van der Waals grain boundaries with inert electrical behaviors in inorganic molecular dielectric film

Domain: neuroscience
Published: 2026-02-02
Editorial outcome: minor_revision

Abstract
Grain boundaries (GBs) in insulating crystal films generally create lattice reconstruction and excess mid-gap states, which may form the transport pathways of charge carriers and lead to serious degradation of insulating properties. Here, we reveal the inert electrical behaviors of GBs in polycrystalline inorganic molecular dielectric film attributed to its special van der Waals structure. Temperature-dependent electrical measurements and first-principles calculations uncovered that such GBs are free of mid-gap states, which explains the unexpectedly low leakage current of Sb2O3 polycrystalline thin film. Through systematic measurements by conductive atomic force microscopy, we further verify the undistinguishable electrical behaviors within grains and at GBs of the polycrystalline film. Our findings may lay a solid foundation for the applications of inorganic molecular film as a compatible gate dielectric in advanced two-dimensional devices.

Introduction
Insulating crystals with van der Waals (vdW) surface, such as hexagonal boron nitride (hBN) are gaining increasing attention for their superior performance as gate dielectrics, which facilitates the research in solid-state physics1–7 and integrated devices based on two-dimensional (2D) materials8–10. When integrated with 2D materials, they can form a well-saturated interface and enable the fabrication of high-performance devices such as field-effect transistors (FETs). However, most reported vdW insulating crystals with layered structure are integrated with 2D materials via the exfoliation-and-transfer method, incompatible with the semiconductor manufacturing processes11–17. A new type of vdW insulating crystal, antimony trioxide (Sb2O3) with a caged inorganic molecular structure, known as an inorganic molecular crystal (IMC), emerged and attracted plenty of research interests18–28. Apart from its excellent performance in 2D devices, it can be fabricated via thermal sublimation process. This foundry-compatible fabrication technique offers unparalleled convenience for the scalable integration of 2D circuits18,19. A puzzling fact, however, remains unexplained for this inorganic molecular dielectric film. A polycrystalline film usually possesses far inferior properties to its single-crystalline counterpart due to the presence of grain boundaries (GBs). For instance, GBs in insulators can create reconstructed lattice bonds and excess mid-gap states, which may act as charge carrier pathways and lead to serious degradation of their insulating performance29–37. Contrary to this classic theory, the fabricated polycrystalline inorganic molecular film (PIMF) of Sb2O3 with nanometer-scale grains exhibits an unexpectedly high insulating property18.

In this work, we present theoretical and experimental results on the electrical behaviors of Sb2O3 PIMF. The common GBs in conventional dielectric crystals can result in lattice reconstruction and excess mid-gap states, which form leakage pathways of charge carriers and degrade the insulating performance (Fig. 1a). We show, in contrast, that the excellent insulating properties of PIMF arise from the inert electrical behaviors of its GBs with a typical vdW structure. The saturated vdW GBs are free of mid-gap states, resulting in almost identical insulating properties of polycrystalline film and its single-crystal counterpart (Fig. 1b).

Results
Fabrication of PIMF and electrical measurements
The PIMF of Sb2O3 can be fabricated via a thermal sublimation evaporation deposition method18,20. The deposited molecules remain in the cage-like structure and grow into a polycrystalline film on any given substrate, as illustrated in Fig. 2a. We first demonstrate the polycrystalline structure of the Sb2O3 film with a thickness of 10 nm grown on substrates of few-layer graphene (see Methods for details). This is the minimum thickness necessary to prevent the direct tunneling of charges18. As shown in Fig. 2b, the selected area electron diffraction (SAED) pattern confirms the single-crystalline nature of the underlying graphene, whereas the multi-oriented Sb2O3 domains give rise to grain size of around 9.6 nm (see Figure S1), close to the film thickness of 10 nm. This result implies that there may exist high-density transverse GBs (crossing from the top of the film to the bottom) within the film. For electrical characterizations, the Sb2O3 film was directly on a degenerately doped Si substrate, which serves as a flat bottom electrode. We tried to observe the Sb2O3 grains GBs from the cross-section HR-TEM image (Fig. 2d). We can clearly identify the Sb2O3 grains as well as the transverse GBs. Such an insulating film with a large number of continuous pathways for charge carrier transport is theoretically expected to possess a poor current-blocking property. In contrast, it exhibits a low leakage current in our device measurements at room temperature using a parallel plate capacitor (Figure S2). The current density (J) as a function of electric field (E) is furthermore investigated at various temperatures (Fig. 2e). We estimate that each device contains over 108 grains on average between the two electrodes with an area of 200 μm × 200 μm. Despite the presence of such high-density GBs, the measured leakage current density remains as low as 10−7 A/cm2 at an electrical field of 2 MV/cm. Moreover, as we can see in Fig. 2e, the measured leakage current density at varying electric field is independent of temperature. We analyze the electrical properties using Fowler-Nordheim tunneling (FNT) theory for a 10 nm thick insulating film at high electric field. The current density J and bias voltage V can be related using the following equation38–41:

ln(J/V2) = ln(q3m/8πhФB d2m*) - (8π(2m*)1/2 ФB3/2 d / 3hqV) (1)

where m and m* are electron mass and effective electron mass, q is electron charge, ФB is energy barrier, d is the thickness of the insulating layer. The strong linearity between ln(J(V))/V2 and 1/V can be identified from the plots (Fig. 4e inset), and they also exhibit clear independence on temperature, which is in good agreement with FNT theory. For an insulating layer with mid-gap states, the tunneling current generally follows the defect-assisted or trap-assisted tunneling theories42,43. For instance, the charge carriers tunneling assisted by the trap states located within the insulating layer may follow the Poole-Frenkel emission mechanism42,44,45. Its current density J and bias voltage V are related as:

ln(J(V)) / V ~ 1/V1/2 + 1/kT (2)

where kb is the Boltzmann constant and T is the temperature. We can see that for such a mechanism, ln(J(V))/V shows linear relation with V1/2 instead of V and it, moreover, exhibits clear dependence on temperature T45,46. These characteristics are in clear contrast to our measured results (Fig. 2e). Based on such analysis on the electrical transport behaviors, it can be, in turn, confirmed that the tunneling behaviors through our Sb2O3 insulating layer are free of defect- or trap-assisted mechanisms.

Impact of vdW GBs on DOS by calculations
We now try to gain insights into the impact of GBs on the electronic band structure of Sb2O3 crystals. As the molecular structure of Sb2O3 is preserved intact in the sublimation-deposition process, we reasonably assume that all the GBs in Sb2O3 are of vdW structure, as schematically shown in Fig. 2a. In order to investigate the impact of such GB presence on the insulating properties, we performed first-principles calculations to study the band structure of the Sb2O3 polycrystalline film (see details in supplementary materials). We constructed several typical crystal models with low-index crystal planes of (100), (110), (111), and (210), which have the lowest formation energy. A large enough vacuum layer is constructed to create the surface. In these crystal models, the complete molecular structure of Sb2O3 is maintained on the exposed surfaces (Fig. 3a). Since the possible excess mid-gap states in polycrystalline film originate from the breakage of the periodic crystal structure at the GBs, the band structure of our crystal models can represent the scenario of polycrystalline film47. Their calculated results of DOS are compared with those of bulk single crystal (Fig. 3b). The results show that they possess exactly the same band gap and introduce no excess mid-gap states for all the constructed crystal models, thanks to the termination of complete molecules. We specifically indicated that the DOS contributed from the top-layer exposed molecules, and all of their electronic states also remain out of the band gap (Fig. 3b). More explicitly, we constructed some representative crystal models containing GBs and investigated their DOS (see details in Supplementary Materials). For a face-centered cubic (FCC) crystal of Sb2O3, Σ3 and Σ5 twin GBs are preferentially formed in experiments due to their relatively low GB formation energies, which are chosen as two typical bi-crystal models for studying the effects of GBs. The Σ3 out-of-plane twist twin boundary (denoted as GB1, Fig. 3c) and the Σ5 in-plane tilt twin boundary (denoted as GB2, Fig. S3) were therefore selected as representative computational models due to their relatively small number of atoms. They can effectively balance computational efficiency and the accurate description of their physical properties. Their crystal structures were optimized, and electronic structures were calculated (Fig. 3d). The two bi-crystal models possess very similar band gap, which is slightly smaller than the bulk crystal calculated via the same approximation method (see detailed analysis in Supplementary Materials). No excess mid-gap states are created despite the presence of GBs. Such theoretical results imply that the presence of vdW GBs in Sb2O3 PIMF will not result in any mid-gap states, in clear contrast to conventional oxide dielectric materials30,31. The PIMF Sb2O3 possesses an identical band gap to the single-crystal film.

Electrical measurement of Grains and GBs in PIMF via C-AFM
To directly investigate the insulating properties of PIMF at GBs, we employ conductive atomic force microscopy (C-AFM) to probe the nanoelectronic properties of Sb2O3 PIMF at the GBs and within the grains (see experimental details in supplementary materials). C-AFM allows for electrical measurements at local positions with nanometer resolution, and the results can be conveniently correlated with the morphology of the sample surface48–51, enabling us to access the electrical behaviors of GBs and grains simultaneously (Fig. 4a). We first obtain the morphology of the PIMF. Thanks to the effect of GB grooving in the film that grows via deposition, we can identify the GBs and grains from the AFM images (Fig. 4b). We then apply ramp voltage stress on specific positions (at GBs or in grains) and carry out the electrical measurements. Figure 4c shows the forward and backwards sweeping E-I curves obtained at GBs and within grains from over 100 positions, with a current limitation of 100 pA to protect the tip and the sample52. Statistically, we find no discernible difference between GBs and grains' E-I curves. The average E-I curves obtained from GBs and grains are almost overlapped (thick curves in Fig. 4c), both for forward and backwards sweeping, which implies an identical electrical property for GBs and grains of our Sb2O3 PIMF. We also analyzed the average E-I curves using FNT theory, as shown in Fig. 4d. Their linear relation implies that both the electrical behaviors of GBs and grains are in good agreement with the FNT as well (analysis of the measured data is shown in Fig. S3). The required electrical field to reach a fixed leakage current of 3 pA for GBs and grains is plotted statically in Fig. 4e, from which we can see that they exhibit very similar values. C-AFM also allows for mapping leakage currents over a given area, which can provide the insulating properties over a continuous area. Applying a constant bias voltage of 3.5 V on the C-AFM tip, the leakage currents in a 500 nm × 500 nm area are mapped for three times (Fig. 4f). As we can observe, most area exhibits an ultra-low conductivity while some regions are more conductive (dark points in Fig. 4f), however, it is clear that such highly-conductive regions do not correlate to the positions of GBs and the position do not repeat in multiple scans; moreover, the currents decrease as the stress proceed due to the presence of charge trapping effect, i.e. some charges get trapped and released from the trapping points. This result is in contrast with multiple observations of enhanced currents and fast degradation at the grain boundaries of metal oxides like HfO253,54. Therefore, this behavior observed in GBs of Sb2O3 PIMF is quite unique and offers higher opportunities for being used as a gate dielectric.

Methods
Thermal evaporation deposition of PIMF Sb2O3
The deposition of Sb2O3 was carried out in a standard thermal evaporation deposition system (Nexdep, Angstrom Engineering) in a high vacuum (10−6 torr). Sb2O3 powder was sublimated by heating and deposited on substrates. The deposition rate was precisely controlled by an in-situ quartz crystal oscillator. To maintain the flatness of the obtained Sb2O3 film, the deposition rate in this work was 0.06 Å s−1 for the entire fabrication process.

Sample preparation for TEM characterizations
For plan-view TEM samples, we exfoliated a few-layer graphene flakes onto SiO2/Si substrate and then transferred them onto a TEM grid assisted by a PMMA membrane. Then the PMMA membrane on the TEM grid is dissolved in acetone. Afterwards, the TEM grid with graphene flakes is annealed in an Ar atmosphere to remove the PMMA residues on graphene flakes, which is then loaded into the thermal evaporation deposition system, and Sb2O3 is deposited. For the cross-section TEM lamella, 10 nm of Sb2O3 was deposited onto a degenerately doped silicon substrate, and then the lamella was fabricated by a dual focused ion beam system (Helios Nanolab G3 UC, FEI). TEM images and SAED were obtained using an FEI Tecnai G2 20.

Preparation and characterization of capacitor devices
10 nm of Sb2O3 was deposited onto a degenerately doped silicon substrate. A shadow mask with a predefined size of 200 μm × 200 μm was placed over the film, followed by the deposition of 40 nm of Au via thermal evaporation to form the top metal electrode. In such a way, the devices for electrical characterizations can be maintained free of contamination resulting from the fabrication processes.

Electrical measurements
Current-voltage measurements were performed in a probe station (Lakeshore) equipped with a semiconductor analyzer (Keithley 4200). We pump the chamber and keep it in a high vacuum (10−6 torr) for 3 h to eliminate the gas adsorption on device surfaces before the device test. Afterwards, the device tests are carried out at various temperatures.

Theoretical calculations
The details of the theoretical calculations are described in the Supplementary Materials.

C-AFM characterization
Conductive atomic force microscopy (C-AFM) experiments were carried out on a Bruker Dimension Icon instrument fitted with a Nanoscope VI controller and PFTUNA module. Measurements were performed in ambient air (relative humidity ≈ 54%). Surface topography was mapped in tapping mode using an NCHV-A tip (spring constant 42 N/m), whereas nanoelectronic characterization, including current mapping and I–V spectroscopy, was obtained in PF-TUNA (tunneling current) mode with a solid platinum RNM25PT300B probe (spring constant 18 N/m). Imaging scans were acquired at 1 Hz, and all I–V curves were collected under a compliance current of 100 pA to prevent damage to both tip and sample. The onset potential (VON) was defined as the voltage at which the measured current first exceeded the system noise level (≈ 3 pA).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors investigated the insulating properties of Sb2O3 polycrystalline inorganic molecular film while paid particular\nattentions to its grain boundaries. This kind of film attract research interests recently for its great potentials as a decent van\nder Waals dielectric film in advanced 2D-semiconductor-based devices, which can be conveniently fabricated and\nintegrated in a scalable way. A polycrystalline film is expected to have poor insulating properties in theory since the grain\nboundaries as typical crystal defects can form the leakage paths. However, in this work, the authors revealed that the grain\nboundaries in Sb2O3 polycrystalline film with van der Waals structure create no defects. They provided robust evidences of\ndevice measurements and theoretical calculations and explain a puzzling fact: why Sb2O3 polycrystalline film possesses an\nexcellent current-blocking property. This work is of significance for applications of this promising dielectric material in future\n2D integrated circuits. I recommend it be accepted for publication in Nature Communications after my concerns as follows\nare well addressed.\n1.In Fig.1a, the schematic figure depicting defect-assisted tunneling is probably incorrect. The charge carriers are supposed\nto hop between defect states via emission mechanism instead of tunneling. The leakage current is temperature-dependent\nonly via emission mechanism in theory. The authors should reconsider the mechanism, correct the figure and the related\ncontent in the manuscript.\n2.The standard of leakage current for a gate dielectric (DRAM for instance) should be marked in Fig.2e so that the insulating\nperformance of Sb2O3 film can be clearly identified.\n3.In the current mappings Fig.4 f, there are some points that show high leakage current. What has caused this leakage?\n4.As we know, the dielectric materials used in many organic devices are made of organic molecules. Is the conclusion also\napplicable to organic molecular dielectric materials? I think it would be interesting if this phenomenon can be extended to\norganic molecular dielectric materials and added relevant content in the part of Discussion.", "reviewer_2": "The manuscript by Liu et al. reports an intriguing observation that the grain boundaries (GBs) of Sb₂O₃ do not exhibit\nleakage current, in stark contrast to conventional insulating films such as HfO₂. The authors attribute this behavior to the\nintrinsic van der Waals (vdW) structure of Sb₂O₃, which purportedly suppresses the formation of charge transport pathways\nvia mid-gap states at the GBs. If validated, this could have substantial implications for the future design of dielectric materials\nin next-generation electronic devices.\nHowever, I believe that further clarification is required to disentangle the effects of the Sb₂O₃ material itself from those\npotentially introduced by the graphene layers used in the experiments. I raise the following concerns:\n1. The suppression of leakage current might not be solely due to the intrinsic properties of Sb₂O₃. As noted on page 3,\nmultiple layers of graphene were intentionally inserted to block direct tunneling of charge carriers. It is therefore critical to\nclarify whether the absence of leakage at GBs is a result of the Sb₂O₃ properties alone or whether it is influenced—partially\nor substantially—by the presence of graphene. The authors should provide a clear explanation or experimental evidence\nruling out the contribution of graphene to the observed leakage suppression.\n2. Related to the above point, Figure 2d is said to show the cross-sectional TEM image, but it is unclear whether the multiple\ngraphene layers are visible or identifiable in this image. If graphene is indeed present, it should be explicitly marked or\nreferenced, and the number of layers should be specified.\n3. It is also unclear whether the measurements presented in Figure 4 were performed on structures that include the\ngraphene layers. Since graphene may strongly influence the electronic properties, especially near GBs, this information is\nessential. If graphene is present in these measurements, it should be consistently annotated throughout the figures and text.\nThe current description only briefly mentions graphene on page 3, with no further indication of its presence in subsequent\nexperiments, which could lead to misunderstandings about the experimental conditions.\n4. On page 7, the authors state: “We first obtain the morphology of the PIMF, from which the GBs and grains can be identified\n(Figure 4b).” However, Figure 4b does not appear to show atomic-resolution imaging, which casts doubt on whether the\nfeatures identified can be definitively assigned as grain boundaries. The authors should clarify the resolution of this image\nand discuss any supporting evidence that validates the interpretation of the observed features as GBs.\nIn summary, while the results are promising, I recommend that the authors provide more detailed and unambiguous\nevidence to isolate the intrinsic effects of Sb₂O₃ from potential contributions of the graphene interlayers. Without this\nclarification, the claim that Sb₂O₃ GBs intrinsically suppress leakage remains open to alternative interpretations.\nMinor comment: The abbreviation IMC appears in the manuscript but is not defined upon first usage. The authors are\nadvised to ensure that all abbreviations, including IMC and others throughout the text, are clearly defined when first\nintroduced for clarity.", "reviewer_3": "Kailang Liu et al. study leakage currents across polycrystalline dielectric films deposited by thermal evaporation of Sb₂O₃.\nWhile the basic dielectric properties of these films, including dielectric permittivity and leakage current, were previously\ncharacterized by the authors [Nature Electronics 4, 906–913 (2021)], they show here that the leakage currents are fairly\nuniform across both grain interiors and grain boundaries (GBs), and they attribute this uniformity to the absence of mid-gap\nstates at GBs. My specific comments are below.\n1. The dielectric film exhibits decent insulating properties, with a low leakage current of ~10⁻⁷ A/cm² at a thickness of 10 nm\n(equivalent oxide thickness ~3.5 nm). However, although the authors compare their results with HfO₂—where GBs are\nknown to introduce mid-gap states and enable defect-assisted tunneling—the advantage of Sb₂O₃ remains somewhat\nunclear. Reported leakage currents for HfO₂ at similar EOTs are comparable, despite its polycrystallinity. What is the\nleakage current of the Sb₂O₃ dielectric at sub-1 nm EOT for state-of-the-art MOSFETs? The authors should clarify the\nsignificance of their films as gate dielectrics.\n2. The grain size in Fig. 4 (a few tens of nanometers) is too small to fully isolate current through GBs from that through grain\ninteriors using C-AFM in ambient conditions. Measurements on samples with much larger grains (>~100 nm) would be\nrequired for a proper comparison, given the spatial resolution of C-AFM and the film thickness.\n3. Do the deposited dielectric films retain the pristine caged inorganic molecular structures proposed in the schematics (Fig.\n2a)? In particular, after thermal deposition, the individual Sb₂O₃ molecules could contain various atomic defects (e.g.,\nvacancies) or form polymeric chains with different stoichiometries. If such atomic defects are uniformly present and govern\nthe leakage current level, GB-specific effects would be difficult to observe.\n4. In Fig. 3, the results show changes in electronic states associated with different crystalline surfaces only. To assess GB\neffects, simulations should be performed on structures that explicitly contain a GB, where two different crystalline domains\nare interfaced.\n5. In Fig. 4f, the locations of high-leakage spots change as the scan is repeated, suggesting structural evolution of the\ndielectric during measurement. What is the structural origin of these local high-leakage currents, and why do their positions\nshift during repeated scans?"}, "author_response": "Responses to reviewers’ comments\nWe thank the reviewers for their comments on our manuscript titled “van der\nWaals grain boundaries with inert electrical behaviors in inorganic molecular\ndielectric film”, based on which we made significant corrections and great\nimprovement on our manuscript. Penglai Gong and Xiaofu Wei are included in\nthe author list for his great contributions to the theoretical calculations of band\nstructure for Sb O with grain boundaries and insightful discussions in the revision\n2 3\nworks. The point-to-point response to the reviewers’ comments are listed as below\nand all the corresponding modifications are highlighted in our revised manuscript.\nResponses to Reviewer #1\nGeneral Comments: The authors investigated the insulating properties of\nSb O polycrystalline inorganic molecular film while paid particular\n2 3\nattentions to its grain boundaries. This kind of film attract research interests\nrecently for its great potentials as a decent van der Waals dielectric film in\nadvanced 2D-semiconductor-based devices, which can be conveniently\nfabricated and integrated in a scalable way. A polycrystalline film is\nexpected to have poor insulating properties in theory since the grain\nboundaries as typical crystal defects can form the leakage paths. However,\nin this work, the authors revealed that the grain boundaries in Sb O\n2 3\npolycrystalline film with van der Waals structure create no defects. They\nprovided robust evidences of device measurements and theoretical\ncalculations and explain a puzzling fact: why Sb O polycrystalline film\n2 3\npossesses an excellent current-blocking property. This work is of\nsignificance for applications of this promising dielectric material in future\n2D integrated circuits. I recommend it be accepted for publication in\nNature Communications after my concerns as follows are well addressed.\nResponse: We thank the reviewer for the positive comments to the\nsignificance of this work. We tried to addressed the reviewer’s concerns as\nlisted below.\nComment 1：In Fig.1a, the schematic figure depicting defect-assisted\ntunneling is probably incorrect. The charge carriers are supposed to hop\nbetween defect states via emission mechanism instead of tunneling. The\nleakage current is temperature-dependent only via emission mechanism in\ntheory. The authors should reconsider the mechanism, correct the figure\nand the related content in the manuscript.\nResponse: We thank the reviewer for pointing out this mistake in our\nmanuscript. We have corrected the figure depicting the transport of charge\ncarriers between defect states to be the thermionic emission, as shown\nbelow.\nComment 2：The standard of leakage current for a gate dielectric (DRAM\nfor instance) should be marked in Fig.2e so that the insulating performance\nof Sb O film can be clearly identified.\n2 3\nResponse: We thank the reviewer for this suggestion. We have added a\ndashed line in Fig.2e that marks the technological requirement for DRAM\ndevices, from which we can clearly see the insulating performance of\nSb O film satisfies at an average electric field around 1.7 MV/cm.\n2 3\nComment 3：In the current mappings Fig.4f, there are some points that\nshow high leakage current. What has caused this leakage?\nResponse: We thank the reviewer for this comment. As we mentioned in\nthe main text, the currents decrease as the stress proceed due to the\npresence of charge trapping effect. More specifically, the locations of high-\nleakage spots may shift between repeated scans due to the dynamic filling\nand release of the trap states rather than permanent structural changes. In\nthe revised manuscript, we have more clearly explained this phenomenon.\nComment 4：As we know, the dielectric materials used in many organic\ndevices are made of organic molecules. Is the conclusion also applicable to\norganic molecular dielectric materials? I think it would be interesting if this\nphenomenon can be extended to organic molecular dielectric materials and\nadded relevant content in the part of Discussion.\nResponse: We thank the reviewer for this great suggestion. It is true that a\nlot of organic molecular dielectric materials are used in organic devices for\ntheir compatibility. For instance, self-assembled monolayer PhO-OTS\n(Nature 431, 963, 2004) and poly(vinylidene fluoride) (PVDF)\n(Phys.Rev.Lett.118, 236801, 2017) are widely used either as dielectric or\nferroelectrics. We have added the relevant content about organic molecular\ndielectric materials in the part of discussion in our revised manuscript.\nResponses to Reviewer #2\nGeneral Comments: The manuscript by Liu et al. reports an intriguing\nobservation that the grain boundaries (GBs) of Sb₂O₃ do not exhibit leakage\ncurrent, in stark contrast to conventional insulating films such as HfO₂. The\nauthors attribute this behavior to the intrinsic van der Waals (vdW) structure of\nSb₂O₃, which purportedly suppresses the formation of charge transport pathways\nvia mid-gap states at the GBs. If validated, this could have substantial\nimplications for the future design of dielectric materials in next-generation\nelectronic devices. However, I believe that further clarification is required to\ndisentangle the effects of the Sb₂O₃ material itself from those potentially\nintroduced by the graphene layers used in the experiments. I raise the following\nconcerns.\nResponse: We thank the reviewer for such supportive comments. The\nreviewer’s major concern is responded as shown below.\nComment 1: The suppression of leakage current might not be solely due to\nthe intrinsic properties of Sb₂O₃. As noted on page 3, multiple layers of\ngraphene were intentionally inserted to block direct tunneling of charge\ncarriers. It is therefore critical to clarify whether the absence of leakage at\nGBs is a result of the Sb₂O₃ properties alone or whether it is influenced—\npartially or substantially—by the presence of graphene. The authors should\nprovide a clear explanation or experimental evidence ruling out the\ncontribution of graphene to the observed leakage suppression.\nResponse: We thank that the reviewer for pointing out this unclear\nstatement in our manuscript, which leads to some misunderstandings. In\nfact, all the samples, except the one used for plan-view TEM\ncharacterizations, were fabricated without few-layer graphene. For\nsamples that are used for electrical measurements in Fig.2d and 2e and for\nC-AFM measurements, Sb O polycrystalline film is deposited on\n2 3\ndegenerately doped Si substrates without few-layer graphene. For plan-\nview TEM characterizations, we transferred few-layer graphene first onto\nTEM grid and then deposit Sb O so that the damages to Sb O film during\n2 3 2 3\nthe transfer process can be avoided. We have now more clearly described\nthe fabrication processes of samples and devices that are used in our\nexperiments and hope that it will no longer lead to similar\nmisunderstandings.\nComment 2: Related to the above point, Figure 2d is said to show the cross-\nsectional TEM image, but it is unclear whether the multiple graphene\nlayers are visible or identifiable in this image. If graphene is indeed present,\nit should be explicitly marked or referenced, and the number of layers\nshould be specified.\nResponse:Graphene is not used in the sample for the cross-sectional TEM\ncharacterizations in Figure 2d. Sb O polycrystalline film is deposited on\n2 3\ndegenerately doped Si substrate and all the materials can be identified and\nhave been indicated in Figure 2d. We have more clearly described the\nfabrication processes of samples and devices in our revised manuscript.\nComment 3: It is also unclear whether the measurements presented in\nFigure 4 were performed on structures that include the graphene layers.\nSince graphene may strongly influence the electronic properties, especially\nnear GBs, this information is essential. If graphene is present in these\nmeasurements, it should be consistently annotated throughout the figures\nand text. The current description only briefly mentions graphene on page\n3, with no further indication of its presence in subsequent experiments,\nwhich could lead to misunderstandings about the experimental conditions.\nResponse: We have modified the description about the fabrication\nprocesses of samples and devices both the main manuscript and Methods.\nFew-layer graphene is actually only used in the sample preparation of plan-\nview TEM. We hope that the revised manuscript will not lead to such\nmisunderstandings.\nComment 4: On page 7, the authors state: “We first obtain the morphology\nof the PIMF, from which the GBs and grains can be identified (Figure 4b).”\nHowever, Figure 4b does not appear to show atomic-resolution imaging,\nwhich casts doubt on whether the features identified can be definitively\nassigned as grain boundaries. The authors should clarify the resolution of\nthis image and discuss any supporting evidence that validates the\ninterpretation of the observed features as GBs.\nResponse: It is true that Figure 4b does not show atomic resolution and\nindeed AFM can hardly provide atomic-resolution images to identify the\nGBs in a film via the crystal lattice structure. However, for a polycrystalline\nfilm that grows on arbitrary substrates, we can usually identify the GBs\nfrom the morphology since there are always grooves at GBs. The\ngrooves at grain boundaries (GBs) are very common and arise from a\ncombination of thermodynamic driving forces and kinetic processes during\nfilm growth or post-growth annealing, which is called grain-boundary\ngrooving. The physical mechanism was revealed and described in some\npapers (J. Appl. Phys. 28, 333,1957; Phys. Rev. Lett. 98, 085503, 2007). In\nthis work, we actually identify the GBs from the grooves within the Sb O\n2 3\nfilm from the AFM images. We can identify grain sizes of about10 nm,\nwhich is in good agreement with the results by TEM in Figure 1. In such a\nway, it is convenient to positioning GBs and carried out the electrical\nmeasurements via C-AFM. In our revised manuscript, we explained how\nwe identify the GB from the AFM images.\nComment 5: In summary, while the results are promising, I recommend\nthat the authors provide more detailed and unambiguous evidence to isolate\nthe intrinsic effects of Sb₂O₃ from potential contributions of the graphene\ninterlayers. Without this clarification, the claim that Sb₂O₃ GBs\nintrinsically suppress leakage remains open to alternative interpretations.\nResponse:We are so grateful that the reviewer has pointed out this critical\nissue in our initial manuscript. We hope that in our revised manuscript the\ndescriptions of various sample fabrication are clear enough and will not\nlead to similar misunderstandings.\nComment 6: Minor comment: The abbreviation IMC appears in the\nmanuscript but is not defined upon first usage. The authors are advised to\nensure that all abbreviations, including IMC and others throughout the text,\nare clearly defined when first introduced for clarity.\nResponse: We appreciate this suggestion. In our revised manuscript, we\nhave addressed such problems and double check all the used abbreviations.\nReviewer #3 (Remarks to the Author):\nGeneral Comments: Kailang Liu et al. study leakage currents across\npolycrystalline dielectric films deposited by thermal evaporation of Sb₂O₃.\nWhile the basic dielectric properties of these films, including dielectric\npermittivity and leakage current, were previously characterized by the\nauthors [Nature Electronics 4, 906–913 (2021)], they show here that the\nleakage currents are fairly uniform across both grain interiors and grain\nboundaries (GBs), and they attribute this uniformity to the absence of mid-\ngap states at GBs. My specific comments are below.\nResponse: In our previous works, we have measured the basic dielectric\nproperties of Sb O film. For instance, the polycrystalline Sb O film\n2 3 2 3\ndeposited at room temperature on degenerately doped Si substrate [Nature\nElectronics 4, 906–913 (2021)]. The current blocking property is not only\ndependent on the intrinsic materials, but also on the film quality. In another\nwork [National Science Review 2024,11, nwae358], we carefully controlled\nthe growth behaviors of Sb O and managed to improve the film quality\n2 3\nwith higher uniformity, which exhibited better current blocking property\nand improved device performance. In this work, we focus on the very\nspecial GBs within the Sb O film and provide an explanation to its\n2 3\nunexpected current blocking properties. We believe that this work can lay\na robust foundation for its application in integrated 2D devices.\nComment 1: The dielectric film exhibits decent insulating properties, with\na low leakage current of ~10⁻⁷ A/cm² at a thickness of 10 nm (equivalent\noxide thickness ~3.5 nm). However, although the authors compare their\nresults with HfO₂—where GBs are known to introduce mid-gap states and\nenable defect-assisted tunneling—the advantage of Sb₂O₃ remains\nsomewhat unclear. Reported leakage currents for HfO₂ at similar EOTs are\ncomparable, despite its polycrystallinity. What is the leakage current of the\nSb₂O₃ dielectric at sub-1 nm EOT for state-of-the-art MOSFETs? The\nauthors should clarify the significance of their films as gate dielectrics.\nResponse: As we have stated in the Introduction part of our manuscript\nand have demonstrated in our previous work [Nature Electronics 4, 906–\n913 (2021)], the greatest advantage of Sb O film as van der Waals gate\n2 3\ndielectric for 2D devices is high compatibility with CMOS processes. It\ncan be facilely fabricated via thermal evaporation deposition method in a\nscalable way on arbitrary substrates and remain its van der Waals structure.\nWith respect to the gate capacitance (or EOT) of Sb O film that the\n2 3\nreviewer pointed out, it not only determined by intrinsic dielectric\nproperties (dielectric constant and band gap), but also greatly depend on\nthe film quality. For Sb O film deposited at room temperature without\n2 3\nprecise growth process control [Nature Electronics 4, 906–913 (2021)],\nthe EOT that meets leakage current standard is 3.5 nm. We more carefully\ncontrolled the nucleation and growth behaviors of Sb O and managed\n2 3\nimprove the performance of Sb2O3 film, exhibiting low gate leakage at 5\nnm (or EOT=1.7 nm) [National Science Review 2024, 11, nwae358]. To\nfurther push its EOT to the requirement of IRDS, we devised the\nSb O /HfO hybrid dielectric integrated on 2D semiconductors with a\n2 3 2\nrecord low EOT of 0.67 nm. While in all the above dielectrics based on\nSb O with high-density grain boundaries, a shared question is that its grain\n2 3\nboundaries do not lead to excess current leakage. This is exactly the\nquestion that our current research work tries to answer. The findings\npresented in this work is an important foundation for the Sb O -based gate\n2 3\ndielectrics in integrated 2D devices.\nComment 2: The grain size in Fig. 4 (a few tens of nanometers) is too small\nto fully isolate current through GBs from that through grain interiors using\nC-AFM in ambient conditions. Measurements on samples with much larger\ngrains (>~100 nm) would be required for a proper comparison, given the\nspatial resolution of C-AFM and the film thickness.\nResponse: We thank the reviewer for this comment. However, we\nrespectfully disagree with this comment. With a resolution of 512 × 512\npixels over a scan area of less than 500 × 500 nm2, the spatial resolution of\nour CAFM measurements is sufficient to resolve features on the scale of\nindividual GBs with lateral dimensions of a few tens of nanometers. More\nspecifically, as shown in Fig. 4f, we are able to detect current spots with\ndiameters below 4 nm, demonstrating that our setup can clearly distinguish\nlocal conduction at the GBs from that within the grain interiors under\nambient conditions.\nComment 3: Do the deposited dielectric films retain the pristine caged\ninorganic molecular structures proposed in the schematics (Fig. 2a)? In\nparticular, after thermal deposition, the individual Sb₂O₃ molecules could\ncontain various atomic defects (e.g., vacancies) or form polymeric chains\nwith different stoichiometries. If such atomic defects are uniformly present\nand govern the leakage current level, GB-specific effects would be difficult\nto observe.\nResponse: The fact that the molecular structure can be remained during\nthe thermal deposition process has been demonstrated and verified in our\nprevious reported works. Due to the weak van der Waals interaction, the\nSb O molecules will sublime before melting when heated up under high\n2 3\nvacuum in the thermal evaporation deposition process. We have verified\nthis phenomenon with a bunch of evidences (Nature Electronics 4, 906–\n913 (2021)), including Raman spectroscopy and thermogravimetry\nanalysis. We also exhibited atomic images of Sb O crystals grown on\n2 3\ngraphene substrates via STM [National Science Review 2024, 11, nwae358].\nWe have demonstrated that: 1) the deposited Sb O film exhibits the same\n2 3\nRaman spectrum as Sb O source powder and all the peaks in spectra are\n2 3\nassigned to the molecular vibration mode, which indicates that Sb O\n2 3\nremains the molecular structure; 2) the sublimation temperature of Sb O\n2 3\npowder is measured to be 490 ℃ at ambient pressure and 186 ℃ at 10-6\ntorr, both far below its melting point of 656 ℃, indicating the sublimation\nof molecules before melting. 3) the formation energy is molecular structure\nof Sb O can be clearly observed STM and none of atomic defects have\n2 3\nbeen identified. The excellent performance of Sb O film in our integrated\n2 3\ndevices is also an indirect evidence. A defective Sb O film can not serve\n2 3\nas an excellent dielectric layer, which may lead to degraded device mobility\nand large hysteresis.\nComment 4: In Fig. 3, the results show changes in electronic states\nassociated with different crystalline surfaces only. To assess GB effects,\nsimulations should be performed on structures that explicitly contain a GB,\nwhere two different crystalline domains are interfaced.\nResponse: In our initial manuscript, as demonstrated in Figure 3a and 3b,\nwe constructed some typical crystal models with low-index crystal planes\nwith exposed surfaces. These structures, though in an indirect way, can in\nprinciple reflect how the presence of GB may impact the band structures\nin comparison with the single-crystal counterpart. Definitely a more\nexplicit approach is to construct crystal models containing as many GB\ntypes as possible and investigate their band structures. However, it is\nextremely difficult to calculate for crystal models containing GBs since\nthey possess a large number of atoms. Limited by the calculation resources,\nwe constructed two representative crystal models with low formation\nenergies: (111)[111] Σ3 denoted as GB1 (Fig. R1)and (310)[100] Σ5\ndenoted as GB2 (Fig. R2). We optimized the structure and calculated their\nelectronic structures (Fig. R3). The calculated results provide a direct\nevidence to our primary conclusion that such vdW GBs of Sb O film do\n2 3\nnot create excess mid-gap states as conventional dielectric crystals.\nFig. R1. The atomic structure of GB1.\nFig. R2. The atomic structure of GB2.\nFig. R3. Comparison of the density of states (DOS) for the twin boundaries\nGB1 and GB2 with the bulk, calculated using numerical atomic orbitals.\nComment 5: In Fig. 4f, the locations of high-leakage spots change as the\nscan is repeated, suggesting structural evolution of the dielectric during\nmeasurement. What is the structural origin of these local high-leakage\ncurrents, and why do their positions shift during repeated scans?\nResponse: We thank the reviewer for this comment. As we mentioned in\nthe main text, the currents decrease as the stress proceed due to the\npresence of charge trapping effect. More specifically, the locations of high-\nleakage spots may shift between repeated scans due to the dynamic filling\nand release of the trap states rather than permanent structural changes."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have addressed all comments; this current version can be published as it is.", "reviewer_2": "The authors have adequately addressed all the reviewers’ comments, and the revised manuscript is significantly improved. I\nbelieve the paper is now suitable for publication.", "reviewer_3": "The authors have answered most of my previous questions and revised the manuscript. In particular, they have added\nadditional DFT calculations on twin boundary structures as a representative boundary case to show that mid-gap states are\nabsent. However, I still have a concern regarding the spatial resolution of C-AFM measurements.\nThe spatial resolution of typical C-AFM is generally larger than 10 nm in ambient conditions, and it is not correlated with the\ndensity of data acquisition points (pixels). Furthermore, the probe tip (RNM25PT300B) used for the measurement appears to\nhave a tip radius < 20 nm. If the measurement has a resolution on the scale of a few nm to effectively distinguish the\ntransport between grain boundary (GB) and grain interior (GI) regions, clearly higher tunneling currents should have been\nidentified in GBs according to FNT theory. This is because there are grooves along the GBs with a smaller d than the GI,\neven though there are no additional defects for leakage pathways (Fig. 4b). Demonstrating a low leakage current despite the\nhigh density of GBs still supports the authors’ main claims. However, I believe that currents through both adjacent GB and GI\nregions contribute to the total current due to current spreading, resulting in spatially averaged data, and this needs to be\ncorrectly commented on in the manuscript."}, "author_response": "Responses to reviewers’ comments\nWe thank the reviewers for their comments on our manuscript titled “van der Waals grain\nboundaries with inert electrical behaviors in inorganic molecular dielectric film”. The\nresponse to the comment is listed as below\nReviewer #3 (Remarks to the Author):\nThe authors have answered most of my previous questions and revised the manuscript. In\nparticular, they have added additional DFT calculations on twin boundary structures as a\nrepresentative boundary case to show that mid-gap states are absent. However, I still have a\nconcern regarding the spatial resolution of C-AFM measurements. The spatial resolution of\ntypical C-AFM is generally larger than 10 nm in ambient conditions, and it is not correlated\nwith the density of data acquisition points (pixels). Furthermore, the probe tip (RNM25PT300B)\nused for the measurement appears to have a tip radius < 20 nm. If the measurement has a\nresolution on the scale of a few nm to effectively distinguish the transport between grain\nboundary (GB) and grain interior (GI) regions, clearly higher tunneling currents should have been\nidentified in GBs according to FNT theory. This is because there are grooves along the GBs with a smaller d than the GI,\neven though there are no additional defects for leakage pathways (Fig. 4b). Demonstrating a low leakage current despite the\nhigh density of GBs still supports the authors’ main claims. However, I believe that currents through both adjacent GB\nand GI regions contribute to the total current due to current spreading, resulting in spatially\naveraged data, and this needs to be correctly commented on in the manuscript.\nReply：We thank the reviewer for raising this point regarding the spatial resolution of CAFM\nmeasurements. However, we respectfully disagree with the implication that the spatial\nresolution in our experiments is limited by the nominal tip radius or by current spreading\nbetween adjacent regions.\nAlthough the C-AFM tip radius is typically larger than a few nanometers, the effective electrical\ncontact is governed by the location of highest local conductivity within the contact area. As a\nresult, charge transport is dominated by the most conductive nanoscale region rather than being\nuniformly distributed across the full tip and sample contact. This enables the detection of highly\nlocalized current spots with resolution well below the nominal tip radius, as shown in Fig. R1.\nFig. R1 | Top view schematic of CAFM contact area and highly conductivity area. [Nanosurf\nCAFM atomic-resolution. Technical note. Online accessed on December 13 th, 2025.\nhttps://www.nanosurf.com/fridayafm/conductive_stick_slip?utm_campaign=%23FridayAFM\n&utm_content=286162975&utm_medium=social&utm_source=linkedin&hss_channel=lis-\ngjO05USkfG]\nIn practice, CAFM can also detect lattice resolution in air. We cite several representative studies\nwhere lattice resolution or atomic resolution was obtained using CAFM in air, despite\nemploying tips with radii significantly larger than the resolution detected in the present work:\n1. Xu K, Holbrook M, Holtzman L N, et al. ACS Nano, 2023, 17(24): 24743-24752.\n(CAFM tip: All-In-One DD, R = 250 nm)\ntip\n2. Yang Y, Xu K, Holtzman L N, et al. ACS Nano, 2024, 18(9): 6887-6895.\n(CAFM tip: All-In-One DD, R = 250 nm)\ntip\n3. Sumaiya S A, Liu J, Baykara M Z. ACS Nano, 2022, 16(12): 20086-20093.\n(CAFM tip: CDT-CONTR, R = 100-200 nm)\ntip\n4. Nanosurf CAFM atomic-resolution. Technical note. Online accessed on December 13 th,\n2025.\nhttps://www.nanosurf.com/fridayafm/conductive_stick_slip?utm_campaign=%23FridayA\nFM&utm_content=286162975&utm_medium=social&utm_source=linkedin&hss_channe\nl=lis-gjO05USkfG\n(CAFM tip: Multi 75E, R = 20 nm)\ntip"}]

Decision letter