High-κ KBe_2BO_3F_2 dielectric material with wide bandgap for two-dimensional electronics

Domain: physics
Published: 2026-03-23
Editorial outcome: minor_revision

Abstract
Further transistor scaling requires gate dielectric materials with both high dielectric constant and wide bandgap to improve gate control and suppress leakage current. However, these two properties typically exhibit an inverse relationship, making it challenging to simultaneously optimize both. Here, we report the exfoliation of KBe2BO3F2 (KBBF) dielectric nanosheets that overcome this trade-off. The material possesses a wide band gap exceeding 8 eV and a bulk dielectric constant of 63. Such dielectric properties give rise to a low leakage current of 10−6 A cm−2 at an equivalent oxide thickness of 0.62 nm and a high gate voltage of 15 V, and is predicted to work stably for 10 years at 6.6 V. 2D MoS2 transistors gated by KBBF show a subthreshold swing of 60 mV dec−1, reaching the theoretical limit at room temperature, and an on/off ratio up to 109. Moreover, the good electrostatic controllability of KBBF enables the fabrication of short-channel devices and inverter circuits. Our research broadens the scope of dielectrics and provides promising opportunities for the development of low-power 2D electronics and integrated circuits.

Introduction
The down scaling of field-effect transistor (FET) dimensions has been continuously driven the development of integrated circuits1-3. However, as the complexity of the process increases and the limit of minimum size is approached, the increase in leakage current and subthreshold swing (SS) caused by short-channel effects leads to a significant rise in device power consumption4-7. Therefore, there is an urgent need to develop new gate dielectric materials that are capable of enhancing gate control and suppress the short-channel effects8,9.

Ideal dielectrics should possess a high dielectric constant (κ) and a wide bandgap (Eg)10,11. On the one hand, a high-κ value can offer a larger gate capacitance, thus enhance gate control ability, lower the operating voltage and dynamic power consumption of the device. On the other hand, a wide bandgap can provide sufficient band offset to reduce leakage current, thereby increasing the current on/off ratio and reducing the static power consumption of the device12-14. Nevertheless, achieving both a high-κ and a wide bandgap in one dielectric remains challenging. In typical inorganic dielectrics, the dielectric constant and bandgap often exhibit an inverse relationship, such as SiO2 (κ~3.9, Eg~9 eV) and TiO2 (κ~80, Eg~3.4 eV)5,15,16. This is mainly because the electronic contribution to the dielectric constant has a prominent inverse relationship with the bandgap.

Therefore, to obtain a high dielectric constant while maintaining a wide bandgap, one needs to focus on the ionic contribution to the dielectric constant, which is related to the bond strength of the material17,18. Therefore, developing materials composed of elements with large electronegativity differences, small atomic sizes, and short bond lengths is an effective strategy for achieving dielectrics with both high-κ value and wide bandgap.

In this work, we report a dielectric of KBe2BO3F2 (KBBF), which exhibits both a high bulk dielectric constant (63) and a wide bandgap (>8 eV). Among its constituent elements, fluorine has the highest electronegativity and the smallest ionic size among all anions. Additionally, KBBF features short chemical bond lengths, providing a foundation for its high dielectric constant and wide bandgap. As a result, KBBF demonstrates an low leakage current (<10−6 A cm−2) at an equivalent oxide thickness (EOT) of 0.62 nm and a high gate voltage of 15 V, and is predicted to work stably for 10 years at 6.6 V. The inert fluorine atom-terminated surface of KBBF enables its integration with two-dimensional (2D) semiconductors via van der Waals (vdW) forces19-21, creating high-quality dielectric/channel interfaces. MoS2 FETs gated by KBBF exhibit a maximum on/off current ratio exceeding 109, an ultimate SS of 60 mV dec−1. Additionally, we utilize KBBF to fabricate high-gain inverters, demonstrating its potential in advanced integrated circuit applications.

Results
Preparation and structure of KBBF thin layer
Unlike other typical 2D vdW materials, KBBF crystal features of a six-membered ring network structure of Be2BO3F2 and K ions distributed between the layers. The sharp X-ray diffraction (XRD) peaks confirm the high crystallinity of our KBBF crystal with a lattice parameter of a=b=4.427 Å and c=18.744 Å (Supplementary Fig. 1). To integrate the 2D dielectric KBBF with 2D channel materials, we prepared KBBF thin layers via mechanical exfoliation from the bulk crystal using Scotch tape, as illustrated in Fig. 1a. For more efficient preparation, we employed the sliding layer method22. For brief, a few KBBF crystals were sandwiched between two pieces of weighing paper and a plastic rod was then rolled gently in one direction on the surface to apply a shear force on the crystals, causing sliding between adjacent layers and enhancing exfoliation. This method enables the preparation of KBBF thin layers with varying thicknesses (Supplementary Fig. 2), and the great surface uniformity of KBBF was also demonstrated by the scanning electron microscope (SEM) image and energy dispersive spectroscopy (EDS) mapping of K and F elements (Supplementary Fig. 3).

The optical microscopy (OM) and atomic force microscopy (AFM) images in Fig. 1b reveal that the as-exfoliated KBBF thin layer has a smooth and uniform surface, with a minimum thickness of 2 nm, corresponding to around three atomic layers of the KBBF crystal. High-resolution transmission electron microscopy (HRTEM) image and selected-area electron diffraction (SAED) pattern demonstrate the high-quality single-crystal nature of the KBBF, with very limited defects in the probed areas, which is also demonstrated by the EDS mapping (Fig. 1c and Supplementary Fig. 4). The interplanar spacing of the periodic atomic distribution d = 2.21 Å, consistent with (-120) the unit cell parameters of KBBF. Cross-sectional TEM images, obtained cutting the sample with a focused-ion beam, reveal that both the KBBF dielectric and the underlying MoS2 channel show typical layered structures with clean and flat surfaces. The flat and clear interface demonstrates that the integration process does not damage the structure of 2D materials, which is crucial for effective gate control and device performance. Additionally, an identified vdW gap between the KBBF and MoS2 will reduce the tunneling probability of charge carriers and help minimize the gate leakage current (Fig. 1d and e). The electron energy loss spectroscopy (EELS) mapping in Fig. 1f confirms the uniform distribution of the characteristic elements in each layer, aligning well with the stacked two-layer materials.

Dielectric properties of ultrathin KBBF
For investigating the dielectric properties of KBBF thin layer, we fabricated the metal–insulator–metal (MIM) parallel-plate capacitor. In this structure, the KBBF layer is sandwiched by an Au-coated SiO2/Si substrate and a top Au electrode (Fig. 2a and b). Fig. 2c presents that the measured capacitance density remain stable with changes in voltage and frequency, indicating that there are almost no deep-level impurities and structural defects in the crystal and the potential of KBBF for high-frequency applications. The specific capacitance–voltage (C–V) and capacitance–frequency (C–f) curves of KBBF with different thickness was shown in Supplementary Fig. 5. According to the test results, the dielectric constant value ε of KBBF can be calculated by the formula: ε = Ct/Aε0, where C, t and A are the capacitance, thickness and effective area of the KBBF, respectively, and ε0 is the vacuum dielectric constant. The thickness dependence of dielectric constant obtained from calculations were shown in Fig. 2d. It can be seen that the KBBF with a thickness of 12 nm has a high dielectric constant of 26.5, and the relationship between the dielectric constant and thickness aligns well with the dead layer model in high-κ capacitors23,24. While there is still debate about whether there is a thickness-related suppression of the dielectric constant on the surface of high-κ dielectric materials, the presence of a low interfacial capacitance region, commonly referred to as the dead layer between the electrode and the dielectric material, which is in series with the bulk capacitance, reduces the overall capacitance and leads to a decrease in the effective dielectric constant (Supplementary Fig. 6a). The fitting of the dead layer model can be performed according to formula: t/ε = t/εbulk + D, where εbulk is the bulk constant of the dielectric material, and D is a constant related to the interfacial dead layer. According to the fitting results, εbulk ≈ 63 and D ≈ 0.353 can be extracted, indicating that KBBF has excellent quality and the characteristic of a high dielectric constant (Supplementary Fig. 6b).

In addition, considering the presence of vdW gap between the electrode and KBBF, the experimentally measured capacitance incorporates the contribution from the vdW gap. We have therefore attempted to deduct this specific capacitance component, as shown in Supplementary Fig. 7. Based on the calculation formula for series capacitance, we established a functional relationship between the measured capacitance and KBBF thickness. The fitting results indicate that, after excluding the capacitance contribution of the vdW gap, the dielectric constant of KBBF is determined to be 63, with the thickness of vdW gap measured at 0.353 nm. This result is consistent with the fitting outcome derived from the dead layer model, which verifies that the dead layer in this work originates from the vdW gap between the electrode and KBBF, and that the intrinsic dielectric constant of KBBF is 63. The EOT of KBBF with different thicknesses were shown in Fig. 2d. Due to the large dielectric constant, the minimum measured EOT can be calculated as 0.25 nm (t=4 nm) according to the formula EOT=3.9t/εKBBF.

An ideal gate dielectric must possess a wide bandgap to guarantee a sufficiently high energy barrier, thereby reducing leakage current to negligible levels. We calculated the bandgap of KBBF to be 8.03 eV using the HSE06 functional within the framework of density functional theory (DFT) (see Methods for detailed computational details), which is consistent with literature reports (~8.31 eV)25. Generally, a large band gap will cause a low electronic contribution to the dielectric constant, thus making the band gap inversely proportional to the dielectric constant, as shown in Fig. 2f. However, KBBF simultaneously exhibits the characteristics of high dielectric constant and wide band gap. This is mainly due to its large atomic electronegativity difference and small chemical bond length, which enhances the ionic contribution in the dielectric constant (Supplementary Fig. 8 and 9).

The wide bandgap and high crystal quality make KBBF have an enhanced EBD and reduced leakage current (Jleak), which are critical parameters of advanced FETs to improve reliability and reduce power consumption. To describe the breakdown characteristics of the KBBF more accurately, we conducted a systematic ramped voltage stress (RVS) test, which is a well-known method for evaluating the breakdown properties of dielectric materials39. Supplementary Fig. 10 presents the statistical results of the EBD of KBBF with different thicknesses (5-30 nm) under varying temperatures (150-350 K) and sweep rates (0.1-1 V s−1). It can be observed from the figure that the EBD of KBBF decreases slightly with increasing temperature and decreasing sweep rate. This phenomenon is mainly attributed to two factors: on one hand, the efficiency of electron energy accumulation in the material improves with rising temperature, making it easier to form breakdown paths; on the other hand, a slower sweep rate allows more time for charge injection, defect activation, or thermal accumulation to occur, thereby reducing the breakdown threshold. For the sample with a thickness of approximately 5 nm, it exhibits an EBD of about 28.4 MV cm−1 at a temperature of 150 K and a sweep rate of 1 V s−1. Even at room temperature, its EBD still exceeds 26 MV cm−1, which is more than four times that of the breakdown field strengths of SrTiO3 and SiO2 reported in the literature24,40. In addition, the measured leakage current of KBBF remains below 10−6 A cm−2 before the breakdown occurs, far below the low-power limit (1.5 × 10−2 A cm−2) and standard complementary metal–oxide–semiconductor (CMOS) gate limit (10 A cm−2) even when the EOT is less than 1 nm41. Furthermore, we evaluated the electrical reliability of KBBF by measuring the time to device failure under constant voltage stress, a characteristic metric defined as time-dependent dielectric breakdown (TDDB). Fig. 2g summarizes the stress-dependent leakage current breakdown transients of a 10 nm-thick KBBF nanosheet under various test voltages. Data fitting further predicts that the nanosheet can achieve a 10-year long-term lifetime at an operational voltage of 6.6 V. Compared with the reported dielectric materials applied in state-of-art silicon and 2D semiconductor technologies, the KBBF crystals demonstrate the high breakdown strength at different dielectric constant (Supplementary Fig. 11)7,9,10,12,13,15,24,26,29-33,35,37,38,42-45. The key features of the gate insulator, namely bandgap, dielectric constant and EBD, are summarized in Supplementary Table 1. It should be noted that Be is slightly toxic. Materials with the same structure but free of Be can also be explored as dielectric materials. However, the excellent dielectric properties and electrical stability of KBBF still make it a highly promising insulating material for high-performance 2D devices.

High-performance 2D FETs with KBBF dielectrics
To assess the electrostatic control capability of KBBF in 2D electronic devices, we integrate the KBBF thin layer onto 2D semiconductors to construct the top-gated 2D FETs and evaluate their device performance. In these FETs (Fig. 3a), MoS2 serves as the channel material, Bi/Au electrode were used to minimize contact resistance46, and the KBBF layer was positioned above the MoS2 as the gate dielectric (see Methods for details), the OM picture of the prepared FET was shown in Fig. 3b. For the dielectric and semiconductor stacks, band alignment is crucial for achieving small SS, minimal leakage current, and enhanced electrical stability in FETs. According to DFT calculations and ultraviolet photo-electron spectroscopy (UPS) measurements, ultrathin KBBF nanosheets have a wide bandgap of up to 8.03 eV, much larger than that of monolayer MoS2 (~1.78 eV). This substantial difference creates pronounced energy band offsets between the KBBF dielectric and the MoS2 channel, with offsets of 3.57 eV for the conduction band minimum and 2.61 eV for the valence band maximum (Fig. 3c and Supplementary Fig. 12). These values far exceed the threshold (> 1 eV) required for high-quality gate dielectrics, thereby effectively preventing electrons or holes from tunneling through the dielectric via direct tunneling or FN tunneling to induce substantial leakage current, which contributes to the development of low-power-consumption and high-performance devices12,47,48.

The typical transfer characteristics curves of KBBF/MoS2 FETs at room temperature and a sweep rate of 1 V s−1 were depicted in Fig. 3e, showcasing a remarkable on/off current ratio exceeding 109 and a low gate leakage current. The ideal heterointerface, characterized by minimal defects, enables the device to achieve good performance with a small hysteresis. We performed transfer characteristic measurements on the devices at different sweep rates and temperatures, and extracted the corresponding hysteresis widths, as shown in Supplementary Fig. 13. It can be observed that the devices exhibit excellent switching characteristics under all tested conditions. The hysteresis width increases slightly with the rise in temperature and the decrease in sweep rate, the maximum hysteresis is 35 mV and 12 mV at sweep rates of 0.1 V s−1 and 1 V s−1 at room temperature, respectively. More importantly, the channel current exhibits a sharp rise with a low threshold slope of 60 mV dec−1, we can identify that the SS can remain close to the Boltzmann thermionic limit over three orders of magnitude (Fig. 3f). To verify the reliability of KBBF as the dielectric, we fabricated ten FETs with the same procedure. The specific transfer characteristic curves of ten MoS2 FETs were shown in Supplementary Fig. 14, and all the devices exhibit excellent on/off characteristics and low gate leakage current. Fig. 3g summarizes the SS, on/off ratio, and hysteresis of all devices. It can be seen that most devices are located within the region of low SS and low hysteresis, the average SS, on/off ratio, and hysteresis are 64.5 mV dec−1, 4×108, and 9.1 mV, respectively. This performance highlights the good electrostatic control and interface quality of the KBBF dielectric. Supplementary Fig. 15 illustrates the output characteristics curves of the device. The linear behavior of Ids−Vds curves at low bias confirms the Ohmic contact and effective current control. The electrical performance of the device can be further modulated through dual-gate operation. When a back-gate voltage is applied, the channel region not dominated by the top gate is activated, leading to a significant increase in channel current and a leftward shift in the threshold voltage (Fig. 3h). In addition, the maximum output current of the FET is enhanced by threefold with the incorporation of the back gate (Fig. 3i).

The performance of 2D semiconductors with atomic-scale thickness is highly sensitive to interface defects. These defects can capture charges during device operation, resulting in increased SS, pronounced hysteresis, and threshold voltage shift11. It is worth noting that the high crystal quality in single-crystalline KBBF minimizes charge trapping events. The calculated density of states (DOS) for pristine monolayer MoS2 and the KBBF/MoS2 heterostructure (Fig. 3d) demonstrates that KBBF integration on the MoS2 surface is devoid of defect-related gap states within the MoS2 electronic structure. The interface state density (Dit) at the KBBF/MoS2 heterointerface can be calculated from
Dit = Ci( q∙SS / kTln10 - 1) (1)
where Ci is the capacitance of top-gate dielectrics, q signifies the electron charge, k is the Boltzmann constant and T represents the test temperature. A remarkably low Dit ≈5.5×1010 cm−2 eV−1 can be obtained, indicating its advantage over previously reported MoS2 FETs with high-κ gate dielectrics. In addition, since K+ ions are located between the layers, any migration behavior of these ions would also affect the device performance. We calculated the migration energy barriers of K+ ions for both intralayer and interlayer migration. As shown in Supplementary Fig. 16, the maximum intralayer migration energy barrier of K+ ions is 1.1 eV, while the interlayer migration energy barrier for K+ ions passing through the Be2BO3 layer reaches 6.8 eV. These results indicate the absence of ionic migration behavior in KBBF, which is also one of the reasons for its small hysteresis.

These results demonstrate that our devices exhibit excellent performance in terms of SS, on/off ratio, hysteresis and Dit. To further highlight the advantages of the KBBF dielectric layer, we have also summarized key parameters of state-of-the-art 2D transistors, such as dielectric constant, Ebd, on/off ratio, SS and hysteresis, as presented in Supplementary Table 1. Furthermore, we also conducted tests on the stability of the device. As shown in Supplementary Fig. 17, our FETs demonstrate excellent air environmental stability over a six-month period, underscoring the durability of the KBBF dielectric layer. Bias temperature instability (BTI) measurements serve as a complementary for evaluating the reliability of transistors. By applying a gate voltage stress of -2 V for different durations to the devices with an EOT of 0.9 nm at 350 K, we characterized the shift in their threshold voltage. It can be seen that although the traps present in the KBBF dielectric may alter the charge state of the devices under negative gate voltage, the threshold voltage of the MoS2 FETs exhibits only a slight variation with gate-biasing time (Fig. 3j). To evaluate the operational stability of the devices, we conducted continuous on/off switching tests. As shown in Supplementary Fig. 18, the devices maintained stable performance over 1000 switching cycles at Vtg = ±2 V and Vds = 50/500 mV. These findings suggest that the transistors with KBBF dielectrics exhibit excellent stability and reliability, which may enable them to play a pivotal role in the development of next-generation 2D devices.

Shorter channel FETs and logic inverter
Although the top-gated FETs with KBBF dielectrics exhibit excellent performance in terms of on/off ratio and SS, the on-state current is still limited by the relatively long channel length and the partial control over the channel semiconductor from the local top gate. Therefore, we fabricated short-channel MoS2 FETs with a back-gate configuration using ultrathin KBBF dielectrics. The FETs with different channel length (40, 80, and 200 nm) were integrated by graphene gate, MoS2 channel and KBBF gate dielectrics. The SEM image of the FET was shown in Supplementary Fig. 19a and the specific preparation process was depicted in Supplementary Fig. 20. The shorter channel MoS2 FETs gated by KBBF dielectrics (EOT=1.7 nm) exhibit great switching characteristics at different channel lengths (Supplementary Fig. 19b). An excellent on/off ratio of over 1010 and a small SS of 80 mV dec−1 was obtained for the 80 nm short channel device (Fig.4b). The corresponding output characteristic curves also confirms the promising on-state current over 400 μA μm−1 due to the reduction in channel length and excellent electrostatic control of the gate insulator (Fig.4c). With the decrease of the channel length, drain-induced barrier lowering (DIBL) becomes predominant for the device performance12. The use of an ultrathin KBBF insulator allows for better channel control, thereby mitigating the DIBL in short channel devices, which can be calculated to be as low as 96 mV V−1 for devices with 80 nm channel lengths.

To assess the performance of our KBBF dielectrics in functional devices, a logic inverter (NOT gate) was constructed using a top-gated configuration (Fig. 4d and Supplementary Fig. 21). Thanks to the superior gate modulation properties of KBBF/MoS2 FETs, the transfer characteristics of inverter exhibit a rapid state transition within a specific voltage range, resulting in a large voltage gain of approximately 29 at Vdd = 2 V (Fig. 4e and f). It is worth noting that even if the Vdd is reduced to 0.1 V, the inverter retains its ability to perform logical inversion. The combination of high voltage gain and compatibility with low operating voltages makes KBBF-based inverters highly promising for integration into high-density, low-power logic circuits.

Methods
Growth of crystalline KBBF
The KBBF crystals were synthesized in two steps, mainly following the procedures described in previous references49,50. First, polycrystalline KBBF was prepared via a conventional solid-state reaction according to the following equation:
6BeO + 3KBF4 + B2O3 → KBe2BO3F2 + BF3 ↑
Stoichiometric amounts of BeO (purity 99.9%), KBF4 (purity 99%), and B2O3 (purity 99.99%) were thoroughly mixed and placed in a platinum crucible. The mixture was heated above 700 oC and maintained at this temperature for 48 h to obtain polycrystalline KBBF. Subsequently, single crystals of KBBF were grown by the flux method using KF-B2O3 as the flux. An appropriate mixture of the KBBF polycrystalline powder and the flux was charged into a platinum crucible, heated to 800 oC, and held for 48 h. The melt was then cooled to 750 oC at a rate of 10 oC h⁻1, followed by slow cooling to 630 oC at 3 oC day⁻1. Afterward, the temperature was lowered to room temperature within two days. The as-grown KBBF crystals were obtained by dissolving the remaining flux in dilute acid.

Preparation of ultrathin KBBF nanosheets
Thinner KBBF nanosheets were obtained by mechanically exfoliating the bulk crystal using Scotch tape after layer sliding, and then using polydimethylsiloxane (PDMS) as an intermediate carrier and with the help of a transfer platform to transfer it onto the target substrates22. In a typical process, a few KBBF crystals were sandwiched between two pieces of weighing paper and a plastic rod was then rolled gently in one direction on the surface to apply a shear force on the crystals, causing sliding between adjacent layers. A certain amount of the treated KBBF crystals was then cleaved repeatedly using Scotch tape.

Materials characterization
The morphological characterization and thickness measurement of exfoliated KBBF nanosheets were performed by an optical microscope (BX51, Olympus) and AFM (Dimension Icon, Bruker). The XRD (D2 PHASER, Bruker) was carried out to determine the crystal structure of bulk KBBF. HRTEM images were characterized using an aberration-corrected TEM (JEM-ARM200F, JEOL) operated at 200 kV. UPS was obtained from AXIS SUPPRA using a helium lamp source emitting.

Dielectric properties measurements
The dielectric properties of KBBF were measured in the metal–insulator–metal device. The bottom electrodes (10/40 nm Cr/Au) were first patterned onto the SiO2/Si substrate by the electron-beam lithography (EBL, ELPHY Plus, Raith GmbH) and electron-beam evaporation (Nexdep, Angstrom Engineering). KBBF nanosheets were then transferred onto the bottom electrode using PDMS on an optical transfer platform. Top electrodes were finally patterned with the same procedure. The current versus voltage curve and capacitance measurements were conducted using a Keithley B1500A semiconductor characterization system.

Computation details
The calculations of bandgap and DOS were conducted using the Vienna Ab initio Simulation Package (VASP)51. The projected augmented wave (PAW) method was employed to describe the ion-electron interactions, with a plane-wave basis set cutoff energy set to 520 eV52. The generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional was utilized53, along with hybrid functional calculations based on the Heyd-Scuseria-Ernzerhof (HSE06) parameters54,55. Specifically, the HSE06 functional was utilized to yield a precise bandgap value for bulk KBBF. A gamma-centered k-point sampling grid for Brillouin zone integration are generated by VASPKIT with a resolution of 0.0456. The convergence thresholds for total energy and atomic forces were set to 10−5 eV and 2×10−2 eV Å⁻1, respectively. The DFT-D3 dispersion correction method developed by Grimme, was included to account for van der Waals interactions57.
The calculations of dielectric constant and ionic migration were performed using the PAW method, as implemented in the VASP 6.4.3 code65. A plane-wave energy cutoff of 520 eV and the semilocal PBE functional were employed throughout all calculations60. The Brillouin zones were sampled using Γ-centered k-meshes with a k-spacing of 0.2 Å−1. The structures were fully relaxed until the total force on each atom was less than 0.01 eV Å−1. The ionic and electronic components of the material’s dielectric constant were acquired via the Density Functional Perturbation Theory (DFPT) approach and the frequency-dependent linear response method, respectively. Specifically, the electronic component of the dielectric constant was calculated using the HSE06 hybrid functional61, 62. Additionally, the ionic migration energy barrier was determined using the Climbing Image Nudged Elastic Band (CINEB) method66, 67 .

Device fabrication and electrical measurements
First, monolayer or few–layer MoS2 flakes were obtained with mechanical exfoliation onto the SiO2/Si substrate. Bi/Au (10/50 nm) electrodes were patterned using EBL followed by deposition of metal. After lift-off of metal in acetone, the KBBF nanosheet was transferred onto the MoS2 channel using PDMS films and a gate electrode was fabricated onto the KBBF nanosheet. The short-channel device was prepared by using few–layer graphene as gate electrodes, and then successively transferring KBBF and MoS2 as the dielectric and channel material. Electrical characterization of the devices was performed using a Keithley 4200 semiconductor parameter analyser. All measurements were carried out under the high vacuum (10⁻6 torr) condition to reduce the gas adsorption on device surface.

Data availability
Relevant data supporting the key findings of this study are available within the article and the Supplementary Information file. All raw data generated during the current study are available from the corresponding authors upon request.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This is a very nice manuscript introducing KBBF for its use as a high-quality gate dielectric for 2D transistors. The work is very thorough and I only have a few suggestions.\nIn general, the authors mention a dielectric constant of 26.5, which is, as discussed, thickness dependent. Contrary to most manuscripts, where just a single thickness and dielectric constant is investigated, the authors do it properly anyway and do study the thickness dependence, so I would update the text accordingly. One option would be to mention the bulk value together with say a value at an EOT of 1nm, or, even better, 0.5nm?\nSimilarly for the leakage currents, where 1e-6 A/cm^2 is mentioned. How about reporting this leakage current for relevant values, e.g. according to the IRDS at an EOT of 0.5nm of 1nm for VG=0.6V (or the corresponding overdrive, depending on what node is chosen)\nThe only technical criticism I would have is the breakdown field. While unfortunately most manuscripts treat the problem similarly, this is still not correct, please see Ernest Wu, IRPS 25 for a thorough discussion. In a RVS setting, breakdown depends on the sweep rate and the temperature and is a statistical quantity. I would suggest the authors try to update the manuscript accordingly. I understand that all devices are manually fabricated and large statistics thus impossible, but I would still suggest to attempt it.\n> Therefore, to obtain a high dielectric constant while maintaining a wide bandgap, one needs to focus on the ionic contribution\nThe problem here would be that the larger the ionic contribution, the large the susceptibility to dead layer effects, so a sweet spot seems to be required.\nI understand this is the first time KBBF is used for devices and the authors use exfoliation. Could they speculate on some possible fab-compatible growth methods? In the Methods section there is only a single sentence on how the crystals were grown, please expand significantly. What precursors, substrates, temperatures, etc.?\n> equivalent capacitance thickness\nThe conventional term is \"capacitance equivalent thickness (CET)\"\n> Due to the large dielectric constant, the minimum measured EOT is 0.74 nm, and even smaller EOT can be obtained\nHow small can you go? This does not appear to be consistent throughout the manuscript. What is the minimum thickness where KBBF is still KBBF?\n> Generally, the dielectric constant of dielectrics\nlike the authors said themselves, it's the electronic contribution ...\n> However, KBBF simultaneously exhibits the characteristics\nDoes KBBF fall into the fluoride category? This inverse relationship is even better fulfilled if materials are put into different categories, see e.g. Fig.3 in [17]. Fluorides stand out as they can have very large bandgaps despite having a large permittivity, so KBBF seems to fit this pattern?\n> Fig. 3c\nThe inset should use a log-x scale (same for SI Fig. 5, lower row)\n> Fig. 3d\nWhy is the 6nm data not shown? What about the 4nm device from the SI? Same for Fig 5 in the SI, why is the thinnest 14nm?\nCould this be redone for devices rather than MIM structures? Device results would be much more relevant.\n> Fig. 3f\nWouldn't it be better to show this for the corresponding material class, e.g. fluorides?\nAlso, these values are bulk dielectric constants, the authors seem to show 5 values for KBBF, but these are contaminated by dead-layer effects.\n> Fig. 3g\nThis is too simplistic, please do this statistically and for different sweep rates, as discussed above\n> which is 4.5 times higher than that of the perovskite SrTiO3 dielectrics reported in the literature\nWhy compare to STO? Why not to SiO2?\n> ultrathin KBBF crystals demonstrate the highest breakdown strength at different dielectric\nPlease do this properly\n> These values exceed the threshold (>1 eV) required for effective gate dielectrics, thereby facilitating the development of devices with low leakage current and superior reliability12\nHere the Robertson papers should be cited.\n> with a hysteresis width ΔVg as low as 1.6 mV\nThis is also somewhat meaningless, please analyse hysteresis for different sweep rates and temperatures, see e.g. Knobloch IEDM 23\n> capture charges during device working\ndevice operation?\n> performance instability primarily arises from intrinsic defects within the MoS2 channel itself.\nHow can this be demonstrated? Channel defects are typically very very fast and only impact SS and not hysteresis. So maybe there are still plenty of defects in KBBF?\n> The FETs with different channel length (40, 80, and 200 nm) were integrated by graphene gate, MoS2 channel and KBBF gate dielectrics\nWhat EOT?\n> To assess the practicability of our KBBF\nthe performance?\n> and excellent electrical reliability\nthe reliability was not really assessed. BTI?\n> which takes about two months\nReally? Two months? Not overly convenient for fabrication?\n> and then transferring it to the target substrate\nHow? PMMA? PDMS?\n> Supplementary Fig. 10 | Reliability of KBBF\nThis is (short term) stability rather than long-term reliability\n> Supplementary Fig. 13 | Long-term stability. Transfer characteristic curves of our top-gated MoS2 FET, presenting an excellent stability after six-month storage.\nHow stored? Vacuum? Desiccator? Air? Unbiased?\n> Supplementary Fig. 14\nThe 200nm device seems to have a positive Vth, while all other devices shown have a negative one? Ideas?", "reviewer_2": "In this manuscript, the authors report a new 2D dielectric material KBe2BO3F2, which has a high dielectric constant and large bandgap achieving ultralow leakage current and the highest breakdown field strength. They also perform the transport test of MoS2 transistors gated by KBBF showing a very small subthreshold swing and a high on/off current ratio. This work provides a new high-performance dielectric material for the development of electronic devices. Overall, I consider this work suitable for publication in Nature Communications.\nNevertheless, I would appreciate clarification on a few points:\n1. It is well-known that the large-scale and controllable synthesis of dielectric materials is crucial for their application in integrated circuits. The KBe₂BO₃F₂ material investigated in this work is currently prepared using mechanical exfoliation, which poses limitations for practical applications. Have the authors considered employing epitaxial growth or other scalable preparation methods to directly achieve high-quality thin layers on substrates? A discussion on the large-scale synthesis pathway for this material would significantly enhance its application potential.\n2. According to the crystal structure provided by the authors, K⁺ ions are located in the interlayer spaces. An important concern is whether these K⁺ ions might migrate under applied gate voltage, particularly posing a risk of intercalation into the MoS₂ channel layer. If ion migration does occur, how might it affect the material's dielectric constant (possibly originating from ionic polarization contributions) and device stability? It is recommended that the authors discuss this aspect through electrical characterization or theoretical calculations.\n3. KBe₂BO₃F₂ exhibits a high dielectric constant and wide bandgap simultaneously, as it contrasts with the general trend observed in conventional dielectric materials. The authors attribute this to the large atomic electronegativity difference and short chemical bond lengths, which is a reasonable explanation. However, providing deeper theoretical evidence—such as quantitative first-principles calculations of the contribution of ionic polarization to the dielectric constant, or a comparative analysis of bond lengths and electronegativity parameters with other known dielectric materials—would strengthen the argument.\n4. The authors' validation of the device-to-device reproducibility and environmental stability of the transistors is commendable. Beyond these, the operational stability of transistors is also a critical metric for practical applications. Including such data would offer a more comprehensive assessment of device reliability.\n5. The demonstration of a logic inverter based on KBe₂BO₃F₂ dielectric highlights its potential for practical applications, which is a valuable extension of the work. However, as previously noted, the practical adoption of this material largely depends on its compatibility with existing semiconductor manufacturing processes, specifically the ability to achieve large-area, uniform, and low-cost synthesis. It is recommended that the authors explore epitaxial growth or large-area thin-film synthesis routes for this material in future studies, which would greatly enhance the completeness and impact of this work.", "reviewer_3": "The manuscript by Xu et al. reported a van der Waals dielectric material KBBF with both high dielectric constant and wide bandgap.Its properties as a dielectric material were systematically studied and its application in 2D electronics and the corresponding performance were well demonstrated, showing good results. The choice of the material based on electronegativity, atomic size and bond length can be a good reference for new dielectric material exploration in the future.Therefore, I think the manuscript can meet the standard of Nature Communications and recommend publication after revision.\n1.Are there other dielectric materials that may also accord with the rule based on the electronegativity, atomic size and bond length?\n2.The growth of KBBF crystal was not provided in detail. The authors should at least briefly describe the precursors and process they used.\n3.What were the typical thicknesses that were used in the transistors and what was the smallest thickness possible?\n4.SEM is known to reduce the contrast of small defects on the surface of matreials, so it may not be appropriate to describe the material has flat surface with SEM and EDS data. Uniformity can be shown instead.\n5.There are errors in the sentence \"The calculated density of states (DOS) of single MoS2 and KBBF/MoS2 heterostructure in Fig. 3d resolves the integration of KBBF on the surface of MoS2 does not introduce defect-related energy levels into MoS2.\""}, "author_response": "Responses to reviewers’ comments\nResponses to Reviewer #1\nGeneral Comments:\nThis is a very nice manuscript introducing KBBF for its use as a high-quality gate dielectric for 2D transistors. The work is very thorough and I only have a few suggestions.\nResponse: We appreciate the reviewer’s positive comments for our manuscript and the suggestions made for improving the quality of the article.\n1. In general, the authors mention a dielectric constant of 26.5, which is, as discussed, thickness dependent. Contrary to most manuscripts, where just a single thickness and dielectric constant is investigated, the authors do it properly anyway and do study the thickness dependence, so I would update the text accordingly. One option would be to mention the bulk value together with say a value at an EOT of 1 nm, or, even better, 0.5 nm?\nResponse: In accordance with the suggestions, we have added discussions on the bulk dielectric constant and the corresponding EOT in both the abstract and the main text.\nThe bulk dielectric constant, extracted by fitting the “dead-layer model”, is 63, and the minimum measured EOT is 0.25 nm. The revised content is as follows:\n“Here, we report a KBe BO F (KBBF) dielectric that overcomes this trade-off. It\n2 3 2\npossesses an ultrawide band gap exceeding 8 eV and a bulk dielectric constant of 63,\nwhile also exhibiting a high dielectric constant of 26.5 even at an ultrathin thickness.”\n“The fitting of the “dead layer” model can be performed according to formula: t/ε =\nt/ε + D, where ε is the bulk dielectric constant of the dielectric material, and D is\nbulk bulk\na constant related to the interfacial dead layer. According to the fitting results, ε ≈\nbulk\n63 and D ≈ 0.353 can be extracted, indicating that KBBF has excellent quality and the\ncharacteristic of an ultrahigh dielectric constant (Supplementary Fig. 6b). Due to the\nlarge dielectric constant, the minimum measured EOT can be calculated as 0.25 nm\n1\n(t=4 nm) according to the formula EOT=3.9t/ε , and even smaller EOT can be\nbulk\nobtained if the thickness is further reduced.”\n2. Similarly for the leakage currents, where 10-6 A/cm2 is mentioned. How about\nreporting this leakage current for relevant values, e.g. according to the IRDS at an EOT\nof 0.5 nm of 1 nm for V =0.6V (or the corresponding overdrive, depending on what\nG\nnode is chosen)\nResponse: According to the suggestion, we have added the relevant parameter values\nin the manuscript, including the EOT corresponding to the measured leakage current of\n10-6 A cm-2 and the comparison with commercial technical standards. The specific\nrevisions are as follows:\n“Such excellent dielectric properties give rise to an ultralow leakage current of 10−6 A\ncm−2 and a highest breakdown field strength of 26.8 MV cm−1 even when the equivalent\noxide thickness is less than 1 nm.”\n“In addition, the measured leakage current of KBBF remains below 10−6 A cm−2 before\nthe breakdown occurs, far below the low-power limit (1.5 × 10−2 A cm−2) and standard\ncomplementary metal–oxide–semiconductor (CMOS) gate limit (10 A cm−2) even when\nthe EOT is less than 1 nm.”\n3. The only technical criticism I would have is the breakdown field. While unfortunately\nmost manuscripts treat the problem similarly, this is still not correct, please see Ernest\nWu, IRPS 25 for a thorough discussion. In a RVS setting, breakdown depends on the\nsweep rate and the temperature and is a statistical quantity. I would suggest the authors\ntry to update the manuscript accordingly. I understand that all devices are manually\nfabricated and large statistics thus impossible, but I would still suggest to attempt it.\nResponse: Thanks for your comments. Following the suggestions, I have carefully\nreviewed the relevant literature. To describe the breakdown field strength of KBBF\nmore accurately, I conducted statistical analyses on the breakdown behavior of KBBF\nsamples with different thicknesses (5-30 nm) under varying temperatures (150-350 K)\nand different sweep rates (0.1-1 V s-1). The statistical results indicate that KBBF\nexhibits excellent breakdown resistance: its breakdown field strength decreases slightly\n2\nwith the increase of test temperature, while it increases slightly as the sweep rate rises.\nFor the sample with a thickness of approximately 5 nm, under the conditions of 150 K\nand a sweep rate of 1 V s-1, its breakdown field strength reaches about 28.4 MV cm-1,\nwhich is far superior to that of other dielectric materials reported so far. Relevant\ncontent has been revised in the manuscript, with specific revisions as follows:\n“To describe the breakdown characteristics of the KBBF more accurately, we conducted\na systematic ramped voltage stress (RVS) test, which is a well-known method for\nevaluating the breakdown properties of dielectric materials (Supplementary Fig. 9)37.\nFig. 2g presents the statistical results of the E of KBBF with different thicknesses (5-\nBD\n30 nm) under varying temperatures (150-350 K) and sweep rates (0.1-1 V s-1). It can\nbe observed from the figure that the E of KBBF decreases slightly with increasing\nBD\ntemperature and decreasing sweep rate. This phenomenon is mainly attributed to two\nfactors: on one hand, the efficiency of electron energy accumulation in the material\nimproves with rising temperature, making it easier to form breakdown paths; on the\nother hand, a slower sweep rate allows more time for charge injection, defect activation,\nor thermal accumulation to occur, thereby reducing the breakdown threshold. For the\nsample with a thickness of approximately 5 nm, it exhibits an E of about 28.4 MV cm-\nBD\n1 at a temperature of 150 K and a sweep rate of 1 V s-1. Even at room temperature, its\nE still exceeds 26 MV cm-1, which is more than four times that of the breakdown field\nBD\nstrengths of SrTiO and SiO reported in the literature21, 38.”\n3 2\nthickness under varying temperatures and sweep rates. Breakdown characteristics\nof (a) 5, (b) 10, (c) 20 and (d) 30 nm KBBF at different temperatures at sweep rate of\nKBBF at different sweep rates at room temperature.\nFig. 2 | Dielectric properties of KBBF thin layers. a, The structure diagram and b, a\nfalse-coloured SEM image of the MIM device. Scale bar, 5 μm. c, Voltage-dependent\ncapacitance density for MIM devices of 12 nm-thick KBBF layer at five different\nfrequencies. Inset, frequency-dependent capacitance density at four different voltages.\nd, Dielectric constant and CET as a function of various KBBF thickness measured from\nMIM capacitors. The gray line is the fitted curve according to the ‘dead layer’ model.\ne, Bandgap of KBBF obtained from DFT calculation. f, Bandgap versus dielectric\nconstant of typical dielectrics5, 9, 10, 12, 13, 15, 23-36. The dashed black line serves as a guide\nto illustrate the inverse proportionality between these two properties. g, Breakdown\ncharacteristics of KBBF with different thickness under varying temperatures (top) and\nsweep rates (bottom).\n4. Therefore, to obtain a high dielectric constant while maintaining a wide bandgap, one\n4\nneeds to focus on the ionic contribution. The problem here would be that the larger the\nionic contribution, the large the susceptibility to dead layer effects, so a sweet spot\nseems to be required.\nResponse: As pointed out by the reviewer, maximizing the contribution of ionic\npolarization is crucial for achieving a high dielectric constant while maintaining a wide\nband gap. However, the enhancement of ionic polarization is usually accompanied by\nan increased susceptibility of the material to the dead-layer effect. Therefore, it is an\nessential approach to minimize the dead-layer effect while preserving a high ionic\npolarization contribution. The dead-layer effect originates from the interfacial charge\naccumulation in the dielectric layer, which is associated with issues such as lattice\nmismatch or chemical bonding disorder between the dielectric and the electrodes.\nCurrently, the main strategies for mitigating the dead-layer effect include using metal\nelectrodes with low chemical activity (e.g., Pt, Au) to enhance electron shielding\n(Nature 2006, 443, 679-682), and inserting buffer layers at the interface to achieve\nstrain modulation (ACS Appl. Mater. Interfaces 2022, 14, 39673-39678). In our\ncapacitance measurements of KBBF, Au electrodes with low chemical activity were\nadopted, which also mitigated the dead-layer effect to a certain extent.\n5. I understand this is the first time KBBF is used for devices and the authors use\nexfoliation. Could they speculate on some possible fab-compatible growth methods? In\nthe Methods section there is only a single sentence on how the crystals were grown,\nplease expand significantly. What precursors, substrates, temperatures, etc.?\nResponse: At present, the primary preparation method for KBBF is the high-\ntemperature flux method, which enables the production of centimeter-scale single-\ncrystal samples. To obtain thin-layer samples, the as-grown single crystals can be\nthinned via slicing. Moreover, since KBBF single crystals are derived from their\npolycrystalline powders, it is hypothesized that wafer-scale fabrication of KBBF may\nbe achievable using thermal evaporation with polycrystalline KBBF powders as the\nevaporator source.\nIn addition, our description of the crystal growth section may have been overly brief,\n5\nso we have also supplemented this part. The specific growth method is as follows:\n“The KBBF crystals were synthesized in two steps, mainly following the procedures\ndescribed in previous references56, 57. First, polycrystalline KBBF was prepared via a\nconventional solid-state reaction according to the following equation:\n6BeO + 3KBF + B O → KBe BO F + BF ↑\n4 2 3 2 3 2 3\nStoichiometric amounts of BeO (purity 99.9%), KBF (purity 99%), and B O (purity\n4 2 3\n99.99%) were thoroughly mixed and placed in a platinum crucible. The mixture was\nheated above 700 oC and maintained at this temperature for 48 h to obtain\npolycrystalline KBBF. Subsequently, single crystals of KBBF were grown by the flux\nmethod using KF-B O as the flux. An appropriate mixture of the KBBF polycrystalline\n2 3\npowder and the flux was charged into a platinum crucible, heated to 800 oC, and held\nfor 48 h. The melt was then cooled to 750 oC at a rate of 10 oC h⁻1, followed by slow\ncooling to 630 oC at 3 oC day⁻1. Afterward, the temperature was lowered to room\ntemperature within two days. The as-grown KBBF crystals were obtained by dissolving\nthe remaining flux in dilute acid.”\n6. Equivalent capacitance thickness. The conventional term is \"capacitance equivalent\nthickness (CET)\".\nResponse: We have modified the “equivalent capacitance thickness (ECT)” to the\n“capacitance equivalent thickness (CET)” in the manuscript.\n7. Due to the large dielectric constant, the minimum measured EOT is 0.74 nm, and\neven smaller EOT can be obtained. How small can you go? This does not appear to be\nconsistent throughout the manuscript. What is the minimum thickness where KBBF is\nstill KBBF?\nResponse: Without considering the influence of the interfacial dead-layer effect, the\nthickness of KBBF that we obtained for device testing is approximately 4 nm, with a\ncorresponding EOT of 0.25 nm. Currently, the thinnest KBBF we can obtain via\nmechanical exfoliation is 2 nm; at this thickness, it can still maintain a complete crystal\nstructure and exhibit a regular shape, as shown in the figure below:\nimages of the KBBF thin layer. Scale bars, 2 μm in OM image and 1 μm in AFM image.\n8. Generally, the dielectric constant of dielectrics. Like the authors said themselves, it's\nthe electronic contribution ...\nResponse: Thank you for pointing this out. We have modified the manuscript to\n“Generally, a large band gap will cause a low electronic contribution to the dielectric\nconstant, thus making the band gap inversely proportional to the dielectric constant”.\n9. However, KBBF simultaneously exhibits the characteristics. Does KBBF fall into\nthe fluoride category? This inverse relationship is even better fulfilled if materials are\nput into different categories, see e.g. Fig.3 in [17]. Fluorides stand out as they can have\nvery large bandgaps despite having a large permittivity, so KBBF seems to fit this\npattern?\nResponse: Strictly speaking, KBBF does not belong to the category of “fluorides” in\nthe traditional sense. Typically, fluorides have F⁻ as the sole or primary anion, with\nionic bonds as the dominant chemical bonding. In contrast, F⁻ in KBBF is only a part\nof the structure, coexisting with O2⁻ to form [BeO F] tetrahedra and [BO ] triangular\n3 3\nnetworks, which constitute a layered structure. Therefore, although its chemical\nformula contains fluorine, its crystal structure and chemical bonding characteristics are\ncloser to those of fluoro-oxoborates rather than typical fluorides (e.g., CaF , NaF, etc.).\nenables them to form large electronegativity differences with other elements and shorter\nchemical bonds. Consequently, KBBF also exhibits the characteristics of high dielectric\nconstant and wide band gap typical of fluorides.\nIn addition, in accordance with the suggestions, we have attempted to classify materials\n7\ninto different categories, similar to Fig. 3 in Ref. [17]. However, apart from oxides, the\ntypes of other categories of materials reported experimentally are relatively few. For\ninstance, there are only a few types of nitrides, fluorides, and chlorides, making it\ndifficult to distinguish them separately. To emphasize this inverse relationship more\neffectively, we have used the same symbol to represent materials belonging to the same\ncategory for clearer differentiation. The revised Fig. 2f is as follows:\nFig. 2f | Bandgap versus dielectric constant of typical dielectrics. The dashed black line\nserves as a guide to illustrate the inverse proportionality between these two properties.\n10. Fig. 3c. The inset should use a log-x scale (same for SI Fig. 5, lower row).\nResponse: The picture you pointed out should be Fig. 2c. We have modified the inset\nimage in Fig. 2c and the lower row in SI Fig. 5 to log-x scale form. The modified images\nare presented as follows:\nFig. 2c | Frequency-dependent capacitance density at four different voltages.\nplate capacitors. C–V measurements (left) and C–f measurements (right) of the MIM\ndevices based on (a) 4 nm, (b) 6 nm, (c) 25 nm, (d) 50 nm, (e) 80 nm, (f) 103 nm, and\n(g) 155 nm, respectively.\n11. Fig. 3d. Why is the 6nm data not shown? What about the 4nm device from the SI?\nSame for Fig 5 in the SI, why is the thinnest 14nm? Could this be redone for devices\nrather than MIM structures? Device results would be much more relevant.\nResponse: According to the suggestions, we have supplemented the device data for the\n4 nm and 6 nm thicknesses, including the capacitance measurement results of the MIM\nstructures and the test results of the FET devices. The results demonstrate that the\ncapacitance values of KBBF with these two thicknesses remain stable under different\nvoltages and frequencies, while the FETs also exhibit a subthreshold swing close to the\n9\ntheoretical limit, a high on/off ratio, and a low hysteresis width. The specific test results\nare as follows:\nFig. R2 | The (a, d) CV, (b, e) Cf, and (c, f) FET transfer characteristic curve test result\nof the devices based on 4 nm (top) and 6 nm (bottom) KBBF as dielectric.\n12. Fig. 3f. Wouldn't it be better to show this for the corresponding material class, e.g.\nfluorides? Also, these values are bulk dielectric constants, the authors seem to show 5\nvalues for KBBF, but these are contaminated by dead-layer effects.\nResponse: We have attempted to classify materials into different categories. However,\napart from oxides, the types of other categories of materials reported experimentally are\nrelatively few. For instance, there are only a few types of nitrides, fluorides, and\nchlorides, making it difficult to distinguish them separately. For a clearer expression,\nwe have used the same symbol to represent materials belonging to the same category\nfor clearer differentiation.\nRegarding the selected dielectric constant values, we have included both those of thin-\nfilm materials and bulk materials. This is because some materials have only been\nreported as 2D thin films for dielectric layer applications (e.g., hBN, MgNb O , and\n2 6\nIn P S ), while others exist solely in 3D bulk structures (e.g., SiO , HfO , and TiO ).\n2 3 9 2 2 2\nTo enhance comparability, we have also presented both the dielectric constant of KBBF\n10\nin its 2D thin-film form and that of its bulk form in the figure. The revised Fig. 2f is as\nfollows:\nFig. 2f | Bandgap versus dielectric constant of typical dielectrics. The dashed black line\nserves as a guide to illustrate the inverse proportionality between these two properties.\n13. Fig. 3g. This is too simplistic, please do this statistically and for different sweep\nrates, as discussed above.\nResponse: We have re-conducted statistical tests on the breakdown behavior of KBBF,\ninvestigating the breakdown characteristics of KBBF with different thicknesses under\nvarying temperatures and sweep rates. Detailed information has been described in\nQuestion 3.\n14. which is 4.5 times higher than that of the perovskite SrTiO dielectrics reported in\n3\nthe literature. Why compare to STO? Why not to SiO ?\nnovel two-dimensional dielectric material reported in recent years, with excellent\ndielectric properties (Nature 2022, 605, 262-267; Nat. Electron. 2022, 5, 233-240). To\nbetter demonstrate the advantages of KBBF dielectric material, we have also compared\nits breakdown strength with that of SiO . The specific modifications are as follows.\n2\n“For the sample with a thickness of approximately 5 nm, it exhibits an EBD of about\n28.4 MV cm−1 at a temperature of 150 K and a sweep rate of 1 V s−1. Even at room\ntemperature, its EBD still exceeds 26 MV cm−1, which is more than four times that of\nthe breakdown field strengths of SrTiO and SiO reported in the literature21, 38”\n3 2\n11\n15. Ultrathin KBBF crystals demonstrate the highest breakdown strength at different\ndielectric. Please do this properly.\nResponse: We have re-conducted statistical tests on the breakdown behavior of KBBF,\ninvestigating the breakdown characteristics of KBBF with different thicknesses under\nvarying temperatures and scan rates. The results indicate that KBBF exhibits a high\nbreakdown field strength under all tested conditions. Specifically, the 5 nm-thick KBBF\nachieves a breakdown field strength of 28.4 MV cm−1 at 150 K with a sweep rate of 1\nV s−1, and its breakdown field strength at room temperature also exceeds 26 MV cm−1,\nwhich is significantly higher than that of other dielectric materials.\n16. These values exceed the threshold (>1 eV) required for effective gate dielectrics,\nthereby facilitating the development of devices with low leakage current and superior\nreliability12. Here the Robertson papers should be cited.\nResponse: We have cited Robertson’s relevant literature here, including [Phys. Stat.\nSol. (a), 2010, 207, 261-269] and [J. Vac. Sci. Technol. A, 2013, 31, 050821].\n17. With a hysteresis width ΔV as low as 1.6 mV. This is also somewhat meaningless,\ng\nplease analyse hysteresis for different sweep rates and temperatures, see e.g. Knobloch\nIEDM 23.\nResponse: We performed transfer characteristic measurements on the devices at\ndifferent sweep rates and temperatures, and extracted the corresponding hysteresis\nwidths. It can be observed that the devices exhibit excellent switching characteristics\nunder all tested sweep rates and temperatures. The hysteresis width increases slightly\nwith the rise in temperature and the decrease in sweep rate, yet remains at a low level\n(< 35 mV) across all conditions. Lowering the temperature and employing fast\nsweeping can effectively reduce the hysteresis width. This is mainly because reduced\ntemperatures decrease the thermally activated charge trapping/releasing rates, while\nfast scanning prevents mobile defects or dipoles from following the variation of gate\nvoltage in time, thereby suppressing charge trapping and releasing processes. The\nspecific modifications are as follows.\n“We performed transfer characteristic measurements on the devices at different sweep\n12\nrates and temperatures, and extracted the corresponding hysteresis widths, as shown in\nSupplementary Fig. 12. It can be observed that the devices exhibit excellent switching\ncharacteristics under all tested conditions. The hysteresis width increases slightly with\nthe rise in temperature and the decrease in sweep rate, yet remains at a low level (< 35\nmV) across all conditions.”\nSupplementary Fig. 12 | Hysteresis of MoS FET with KBBF as the dielectric. a,\ntemperatures. b, The transfer characteristic curves of the device with a sweep rate of 1\nV s−1 at different temperatures. c, Statistics on the hysteresis of devices with different\nsweep rates and temperatures.\n18. Capture charges during device working? device operation?\nResponse: We have modified “device working” to the more precise “device operation”.\n19. Performance instability primarily arises from intrinsic defects within the MoS\n2\nchannel itself. How can this be demonstrated? Channel defects are typically very fast\nand only impact SS and not hysteresis. So maybe there are still plenty of defects in\nKBBF?\nResponse: We conclude that KBBF has a low defect density based on the following\nthree lines of analysis: (1) Defects in the dielectrics act as slow border traps that capture\nand release charges during device testing, thereby inducing significant hysteresis.\nHowever, devices using KBBF as the dielectric layer exhibit negligible hysteresis under\nvarious test conditions, as shown in Fig. R3a. (2) When measuring the capacitance of\nKBBF via MIM structured capacitors, the capacitance value shows minimal variation\nwith frequency, indicating a low concentration of deep-level impurities and defects\n13\nwithin the material, as shown in Fig. R3b. (3) TEM characterization also proved that\nKBBF has a very high crystallization quality, as shown in Fig. R3c. Therefore, we\nbelieve that the KBBF employed in this work has a low defect density.\nFig. R3 | a, Statistics on the hysteresis of devices with different sweep rates and\ntemperatures. b, Voltage/frequency-dependent capacitance density for MIM devices of\nKBBF. c, HRTEM image of the KBBF thin layer.\n20. The FETs with different channel length (40, 80, and 200 nm) were integrated by\ngraphene gate, MoS channel and KBBF gate dielectrics. What EOT?\nand the corresponding EOT is 1.7 nm.\n21. To assess the practicability of our KBBF. The performance?\nResponse: Based on your suggestion, we have revised the manuscript as “To assess the\nperformance of our KBBF dielectrics in functional devices”.\n22. And excellent electrical reliability. The reliability was not really assessed. BTI?\nResponse: To better characterize the reliability of the devices, we performed bias\ntemperature instability (BTI) measurements, with the results presented in the\nSupplementary Fig. 17. It can be observed that although the small number of trap states\npresent in the KBBF dielectric may alter the charge state of the devices under negative\ngate voltage, the threshold voltage of the MoS FETs exhibits only a slight variation\n2\nwith gate-biasing time, indicating that the devices possess excellent reliability.\ntg, stress\n23. Which takes about two months. Really? Two months? Not overly convenient for\nfabrication?\nResponse: Yes, the preparation of KBBF is achieved through the slow crystallization\nof flux methods, and this process takes approximately two months to complete. We\nhave also added a detailed experimental scheme in the text.\n“The KBBF crystals were synthesized in two steps, mainly following the procedures\ndescribed in previous references [Journal of Crystal Growth 318 (2011) 610–612] and\n[J. Mater. Res., Vol. 18, No. 10, Oct 2003]. First, polycrystalline KBBF was prepared\nvia a conventional solid-state reaction according to the following equation:\n6BeO + 3KBF + B O → KBe BO F + BF ↑\n4 2 3 2 3 2 3\nStoichiometric amounts of BeO (purity 99.9%), KBF (purity 99%), and B O (purity\n4 2 3\n99.99%) were thoroughly mixed and placed in a platinum crucible. The mixture was\nheated above 700 oC and maintained at this temperature for 48 h to obtain\npolycrystalline KBBF. Subsequently, single crystals of KBBF were grown by the flux\nmethod using KF-B O as the flux. An appropriate mixture of the KBBF polycrystalline\n2 3\npowder and the flux was charged into a platinum crucible, heated to 800 oC, and held\nfor 48 h. The melt was then cooled to 750 oC at a rate of 10 oC h⁻1, followed by slow\ncooling to 630 oC at 3 oC day⁻1. Afterward, the temperature was lowered to room\n15\ntemperature within two days. The as-grown KBBF crystals were obtained by dissolving\nthe remaining flux in dilute acid.”\n24. And then transferring it to the target substrate. How? PMMA? PDMS?\nResponse: Yes, we used PDMS as an intermediate carrier for transfer when exfoliating\nthe sample. To make this clearer, we have added relevant content to the manuscript, as\ndetailed below.\n“Thinner KBBF nanosheets were obtained by mechanically exfoliating the bulk crystal\nusing Scotch tape after layer sliding, and then using polydimethylsiloxane (PDMS) as\nan intermediate carrier and with the help of a transfer platform to transfer it onto the\ntarget substrates”\n25. Supplementary Fig. 10 | Reliability of KBBF. This is (short term) stability rather\nthan long-term reliability\nResponse: Supplementary Fig. 10 is, in fact, a set of repeated experiments on multiple\ndevices performed to verify the reliability of KBBF as the dielectric layer, rather than\na test of long-term device stability. As shown in the figure, all devices exhibit low\nsubthreshold swing, high on/off ratio, low gate-leakage current, and negligible\nhysteresis. The corresponding statistical data are presented in Fig. 3g, demonstrating\nthe excellent dielectric properties and electrostatic control capability of KBBF. The\nlong-term reliability was shown in Supplementary Fig. 16.\n26. Supplementary Fig. 13 | Long-term stability. Transfer characteristic curves of our\ntop-gated MoS FET, presenting an excellent stability after six-month storage. How\n2\nstored? Vacuum? Desiccator? Air? Unbiased?\nResponse: We have preserved this device in an air environment, and the corresponding\nstorage conditions have also been supplemented in the manuscript.\ntop-gated MoS FET, presenting an excellent stability after six-month storage in air\n2\nenvironment.\n27. Supplementary Fig. 14. The 200 nm device seems to have a positive Vth, while all\nother devices shown have a negative one? Ideas?\nResponse: The threshold voltages of the devices with channel lengths of 200 nm,\n80\nnm, and 40 nm, obtained via the linear-region extrapolation method, are -0.48 V,\n-1.36\nV, and -1.68 V, respectively. The reason why the threshold voltage shifts negatively\nwith the shortening of the channel length is that the reduction in channel length leads\nto a larger on-current of the device at zero gate voltage, requiring a more negative gate\nvoltage to turn the device off. The same phenomenon has also been observed in relevant\nliterature (Nat. Electron. 2024, 7, 1137-1146).\nGeneral Comments:\nIn this manuscript, the authors report a new 2D dielectric material KBe BO F , which\n2 3 2\nhas a high dielectric constant and large bandgap achieving ultralow leakage current and\nthe highest breakdown field strength. They also perform the transport test of MoS\n2\ntransistors gated by KBBF showing a very small subthreshold swing and a high on/off\ncurrent ratio. This work provides a new high-performance dielectric material for the\ndevelopment of electronic devices. Overall, I consider this work suitable for publication\nin Nature Communications.\nNevertheless, I would appreciate clarification on a few points:\nResponse: We thank the reviewer very much for the very positive comments to our\nmanuscript and for supporting our work to be published.\n1. It is well-known that the large-scale and controllable synthesis of dielectric materials\nis crucial for their application in integrated circuits. The KBe BO F material\n2 3 2\ninvestigated in this work is currently prepared using mechanical exfoliation, which\nposes limitations for practical applications. Have the authors considered employing\nepitaxial growth or other scalable preparation methods to directly achieve high-quality\nthin layers on substrates? A discussion on the large-scale synthesis pathway for this\nmaterial would significantly enhance its application potential.\nResponse: As noted by the reviewer, the large-scale and controllable synthesis of\ndielectric materials is crucial for their application in integrated circuits. At present, the\nprimary preparation method for KBBF is the high-temperature flux method, which\nenables the production of centimeter-scale single-crystal samples. To obtain thin-layer\nsamples, the as-grown single crystals can be thinned via slicing. Moreover, since KBBF\nsingle crystals are derived from their polycrystalline powders, it is hypothesized that\nwafer-scale fabrication of KBBF may be achievable using thermal evaporation with\npolycrystalline KBBF powders as the evaporator source. As for the method of epitaxial\ngrowth, the lattice constants of KBBF are a = b = 4.427 Å and c = 18.744 Å, it is\nnecessary to match both the 4.4 Å six-membered ring and the long-period layer spacing\n18\nof 18 Å at the same time, which poses great challenges for substrate selection. In\naddition, we believe that high-quality thin-layer samples can also be obtained by\ndeveloping large-scale exfoliation methods, such as gold-assisted exfoliation or liquid-\nphase exfoliation, etc.\n2. According to the crystal structure provided by the authors, K⁺ ions are located in the\ninterlayer spaces. An important concern is whether these K⁺ ions might migrate under\napplied gate voltage, particularly posing a risk of intercalation into the MoS channel\n2\nlayer. If ion migration does occur, how might it affect the material's dielectric constant\n(possibly originating from ionic polarization contributions) and device stability? It is\nrecommended that the authors discuss this aspect through electrical characterization or\ntheoretical calculations.\nResponse: Based on the suggestions, we conducted a theoretical calculation of the\nmigration behavior of K+ ions in KBBF. We simulated the migration energy barriers of\nK+ at different positions in KBBF via first-principles calculations, with the results\npresented in Supplementary Fig. 15. Two migration scenarios of K+ were considered in\nthe calculations: intralayer migration and interlayer migration. For intralayer migration,\nthe maximum migration energy barrier of K+ is 1.1 eV, indicating that intralayer\nmigration of K+ is relatively difficult. In contrast, for interlayer migration—especially\nwhen K+ passes through the Be BO layer—the maximum migration energy barrier can\n2 3\nreach 6.8 eV. This is mainly attributed to the size effect, which causes significant\nstructural distortion when K+ penetrates the Be BO layer, leading to an increase in\n2 3\nenergy. Therefore, K+ does not migrate and embed into the MoS₂ layer during device\ntesting. In addition, if K+ migration were to occur, the polarization induced before and\nafter migration would introduce considerable hysteresis to the devices. However, the\ntransfer characteristic measurements of the transistors demonstrate a small hysteresis,\nwhich also confirms that K+ migration does not occur during device testing. We have\nalso added relevant discussions to the manuscript.\n“In addition, since K+ ions are located between the layers, any migration behavior of\n19\nthese ions would also affect the device performance. We calculated the migration\nenergy barriers of K+ ions for both intralayer and interlayer migration. As shown in\nSupplementary Fig. 15, the maximum intralayer migration energy barrier of K+ ions is\n1.1 eV, while the interlayer migration energy barrier for K+ ions passing through the\nBe BO layer reaches 6.8 eV. These results indicate the absence of ionic migration\n2 3\nbehavior in KBBF, which is also one of the reasons for its negligible hysteresis.”\nSupplementary Fig. 15 | Theoretical calculation of ionic migration. The energy\nbarrier of K+ ions migrates at intralayer and interlayer in KBBF.\n3. KBe BO F exhibits a high dielectric constant and wide bandgap simultaneously, as\n2 3 2\nit contrasts with the general trend observed in conventional dielectric materials. The\nauthors attribute this to the large atomic electronegativity difference and short chemical\nbond lengths, which is a reasonable explanation. However, providing deeper theoretical\nevidence—such as quantitative first-principles calculations of the contribution of ionic\npolarization to the dielectric constant, or a comparative analysis of bond lengths and\nelectronegativity parameters with other known dielectric materials—would strengthen\nthe argument.\nResponse: To better support our interpretation that KBBF exhibits both a wide band\ngap and a high dielectric constant, we performed first-principles calculations on the\nelectronic/ionic contributions to its dielectric constant, and statistically compared the\n20\nelectronegativity differences and bond lengths of several typical dielectric materials,\nas shown in Supplementary Fig. 7 and Supplementary Fig. 8. As observed from the DFT\ncalculation results, compared with the conventional dielectric material SiO and the\n2\ntypical 2D dielectric material hBN, KBBF has a larger proportion of ionic contribution\nto its dielectric constant, indicating that ionic polarization plays a dominant role in its\ndielectric constant. This characteristic is conducive to the realization of its wide band\ngap and high dielectric constant properties, which is consistent with our theoretical\ninterpretation. In addition, the comparison of electronegativity differences and bond\nlengths among different dielectric materials shows that KBBF has the largest\nelectronegativity difference and the shortest bond length, which also serves as strong\nevidence for its high ionic contribution.\nSupplementary Fig. 7 | Comparison of the electronegativity difference and\nchemical bond length between KBBF and other typical dielectric materials. KBBF\nexhibits the largest electronegativity difference and the smallest chemical bond length.\ncontribution and ionic contribution in dielectric constant.\n4. The authors' validation of the device-to-device reproducibility and environmental\nstability of the transistors is commendable. Beyond these, the operational stability of\ntransistors is also a critical metric for practical applications. Including such data would\noffer a more comprehensive assessment of device reliability.\nResponse: Thanks for your suggestions. To better characterize the reliability of the\ndevices, we performed bias temperature instability (BTI) measurements and continuous\non/off switching tests, with the results presented in the Supplementary Fig. 17 and\nSupplementary Fig. 18. It can be observed in BTI measurements that the threshold\nvoltage of the MoS FETs with KBBF dielectric exhibits only a slight variation with\n2\ngate-biasing time. In continuous on/off switching tests, the devices maintained stable\nperformance over 1000 switching cycles at V = ±2 V and V = 50/500 mV, indicating\ntg ds\nthat the devices possess excellent reliability. The detailed were shown below:\n“Bias temperature instability (BTI) measurements serve as a complementary for\nevaluating the reliability of transistors. By applying a gate voltage stress of -2 V for\n22\ndifferent durations to the devices at 350 K, we characterized the shift in their threshold\nvoltage. It can be seen that although the traps present in the KBBF dielectric may alter\nthe charge state of the devices under negative gate voltage, the threshold voltage of the\nMoS FETs exhibits only a slight variation with gate-biasing time (Supplementary Fig.\n2\n17). To evaluate the operational stability of the devices, we conducted continuous on/off\nswitching tests. As shown in Supplementary Fig. 18, the devices maintained stable\nperformance over 1000 switching cycles at V = ±2 V and V = 50/500 mV. These\ntg ds\nfindings suggest that the transistors with KBBF dielectrics exhibit excellent stability\nand reliability, which may enable them to play a pivotal role in the development of next-\ngeneration 2D devices.”\nSupplementary Fig. 17 | Negative bias-temperature instability (NBTI) of the MoS\ntg, stress\n2\ncontinuous gate voltage switching. a, Vtg = ± 2V, V = 50 mV. b, Vtg = ± 2V, V =\nds ds\n500 mV.\n5. The demonstration of a logic inverter based on KBe BO F dielectric highlights its\n2 3 2\npotential for practical applications, which is a valuable extension of the work. However,\nas previously noted, the practical adoption of this material largely depends on its\ncompatibility with existing semiconductor manufacturing processes, specifically the\nability to achieve large-area, uniform, and low-cost synthesis. It is recommended that\nthe authors explore epitaxial growth or large-area thin-film synthesis routes for this\nmaterial in future studies, which would greatly enhance the completeness and impact\nof this work.\nResponse: Thank you for the reviewer’s suggestions. In future work, we will further\ninvestigate suitable fabrication processes for large-area KBBF. These include exploring\nappropriate epitaxial substrates for the epitaxial growth of KBBF, attempting to obtain\nlarge-area thin films via thermal evaporation approach, and preparing thin-layer\nsamples through liquid-phase exfoliation followed by spin-coating.\nGeneral Comments:\nThe manuscript by Xu et al. reported a van der Waals dielectric material KBBF with\nboth high dielectric constant and wide bandgap. Its properties as a dielectric material\nwere systematically studied and its application in 2D electronics and the corresponding\nperformance were well demonstrated, showing good results. The choice of the material\nbased on electronegativity, atomic size and bond length can be a good reference for new\ndielectric material exploration in the future. Therefore, I think the manuscript can meet\nthe standard of Nature Communications and recommend publication after revision.\nResponse: We appreciate this inspiring comment. Following the reviewer’s\nsuggestions, we revised the manuscript and further improved the quality of the article.\n1. Are there other dielectric materials that may also accord with the rule based on the\nelectronegativity, atomic size and bond length?\nResponse: If a dielectric material complies with the rules based on electronegativity,\natomic size, and bond length, its elemental composition must contain elements with\nhigh electronegativity, and the groups of its constituent elements in the periodic table\nshould differ significantly. According to predictions from theoretical calculation\nliteratures (Sci. Rep. 2018, 8, 14794), fluorides tend to satisfy the aforementioned rules,\nsuch as BaBeF and LaF . Furthermore, experimental literatures (Nat. Nanotechnol.\n4 3\n2024, 19, 932-940) have reported that the synthesized LaF exhibits the characteristics\n3\nof a wide band gap (E ~ 10.5 eV) and a high dielectric constant (κ ~ 30). However, at\ng\npresent, LaF can only be obtained as polycrystalline samples via thermal evaporation,\n3\nwhich suffer from poor crystalline quality. In contrast, KBBF single-crystal nanosheets\nprepared by mechanical exfoliation exhibit higher crystalline quality and thus\ndemonstrate lower leakage current.\n2. The growth of KBBF crystal was not provided in detail. The authors should at least\nbriefly describe the precursors and process they used.\nResponse: Thanks for your suggestion, we have added a detailed experimental scheme\n25\nin the manuscript.\n“The KBBF crystals were synthesized in two steps, mainly following the procedures\ndescribed in previous references56, 57. First, polycrystalline KBBF was prepared via a\nconventional solid-state reaction according to the following equation:\n6BeO + 3KBF + B O → KBe BO F + BF ↑\n4 2 3 2 3 2 3\nStoichiometric amounts of BeO (purity 99.9%), KBF (purity 99%), and B O (purity\n4 2 3\n99.99%) were thoroughly mixed and placed in a platinum crucible. The mixture was\nheated above 700 oC and maintained at this temperature for 48 h to obtain\npolycrystalline KBBF. Subsequently, single crystals of KBBF were grown by the flux\nmethod using KF-B O as the flux. An appropriate mixture of the KBBF polycrystalline\n2 3\npowder and the flux was charged into a platinum crucible, heated to 800 oC, and held\nfor 48 h. The melt was then cooled to 750 oC at a rate of 10 oC h⁻1, followed by slow\ncooling to 630 oC at 3 oC day⁻1. Afterward, the temperature was lowered to room\ntemperature within two days. The as-grown KBBF crystals were obtained by dissolving\nthe remaining flux in dilute acid.”\n3. What were the typical thicknesses that were used in the transistors and what was the\nsmallest thickness possible?\nResponse: The typical thickness of KBBF used in transistors is approximately 12 nm.\nThis thickness facilitates the acquisition of large-sized flakes, which are conducive to\ndevice fabrication. Moreover, due to the influence of the interfacial dead-layer effect,\nits capacitance equivalent thickness (CET) is comparable to that of thinner KBBF films.\nFor instance, the CET is 1.76 nm at a thickness of 12 nm, versus 1.63 nm at 4 nm,\nresulting in negligible differences in their gate control capabilities. Currently, the\nthinnest KBBF thickness that can be used for device fabrication is 4 nm, and the\ncorresponding device test results are presented in the figure below.\n4. SEM is known to reduce the contrast of small defects on the surface of materials, so\nit may not be appropriate to describe the material has flat surface with SEM and EDS\ndata. Uniformity can be shown instead.\nResponse: Thank you for your professional advice. We have revised the manuscript,\nreplacing the “flat surface” with “great surface uniformity”.\n5. There are errors in the sentence \"The calculated density of states (DOS) of single\nMoS and KBBF/MoS heterostructure in Fig. 3d resolves the integration of KBBF on\n2 2\nthe surface of MoS does not introduce defect-related energy levels into MoS .\"\n2 2\nResponse: Thank you for pointing this out. We have revised this sentence to “The\ncalculated density of states (DOS) for pristine monolayer MoS and the KBBF/MoS\n2 2\nheterostructure (Fig. 3d) demonstrates that KBBF integration on the MoS surface is\n2\ndevoid of defect-related gap states within the MoS electronic structure.”\n2\nResponses to Reviewer #1\nGeneral Comments:\nI wish to thank the authors for the diligent reply. Still, some concerns remain.\nResponse: We appreciate the reviewer’s comments for our manuscript and the\nsuggestions made for improving the quality of the article.\n1. While trying to improve on the understanding of insulator breakdown, the authors\nstill speak of \"breakdown field\". As discussed in Wu 25 (IRPS), there is no such thing.\nThe field at which the insulator breaks down depends on ramp rate, area, and\ntemperature, if one uses ramped voltage stress, so this number is not a material\nparameter and should no longer be reported. I understand that most groups in the 2D\nfield report some \"random numbers\" called \"breakdown field\", but this doesn't make\nthis correct. Rather report the maximum voltage (V ) at which the insulator can\nmax\nsurvive for 10 years given a meaningful area.\nResponse: To further characterize the dielectric properties of KBBF, we have\nsupplemented its time-dependent dielectric breakdown (TDDB) performance following\nthe reviewers’ suggestions, and extracted the maximum operating voltage for its stable\n10-year service, as shown in Fig. R1. By testing the TDDB behavior of 10 nm-thick\nKBBF (EOT=0.62 nm) under different voltages, the maximum operating voltage for its\n10-year stable service was extrapolated to be 6.6 V, and the relevant content has been\nrevised in the main text accordingly.\nnm-thick KBBF at various voltage stresses. b, TDDB versus stress voltage\ncharacteristics, where the black dash-line represents the lifetime prediction.\n2. the great surface uniformity of KBBF. That's not scientifically rigorous, please give\nRMS surface roughness.\nResponse: According to the suggestion, we extracted the surface roughness of KBBF\nand supplemented it in manuscript. As can be seen from Supplementary Fig. 2, the\nsurface roughness of KBBF of different thicknesses is all less than 1 nm, which proves\nthat it has good uniformity.\nSupplementary Fig. 2 | Exfoliation of KBBF. Optical images, AFM images and\nheight curves of (a) 4 nm, (b) 15 nm, (c) 25 nm, (d) 40 nm KBBF, respectively.\n2\n3. According to the test results, the dielectric constant value ε of KBBF can be\ncalculated by the formula: ε = Ct/Aε . The measured C contains the contribution of the\n0\ntwo vdW gaps which would have to be subtracted.\nResponse: According to the suggestion, we attempted to subtract the vdW gaps\nbetween the electrode and the insulator to calibrate the capacitance and calculate the\ndielectric constant. The details are as follows:\nIn the MIM structured capacitors, the vdW gap between the electrode and KBBF forms\na series configuration with the KBBF layer, and the total capacitance can be derived\nfrom the following equation:\n1 1 1 1 1 2\n= + + = + (1)\nCtotal Cgap1 CKBBF Cgap2 CKBBF Cgap\nwhere C , C , and C denote the total capacitance, vdW gap capacitance, and\ntotal gap KBBF\nKBBF capacitance, respectively. The formula for calculating the capacitance per unit\narea is given by:\nC=\nε0εr\n(2)\nd\nwhere ε and ε are the vacuum dielectric constant and relative dielectric constant,\n0 r\nrespectively, and d is the thickness. Combining Equations (1) and (2), we can obtain:\n1\n=\nd2\n+\nd1\n=\nd2\n+\nd1\n(3)\nCtest ε0εKBBF ε0εvdW gap ε0εKBBF ε0\nwhere C is the experimentally measured capacitance, ε and ε are the\ntest KBBF vdW gap\ndielectric constant of KBBF and the vdW gap, respectively. Herein, ε is set to 1,\nvdW gap\nand d and d represent the thicknesses of the vdW gap and KBBF, respectively. At this\n1 2\npoint, a functional relationship between the C and the KBBF thickness d is\ntest 2\nestablished, as illustrated in Supplementary Fig. 7. By fitting the experimental data, the\ndielectric constant of KBBF is determined to be 63, with the thickness of two vdW gap\nbeing 0.353 nm. Notably, this dielectric constant value is obtained after excluding the\ncapacitance contribution from the vdW gap. It is found that this value is consistent with\nthe result derived from the “dead layer” model. Therefore, it can be concluded that the\n“dead layer” in this work mainly originates from the vdW gap between the electrode\nand KBBF, and the intrinsic dielectric constant of KBBF is 63.\ngaps. a, Schematic of a metal–insulator–metal (MIM) capacitor. b, 1/C as a function of\nvarious KBBF thickness measured from MIM capacitors.\n4. The thickness dependence of dielectric constant and capacitance equivalent thickness\n(CET). CET is used to MIS structures and includes the channel capacitance. Here, the\nauthors use MIM structures, so they should report the EOT.\nResponse: Thank you for your professional suggestions. We have extracted the EOT\nvalues of KBBF samples with different thicknesses and replaced the original CET data\naccordingly, as shown in Fig. 2d.\nFig. 2d. Dielectric constant and EOT as a function of various KBBF thickness measured\nfrom MIM capacitors.\n5. Due to the large dielectric constant, the minimum measured EOT can be calculated\nas 0.25 nm (t=4 nm) according to the formula EOT=3.9t/ε , and even smaller EOT\nbulk\ncan be obtained if the thickness is further reduced. Not sure what the authors are aiming\n4\nat. Minimum EOT in what sense? Should this be based on estimated leakage currents?\nAccording to the IRDS, only a certain leakage current is acceptable.\nResponse: The minimum EOT value reported herein is not intended for comparison\nwith those reported in other studies, nor does it represent the minimum EOT that can\nmaintain a specific leakage current. Instead, it simply corresponds to the EOT of the\nthinnest KBBF flake obtainable via mechanical exfoliation that could be used for\ncapacitance measurements. To date, the thinnest KBBF flake we have exfoliated for\ndevice fabrication is 4 nm, with a corresponding EOT of 0.25 nm.\n6. Density functional theory (DFT) calculations determined. Please mention the\nfunctional used.\nResponse: The HSE06 hybrid functional is well recognized for its accuracy in bandgap\ncalculations. In order to obtain an accurate bandgap for KBBF, HSE06 functional is\nused in the DFT calculations. To further improve the readability of the manuscript, as\nyou suggested, the functional employed in the calculations are described directly in the\narticle, and detailed computational procedures were described in the Methods section.\n“We calculated the bandgap of KBBF to be 8.03 eV using the HSE06 functional within\nthe framework of density functional theory (DFT) (see Methods for detailed\ncomputational details)”;\n“The calculations of bandgap and DOS were conducted using the Vienna Ab initio\nSimulation Package (VASP)58. The projected augmented wave (PAW) method was\nemployed to describe the ion-electron interactions, with a plane-wave basis set cutoff\nenergy set to 520 eV59. The generalized gradient approximation (GGA) with the\nPerdew-Burke-Ernzerhof (PBE) functional was utilized60, along with hybrid functional\ncalculations based on the Heyd-Scuseria-Ernzerhof (HSE06) parameters61,62.\nSpecifically, the HSE06 functional was utilized to yield a precise bandgap value for\nbulk KBBF. A gamma-centered k-point sampling grid for Brillouin zone integration are\ngenerated by VASPKIT with a resolution of 0.0463. The convergence thresholds for total\nenergy and atomic forces were set to 10−5 eV and 2×10−2 eV/Å, respectively. The DFT-\nvan der Waals interactions64.”\n7. Fig 2d. Please label the curves, which is which?\nResponse: Following the suggestions, we have labeled the different curves with arrows\nto facilitate their easier differentiation, as shown in the Fig. 2d.\nFig. 2d. Dielectric constant and EOT as a function of various KBBF thickness measured\nfrom MIM capacitors.\n8. These values exceed the threshold (>1 eV) required for effective gate dielectrics,\nthereby facilitating the development of devices with low leakage current and superior\nreliability. Not much is said about reliability. How would the band offset impact\nreliability? Reliability will depend on the density of trap states, the band offset is of\nsecondary importance.\nResponse: Thank you for pointing this out. To address this, we have supplemented the\ndiscussion regarding the impact of band offset between the dielectric and\nsemiconductor on device reliability. Specifically, a large band offset can effectively\nprevent electrons and holes from passing through the dielectric via Schottky emission,\nwhich would otherwise induce substantial leakage current, degrade device reliability,\nand increase power consumption. We also fully agree with your viewpoint: trap states\nnot only induce defect-assisted carrier tunneling, but also cause threshold voltage drift,\nthereby compromising device reliability. The revised content is as follows:\n“These values far exceed the threshold (> 1 eV) required for high-quality gate\n6\ndielectrics, thereby effectively preventing electrons or holes from tunneling through the\ndielectric via Schottky emission to induce substantial leakage current, which\ncontributes to the development of low-power-consumption and high-performance\ndevices.”\n9. For verify the reliability of KBBF. To verify?\nResponse: We have revised the original sentence to “To verify the reliability of KBBF\nas the dielectric”.\n10. Fig 3i. This comparison is somewhat meaningless. At what overdrives where the\nIon measured? Did these devices have proper V ? Was I measured at 0V? What were\nth off\nthe EOTs?\nResponse: This comparison primarily focuses on the maximum on/off ratio and\nminimum SS achievable by a complete switching cycle in FETs. Following your\nreminder, we have also recognized that different drain-source voltages (V ) and\nds\noverdrive voltages (V ) will indeed yield distinct results. Therefore, to enable a more\nov\nequitable comparison, we have screened relevant studies and only compared the on/off\nratios obtained under the same V conditions. Meanwhile, we have labeled both the\nds\nV and EOTs under actual operating conditions of the FETs (note that we were unable\nov\nto calculate the overdrive voltages for all studies due to the lack of reported threshold\nvoltage (V ) data in some cases), as shown in Fig. 3i.\nth\nIn addition, the core objective of this comparison is to demonstrate the modulation\ncapability of different dielectric materials on the magnitude of channel current. For this\nreason, we did not take into account whether the devices have proper V or whether the\nth\nI is achieved at 0 V. We have also compiled the relevant performance parameters of\noff\nthe dielectric materials that have been reported so far, as shown in Supplementary Table\n1. We hope this will be helpful for readers to compare the performance of different\ndielectric materials at present.\nκ dielectrics in terms of SS and on/off ratios. The values on the left side of the brackets\nrepresent the EOT values actually applied in the FET test, while the values on the right\nside are the overdrive voltages.\n11. Fig 3j. The hysteresis should be normalized by EOT. (10.1038/s41467-025-66210-\nz).\nResponse: Following the suggestion, we have normalized the hysteresis widths of the\ndevices used for comparison by their EOT values to enable a fairer comparison.\nFig. 3j. Normalized hysteresis coupled with D of KBBF-gated MoS FETs compared\nit 2\nwith literature values. The hysteresis was normalized using EOT.\n8\n12. confirms the promising on-state current over 400 μA μm−1. At what overdrive? EOT?\nResponse: The reported on-state current over 400 μA·μm−1 was obtained from the\noutput characteristic curves at a gate voltage of 10 V and a source-drain voltage of 2 V.\nWith a threshold voltage of -1.36 V, the overdrive voltage under this condition was\n11.36 V, and the EOT was 1.7 nm.\nGeneral Comments:\nI thank the authors for carefully addressing my comments. I am satisfied with the\nrevised manuscript and recommend it for publication.\nResponse: We sincerely appreciate your positive feedback on our revised manuscript\nand your kind recommendation for publication.\nGeneral Comments:\nMy concerns have been addressed in the revised manuscript. Meanwhile, some\nadditional information, which I believe was useful and suggested by reviewer #1, was\nalso provided, such as the performance versus sweep rate. I think the revised manuscript\ncan now be considered for publication.\nResponse: We are deeply grateful for your favorable evaluation of our revised\nmanuscript and your kind recommendation for publication.\nResponses to Reviewer #1\nGeneral Comments:\nThe revised manuscript is significantly improved, I have only a few minor concerns\nremaining.\nResponse: We appreciate the reviewer’s comments for our manuscript and the\nsuggestions made for improving the quality of the article.\n1. KBe\n2\n. Call it potassium beryllium fluoroborate or potassium beryllium borate\nfluoride at some point. Also, at some point it should be mentioned that beryllium is\nhighly toxic and beryllium free alternatives should also be explored.\nResponse: Thank you for pointing this out. We have added the relevant content at the\nend of the paper.\n“It should be noted that Be is slightly toxic. Materials with the same structure but free\nof\nfree\nof Be can also be explored as dielectric materials.”\n2. thickness of the vdW gap. In one place it is given as 0.41 nm, in another as 0.353.\nHow was this determined? As the distance between the cores? This is unlikely correct,\nsince then also the parts of the gap that include the atoms is counted, which, however,\ncan be polarized, so would not have a vacuum permittivity. It has been suggested to\nsubtract the core radii and treat the rest as a quasi-vacuum gap, with somewhat higher\npermittivity of about 2 (see Pourfath 2025). In the SI, Eq (3) should contain two vdW\ngaps, as also shown in Fig S7.\nResponse: The vdW gap value of 0.41 nm labeled in the manuscript was determined\nfrom cross‑sectional TEM data, and some deviation may exist due to manual\nmeasurement. In contrast, the vdW gap value of 0.353 nm was obtained by fitting the\ncapacitance measurement results. According to your suggestion, we have reviewed the\nrelevant literature (Pourfath 2025) and corrected both the dielectric constant and\nnumber of the vdW gaps used in the calculation. The fitting results indicate that the\n1\nvdW gap in our devices is 0.353 nm. To avoid ambiguity, we have standardized the\nvdW gap value to 0.353 nm throughout the manuscript.\n3. bulk dielectric constant of 63, while also exhibiting a high dielectric constant of 26.5\neven at an ultrathin thickness. That's a massive drop, don't recall seeing something like\nthis. Were the vdW gaps properly considered?\nResponse: According to the suggestion for Question 2, we have recalculated the\nrelevant parameters of the vdW gap. Therefore, we believe that the vdW gap in our\nstudy has been appropriately considered. The significant reduction in the dielectric\nconstant has also been reported in SrTiO (from 270 to 30, Nature 2022, 605, 262) and\n3 4\n4. an ultralow leakage current of 10−6 A cm−2 and enables it to maintain for 10 years at\na high working voltage of 6.6 V even when the equivalent oxide thickness is less than\n1 nm. This is an unfortunate statement and mixes a lot of things together, state clearly\nat what conditions what leakage is obtained, leakage depends exponentially on V and\ng\nEOT.\nResponse: Thank you for your suggestion. We have supplemented the specific\nmeasurement conditions in the manuscript.\n“Such dielectric properties give rise to a low leakage current of 10−6 A cm−2 at an\nequivalent oxide thickness of 0.62 nm and a high gate voltage of 15 V, and is predicted\nto work stably for 10 years at 6.6 V”\n5. which exhibits both a high dielectric constant (63). a high BULK dielectric.\nResponse: We have revised the relevant content to “which exhibits both a high bulk\ndielectric constant (63) and a ultrawide bandgap (>8 eV)”.\n6. The inert fluorine atom-terminated surface of KBBF. Maybe cite other fluorides\nwhich all seem to have this property, making them nicely integrable with 2D materials.\nResponse: To better support this viewpoint, we have added relevant references as\nsuggested, including [Nat. Electron. 2019, 2, 230-235], [Appl. Surf. Sci. 1990, 41-42,\n451-456] and [2D Mater. 2019, 6, 045004].\n2\n7. an identified vdW gap (~0.41 nm) between the KBBF and MoS\n2\nwill reduce the\ntunneling probability of charge carriers and help minimize the gate leakage current. Yes,\nthat's true, but unfortunately, the vdW gap has a low permittivity, which will result in a\nlarge penalty in terms of EOT.\nResponse: We agree with your point that the presence of vdW gaps helps reduce\nleakage current but at the expense of the overall EOT. In future work, we will further\nattempt to exclude the contribution of vdW gaps to restore the intrinsic EOT of the\ndielectrics as much as possible.\n8. which verifies that the “dead layer” in this work originates from the vdW gap.\nTwo\nvdW gaps? What is D when the vdW gaps are considered?\nResponse: Yes, since the fitting result from the dead-layer model is consistent with the\ncapacitance fitting result after subtracting the vdW gap, we conclude that the dead layer\nin this study mainly originates from the two vdW gaps between the electrode and KBBF.\nIn the dead-layer model, we think D is the thickness of the dead-layer region, and when\nthe vdW gaps are taken into account, D corresponds to the actual thickness of the vdW\ngaps.\n9. Fig. 2a. please add the vdW gaps.\nResponse: Following the suggestion, we have revised Fig. 2a by adding the vdW gap.\nFig. 2a. The structure diagram of the capacitor device.\n10. tunneling through the dielectric via Schottky emission. Even for 1eV, the dominant\nmechanism is not Schottky emission but direct/FN tunneling through the small barrier.\nResponse: Thank you for pointing this out. We have revised the relevant content to\n“thereby effectively preventing electrons or holes from tunneling through the dielectric\nvia direct tunneling or FN tunneling to induce substantial leakage current”.\n3\n11. outstanding performance with a minimum hysteresis width ΔV\ng\nas low as 1.6 mV.\nThe minimum hysteresis width is irrelevant, the maximum is much more interesting.\nThis is even more so as this minimum seems to be have achieved at 4K, where charge\ntrapping is mostly frozen out. Please report the maximum value at RT (using a few more\nsweep frequencies).\nResponse: Thank you for your comment. In fact, the hysteresis of 1.6 mV represents\nthe minimum value measured at room temperature. Following your suggestion, we have\nrevised it to the maximum hysteresis at different sweep rates: the maximum hysteresis\nis 35 mV and 12 mV at sweep rates of 0.1 V s-1 and 1 V s-1, respectively.\n12. The calculated density of states (DOS) for pristine monolayer MoS\n2\nand the\nKBBF/MoS heterostructure (Fig. 3d) demonstrates that KBBF integration on the MoS\n2 2\nsurface is devoid of defect-related gap states within the MoS electronic structure. I am\n2\nnot sure what the authors mean, how can a calculation using an ideal structure prove\nanything? Calculated how?\nResponse: Here, we adopted the method reported in [Nat. Electron. 2022, 5, 849-858]\nto interpret and verify the superior performance of the KBBF/MoS heterostructure via\n2\ntheoretical calculations. The detailed calculation methods were described in the\n“Computation details” section of the manuscript. In our experimental results, the MoS\nindicating an excellent interface quality between KBBF and MoS . No chemical\n2\nbonding or charge carrier exchange occurs at the interface, preserving the independent\nelectronic properties of the MoS channel. Theoretically, this is manifested by the\n2\nabsence of interaction-induced gap states in the DOS of MoS . Although the\n2\ncalculations were performed using an ideal model structure, which may not fully match\nthe realistic experimental conditions, they theoretically demonstrate the feasibility of\nKBBF as an ideal gate dielectric material and are generally consistent with our\nexperimental observations.\n4\n13. Consequently, in KBBF/MoS\n2\ndevices, performance instability primarily arises\nfrom intrinsic defects within the MoS channel itself. Also not sure how this should\n2\nfollow from anything? The MoS is also (poly)crystalline?\n2\nrepresents a conjecture regarding the instability observed in the device performance.\nSince our theoretical calculations confirmed that KBBF does not introduce gap states\ninto the electronic structure of MoS , we speculate that the performance may be affected\n2\nby defects generated during the synthesis of MoS . Alternatively, impurities and defects\n2\nintroduced during the device fabrication process could also contribute to this effect. To\navoid any misinterpretation, we have removed the relevant descriptions.\n14. Fig. 3a. Please add the vdW gaps.\nResponse: We have added the vdW gap in Fig. 3a.\nFig. 3a. The schematic of the MoS FET with KBBF dielectric.\n2\n15. Fig. 3. Please report the normalized currents.\nResponse: We have normalized the current values shown in Fig. 3.\n16. Fig. 3i. Not sure this is a fair comparison. Did the authors make sure all Ion are\nreported for the same overdrive? For the same EOT and the same channel length?\nResponse: We aimed to conduct a fair comparison. However, there are very few\nsamples under identical measurement conditions, and we could not ensure they have\nthe same overdrive voltage, EOT, and channel length. Therefore, we decided not to\nperform this comparison.\n17. Fig. 3j. where the hysteresis conditions comparable (similar voltage ranges? similar\nsweep ranges).\nreported in the literature without considering factors such as voltage range and sweep\nrate. For greater rigor, we will not perform this comparison.\n18. By applying a gate voltage stress of -2 V for different durations to the devices at\nResponse: The BTI test was conducted under the condition of EOT = 0.9 nm. The\nrelevant parameters are provided in the manuscript.\n“By applying a gate voltage stress of -2 V for different durations to the devices with an\nEOT of 0.9 nm at 350 K, we characterized the shift in their threshold voltage.”\n19. At this point, the short-channel effects (SCEs) of device become significant, causing\nthe decrease in the gate electrostatic control ability, and leading to an increase in the\nleakage current and SS. SCE should be minimal for monolayers of 2D materials? High-\nk only becomes important to increase the carrier density in the channel.\nResponse: We agree with your point that 2D materials possess excellent immunity to\nshort-channel effects. The channel length of our fabricated devices is not sufficient to\ninduce significant short-channel effects, so we have revised the corresponding\ndescription in the manuscript.\n“Although the top-gate FETs with KBBF dielectrics exhibit excellent performance in\nterms of on/off ratio and SS, the on-state current is still limited by the relatively long\nchannel length and the partial control over the channel semiconductor from the local\ntop gate. Therefore, we fabricated short-channel MoS FETs with a back-gate\n2\nconfiguration using ultra-thin KBBF dielectrics.”\n20. Fig. 4a. Please add the vdW gaps. Shot->Short.\nResponse: We have added the vdW gaps in Fig. 4a and corrected the misspelled words.\nFig. 4a. Schematic of short-channel MoS FET.\n2\n6\n21. a negligible hysteresis (2.3 mV nm−1). Please don't report the 4K hysteresis here,\nuse the much larger average value at RT. This value is not negligible, it is higher than\nthe life-time criterion for Si technology (30 mV after 10 years).\nResponse: According to the suggestion, we calculated the average hysteresis of 10\ndevices at room temperature and revised the manuscript to “a small hysteresis (9.1 mV\non average)”."}]

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