Introduction

Electromagnetic wave absorbing (EWA) materials are undergoing unprecedented technological innovations to address the billion-fold surge in electromagnetic radiation1,2,3,4,5. Impressively, the heteroatom doping strategy offers microscopic modification capabilities down to the atomic scale, fundamentally reshaping the atomic configuration and EWA properties of materials6,7,8. Theoretically, countless mapping relationships from microstructures to macrofunctions can be derived by designing the doping sequence and cleverly combining different heteroatoms. However, revealing the interatomic interactions and inheritance rules during complex doping processes, as well as how these factors collectively determine the EWA mechanism and manipulate electromagnetic properties, poses a formidable challenge.

Inspired by the traditional concept of high entropy (HE), doping engineering with five or more types of heteroelements (not limited to near-equimolar ratios) is defined as high-entropy doping (HED). Technically, HED directly belongs to the emerging branch of doping engineering, while conceptually, it has HE advantages9,10. Prior HE studies have outlined preferred modification pathways (e.g., enhancing the defect density, and creating heterogeneous interfaces) and core effects (e.g., lattice distortion, and cocktail effects) that are highly relevant for guiding EWA material design11,12,13,14. Upon examination of seminal EWA works from prestigious teams on HE systems spanning metals, oxides, ceramics, and sulfides, a unifying principle emerges: minimizing short-range ordering and maximizing the energy density within the system15,16,17,18. Although HED engineering has yet to be reported in the EWA field, it has already demonstrated comparable or even superior value to conventional HE strategies in energy applications, including conformational entropy maximization, electronic structure optimization, and robustness enhancement19. Therefore, HED engineering can provide new degrees of freedom for electromagnetic property regulation and expand the development horizons of EWA materials20,21.

To date, the lack of two categories of pivotal investigations has hindered progress in HED research and the EWA field. The first category is HED research focusing on two-dimensional van der Waals (2D-vdW) systems22. Compared with 3D materials, the weak interlayer interactions of 2D-vdW materials provide them with a larger atomic modulation space in the vertical direction23. Moreover, the fewer interfacial defects and large specific surface area synergistically suppress phase separation, ensuring phase homogeneity and doping uniformity. This research is crucial for elucidating the origins of the EWA mechanism, as it eliminates interfacial interference and facilitates clearer cross-scale correlations between atomic configurations and electromagnetic functionalities. The other missing category is anionic HED studies. Anions have a greater difference in electronegativity than cations, which means that strongly polar dipole pairs can be more easily introduced and that the conductivity can be more easily regulated24. Interestingly, codoped systems exhibit more significant spin density redistribution and stronger carrier migration ability than single-doped systems, which is beneficial for energy storage and conversion25,26,27. Researchers have begun to consciously regulate the doping sequence of up to three elements, and preliminary success has been achieved28. Given this, there is potential to further selectively manipulate localized/delocalized electronic states through anionic HED engineering, thus transitioning the cocktail effect in HE materials from unpredictable to programmable.

In this work, we conduct an anionic HED study on a thin graphite framework and demonstrate its effectiveness in the EWA field. Five anions (O/N/S/P/B) are sequentially doped into a unified two-dimensional thin graphite framework through a synergistic strategy of in-situ pyrolysis and solvothermal treatment. Throughout the HED process, the pivotal anion multibody interactions and underlying inheritance principles encompass the following: 1) N/S codoping greatly increases the electron concentration. 2) A sixfold B-doping efficiency is achieved because of the preexisting N, which results in electronic traps. 3) Both the P and B doping processes introduce many O-containing groups, resulting in electron localization. 4) The heteroatom content increases across successive doping processes, maximizing the configuration entropy and polarity. Notably, perfectly balanced delocalized charges and wide-area imbalanced local charges lead to a ‘directional cocktail effect’ that ensures the dominance of dipole polarization in the dielectric loss. In addition, we apply the product to electronic chips and reduce electromagnetic radiation by more than 90%. In conclusion, this work fills the gap in HED and HE research and provides ideas for designing high-performance EWA materials.

Results and discussion

Motivation and approach for anion doping engineering

In the design of broadband EWA materials, adherence to the principles of complex variable function theory is essential. For dielectric materials, the complex permittivity, which includes the storage (real part, ε’) and loss (imaginary part, ε’’) components of electrical energy, is a primary consideration29. By utilizing the Kramers-Kronig relations30, we derived a formulation that ensures causality and regularity, thereby establishing an integral relationship among various physical parameters, including the material thickness (2, 2.5, and 3 mm), frequency range (2–18 GHz), and absorption intensity (<−10 dB). The computational results indicate that the required complex permittivity variation trend is impractical, as such strong dielectric dispersion cannot occur at low frequencies. (Figure S1, Supporting Information). Although the dielectric requirements for the X-Ku band are less stringent, the initial 2D-vdW system, i.e., carbon nanosheets (CNs), falls short of fulfilling fundamental criteria (Fig. 1a). Consequently, the atomic configuration must be optimized to improve the mixing entropy and surface electronic states until the desired dielectric properties are achieved.

Fig. 1: Motivation and implementation routes for high-entropy doping engineering.
figure 1

a Dynamic prediction of the complex dielectric constant of EWA realized at different thicknesses. The shades of red, blue and orange are the dielectric constant regions where effective reflection loss (RL < −10 dB) can be achieved at 2 mm, 2.5 mm and 3 mm thickness respectively. Frequency coverage is 8–18 GHz. b Preparation of two-dimensional carbon nanosheets and subsequent multistage doping process. White atoms are carbon atoms and other colors indicate different heteroatoms such as O, N, S, P and B. The richer the color indicates the more the variety of heteroatoms and the greater the entropy of the system. c Elemental mapping and low-resolution TEM results for a series of samples that have undergone low-, medium-, and high-entropy doping.

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Anions were doped into the material matrix through formatting steps (Fig. 1b). Initially, glucose molecules were adsorbed onto salt templates and subsequently graphitized in situ. The transformation of carbon materials from micrometer particles to nanosheets leads to a two hundredfold increase in the specific surface area, thus providing a broader doping platform (Figs. S2–3, Supporting Information). The pyrolysis parameters were determined via in situ TGA/DSC-MS-IR tests. To obtain a stable carbon network, we fixed the graphitization temperature near the strongest heat-absorbing site, which helped exclude the influence of the ambient temperature on the parent lattice during the subsequent doping process (Figure S4, Supporting Information). Then, the solvothermal method was employed to introduce other heteroelements into the O-doped carbon lattice. Among the selected dopants, boric acid (P-doped), phosphoric acid (B-doped), and thiourea (N, S-doped) are commonly used. Notably, the reaction between boric acid and phosphoric acid yields substantial precipitates of boric phosphates, so B-doping and P-doping need to be separately implemented. All samples except for CNs are labeled CNs(A) or CNs(A,B), where A represents the element (not limited to one element) of the previous solvothermal doping and B represents the element of the latter doping. Elemental mapping and X-ray diffraction (XRD) analyzes confirm the uniform distribution of all the elements within the carbon matrix, which is devoid of segregation and solid impurities (Fig. 1c and Figure S5, Supporting Information). This uniformity allows us to focus on the atomic configuration without interference from the morphology, interfaces, or other extrinsic factors. To provide a detailed discussion of doping engineering, the eight sample groups are categorized into low-entropy systems (n = 1, 2), medium-entropy systems (n = 3, 4), and HE systems (n = 5) according to the number of heteroelements.

Inspiration and guidance from low- and medium-entropy doping

Beginning with low- and medium-entropy doping, we meticulously examined the direct effects implications of individual dopant elements and their simple combinations on the atomic structure. First, we affirmed that B and P can be individually or jointly incorporated into carbon. On the one hand, a new peak at 1070 cm−1 in the infrared spectrum, which is attributed to P-C/B-C bonds, is discernible from the C-O peak at 1092 cm−1 (Figure S6, Supporting Information)31,32. On the other hand, although the crystallinity of the samples is relatively weak, subtle differences in the lattice spacings are evident in the selected area electron diffraction and high-resolution transmission electron microscopy (TEM) images (Fig. 2a). For example, P doping results in larger lattice spacings compared than B doping, with CNs(P,B) occupying an intermediate position between CNs(B) and CNs(P). This phenomenon stems from atomic size effects, in which the larger radii of B (82 pm) and P (110 pm) relative to those of C (77 pm) and O (66 pm) in the matrix lead to various degrees of carbon lattice expansion upon doping. Notably, the pronounced size disparity of P atoms leads to distortion of the hexagonal graphite framework plane, necessitating system-wide strain energy adjustments to counteract local structural perturbations. In other words, P atoms may be prone to detachment from the carbon framework. Elemental content measurements (Tables S1–S2, Supporting Information) corroborate this notion, with initial P doping diminishing upon subsequent B-doping, whereas P/B codoping minimally affects the B content. Moreover, the entire doping process influences the O content, notably enhancing it upon P/B codoping, which is attributable to intensified carbon surface oxidation arising from oxygen-containing species generated by various acidic dopants.

Fig. 2: Effect of low- and medium-entropy doping.
figure 2

a High-resolution TEM and SAED results for CNs, CNs(B), CNs(P), and CNs(P,B). b, c B1s spectra and P 2p spectra obtained from XPS tests. d Complex permittivity and dielectric loss tangent, (e) Cole-Cole curves corresponding to 12−16 GHz, (f) reflection loss curves at 2.5 mm thickness, and (g) polarization loss/conductivity loss ratios of CNs, CNs(B), CNs(P), and CNs(P,B).

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To further reveal the doping details, X-ray photoelectron spectroscopy (XPS) characterization was conducted. Typically, the B 1 s spectrum can be deconvoluted into BCO2 (194.1 eV), BC2O (192.4 eV), BC3 (190.6 eV), and B4C (186 eV) peaks, whereas the P 2p spectrum can be deconvoluted into P-C (133.4 eV) and P-O (134.6 eV) peaks10,33. Fig. 2b, c demonstrate that B-containing species undergo more pronounced alterations than those containing P, which is marked by a substantial increase in the amount of BCO2 (from 5% to 40%) and a corresponding decrease in the amount of BC2O (from 64.3% to 36.2%). These observations underscore the advantages of medium-entropy doping over low-entropy doping in fostering functional group diversity and increasing heteroatom concentrations, as reflected in the schematic roadmap of atomic configuration changes (Figure S7, Supporting Information).

Additionally, we investigated the impact of low- and medium-entropy doping with O, P, and B on the dielectric properties. In conventional atomic substitution models, B acts as an acceptor impurity, decreasing the electron concentration, whereas O and P function as donor impurities, potentially increasing the electron concentration30,34. However, constrained by the dopant species and methods, a substantial portion of O atoms and select B and P atoms integrate into edge polar groups via covalent bonds, thereby augmenting localized electrons and diminishing delocalized electrons35. As depicted in Fig. 2d, both the complex permittivity and dielectric tangent (tan δε) decrease with B- and P-doping, which is attributed to the suppressed conductivity. Intriguingly, the dielectric parameters of CNs(P,B) do not fall below those of CNs(B) but reside between those of CNs(B) and CNs(P). We hypothesize that the diverse bonding types and increased heteroelement content give rise to broader charge distribution inhomogeneities, fostering stronger polarization that compensates for the dielectric parameters. Pivotal evidence lies in the marked correlation between the relaxation characteristics and dopant elements, which manifests as distinct resonance peak shifts in the dielectric parameters within 12–16 GHz. Relaxation sites are identified in Cole-Cole plots (Fig. 2e), revealing that the polarization positions vary with the dopants, with medium-entropy doping yielding a compromise between multiple low-entropy dopings. This intrinsic dipole polarization, stemming from heteroatom substitution and polar functional groups, largely dictates the frequency response trends for EWA materials (Fig. 2f). To firmly establish the compensatory impact of polarization on the dielectric parameters, we performed dielectric fitting of the ε’’ values by employing the modified Debye relaxation model, quantifying ε’’ into the conductivity loss (εc”) and polarization loss (εp”) components (Fig. 2g and Figure S8, Supplementary Information). The fitting data indicate that the εc” of CNs(P,B) is the lowest among the four groups of samples and is close to that of CNs(B). Obviously, the contribution of εc” to the dielectric loss is not dominant. Rather, the εp” curve shows a consistent pattern with the ε’’ curve, and εp” plays a pivotal role in determining the capacity to absorb and dissipate electric field energy. CNs(P,B) exhibit a greater εp” contribution to the dielectric loss than low-entropy doped samples within 12–18 GHz, especially since εp”/εc” exceeds 10, encompassing the typical relaxation range in Cole-Cole plots, corroborating our reasoning.

Under stringent conditions of a low filler loading (7.5 wt%) and thin thicknesses (< 3 mm), CNs(P,B) fail to achieve the target impedance range, hindering the existence of an effective absorption bandwidth (EAB) (Figure S9, Supplementary Information). Fortunately, medium-entropy doping with P and B provides two key insights for HED strategies: 1) The polarization timescales in medium-entropy doping are jointly influenced by distinct heteroelements, suggesting that the polarization and EWA frequency bands can be tailored by adjusting the heteroelement types. 2) Compared with low-entropy doping, medium-entropy doping introduces abundant doping sites and polar species, leading to extensive charge imbalance and increased dipole polarization loss contributions.

Impact of HED engineering on material electromagnetism

Through anionic HED engineering, a microstructure characterized by high disorder yet coexistence of ordered atoms can be achieved. The CNs underwent an initial N/S codoping process, followed sequentially by P and B doping. As depicted in Figure S10, Supplementary Information, the resulting CNs(NS) and their derivatives retain a weakly crystalline nature. Moreover, the lattice stripes still follow the atomic size effect, which is indicative of successful doping with these heteroelements. The intricate anion multibody interactions and inherited configurational features, revealed by XPS (Fig. 3a-b), are summarized as follows:

Fig. 3: Effect of high-entropy doping on atomic configuration and dielectric properties.
figure 3

a N1s, S2p, B1s and P2p spectra. b Schematic of the atomic structure of CNs(NS) after B-doping, P-doping and P/B co-doping as the substrate. In the schematic, white atoms are carbon atoms, red atoms are O atoms, purple atoms are S atoms, green atoms are N atoms, blue atoms are B atoms, and yellow atoms are P atoms. c Elemental content of the samples. d ID/IG values in the Raman spectra. e Complex permittivity, (f) fitted conductivity of the coaxial ring as well as measured powder resistivity. Powder resistivity data are presented as mean values  ±  SD (n  =  3). g Electrochemical impedance spectra. and (h) Impedance Smith charts of CNs(NS), CNs(NS,B), CNs(NS,P), and CNs(NS,P,B).

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1) The preexisting S in the carbon matrix minimally interacts with B or P doping, as evidenced by the limited changes in the S atomic content and S 2p spectra.

2) The preexisting N in the carbon matrix more strongly interacts with B or P doping, albeit at different levels. For N and B, the N-containing carbon matrix facilitates enhanced B doping. Specifically, the B atomic contents in CNs(NS,B) and CNs(NS,P,B) reach 3.11 at% and 5.08 at%, respectively, which are significantly higher than those in CNs(B) (0.97 at%) and CNs(P,B) (0.86 at%). With respect to N and P, P doping introduces new NO2 species into the carbon matrix and reduces graphitic N. Thus, in CNs(NS,P,B), these dual interactions coexist, contributing to increased polarity while reducing the conductivity.

3) P/B codoping still heavily introduces O, similar to in the previous medium-entropy doping systems. In contrast, N/S codoping has a minimal effect on O.

In short, within the anionic HED system driven by both in-situ O-doping and ex-situ N/S/P/B codoping, the total heteroelement content and the variety and distribution range of polar units are markedly augmented. Furthermore, structural insights into the carbon lattice were obtained via Raman spectroscopy (Figure S11, Supplementary Information), and the ratio of the D-band (dominated by heteroatoms) to the G-band (dominated by sp2-hybridized carbon atoms, ID/IG) was calculated. The trend in the ID/IG values closely aligns with the heteroatom content (Fig. 3c, d). Undoubtedly, an increase in the amount of dopant elements progressively increases the disorder and mixing entropy of the material system (Figure S12, Supplementary Information).

Typically, the dominance of different types of dielectric loss significantly impacts the EWA characteristics. Polarization-dominated dielectric materials hold potential for broadband absorption8,36,37. Taking dipolar polarization as an example, electromagnetic energy is utilized primarily to overcome the thermal motion of molecular and atomic dipoles, rather than to drive long-range carrier migration, thereby mitigating skin depth effects. Therefore, stronger dipolar polarization is preferable.

HED engineering offers greater advantages in enhancing the electrical properties and modulating the dielectric loss types, which is manifested in two aspects. First, N and S, as electron donors, increase the electron density and conductivity of the material system by introducing valence electrons. Compared with medium-entropy doping systems with O, P, or B, medium- and high-entropy doping systems incorporating N and S exhibit improved complex permittivity and electromagnetic wave attenuation performance (Fig. 3e). However, an excessively high conductivity can lead to the generation of opposing induced currents, thus increasing the surface reflectivity of electromagnetic waves (> 0.32). While conductive losses convert electromagnetic waves into Joule heat dissipation, they also limit the absorption bandwidth. Therefore, reducing excessive conductivity to an appropriate range is crucial. Here, the second advantage of HED engineering lies in balancing impedance matching through the introduction of electron acceptors. The complex permittivity of CNs(NS,B), CNs(NS,P), and CNs(NS,P,B), their complex permittivity undergoes a fluctuating decline, similar to the trends observed without NS elements. We subsequently compared the coaxial ring conductivities and powder resistivities. As shown in Fig. 3f, the materials exhibit consistency in their electrical behavior. Specifically, the conductivity order is CNs(NS) > CNs(NS,P) > CNs(NS,B) > CNs(NS,P,B) and CNs > CNs(P) > CNs(B) > CNs(P,B). The samples containing P and B exhibit the lowest conductivity within their respective series, indicating maximum suppression of εc”. Furthermore, electrochemical impedance spectroscopy data were plotted. As shown in Fig. 3g, CNs(NS,P,B) exhibits a weaker charge transfer rate at high frequencies than the other CNs(NS)-derived samples. A similar phenomenon is observed for CNs(P,B) (Figure S13, Supplementary Information). In conjunction with the Smith circle diagram of the normalized input impedance expressed in complex form (Fig. 3h), the synergistic coordination of anions such as N, S, O, P, and B in carbon helps bring the input impedance of the material close to the air impedance. Importantly, since the enhanced polarization compensates for the dielectric losses, the electromagnetic attenuation capability is not overly suppressed by the already weakened conductive losses. All four groups of samples show the potential for the existence of an EAB, but among them, CNs (NS) have a limited curve length in the inner region of the impedance threshold (orange circle). This means that appropriately reducing εc” and enhancing εp” can help increase the chances of electromagnetic waves being incident inside the material and subsequently being dissipated.

By utilizing density functional theory (DFT), the principle of the modulation effect of HED engineering on the dielectric loss was elucidated. The specific modification of carbon atomic structures by various doping elements and their combinations was considered, leading to the establishment of four corresponding model sets (Fig. 4a). The optimized structures show that the large P atoms cause the graphene lattices to expand out-of-plane, rendering the previously in-plane stable N/S-doped model axially asymmetric. This lattice distortion is inherited in models with additional impurities and may enhance the polarity of the entire system. Subsequently, charge differential density maps were calculated, in which red and yellow colors signify regions of electron accumulation and depletion, respectively (Fig. 4b). Generally, when carbon atoms at internal or edge sites are substituted, charge redistribution occurs. The CNs(NS,P) and CNs(NS,P,B) models exhibit a more severe charge imbalance, which is more evident in the side views. Similarly, the electron localization function reflects these changes in the bonding electrons (Figure S14, Supplementary Information). Charge tends to concentrate at doping sites, with increased doping leading to more severe charge asymmetry on the bonds. To better compare the influences of the doping type and form on electron gain and loss, the Mulliken charges were calculated (Figure S15, Supplementary Information). Theoretically, the charge on C atoms in the graphite region is ~4 eV. The electron count on the other heteroatoms at the doping sites, except for B, is greater than 4 eV. Taking CNs(NS,P,B) as an example, the charge magnitude of the heteroatoms is as follows: O (5.733–6.045 eV) > S (5.773–5.816 eV) > P (5.062–5.153 eV) > N (4.574–4.997 eV) > B (3.597 ~ 3.933 eV). The alteration in the valence electrons of the heteroatoms after doping confirms that B atoms strongly attract free electrons from N and S, reducing the overall conductivity. Moreover, the presence of oxygen-containing polar groups strongly affects the spatial distribution of bound electrons. This change is not confined to the heteroatom or adjacent bonds but radiates to the surrounding areas. We compared the total charges in eight marked typical regions across different doping models (Fig. 4c). The results indicate that B-containing functional groups (regions II and VIII), particularly B4C, significantly reduce the local electric field. In edge-doped regions, the number of electrons increases with the addition of oxygen-containing functional groups, generating extra electric dipoles and increasing the polarity (Fig. 4d). Notably, B doping may decrease the polarizability, as it is detrimental to aggregation of electrons and does not introduce additional lattice distortion. In contrast, P doping increases the polarizability because it both enriches the local charge and increases the axial asymmetry. However, the introduction of B into CNs(NS,P,B) unexpectedly increases the polarizability rather than decreasing it. Based on an analyzing region of VII, P/B codoping leads to concentrated doping or adsorption of oxygen-containing functional groups at edge sites, greatly increasing the electron density in these areas. These electron-rich regions and B-containing electron-deficient regions collectively form a discrete, opposing charge distribution pattern. This established charge asymmetry is subsequently further exacerbated by out-of-plane deformation and displacement of the electron clouds due to lattice distortion. That is, the lattice distortion, electron-rich and electron-deficient regions together maximize the polarity of the material. This field effect induced by an abundance of polar groups unprecedentedly promotes the transition of electrons from delocalized to localized states. Interestingly, the fixed order and combination of doping exhibit reproducibility in their influence on polarization relaxation. For example, N, S, P doping increase the relaxation time, whereas B and O doping decrease it. The multielemental interplay governs the relaxation sites, thus yielding a compromise behavior (Fig. 4e). Additionally, HED engineering aids in enhancing the proportion of polarization loss in the dielectric loss (Fig. 4f). Based on the above, we suggest that HED engineering induces a ‘directional cocktail effect’ that favors polarization and EWA properties.

Fig. 4: Density Functional Theory Calculations for Medium- and High-Entropy Doping.
figure 4

a Structurally optimized medium- and high-entropy doped atom models. White atoms are carbon atoms, light red atoms are O atoms, purple atoms are S atoms, green atoms are N atoms, blue atoms are B atoms, and yellow atoms are P atoms. b Charge density difference plots. c Comparison of Mulliken charges in each region. d Calculated polarizabilities. e Cole-Cole curves of 7−12 GHz. f Polarization loss/conductivity loss ratios of CNs(NS), CNs(NS,B), CNs(NS,P), and CNs(NS,P,B).

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The benefits of anionic HED engineering are demonstrated through the EWA performance. In Fig. 5a, CNs, CNs(B), CNs(P), and CNs(P,B) fail to achieve reflection loss intensities below −10 dB within 2–18 GHz, primarily because of the poor conductivity of CNs. In contrast, samples doped with N and S achieve effective absorption. Specifically, CNs(NS) achieves an EAB of 3.66 GHz at 1.44 mm, CNs(NS,B) achieves an EAB of 3.76 GHz at 2.12 mm, CNs(NS,P) achieves 4.35 GHz at 1.57 mm, and CNs(NS,P,B) achieves an EAB of 7.05 GHz at 2.6 mm. While CNs(NS,B) and CNs(NS,P) outperform CNs(NS), B- or P-doping alone is insufficient to fully balance the excessive enhancement of electrical properties by N/S codoping. N/S/P/B codoping achieves a satisfactory balance, minimizing the drawbacks of conductive losses and promoting polarization advantages, thereby broadening the absorption bandwidth. Variations in the maximum EAB further validate the compromise effect of HED engineering among the O, N/S, and P/B dopants (Figure S16, Supplementary Information). To ascertain the reliability of the excellent EWA performance, we performed S11 parameter measurements on a coaxial ring equipped with an additional metal backplate at a constant thickness (Figure S17, Supplementary Information). The findings demonstrate a high consistency between the experimentally measured values and the reflection loss calculations derived from transmission line theory. Compared with other representative low- and medium-entropy doped carbon absorbers (Fig. 5b and Table S3, Supplementary Information), the high-entropy doped carbon absorber in this work exhibits both broadband absorption (> 7 GHz) and high loss (< −60 dB), which are achieved at an ultralow filling rate (7.5 wt%), positioning it at the cutting edge of research on heteroatom-doped carbon EWA materials. Moreover, effective anionic HED engineering and the accompanying exceptional EWA performance is highlighted through comparisons with recently reported EWA materials of other systems, including MXene-based, ceramic-based, chalcogenide-based, polymer-based, sulfur-compound-based, and metal-organic framework/layered bimetallic hydroxide derivatives (Figure S18 and Table S4, Supplementary Information).

Fig. 5: EWA performance and applications.
figure 5

a two-dimensional performance diagram of the sample. b performance comparison diagram of CNs(NS,P,B) with other low-entropy and medium-entropy doped carbon materials. c three-dimensional diagram of the radar scattering cross-section of the sample at 13.42 GHz. d line drawing of radar scattering cross-section of the metal backplate model and −45 ~ 40°. e EWA performance of CNs(NS,P,B) at different angles of incidence of electromagnetic waves. f Schematic diagrams of chips of electronic devices before and after applying EWA materials. g E-field radiation values before and after applying EWA materials.

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The effectiveness of anionic HED engineering was verified using radar cross-section (RCS) simulations. We constructed a model of a metal backplane coated with an EWA layer and calculated the absorption and scattering of electromagnetic waves at different frequencies under infinite far-field conditions. As shown in Figure 6a, scattering signals of CNs(NS) and its derivatives in the X and Ku bands (with a frequency interval of 1 GHz) are observed (Figures S19-23, Supplementary Information). The pure perfect electric conductor (PEC) model exhibits strong scattering at each frequency point, whereas the EWA-coated model exhibits a frequency preference for a low RCS. These low-RCS frequencies align with the reflection loss patterns calculated by transmission line theory (Figure S24, Supplementary Information). Notably, CNs(NS,P,B) exhibits nearly undetectable scattering signals at 13.42 GHz (Fig. 5c), indicating complete absorption and dissipation of electromagnetic waves. In Fig. 5d, the RCS values from -45° to 45° are represented in a radar chart. The main lobe value represents the maximum radiation in the primary working direction of the radar. Clearly, CNs(NS,P,B) most effectively eliminates electromagnetic interference in this direction. Moreover, the RCS reduction by CNs(NS,P,B) is 21.34-27.13 dBm2 greater than that by the other samples, equivalent to the difference between a regular airplane and a bird. Additionally, CNs(NS,P,B) exhibits narrower sidelobes and lower RCS values on the sidelobes, indicating that HED engineering facilitates electromagnetic energy attenuation over a wide angular range, providing stronger anti-interference capabilities. To prove this, we calculated the EWA performance for different electromagnetic wave incidence angles. As shown in Fig. 5e, CNs(NS,P,B) exhibits wide-angle absorption, maintaining an EAB above 5.7 GHz within a 35° range.

Finally, the applicability of CNs(NS,P,B) in the civilian electronic field was demonstrated. We combined high-entropy doped carbon powder with an elastomer to create elastic patches and applied them to cover chip surfaces in communication devices (Fig. 5f). Radiation measurements were conducted on bare chips and chips covered with EWA materials. The results show that the bare chip emits a high radiation of 103 V/m, whereas our material reduces the radiation by several orders of magnitude to only ~60 V/m. This experiment underscores the importance of anionic HED engineering for promising EWA materials and their potential applications in civilian fields.

In summary, we developed anionic HED engineering and successfully enhanced the dielectric properties and EWA performance of carbon materials. Initially, O-doped two-dimensional CNs was synthesized via a salt-templating method followed by in situ pyrolysis. Subsequently, leveraging the large specific surface area, these CNs underwent sequential N/S codoping, P doping, and B doping via a three-step solvothermal process, yielding HE carbon materials. In the complex step-by-step doping process, heteroatoms with different doping orders show multibody interactions, and the final product inherits their electrical properties. Compared with low- and medium-entropy doping engineering, HED engineering has remarkable advantages in balancing delocalized charges and enhancing localized charges, manifested as a reduced conductivity and a strengthened dipole polarization. Synergistic experimental investigations and DFT calculations collectively revealed a ‘directional cocktail effect’, facilitating modulation of the type and intensity of the dielectric loss. Ultimately, the CNs(NS,P,B) HE sample achieves broadband and efficient EWA performance under ultralightweight conditions. Moreover, this material can be utilized to fabricate absorbing patches to mitigate intense radiation in electronic devices. We believe that anionic HED engineering addresses a crucial gap in doping research and broadens the design paradigm for advanced EWA materials, thereby facilitating advancements in the field of electromagnetic functional materials.

Methods

General

The electromagnetic performance experimental, electromagnetic radiation detection experiment, DFT and RCS are given in the Supplementary Methods.

Preparation of two-dimensional carbon nanosheets (CNs)

A mixture of 5 g glucose and 75 g sodium chloride (NaCl) was homogenously dispersed in 30 milliliters of deionized water through manual agitation for a duration of 10 min. Subsequently, this solution was subjected to a vacuum drying process within an oven maintained at 80 °C for a period of 48 h, resulting in a thoroughly dehydrated specimen. The dried material was then meticulously pulverized into an extremely fine powder. The powdered sample underwent controlled heating at a rate of 2 °C/min until reaching 1000 °C, where it was annealed for 2 h in an argon atmosphere. Following natural cooling to room temperature, the resultant black powder was subjected to an alternating washing process with deionized water and ethanol, each for three cycles, to remove excess salt templates. Finally, the powder was dried overnight in an oven at 60 °C, resulting in the final product designated as CNS.

Preparation of B-doped CNs, labeled CNs(B)

The CNs was redispersed in 80 ml of aqueous solution that also had 0.02 mol of boric acid and sonicated for 10 min to ensure dispersion. The mixed solution was placed in a 100 ml reactor and then heated up to 200°C at a rate of 5 °C/min. After being kept at 200°C for 10 h, the solution was cooled naturally to room temperature. The solution was vacuum filtered to obtain a powder, which was washed three times alternately with water and ethanol. The last time with ethanol and then dried in an oven at 60 °C for 10 min.

Preparation of P-doped CNs, labeled CNs(P)

The CNs was redispersed in 80 ml of phosphoric acid and sonicated for 10 min to ensure dispersion. The other steps were the same as those for the preparation of CNs (B).

Preparation of P/B co-doped CNs, labeled CNs(P,B)

The CNs (P) was redispersed in 80 ml of aqueous solution containing 0.02 mol of boric acid and sonicated for 10 min to ensure dispersion. The solvent heating procedure and subsequent operations were the same as for the preparation of CNs(B).

Preparation of N/S co-doped CNs, labeled CNs(NS)

The solvent was in 80 ml of aqueous solution containing 0.02 mol of thioacetamide, referring to the above experiments for the procedure.

Preparation of N/S/P/B co-doped CNs, labeled CNs(NS,P,B)

The CNs(NS) was redispersed in 80 ml of phosphoric acid and sonicated for 10 min to ensure dispersion. The mixed solution was placed in a 100 ml reactor and heated at 5 °C per minute to 200 °C. After 10 h at 200 °C, the solution was cooled naturally to room temperature. The solution was vacuum filtered to obtain a powder which was washed three times alternately with water and ethanol. The last time it was washed with ethanol and then dried in 60 °C for 10 min to get CNs(NS,P). CNs(NS,P) was again dispersed into 80 ml of aqueous solution containing 0.02 mol of boric acid. The solvent heating, washing and drying processes were repeated to obtain CNs(NS,P,B).

Characterization

Surface architectures were investigated through surface scanning utilizing a field emission scanning electron microscope (FE-SEM), specifically the Zeiss Supra 55 VP model, which provided detailed morphological insights. High-resolution probing of local structures, including selected area electron diffraction (SAED) patterns and elemental distributions, was accomplished with the Thermo Fisher Scientific Titan Themis G3 300 kV double spherical aberration corrected transmission electron microscope (TEM). Adsorption-desorption profiles of N2 were analyzed employing a Micromeritics ASAP 2020 chemisorption analyzer, yielding crucial information on surface interactions. Phase compositions and crystalline arrangements were elucidated through X-ray diffraction (XRD) analysis on the Bruker D8 ADVANCE instrument, operating at λ = 0.15418 nm, complemented by Raman spectroscopy on the Horiba LabRAM HR Evolution setup, excited at λ = 532 nm. Functional group identification was performed using Fourier transform infrared (FT-IR) spectroscopy on the Thermo Fisher Scientific Nicolet iS50 platform, while the valence states of surface elements were determined via X-ray photoelectron spectroscopy (XPS) on the Ulvac-Phi PHI 5000 VersaProbe III system, utilizing Al Kα radiation at 1486.6 eV. Electrochemical impedance spectroscopy (EIS) measurements were conducted on the samples using the CH Instruments CHI660E electrochemical workstation, with a Pt plate serving as the counter electrode, an Ag/AgCl reference electrode, and 3.5 wt% NaCl as the electrolyte solution.