architecture, the overlappedtop and bottom graphene electrodes act as a capacitor (C). Thelarger the C, the higher the modulation efficiency. On the otherhand, the speed of the modulator defined as f3dB= 1/(2πRC) isinversely proportional to C (R being the total resistance). In thisframework, the quality of graphene appears as a valid turnaroundto overcome this fundamental limitation. High electron mobilityis expected to minimize the overall resistance and reduce theinsertion loss (IL)1,9, thus increasing the bandwidth and theextinction ratio (ER). However, the quality of graphene is verysensitive to its environment, e.g., the dielectric to encapsulate it.Indeed, no graphene/dielectric combination has been able toensure high charge carrier mobilities and low levels of residualdoping in existing graphene waveguide-coupled modulators16.The growth of nonlayered (i.e., 3D) dielectrics, e.g., aluminumoxide (Al2O3), silicon nitride (SiN), or HfO2 directly on top ofgraphene leads to low electronic mobility16–18 and/or inhomo-geneous doping19.In this work, we demonstrate the 2D–3D integration of hBNand HfO2 within the dielectric section of a DL graphene EAmodulator. This dielectric combination enhances the capacitanceof the EA modulators without compromising their robustnessagainst high voltages and preserves the high mobility and lowdoping of intrinsic graphene. As a result, we achieved a static anddynamic (at 40 Gbps) modulation efficiency as high as 2.2 and1.49 dBV−1, respectively, a f3dB bandwidth of ~39 GHz, and adevice footprint of 60 μm× 0.45 μm ≈ 27 μm2 (neglecting themetal pads and graphene leads). Moreover, the hBN–HfO2–hBN-based devices show a symmetric and nearly hysteresis-freeoperation. The larger breakdown voltage of this 2D–3D dielec-tric, even beyond the full transparency regime (i.e., Pauli block-ing), increases the ER and reduces the IL of the modulators.ResultsThe EA modulators were fabricated on top of a photonic struc-ture20 formed by two grating couplers21 feeding light in and out ofan optical waveguide (Fig. 1a). The 750-nm-wide waveguide forthe device in Fig. 1 was designed to support a singletransverse–magnetic (TM) optical mode20 (see SupplementaryNote 3). The presented DL graphene modulators were built, withhBN-encapsulated graphene top and bottom electrodes (Fig. 1d).The hBN–graphene–hBN stacks have been fabricated followingstate-of-the-art fabrication techniques22,23. This ensured low levelsof doping and high charge carrier mobilities. We characterized thequality of the resulting modulators (see Supplementary Notes 2and 6) and extracted a carrier density-independent mobility as highdTransmission [dBm]-10 -5 0 5 10-36-37-38-39-40-41V    [V]BTa e-10 0 10-44-43-42  Bottomgraphene    TopgrapheneCr/Pd/AuGCGCSi WGCr/Pd/AuVBThBNhBNSi WGGrapheneHfO2HfO2HfO2hBN0.4E   [eV]F0.30.20.100.10.20.30.4b cFig. 1 Device geometry and static characterization. a Optical image of a photonic device consisting of two grating couplers (GC), a silicon opticalwaveguide (Si WG), and an hBN–HfO2–hBN-based graphene EA modulator on top (see zoom-in optical (panel b) and scanning electron microscope (SEM)(panel c) images for details). In panel c, 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. The white scale bars in panel a, b, and c are 100, 5, and 1 μm, respectively.d Electrical connections and schematic cross-section of an EA modulator with an hBN–HfO2–hBN dielectric. The top and bottom graphene electrodes arefully encapsulated by hBN (in green) protecting both graphene electrodes from the out-of-plane dangling bonds typical of 3D oxide materials, e.g., HfO2(in red). See inset for a molecular representation. e Transmission curves as a function of the voltage between the bottom and top graphene electrodes(VBT axis, bottom) and the Fermi energy at the graphene electrodes (EF axis, top) for the EA modulator in panel a with an hBN–HfO2–hBN dielectric (seesketch). The 1550 nm excitation power was set to 0 dBm. The forward and backward voltage sweeps (black and blue, respectively) show no majorhysteresis compared to a modulator with an hBN–HfO2 dielectric (see inset). The red line is a linear fit to the forward voltage sweep within a 0.5 V voltagespan (extracted slope: 2.2 dBV−1).ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-20926-w2 NATURE COMMUNICATIONS |         (2021) 12:1070 | https://doi.org/10.1038/s41467-021-20926-w |www.nature.com/naturecommunicationswww.nature.com/naturecommunicationsas 30,000 cm2 V−1 s−1 at room temperature23 (see SupplementaryNote 2).Although hBN-encapsulated graphene devices have allowed fordevice designs with unprecedented functionalities24–26 andimproved performance23, such layered dielectric material typi-cally contains impurities and/or crystal defects leading to lowbreakdown voltages27,28. Moreover, the dielectric permittivity ofhBN is rather low compared to existing high-κ dielectrics29, witha value close to that of SiO2 (ϵr ~ 4). This low dielectric constantand reduced breakdown voltage (see Supplementary Note 5)compromises not only the power consumption and the ability toreach high modulation efficiencies at reasonably low drive vol-tages but also limits the IL and the ER of the modulators1,9. Wethus integrate HfO2, a high-κ dielectric material, within the hBN-encapsulated graphene electrodes (see the sketch in Fig. 1d).With such hBN–HfO2–hBN dielectric arrangement, grapheneremains isolated from HfO2, shielded away from any possibleout-of-plane dangling bonds of the 3D oxide material (see inset ofFig. 1d for the molecular representation of the 2D–3D dielectricinterface). More importantly, the hBN–graphene interfacesremain atomically sharp and clean22,23,30. This nanoscale controlof the interfaces brings further advantages to real-world EAgraphene modulators, like a symmetric and hysteresis-freeoperation. This is directly visible in the transmission curves asa function of the applied voltage VBT or, alternatively, as afunction of the Fermi energy EF at the graphene electrodes (seethe bottom and top axis in Fig. 1e and Supplementary Note 9).Both forward and backward voltage sweeps (black and blue tra-ces, respectively) show minor hysteresis and appear symmetricwith respect to the charge neutrality point. For comparison, adevice fabricated with a HfO2–hBN dielectric shows no overlapbetween the forward and backward sweeps (inset of Fig. 1e). Thisstrong hysteresis is nonetheless expected for this HfO2–hBNmodulator since, in that case, the top graphene electrode is indirect contact with HfO2. The hBN–HfO2–hBN modulator deviceexhibits a modulation efficiency as high as ~2.2 dBV−1 within a0.5 V voltage span (see red linear fit to the data in Fig. 1e).Considering the length of our modulator (~60 μm), we obtain anormalized static modulation efficiency of ~0.037 dBV−1 μm−1, athreefold increase compared to previously reported high-speedgraphene EA modulators9.With such a high static modulation efficiency (Fig. 1), one mightexpect the device speed to be compromised14. However, the highmobility of the hBN-encapsulated graphene is expected to increasethe bandwidth. This is visible in Fig. 2a, where we calculated thef3dB bandwidth as a function of the charge carrier-dependentmobility (μ) and contact resistivity (ρc) for a graphene modulatorwith the same geometry and dielectric combination as the device inFig. 1 (see Supplementary Note 11). As observed, the graphenemobility and the contact resistivity have a major influence on themodulator speed. Considering the mobility μ ≈ 12,000 cm2 V−1 s−1(evaluated at VBT= 10.4 V) and the contact resistivity ρc ≈800Ω μm achieved experimentally (see Supplementary Notes 4and 11), we expect a bandwidth of f3dB ~ 46 GHz (dashed lines inFig. 2a). To confirm this value experimentally, we measured theelectro-optical (EO) bandwidth of the device in Fig. 1 at a DCvoltage VBT= 10.4 V and a peak-to-peak voltage VAC= 200mV(Fig. 2b). The bandwidth of the measured device attains f3dB ≈39 GHz (without de-embedding, see Supplementary Note 13). Thisvalue is close to the capabilities of our setup, limited to 40 GHz bythe vector network analyzer and the RF probes (see SupplementaryNote 12). Even though the measured f3dB does not reach theexpected f3dB ~ 46 GHz (Fig. 2a), possibly due to an increasedcontact resistivity of the measuring device (see SupplementaryNote 11), this is still the highest f3dB bandwidth among allgraphene-based modulators reported so far8,9,11,12,31,32.The high-speed operation of our modulator device is alsosupported by non-return-to-zero eye diagram measurements. Thedata were obtained through an electrical pattern generator (PG)driving the modulator with a 231− 1 pseudo-random binarysequence 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 theDC bias was set to 11 V. The device was terminated with a 50 Ωload to avoid reflections due to the impedance mismatch betweenthe PG electrical output and the modulator (when measured at40 Gbps). Open eye diagrams at 28 and 40 Gbps are shown inFig. 2c, with an ER as high as 5.2 dB and a signal-to-noise ratio of2.28 dB for the latter (see Supplementary Note 14 for an eyediagram at 10 Gbps). These results confirm the large modulationefficiency of our hBN–HfO2–hBN-based modulator device,even at high speeds, with a dynamic modulation efficiency of1.49 dBV−1 at 40 Gbps9.a b0c40f  bandwidth  39 GHz3dB-10 -8 -4 0 4S [dB]21Bandwidth [GHz]0 10 20 -6 -2 228 Gbs40 Gbs304 8 12 16 203 2 -1Mobility μ [10 cm (Vs) ]010203040506070f bandwidth [GHz]3dBρ  = 500 Ω·μm cρ  = 800 Ω·μm cρ  = 1.1 kΩ·μm cρ  = 1.4 kΩ·μm cρ  = 1.7 kΩ·μm cFig. 2 Dynamic characterization. a f3dB bandwidth as a function of the charge carrier-dependent mobility (μ) and the contact resistivity (ρc) calculated for adevice with the same geometry and dielectric combination as the device in Fig. 1 (see Supplementary Note 11). The dashed lines indicate the expected f3dB~46 GHz at μ ~12,000 cm2 V−1 s−1 (evaluated at VBT= 10.4 V, refer to panel b). b Measured electro-optical S21 frequency response of the EA modulator atVBT= 10.4 V and VAC= 200mV, without de-embedding, i.e., including the contributions of the setup and photodetector (see Supplementary Note 12). c Inall, 231− 1 pseudo-random binary sequence non-return-to-zero eye diagram at 28 and 40 Gbps. The EA modulator is d.c. biased at VBT= 11 V and driven bya VAC= 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 arrowsindicate the 0W baseline, and the white scale bar corresponds to 10 ps.NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-20926-w ARTICLENATURE COMMUNICATIONS |         (2021) 12:1070 | https://doi.org/10.1038/s41467-021-20926-w |www.nature.com/naturecommunications 3www.nature.com/naturecommunicationswww.nature.com/naturecommunicationsLike the speed of the modulator, the power consumptionunderstood as the switching energy per bit also benefits from thesmall footprint of the device. Ignoring the parasitic pad capaci-tance, we obtain for the modulator in Fig. 1 an energy per bit ofCðVACÞ2=4 � 160 fJbit�1, where C= 52 fF is the capacitancebetween the top and bottom graphene electrodes and VAC= 3.5 Vthe voltage swing12. This value of energy per bit is on par withstate-of-the-art SiGe technologies33,34.To directly compare modulators with different dielectrics, it ismore convenient to compare the transmission as a function of EF(see the EF axis in Figs. 1e and 3b and c) since EF already con-siders the thickness and the relative permittivity of the dielectric(see Supplementary Note 7). Operating the modulators at high EFenhances both ER and IL, with the ER (IL) increasing (decreas-ing) as a function of EF9. In the full transparency regime (Pauliblocking, see Supplementary Note 1), the ER is maximized andthe IL is expected to become nearly zero for high-qualitygraphene1,9 (see Supplementary Note 10). It is thus crucial todetermine which dielectric materials facilitate Pauli blockingoperation. Figure 3a illustrates the expected maximum EF,EmaxF ¼ _vFffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiπϵ0ϵrEBD=qp; ð1Þas a function of the relative permittivity (ϵr) and dielectricstrength (EBD) of any given dielectric. The square boxes in Fig. 3aenclose the expected EmaxF for the HfO2− and hBN-based mod-ulators (in red and green, respectively) and the black star repre-sents the EmaxF ¼ 0:57 eV expected for the hBN–HfO2–hBNmodulator of Fig. 1e (see Supplementary Note 10). The bound-aries of the boxes are taken from literature28,35–37 (marked withdots) and from our dielectric characterization (marked with stars,see Supplementary Notes 5 and 10). All dielectric materials ful-filling EmaxF > 0:5 eV (see white fringe in Fig. 3a) allow fulltransparency, i.e., Pauli blocking. The comparison in Fig. 3ahighlights the advantages of the hBN–HfO2–hBN dielectric (blackstar), achieving higher EF values than the hBN dielectric whileequally preserving the intrinsic qualities of graphene.These results are confirmed by the transmission traces inFig. 3b, c. None of the hBN-based modulators were able towithstand Pauli blocking operation (orange-shaded regionFig. 3b), all breaking their hBN dielectric at a similarEmaxF � 0:4 eV (see vertical dashed lines in Fig. 3b and Supple-mentary Notes 7 and 8). Even though these hBN-based mod-ulators were too fragile, we obtained modulation efficiencies ashigh as 0.3, 1.3, and 2 dBV−1 for device lengths L= 12, 24, and 42μm, respectively. Once normalized by its length, we obtain 0.025,0.054, and 0.047 dBV−1 μm−1. These results exceed the state-of-the-art modulation efficiency of 0.038 dBV−1 μm−110. Still, thepremature hBN breakdown compromises the ER and the IL.Indeed, the measured ER= 0.75, 2.3, and 4.9 dB (data points inFig. 3b) is far from the simulated ER= 1.8, 4.4, and 7.9 dB (solidtraces in Fig. 3b) expected for the 12, 24, and 42 μm-long mod-ulators, respectively (for simulations, refer to SupplementaryNotes 1–3). Likewise, the measured IL= 1, 2.2, and 3.4 dB arehigher than IL ≈0 dB expected for high-mobility graphene mod-ulators1 (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 SupplementaryNote 10).On the other hand, the second hBN–HfO2–hBN modulatordevice attains the Pauli blocking regime (Fig. 3c), in agreementwith the dielectric characterization of hBN–HfO2–hBN (Fig. 3aand Supplementary Notes 5 and 10), reaching a maximum Fermienergy of EmaxF � 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 andred traces of Fig. 3c, b, respectively) and an IL reaching nearlyzero (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 a0.5 V span, see Fig. 3c). We note that the hBN–HfO2–hBN deviceof Fig. 1e has a relatively weak measured ER ≈ 4.4 dB andIL ≈7.8 dB (see Supplementary Note 10) due to an overcautiousVBT= 12.1 V applied voltage (or alternatively EF= 0.41 eV).Normalized transmission [dB]0-1-2-3-4-8b-7-6-50.0 0.2 0.4E  [eV]F0.6c0.0 0.2 0.4 0.60-1-2-3-4-8-7-6-5hBN - - hBNHfO   2hBNL = 12 μmL = 24 μmL = 42 μm L = 44 μmE  [eV]F0 3 6 9 12 15 18V  [V]BT0 3 6 9 12 15V  [V]BT2 4 6 8-1Dielectric strength E  [MV cm ]BDRelative permittivity εr4 81216E [eV]F     0.51.01000 0.0amaxhBNHfO2hBN & HfO2Fig. 3 Dielectric breakdown and Pauli blocking operation. a Maximum Fermi energy, noted EmaxF , expected at the graphene electrodes of a graphenemodulator with a dielectric’s relative permittivity ϵr and dielectric strength EBD. All points lying inside the blue-colored region represent a dielectric allowingfor Pauli blocking operation (EmaxF >0:5 eV, refer to Supplementary Note 1). The red-colored region indicates otherwise (EmaxF <0:5 eV). The white bandrepresents the Pauli blocking boundary condition, defined as EmaxF ¼ 0:5 eV. The expected EmaxF for HfO2 and hBN are represented by the red and greensquares, respectively, taking the values of EBD and ϵr from literature28,35–37 (marked with dots) and our dielectric characterization (marked with stars, seeSupplementary Notes 5 and 10). The black star represents the EmaxF ¼ 0:57 eV expected for the hBN–HfO2–hBN modulator in Fig. 1e (see SupplementaryNote 10). b, c Normalized transmission as a function of EF and VBT for modulators with hBN (b) and hBN–HfO2–hBN (c) dielectric. The data points aremeasurements and the solid curves simulations (see Supplementary Notes 1–3 and 10). The vertical dashed lines indicate the EmaxF achieved at the dielectricbreakdown. The orange-shaded regions show the full transparency range, i.e., Pauli blocking. The top VBT axis in panel b is for the 42 μm-long device only(see Supplementary Note 7 for the other hBN devices). The graphene Dirac cones in panel b show the absorption and Pauli blocking processes at low andhigh Fermi energies, respectively.ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-20926-w4 NATURE COMMUNICATIONS |         (2021) 12:1070 | https://doi.org/10.1038/s41467-021-20926-w |www.nature.com/naturecommunicationswww.nature.com/naturecommunicationsConsidering the breakdown capabilities of hBN–HfO2–hBNdielectric (black star in Fig. 3a), we evaluated a potential ER ≈ 12dB and IL ≈ 0.042 dB for this device (see Supplementary Note 10).DiscussionAlthough material platforms like lithium niobate38 (LiNbO3) orhybrid technologies like Si/indium phosphide39 (InP), Si/SiGe40,or InGaAlAs40 offer outstanding performances in modulatorapplications, those are either not scalable38,41 (LiNbO3) or theirintegration with a CMOS fabrication line remains challenging40,42.Nowadays, Si and graphene are envisaged as the most scalable,cost-effective, and CMOS-compatible materials for amplitudemodulator applications1. To compare our results with state-of-the-art graphene and Si amplitude modulators, both EA andMach–Zehnder interferometer configurations included, we sum-marize our results in Fig. 4 and in Supplementary Notes 15 and16. Figure 4 shows the dynamic modulation efficiency (extractedfrom the eye diagrams and normalized by the device length anddrive voltage) as a function of the modulation speed (red axis andred data point in Fig. 4) and the static modulation efficiency(measured in DC and normalized by the device length), as afunction of the f3dB bandwidth (black axis and black data point inFig. 4). To avoid discrepancies due to the different extractionmethods, we determine the static modulation efficiency of thecompared literature8–12 using the same method as in Fig. 1e, i.e.,by applying a linear fit within a 0.5 V voltage span. The resultshighlight the trade-offs between speed and modulation efficiencyand stress the advantages of an hBN–HfO2–hBN dielectric toobtain large static and dynamic modulation efficiencies even athigh speed. As observed, the modulation efficiency typically dropsfor devices with high speed8,9, being our device the only mod-ulator able to operate at high speed with a large static and dynamicmodulation efficiency (Fig. 4). These results outperform state-of-the-art graphene and not-yet-commercial silicon-based electro-absorption modulators43–45 (see blue/red and green data clouds,respectively in Fig. 4) when considering the modulation efficiencynormalized by the length (i.e., footprint). This figure-of-merit israther an important one since for many envisaged applications(e.g., chip interconnects), multiple modulator devices are expectedto coexist on the same chip.In this work, we demonstrated the advantages of integratinghBN with a 3D high-κ dielectric for high-quality graphene-basedEA modulators. Compared to traditional oxide sputtering oratomic layer deposition (ALD) growth on top of graphene, theintegration of HfO2 in-between hBN prevented any damage tothe underlying graphene and allowed clean graphene–hBNinterfaces. These clean interfaces yielded a symmetric and nearlyhysteresis-free operation. Moreover, this 2D–3D integrationenabled full transparency while maintaining the high mobilityand low doping of intrinsic graphene. More importantly, thehBN–HfO2–hBN-based EA modulators were able to reach highmodulation speeds with strong modulation efficiencies, over-coming the fundamental limitations of the DL graphene config-uration and outperforming state-of-the-art graphene and Sitechnologies. The compatibility of this hBN–HfO2–hBN dielectricwith Si and other 2D materials might allow for considerablescaling improvements and greater device functionality in a broadrange of graphene- and 2D-based electronic and optoelectronicapplications, even beyond graphene-based modulators.MethodsDevice fabrication. The Si photonic waveguide with a core cross-section of 750nm × 220 nm was prepared on the IMEC iSiPP25G silicon-on-insulator platform20.For the fabrication of the electroabsorption modulator, the graphene and hBNflakes were exfoliated from highly oriented pyrolytic graphite and hBN crystals,respectively. The bottom hBN–graphene–hBN stacks were prepared by the van derWaals assembly technique22,23 and transferred directly onto the Si waveguideseparated by a 10 nm spacer of high-quality thermal SiO2. The bottom hBN flake(separating the graphene and the SiO2 layer) thickness of ~5 nm was chosen toenhance the graphene absorption while isolating the graphene from the rough SiO2substrate. The top hBN has a thickness of ~10 nm. The stack has been etched byreactive ion etching in an oxygen (O2) and trifluoromethane (CHF3) (4:40 sccm)environment to expose the graphene edge. The bottom stack was then contacted bya 3/15/30 nm Cr/Pd/Au metal combination. The 10 nm hafnium oxide film hasbeen deposited at 250 °C prior depositions of a 2 nm sputtered SiO2 seed layer byALD. Tetrakis-dimethylamido hafnium (TDMAH) (0.4 s purge time) and watervapor (5 s purge time) as precursors have been used in a Savannah G1 system fromCambridge Nanotech. 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Monolithic 56 Gb/s silicon photonic pulse-amplitudemodulation transmitter. Optica 3, 1060–1065 (2016).46. Sorianello, V. et al. Graphene-silicon phase modulators with gigahertzbandwidth. Nat. Photonics 12, 40–44 (2018).AcknowledgementsWe thank S. Pradhan for his assistance in capacitance measurements and D.A. Iranzo forhis inputs on the illustration in Fig. 1d. We also thank T. Khodkov, D.B. Ruiz, and S.Castilla for technical assistance. The research leading to these results has receivedfunding from the European Union’s Horizon 2020 research and innovation programunder grant agreement No. 881603 (Graphene flagship Core3). H.A. also acknowledgesfunding from the European Union’s Horizon 2020 research and innovation programunder the Marie Skłodowska-Curie grant agreement No. 665884. F.H.L.K. alsoacknowledges support from the Government of Spain (FIS2016-81044, Severo OchoaCEX2019-000910-S), Fundació Cellex, Fundació Mir-Puig, and Generalitat de Catalunya(CERCA, AGAUR, and SGR 1656). K.W. and T.T. acknowledge support from the Ele-mental Strategy Initiative conducted by the MEXT, Japan, Grant NumberJPMXP0112101001, JSPS KAKENHI Grant Number JP20H00354 and the CREST(JPMJCR15F3), JST.Author contributionsB.T., H.A., and F.H.L.K. conceived the idea. H.A. and B.T. fabricated the devices. L.O.and B.T. did the simulations. B.T. and H.A. performed the measurements and dataanalysis. A.M. and V.S. performed high-frequency measurements under the supervisionof M.R. M.P. and D.V.T. provided Si waveguides. K.W. and T.T. synthesized the hBNcrystals. F.H.L.K. and B.T. supervised the project. B.T., H.A., and F.H.L.K. wrote thepaper with input from all authors.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version contains supplementary materialavailable at https://doi.org/10.1038/s41467-021-20926-w.Correspondence and requests for materials should be addressed to B.Tés. or F.H.L.K.Peer review information Nature Communications thanks the anonymous reviewer(s) fortheir contribution to the peer review of this work.Reprints and permission information is available at http://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in any medium or format, as long as you giveappropriate credit to the original author(s) and the source, provide a link to the CreativeCommons license, and indicate if changes were made. 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To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2021ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-20926-w6 NATURE COMMUNICATIONS |         (2021) 12:1070 | https://doi.org/10.1038/s41467-021-20926-w |www.nature.com/naturecommunicationshttps://doi.org/10.1038/s41467-021-20926-whttp://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/www.nature.com/naturecommunications 2D-3D integration of hexagonal boron nitride and a high-κ dielectric for ultrafast graphene-based electro-absorption modulators Results Discussion Methods Device fabrication Data availability References Acknowledgements Author contributions Competing interests Additional information