# Fileset

[Pierret_2022_Mater._Res._Express_9_065901.pdf](https://mdr.nims.go.jp/filesets/5cc708d3-671e-490b-b6bf-f25852d22296/download)

## Creator

A Pierret, D Mele, H Graef, J Palomo, [T Taniguchi](https://orcid.org/0000-0002-1467-3105), [K Watanabe](https://orcid.org/0000-0003-3701-8119), Y Li, B Toury, C Journet, P Steyer, V Garnier, A Loiseau, J-M Berroir, E Bocquillon, G Fève, C Voisin, E Baudin, M Rosticher, B Plaçais

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Dielectric permittivity, conductivity and breakdown field of hexagonal boron nitride](https://mdr.nims.go.jp/datasets/e30e788e-72e1-4b56-aa2d-7d6a9fedee72)

## Fulltext

Dielectric permittivity, conductivity and breakdown field of hexagonal boron nitrideMaterials Research ExpressPAPER • OPEN ACCESSDielectric permittivity, conductivity and breakdownfield of hexagonal boron nitrideTo cite this article: A Pierret et al 2022 Mater. Res. Express 9 065901 View the article online for updates and enhancements.You may also likeBand gap measurements of monolayer h-BN and insights into carbon-related pointdefectsRicardo Javier Peña Román, Fábio J RCosta Costa, Alberto Zobelli et al.-Recent progress in synthesis of two-dimensional hexagonal boron nitrideHaolin Wang, Yajuan Zhao, Yong Xie etal.-Optical absorption of single-layerhexagonal boron nitride in the ultravioletJ C G Henriques, G B Ventura, C D MFernandes et al.-This content was downloaded from IP address 220.150.149.130 on 02/07/2022 at 08:24https://doi.org/10.1088/2053-1591/ac4fe1https://iopscience.iop.org/article/10.1088/2053-1583/ac0d9chttps://iopscience.iop.org/article/10.1088/2053-1583/ac0d9chttps://iopscience.iop.org/article/10.1088/2053-1583/ac0d9chttps://iopscience.iop.org/article/10.1088/1674-4926/38/3/031003https://iopscience.iop.org/article/10.1088/1674-4926/38/3/031003https://iopscience.iop.org/article/10.1088/1361-648X/ab47b3https://iopscience.iop.org/article/10.1088/1361-648X/ab47b3https://googleads.g.doubleclick.net/pcs/click?xai=AKAOjss4cuKfuUIzMbSuM66Pxyu1zMKSNl75GeYR3wQ8wPHf2BMTbgvR-9tU10yG_zW0Z4J29e6Fh-8NC4UYcMDEFzZILHEyBlNC8ZEoUvfh1GvJnKhDTUy9Z8SJMrUSv2WVZj-7XGgjrhO6bAK0lLXD3k63TyeHmuooHUXbuykhh-_TTEdNRxQRfYI0xXczLVCQS_InO1POfJmOlgcOR5kvLGrTEBHTPZBVzQB5ctMdmkV1Yr2y2KpfjGyvq808c8yfpFkoYP8ZfwZf_gUl7PL-vF8Udp9XVxGpxYvZl2hHjhEHGg&sig=Cg0ArKJSzPpY8kKnyscX&fbs_aeid=[gw_fbsaeid]&adurl=https://www.electrochem.org/individual-membership%3Futm_source%3DIOP%26utm_medium%3D1640x440%26utm_campaign%3D2022Membership%23communityMater. Res. Express 9 (2022) 065901 https://doi.org/10.1088/2053-1591/ac4fe1PAPERDielectric permittivity, conductivity and breakdown field of hexagonalboron nitrideAPierret1, DMele1 , HGraef1, J Palomo1, T Taniguchi2, KWatanabe3 , Y Li4, B Toury4, C Journet4 ,P Steyer5, VGarnier5, A Loiseau6, J-MBerroir1, E Bocquillon1,7, G Fève1, CVoisin1, E Baudin1 ,MRosticher1 andBPlaçais1,∗1 Laboratoire de Physique de l’École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, F-75005Paris, France2 AdvancedMaterials Laboratory, National Institute forMaterials Science, Tsukuba, Ibaraki 305-0047, Japan3 AdvancedMaterials Laboratory, National Institute forMaterials Science, Tsukuba, Ibaraki 305-0047, Japan4 Laboratoire des Multimatériaux et Interfaces, UMR CNRS 5615, Univ Lyon, Université Claude Bernard Lyon 1, F-69622 Villeurbanne,France5 Université de Lyon,MATEIS, UMRCNRS 5510, INSA-Lyon, F-69621Villeurbanne cedex, France6 Laboratoire d’Etude desMicrostructures (LEM), ONERA,CNRS,Université Paris-Saclay, 92322Châtillon, France7 Physikalisches Institut, Universität zuKöln, Zülpicher Strasse 77, 50937, Köln, Germany∗ Author towhomany correspondence should be addressed.E-mail: aurelie.pierret@phys.ens.fr and bernard.placais@phys.ens.frKeywords: hexagonal boron nitride, dielectric constant, dielectric strength, dielectric breakdownAbstractIn view of the extensive use of hexagonal boron nitride (hBN) in 2Dmaterial electronics, it becomesimportant to refine its dielectric characterization in terms of low-field permittivity and high-fieldstrength and conductivity up to the breakdown voltage. The present study aims atfilling this gap usingDC andRF transport in twoAu-hBN-Au capacitor series of variable thickness in the 10–100 nm range,made of large high-pressure, high-temperature (HPHT) crystals and a polymer derivative ceramics(PDC) crystals.We deduce an out-of-plane lowfield dielectric constant ò∥= 3.4± 0.2 consistent withthe theoretical prediction ofOhba et al, that narrows down the generally acceptedwindow ò∥= 3–4.TheDC-current leakage at high-field is found to obey the Frenkel-Pool law for thermally-activatedtrap-assisted electron transport with a dynamic dielectric constant ò∥; 3.1 and a trap energyΦB; 1.3 eV, that is comparable with standard technologically relevant dielectrics.1. IntroductionHexagonal boron nitride (hBN) is a van derWaals crystal insulator introduced in graphene electronics a decadeago [1] and since then extensively used as encapsulant [2], tunnel barrier [3–5], or gate dielectric in 2Dmaterialelectronics [6, 7]. In view of its technological relevance, it is important to improve its characterization both interms of low-field permittivity and high-field dielectric conductivity and breakdown field. Accepted values fortheDCdielectric permittivity constant lie in the broad range ò∥= 3–4 [1, 8–10], whereas breakdownfields aremore scattered, with EBD= 4–10MV cm−1 [9, 11], depending onmaterial quality and breakdown-fielddefinition criterion. The purpose of the present study, which is based onDC andRF transport in Au-hBN-Aucapacitorsmade of two types of hBN crystals, is to narrowdown the uncertainty in permittivity, to shed lightonto the dielectric breakdownmechanism, and to use these characterizations to benchmark the two hBN crystalsources.We have used two series of Au-hBN-Au capacitorsmade of large exfoliated hBN crystals. Crystals are growneither under high-pressure high-temperature (HPHT samples) as described in [12], or with a polymer derivativeceramics (PDC) route described in [13]. Exfoliated hBNflakes, of thickness d∼ 10–100 nm, are sandwichedbetweenAu electrodes of lateral dimensions L×W= 10× 10 μm.A significant fraction of samples (17HPHTsand 11 PDCs of the total 41 capacitors) follows the parallel-plate capacitance lawwith a dielectric constantOPEN ACCESSRECEIVED3 January 2022REVISED26 January 2022ACCEPTED FOR PUBLICATION28 January 2022PUBLISHED3 June 2022Original content from thisworkmay be used underthe terms of the CreativeCommonsAttribution 4.0licence.Any further distribution ofthis workmustmaintainattribution to theauthor(s) and the title ofthework, journal citationandDOI.© 2022TheAuthor(s). Published by IOPPublishing Ltdhttps://doi.org/10.1088/2053-1591/ac4fe1https://orcid.org/0000-0002-2250-9671https://orcid.org/0000-0002-2250-9671https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0002-3328-317Xhttps://orcid.org/0000-0002-3328-317Xhttps://orcid.org/0000-0003-3694-9640https://orcid.org/0000-0003-3694-9640https://orcid.org/0000-0003-2408-7393https://orcid.org/0000-0003-2408-7393mailto:aurelie.pierret@phys.ens.frmailto:bernard.placais@phys.ens.frhttps://crossmark.crossref.org/dialog/?doi=10.1088/2053-1591/ac4fe1&domain=pdf&date_stamp=2022-06-03https://crossmark.crossref.org/dialog/?doi=10.1088/2053-1591/ac4fe1&domain=pdf&date_stamp=2022-06-03http://creativecommons.org/licenses/by/4.0http://creativecommons.org/licenses/by/4.0http://creativecommons.org/licenses/by/4.0ò∥; 3.4± 0.2. The other 14 samples deviate from this lawwith lower capacitance values, presumably due toprocess imperfections involving spurious air gaps, due to dust or bubbles between the hBNflake and the bottomelectrode. Besides, we do not see significant differences betweenHPHT and PDCcrystals in terms ofpermittivity.The dielectric strength is characterized bymonitoring the leakage current at high bias which is analyzed interms of a bulk conductivity. This analysis is carried out on a subset of 7 capacitors having survived the high-biastraining. As shown in [9], dielectric conductivity is a three step process, starting by a threshold-less exponentialcurrent growth, followed by a quasi-saturation at a breakdownfield EBD and culminating by an irreversiblecurrent runaway forE EBD usually leading to sample breakdown.Herewe focus on the pre-breakdown regimeE EBDwheremoderate current densities (J< JBD; 0.5 A cm−2) are applied that secure device integrity. Inthese conditions, we observe a bias-reversible, reproducible and polarity-independent behavior. The leakagecurrent obeys a standard exponential growthwith voltagewhich precludes unambiguous determination of adielectric breakdown voltage (see figure 2(a)). However, when using an arbitrary breakdown current criterionJ JBD, wefind an overall increase of the breakdown voltagewith thickness which suggests the relevance of abreakdownfield, i.e. a bulk scenario, and justifies our breakdown analysis in terms of conductivity, e.g. J/E(E)below a breakdown conductivityσBD∼ 1 μΩ cm−1.Wefind that the conductivity,σ= J/E obeys the Frenkel-Pool (FP) law (equation (1) below), corresponding to a trap-assisted, thermally-activated, bulk Schottkytransport [14, 15]. Its signature lies in the linear dependence, s s =  f E Tln BD2( ) (seefigure 2(b)),observed in the [10−4–10−1] μS cm−1 range at room temperature (T= 300 K). The FP activation scenario isconfirmed by the temperature dependencemeasured in one representative sample (inset offigure 2(b)). Therobustness of the field dependence contrasts with the large variability (within a factor 106) of the conductivityprefactor.We assign the latter to a variability in the deep-level donor energyΦB; 0.9–1.3 eV, with alogarithmical precision in theσBD prefactor. Remarkably, five devices show very similar Frenkel-Pool plots withdeep-level traps energyΦB,hBN; 1.27± 0.03 eV, suggesting the existence of a quasi-intrinsic limit. This value isquite typical of that of technology-relevant insulators, such as Si3N4whereΦB; 1.3± 0.2 eV [16], or SiO2whereΦB; 1 eV [17] are reported. Some PDC-grown devices showhowever trapswith a smaller energy, which opensroutes for improvement of this lessmature growth process.2. Capacitor fabrication and setupWehave fabricated 41Au-hBN-Au capacitors, 27 of themwithHPHT-hBN fromNIMS and 14with the PDC-hBN fromLMI. The growth technics, as well as structural and optical characterizations, of these high-qualitycrystals are detailed in [12] and [13, 18] respectively. The capacitors were deposited on high-resistivity Sisubstrates, suitable for RFmeasurement, that are coveredwith a 285 nm-thick SiO2 layer. The bottom electrodeand theRF coplanar waveguide structure arefirst deposited using laser lithography and thermal evaporation.The bottom110/5 nmAu/Cr electrode is buried into SiO2 to ensure a planar surface for hBN-flakes transfer.Planarisation is completed bymechanically polishing the smallmetallic pitches at the gold edges with isopropylalcohol (IPA). This processminimizes air gaps between hBN and the bottom gold electrodewhich are ultimatelylimited byAu roughness of amplitude 2δ; 1.5 nm, asmeasured by atomic forcemicroscopy (AFM). hBNcrystals weremechanically exfoliatedwith polydimethylsiloxane (PDMS).We use poly-propylene carbonatePPC-PDMS stamps to dry transfer the hBNflakes on the bottom electrode. A second lithography step allowscovering the hBNflakewith a secondAu/Cr electrode, which is conformal to the hBNdielectric and thereforeairgap-free. The obtained structures form a nominally 10× 10 μmcapacitor in a parallel-plate configuration.After annealing (1h at 240° Celsius underN2) the capacitor’s hBN thickness is determined byAFMand falls inthe range d= 6–98 nm. This range exceeds theminimal thickness (10–20 nm) formobility-preservingencapsulation, is relevant for gate dielectric applications, and reaches the value (∼100 nm) for fully-developedradiative cooling [19, 20]. It is however not relevant for tunnel-barrier applications which are describedelsewhere [3–5]. The lateral size of capacitors was deliberatelymaximized at the limits of our exfoliationtechnique to increase experimental resolution,minimize spurious edge effects, and address the homogenousproperties of hBN. It is preciselymeasured by scanning electronmicroscopy.We have indifferently used colinearand perpendicular source and drain electrodes, the later geometry being shown in the optical image offigure 1(a).High frequency admittancemeasurements were carried out in a Janis (cryogenic) probe station undervacuumat room temperature (see sketch infigure 1(a)). The two-port scattering parameters Sij of the capacitorweremeasured using anAnritsuMS4644B vectorial network analyzer (VNA) in the 10MHz–10 GHz range. Ashort-open-load-reciprocal protocol was used to calibrate thewave propagation until the probe tips. Asexplained in [21], thewave propagation in the coplanar access of the capacitor is de-embedded by calculating theABCDmatrix from the S parameters of a symmetric thruline reference structure. To correct for residual2Mater. Res. Express 9 (2022) 065901 APierret et alparasitic stray capacitance effects, we convert the previous ABCDmatrices into complex admittancematricesand subtract the contribution of a dummy reference structure of same geometry but devoid of the central Au-hBN-Au capacitor. The total capacitance is directly deduced from the low frequency (sub-GHz) imaginary partY12= jωC.Breakdownmeasurements have been carried out on the same setup bymonitoring the leakage current asfunction of the appliedDC voltage (Keithley 2400 Source-MeasureUnit). The same procedure has been appliedat low temperature on a representative capacitor to check the activationmechanism at stake in the dielectricbreakdown.3.Dielectric constantFigure 1(b) shows capacitances of the full set of 41 tested capacitors versus hBN thickness. Capacitance data,deduced fromVNAmeasurements, are first comparedwith complementary data obtained by sub-MHz Lock-Intechniques (not shown) to ascertain their frequency independence. Data are scattered, but we can stillfind asignificant fraction of devices, of bothHPHTand PDC sources, showing capacitance-data accumulation alongan upper limit given by the parallel-plate capacitance formulaC= ò0ò∥LW/d* (red and blue symbols infigure 1(b)), where ò∥; 3.4± 0.2 and d* = d+ ò∥δ is an effective dielectric thickness accounting for spuriousair-gap contributions due to (bottom)metal roughness 2δ; 2 nm.One third of the series (14 devices, blacksymbols infigure 1(b)), exhibiting lower capacitance values caused by process imperfections including spuriousair gaps, presumably due to dust or bubbles between the hBNflake and the bottom electrode, are discarded.From the selected devices (17HPHTs and 11 PDCs), we are able to narrow down the dielectric constant windowand provide a recommended value of the hBNdielectric constant ò∥= 3.4± 0.2. This value exceeds by 13% theò∥; 3.0 reported inmetal-hBN-graphene quantum-Hall devices [8, 19]. This apparent disagreement can beliftedwhen considering the series quantum capacitance of the graphene electrode in these thin hBN samples[8, 22], as well as roughness-induced air-gaps at the bottom electrodes. Ourmeasured permittivity turns out tobe consistent with the theoretical prediction ò∥= 3.38 of [23], following an ab-initio approachwhich alreadyquantitatively predicts correctly the optical permittivity and its anisotropy [24].4. Breakdown current and conductivityFigure 2(a) shows typical current-voltage characteristics of capacitors showing a strongly non-linear onset ofcurrent. Characteristics become irreversible at large current density, J∼ 0.1 μA cm−2, eventually leading tosample breakdown for J JBD 1 μA cm−2. At the lower bias offigure 2(a), I-V curves are reproducible andbias symmetric (inset offigure 2(a)). As seen in thefigure, the breakdown voltageVBD shows a tendency toincrease with hBN thickness d, suggesting a bulk origin of breakdown.A deeper insight into the breakdownmechanism is provided by figure 2(b)which reveals a µJ E Eln( )scaling of conductivity. It corresponds to the Frenkel-Pool (FP) effect [14–16], where afinite dielectricFigure 1.Dielectric constant deduced from a series of Au-hBN-Au capacitors of thickness d = 6–98 nmand lateral dimensionsL × W = 10 × 10 μm. Panel (a) : scheme of themeasuring setup. Panel (b): capacitance of the series of 41 devices. A subset of 17HPHT-type and 10 PDC-type capacitors follow the parallel-plate formulaC = ò∥ò0LW/(d + ò∥δ), where δ ; 1 nm accounts for air-gap contribution associatedwith bottomAu-plate roughness 2δ. From this subset we can refine the precision of the dielectric constantat ò∥ = 3.4 ± 0.2.3Mater. Res. Express 9 (2022) 065901 APierret et alconductivity J/E arises due to thermal de-trapping of deep-level electrons of energy eΦB? kBT. Conductivityincreases at large voltage as electric field lowers the barrier heightΦB by an amount p eE BD 0 . At ultimatefields, it eventually leads to full ionization of trapswhenever pF -  eE k TB BD B0( )  , which defines abreakdown electric field EBD. In this picture,EBD=ΦB/r0 is on the order of the impurity field, wherer0= e/πòBDò0ΦB is the screening length. The FP conductivity writes [15]:sp= ´ -F -  JEeeEk Texp , 1BDB BDB0⎡⎣⎢⎤⎦⎥ ( )where the breakdown conductivityσBD= JBD/EBD;NTeμ corresponds to the band conductivity (mobilityμ)for fully ionized traps (concentrationNT). Equation (1) holds in thefield rangeEFN E EBD, orJ= 10−4–10−1 μA cm−2, where EFN is the Fowler-Nordheim tunneling limit for a defect-free thin triangularbarrier [16].As seen infigure 2(b), the field dependence of breakdown conductivity does obey the FPmechanism for bothhBN sources, with a slope solely determined by òBD. Data fitting suggests a smallfield-suppression of permittivitywith òBD; 3.1< ò∥; 3.4. In contrast to the universality of slope, the prefactor s - FexpBDek TBB( ) shows samplevariability, exhibiting variations by six orders ofmagnitude. This observation highlights the strong sensitivity ofbreakdown tomaterial quality which, in the FP scenario,mainly stems from the variability in the trap potentialΦB (andEBD), as that ofNT andμ inσBD cannot explain such a large scatter alone. For a quantitative estimationofΦBwe setσBD∼ 0.1 μS cm−1, corresponding to JBD∼ 0.5 A cm−2 andEBD∼ 5MV cm−1. This breakdowncurrent is typical of quasi saturation values observed in our samples, and in the literature (figure 5 in [9]).Withthis procedure, we extractΦB= 0.9–1.3 V infigure 2(b). Remarkably, we observe an accumulation ofconductivity data (4HPHT and 1PDC capacitors) along an upper limit represented by theΦB= 1.27± 0.03 Vline. This suggests the existence of a dielectric strength limit in high-quality hBN crystals. Dispersion among thatdata-subset of highest-quality samples corresponds toΔΦB= 0.06 V, or a variation ofσBD in the range0.01–1 μS cm−1. Taking a typical insulatormobilityμ 1 cm2/Vs, this translates into a trap densityNT∼ 1012–1013 cm−3 and a trap numberNTdLW ∼ 10–100.To further establish the FPmechanism of breakdownwe have added, in the insert of figure 2(b), acomparison between 10 K and 300 K breakdown currentmeasurements performed on an additional sample(NIMS-5-01-98 nm), which illustrates the strong temperature dependence of activated FP transport, at variancewith tunneling-based scenarios.Figure 2.Room temperature dielectric breakdown inHPHT (red symbols/lines) and PDC (blue symbols/lines) hBN capacitors of10 × 10 μmlateral dimension. Panel (a): exponential growth of leakage current at large voltage. Inset shows bipolar characteristicsover a broader current density range. Pre-breakdown voltage increases with hBN thickness and is typically larger inHPHT-baseddevices than in PDC-based ones. Panel (b): Frenkel-Pool plot of the high-field hBN conductivity as function of electric field, showing ascaling of the field-dependence. The dielectric strength (or breakdown field) takes amaximum shared by 4HPHT samples and 1 PDCsample. It obeys the Frenkel-Pool law (red line) in equation (1)withΦB = 1.27 ± 0.03 V, takingσBD = 0.1 μS cm−1 as an estimate ofthe fully ionized donor conductivity, and òBD = 3.1. Two PDC samples (upward- and downward-pointing blue triangles) show thesame Frenkel-Pool field dependence (blue line) howeverwith smaller trap energiesΦB = 0.9 and 1.0 V. Inset shows the temperaturedependence of high-field current,measured on a representative sample. The increase of the slope at 10K illustrates the thermallyactivated nature of transport.4Mater. Res. Express 9 (2022) 065901 APierret et al5. ConclusionOur estimate of hBNdielectric permittivity, º =    3.4 0.2c0 , agrees with the calculations ofOhba et al,which predicts: =¥^ 4.85c , =¥ 2.84c , =^ 6.61c0 , =  3.38c0 [23]. This completes previous results based onopticalmeasurements giving =¥^ 4.95c , =¥ 2.86c , =^ 6.96c0 [24]. The excellent agreement in the fourrelevant dielectric constants of hBN gives strong confidence in the ab-initio technique to provide reliablepredictions of static and dynamical properties of BN crystals including those of the zinc-blende andwurtzitecrystals.The relevance of the 3DFrenkel-Poolmechanism of conductivity in the 2DhBNwas not granted as 2Dmaterialsmay sustain specificmechanisms.We demonstrate here that it works for c-axis transport, but thesituation can be different for in-plane electricfields with the opening of new leakage channels associatedwithcharges gliding in-between hBNplanes. The identification of deep-level traps responsible for breakdown isbeyond the scope of ourwork, especially as leakage current alone cannot identify the acceptor/donor nature ofthe levels.WefindΦB; 1.27± 0.03 eV in hBN,which is larger than the 1 eV reported in SiO2 [17], andcomparable with the 1.3± 0.2 eV in Si3N4 [16]. In the latter case, deep traps are attributed to silicon-dangling-bond centers [25]. This trap energy determines amaximumbreakdown field EBD; 5MV cm−1, defined as thethreshold for current quasi-saturation.Finally we conclude on the strong similarity ofHTHP and PDChBNcrystals in terms of dielectricpermittivity and strength, with however a better yield in terms of intrinsic dielectric breakdown for theNIMSsamples, which can to a large extent be attributed to a longermaturity of the growth technique.AcknowledgmentsThe research leading to these results has received partial funding from the EuropeanUnion ‘Horizon 2020’research and innovation programunder grant agreementNo.881603 ‘GrapheneCore 3’, the ANR-14-CE08-018-05 ‘GoBN’ andANR-21-CE24-0025-01 ‘ELuSeM’.Data availability statementThe data that support thefindings of this study are available upon reasonable request from the authors.ORCID iDsDMele https://orcid.org/0000-0002-2250-9671KWatanabe https://orcid.org/0000-0003-3701-8119C Journet https://orcid.org/0000-0002-3328-317XEBaudin https://orcid.org/0000-0003-3694-9640BPlaçais https://orcid.org/0000-0003-2408-7393References[1] DeanCR et al 2010 Boron nitride substrates for high-quality graphene electronicsNatureNanotechnol 5 722[2] MayorovA S et al 2011Micrometer-Scale ballistic transport in encapsulated graphene at room temperatureNano Lett. 11 2396[3] LeeG-H, YuY-J, Lee C,DeanC, ShepardKL, KimP andHone J 2011 Electron tunneling through atomicallyflat and ultrathinhexagonal boron nitrideAppl. Phys. Lett. 99 243114[4] Britnell L et al 2012Electron tunneling through ultrathin boron nitride crystalline barriersNano Lett. 12 1707[5] KimM,Pallecchi E, GeR,WuX,DucournauG, Lee J C,HappyH andAkinwandeD 2020Analogue switchesmade fromboron nitridemonolayers for application in 5G and terahertz communication systemsNature Electronics 3 479[6] NovoselovK S,MishchenkoA, CarvalhoA andCastroNetoAH2016 2Dmaterials and van derWaals heterostructures Science 353 461[7] Illarionov YY et al 2020 Insulators for 2Dnanoelectronics: the gap to bridgeNat. Commun. 11 3385[8] Yang F, ZibrovAA, Bai R, Taniguchi T,WatanabeK, ZaletelMP andYoungA F 2021 Experimental determination of the energy perparticle in partially filled landau levelsPhys. Rev. Lett. 126 156802[9] Hattori Y, Taniguchi T,Watanabe K andNagashio K 2016Anisotropic dielectric breakdown strength of single crystal hexagonal boronnitrideACSAppl.Mater. Interfaces 8 27877[10] Veyrat L, JordanA, ZimmermannK,Gay F,Watanabe K, Taniguchi T, SellierH and Sacépé B 2019 Low-Magnetic-Field Regime of aGate-DefinedConstriction inHigh-Mobility GrapheneNano Lett. 19 635[11] Ahmed F,Heo S, Yang Z, Ali F, RaCH, LeeH-I, Taniguchi T,Hone J, Lee BH andYooW J 2018Dielectric dispersion and high fieldresponse ofmultilayer hexagonal boron nitrideAdv. Funct.Mater. 28 1804235[12] Taniguchi T andWatanabeK 2007 Synthesis of high-purity boron nitride single crystals under high pressure by using Ba-BN solventJ. Cryst. Growth 303 5255Mater. Res. Express 9 (2022) 065901 APierret et alhttps://orcid.org/0000-0002-2250-9671https://orcid.org/0000-0002-2250-9671https://orcid.org/0000-0002-2250-9671https://orcid.org/0000-0002-2250-9671https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0002-3328-317Xhttps://orcid.org/0000-0002-3328-317Xhttps://orcid.org/0000-0002-3328-317Xhttps://orcid.org/0000-0002-3328-317Xhttps://orcid.org/0000-0003-3694-9640https://orcid.org/0000-0003-3694-9640https://orcid.org/0000-0003-3694-9640https://orcid.org/0000-0003-3694-9640https://orcid.org/0000-0003-2408-7393https://orcid.org/0000-0003-2408-7393https://orcid.org/0000-0003-2408-7393https://orcid.org/0000-0003-2408-7393https://doi.org/10.1038/nnano.2010.172https://doi.org/10.1021/nl200758bhttps://doi.org/10.1063/1.3662043https://doi.org/10.1021/nl3002205https://doi.org/10.1038/s41928-020-0416-xhttps://doi.org/10.1126/science.aac9439https://doi.org/10.1038/s41467-020-16640-8https://doi.org/10.1103/PhysRevLett.126.156802https://doi.org/10.1021/acsami.6b06425https://doi.org/10.1021/acs.nanolett.8b02584https://doi.org/10.1002/adfm.201804235https://doi.org/10.1016/j.jcrysgro.2006.12.061[13] Li Y, Garnier V, Steyer P, Journet C andToury B 2020Millimeter-Scale hexagonal boron nitride single crystals for nanosheetgenerationACSAppl. NanoMater 3 1508[14] Frenkel J 1938OnPre-BreakdownPhenomena in Insulators and Electronic Semi-Conductors Phys. Rev. 54 647[15] Sze SMandNgK2007Physics of Semiconductor Devices III edn (NewYork:Wiley) Section 6.7.2[16] Sze SM1967Current transport andmaximumdielectric strength of silicon nitride films J. Appl. Phys. 38 2951[17] HarrellWR and Frey J 1999Observation of Poole Frenkel effect saturation in SiO2 and other insulating filmsThin Solid Films 352 195[18] Maestre C et al 2022 From the synthesis of hBN crystals to their use as nanosheets for optoelectronic devices 2DMaterials 1 1 in press[19] YangW et al 2018A graphene Zener-Klein transistor cooled by a hyperbolic substrateNatureNanotechnol. 13 47[20] Baudin E, VoisinC and Plaçais B 2019Hyperbolic phonon polariton electroluminescence as an electronic cooling pathwayAdv. Funct.Mater. 30 1904783[21] GraefH et al 2018Ultra-longwavelengthDirac plasmons in graphene capacitors J. Phys.Mater. 1 01LT02[22] Pallecchi E, Betz AC, Chaste J, FèveG,Huard B, Kontos T, Berroir J-M and Plaçais B 2011Transport scattering time probed through rfadmittance of a graphene capacitor Phys. Rev.B 83 125408[23] OhbaN,MiwaK,NagasakoN and FukumotoA 2001 First-principles study on structural, dielectric, and dynamical properties for threeBNpolytypes Phys. Rev.B 63 115207[24] Segura A, Artus L, CuscoR, Taniguchi T, Cassabois G andGil B 2018Natural optical anisotropy of h-BN:Highest giant birefringence ina bulk crystal through themid-infrared to ultraviolet range Phys. Rev.Mat.B 2 024001[25] KrickDT, Lenahan PMandKanicki J 1988Nature of the dominant deep trap in amorphous silicon nitridePhys. Rev.B 38 82266Mater. Res. Express 9 (2022) 065901 APierret et alhttps://doi.org/10.1021/acsanm.9b02315https://doi.org/10.1103/PhysRev.54.647https://doi.org/10.1063/1.1710030https://doi.org/10.1016/S0040-6090(99)00344-2https://doi.org/10.1088/2053-1583/ac6c31https://doi.org/10.1038/s41565-017-0007-9https://doi.org/10.1002/adfm.201904783https://doi.org/10.1088/2515-7639/aadd8chttps://doi.org/10.1103/PhysRevB.83.125408https://doi.org/10.1103/PhysRevB.63.115207https://doi.org/10.1103/PhysRevMaterials.2.024001https://doi.org/10.1103/PhysRevB.38.8226 1. Introduction 2. Capacitor fabrication and setup 3. Dielectric constant 4. Breakdown current and conductivity 5. Conclusion Acknowledgments Data availability statement References