Potential well engineering for self-adaptive dielectric response polymer dielectrics

Domain: biology
Published: 2026-03-26
Editorial outcome: major_revision

Abstract
The existing polymer dielectrics as insulating packaging media can no longer meet the insulation demands in highly integrated power electronic devices. Self-adaptive dielectrics with nonlinear dielectric response have been explored to eliminate electric field distortion caused by charge accumulation, but traditional strategies based on Schottky barriers result in interface defects. Here, we report polymer dielectric composites with customizable potential wells in recycled melamine foam-derived graphitic carbon nitride frameworks that overcome concerns about interface defects. We demonstrate that potential wells can efficiently capture low-energy charge carriers and release them for rapid transport under high electric fields. Notably, by doping donor or acceptor states into the frameworks, precise control over potential well depth and distribution was achieved, allowing customization of both nonlinear conductivity and threshold electric field strength. This work establishes a generalizable strategy for engineering next-generation self-adaptive dielectrics, enabling intelligent insulation behavior and enhanced reliability in high-field, high-temperature electronic packaging environments.

Introduction
The pursuit of high power density and high integration in emerging power electronics technologies has placed unprecedented demands on the electrical insulation performance and reliability of packaging polymer dielectrics1, 2. During extended operation under multiple physical fields (e.g., thermal and electric fields), persistent charge injection and accumulation within polymer dielectrics can induce local field distortions, significantly increasing the risk of partial discharge3. Traditional strategies focus on improving the electrical insulation performance of polymer dielectrics4, 5. Although high breakdown thresholds can delay material failure, the threat of electric field distortion caused by charge injection to material reliability has not been eliminated6. Importantly, these charge effects are exacerbated under complex operating conditions, such as high-frequency excitation, transient surges, and electro-thermal coupling7.

To address these challenges, self-adaptive dielectrics (SADSs) have emerged, characterized by a nonlinear relationship between electrical response and applied electric field8. SADs have reversible insulation-conduction conversion ability near the electric field threshold, fundamentally avoiding electric field distortion caused by charge accumulation (Fig. 1a). To date, the insulation-conduction conversion ability of all SADs derives from the semiconductor particles, which physically depends on the Schottky barrier of semiconductor particles9. Nevertheless, both the grain boundaries within particles and the contact interfaces between particles are uncontrollable, resulting in fluctuating performance from batch to batch. More importantly, the severe mismatch in thermal expansion coefficient between polymer matrix and inorganic filler can lead to interface defects and become the insulation weakness of SADs, raising doubts about their reliability10.

Compared to Schottky barriers (Fig. 1b), we have noticed that potential wells may also serve as a source of nonlinear conductivity (Fig. 1c), which has been widely used in N-type and P-type semiconductors11, 12. Similarly, we can precisely adjust the depth and density of the potential well through doping with heteroatoms or structural design, where density can regulate charge mobility and depth can regulate the switching field threshold. This strategy can not only fundamentally solve the negative effects caused by the large number of interfaces in traditional SADs, but also customize the required performance according to application scenarios (such as shallow wells for electrostatic protection in microelectronic devices and deep wells for high-voltage insulation equipment).

From the perspective of the origin of nonlinear electrical response, the advantage of potential-well-based SADs lies in shifting the nonlinear regulation from barrier heights that depend on interfacial contact states to designable and controllable bulk trapping states. Under low electric fields, charge carriers are trapped in potential wells, suppressing leakage and maintaining insulation, whereas increasing field strength activates field-assisted detrapping and hopping 13, resulting in a rapid and reversible transition to conduction near the threshold. The energy constraint imposed on charge carriers is mainly determined by the depth of the potential wells, while the number and spatial distribution of the wells are governed by their density. Because heteroatom doping with neighboring-group elements can introduce controllable impurity levels or localized states into the semiconducting framework, such as deep wells near the Fermi level or shallow wells near the conduction or valence band edges, the depth and density of potential wells can be tuned in a predictable manner 14, 15, 16. Consequently, constructing potential wells through doping enables effective regulation of the switching field and nonlinear coefficient, such that the nonlinear response is no longer primarily dictated by uncontrollable randomness associated with particle contact states or grain-boundary microstructures, thereby improving performance stability and batch-to-batch reproducibility.

Here, we report a polymer dielectric incorporating customizable potential wells, derived from the pyrolytic conversion of recycled melamine foam into graphitic carbon nitride (g-C3N4) frameworks. Through selective donor-acceptor doping, both the depth and spatial distribution of the potential wells were precisely engineered. The nonlinear current-voltage behavior of the frameworks and their polymer composites was systematically characterized, and a quantitative approach for extracting potential-well parameters was established based on space charge limited current (SCLC) theory. Density functional theory calculations further elucidated the tunable formation mechanism of the potential wells and their correlation with charge transport. Notably, electrostatic discharge measurements confirmed that potential-well engineered SADs enable rapid charge dissipation and highly controllable nonlinear electrical responses, highlighting a new materials design paradigm for adaptive insulation and advanced electronic packaging.

Results
Design and Characterization of Potential-Well Structures
Conventional self-adaptive dielectrics (SADs) typically achieve nonlinear conductivity through grain-boundary barriers within wide-bandgap semiconductor fillers or Schottky barriers at inter-particle interfaces, which rely on continuous filler pathways for charge migration17. In contrast, potential-well type SADs require interconnected carrier transport networks with embedded well distributions, allowing low energy carriers to be temporarily trapped and released under high electric fields for field-dependent regulation. Guided by this concept, we selected waste melamine foam as the structural precursor (Fig. 1d). This lightweight, elastic, and porous thermoset transforms via nitrogen pyrolysis into a carbon-nitride framework while preserving its three-dimensional skeleton18. Scanning Electron Microscopy (SEM) images (Supplementary Figure 1) reveal a well retained open-cell architecture composed of ~5 μm interconnected struts, providing continuous carrier channels and abundant sites for potential-well formation.

As the fundamental structural unit of this three-dimensional framework, graphitic carbon nitride (g-C3N4, CN) serves as a representative medium-bandgap (~2.7 eV) polymeric semiconductor 18, 19. Its heptazine-based backbone-linked through C=N and C–N covalent bonds-forms a π-conjugated aromatic network that endows the material with outstanding thermal and chemical stability20, 21, 22. This robust architecture maintains integrity under elevated temperature and electric field stress while allowing precise modulation of electronic states. Schematic illustration (Fig. 1d) depicts the transformation from melamine foam to CN foam, showing abundant intrinsic trapping sites that naturally constitute the potential-well framework.

To further tune the electronic structure, heteroatom doping was introduced as an efficient means to modulate the depth and density of potential wells. Donor-type dopants such as phosphorus (P) contribute extra electrons, creating shallower wells and facilitating carrier hopping, whereas acceptor-type dopants such as boron (B) generate electron-deficient regions that deepen the wells and enhance trapping capability16. By carefully tailoring the type, and concentration of dopants, either shallow or deep potential wells can be selectively introduced, allowing precise customization of nonlinear conduction characteristics to meet specific application requirements. In practice, melamine foams were impregnated with aqueous ammonium dihydrogen phosphate or boric acid, dried, and pyrolyzed. Energy-dispersive X-ray spectroscopy (EDS) elemental mapping (Fig. 2a, Supplementary Figure 2 and Figure 3) confirms uniform dopant incorporation throughout the framework, verifying the effectiveness of this facile solution-based doping route.

Fourier Transform infrared spectroscopy (FTIR) and X-ray diffraction (XRD) analyses (Supplementary Figure 4 and Figure 5) demonstrate that the CN network derived from melamine pyrolysis retains the heptazine skeleton and layered g-C3N4 structure, ensuring high thermal stability and a well-conjugated backbone23. X-ray Photoelectron Spectroscopy (XPS) spectra (Supplementary Figure 6) reveal that B and P dopants preferentially substitute carbon sites within the heptazine units, forming stable B-N and P-N bonds directly incorporated into the lattice without compromising crystallinity. Such substitutional doping preserves structural integrity while introducing localized electronic states that act as tunable potential wells24. Ultraviolet-visible (UV-vis) absorption spectra (Supplementary Figure 7) further indicates that P doping narrows the bandgap by generating shallow states near the conduction band, thereby promoting electron transport. In contrast, B doping leaves the bandgap largely unchanged but introduces deep traps near the Fermi level, which markedly influence carrier dynamics despite minimal band edge modification.

Electrical Properties of CN Foams and Composites
The electrical properties of CN foams are evaluated through current-voltage (I-V) measurements on individual struts using a microprobe station. Metal probes contact a single strut to apply voltage, and the current response is recorded in real time (Fig. 2b). Compared with the pristine CN foam, which shows a relatively smooth and delayed current increase (Fig. 2c), both B and P doped foams exhibit pronounced nonlinear conduction but with distinct switching fields: B doping shifts the threshold to higher fields (Fig. 2d), reflecting stronger trapping of high-energy carriers, whereas P doping reduces the threshold (Fig. 2e), indicating that the electric field condition for charge dissipation is reached at lower field strengths.

This contrasting behavior arises from the distinct electronic effects of B and P substitution within the g-C3N4 lattice. Because B and P belong to the main groups adjacent to that of carbon in the periodic table, their valence electron numbers differ by one, leading to the introduction of additional holes (B) or electrons (P) upon substitution. At the low doping levels used here (B/P: C < 0.1, as shown in Supplementary Table 1), the holes generated by B doping do not dominate conduction, and the carbon nitride retains its n-type character25. Instead, B doping introduces localized states near the Fermi level that suppress electron transport, thereby shifting the switching field toward higher values. In contrast, P doping introduces shallow trap states near the conduction band, forming shallow potential wells that lower the excitation barrier for electrons and allow earlier charge release under applied fields. Therefore, the opposite switching-field trends induced by B and P doping originate from their distinct effects on potential well depth and the type of additional carriers introduced by the dopants.

The field-dependent conductivity of the EP/CN series composites was determined using a three-electrode setup constructed in accordance with the IEC 62631 standard (Supplementary Figure 8). All three composites display the characteristic nonlinear conductivity behavior of SADs, showing a rapid increase in conductivity with increasing field. Finite-element simulations are conducted to further validate the charge dissipation mechanism in the EP/CN composites (Supplementary Note 1). The simulation results confirm that injected carriers preferentially migrate along the foam skeleton, forming continuous dissipation pathways within the polymer matrix (Fig. 2g). By simulating the current density distributions of the EP/CN, EP/CN-B, and EP/CN-P composites under different electric field strengths (Supplementary Figure 9 and Figure 10), the nonlinear conduction transition can be directly visualized. At low electric fields, the carrier energy is insufficient to overcome the potential well confinement, and the composites remain in an insulating state; as the field increases, carriers are progressively released from the potential wells and transported through the interconnected CN skeleton toward the ground electrode, leading to a pronounced rise in current density. The calculated current density-electric field (J-E) characteristics (Supplementary Figure 11) exhibit the same trend as the experimental results.

The nonlinear response is quantified by the switching field (Es) and nonlinear coefficient (α), obtained by fitting:
σ = σ0(1+(E/Es)α-1) (1)
where σ and σ0 denote the high and low field conductivities, respectively, and E is the electric field strength. Consistent with the intrinsic I-V characteristics of the foams, the EP/CN-B and EP/CN-P composites exhibit conductivity enhancement at higher and lower switching fields, respectively (Supplementary Table 2). These differences in switching fields are closely related to application requirements. Devices such as integrated circuits and optoelectronic components typically contain ultrathin insulating layers with low breakdown thresholds and are therefore highly susceptible to electrostatic discharge. In these systems, rapid charge dissipation is required at relatively low electric-field strengths (0.1-1 kV/mm), to prevent irreversible damage induced by charge accumulation26. In contrast, high-voltage insulation and overvoltage protection systems, such as those used in power electronics, must maintain extremely low leakage current under normal operating conditions and are therefore required to exhibit much higher switching fields, generally exceeding 5-10 kV/mm 2. In these applications, conductive pathways should only be activated under abnormal electrical stress, such as overvoltage or transient surge events. Consequently, materials intended for adaptive dielectric regulation must balance low-field charge dissipation capability with high-field insulation stability, depending on the targeted application scenario.

The nonlinear coefficient α provides further insight into charge-dissipation efficiency under strong electric fields. In potential well-type SADs, deeper wells correspond to larger α values because deep traps confine electrons more strongly and delay their release at low fields. Once the field becomes sufficiently high, these trapped electrons are excited or hop between wells with increased kinetic energy, resulting in enhanced mobility after release. The emergence of such high energy carriers produces a steeper rise in conductivity at elevated fields, thereby increasing α. This correlation between trap depth and nonlinear response highlights the complementary roles of shallow and deep wells in regulating carrier transport.

Thermally stimulated depolarization-current (TSDC) measurements provide direct evidence of this well-depth distribution (Fig. 2h): the P- and B-doped samples show distinct depolarization peaks at ~130 °C and ~220 °C corresponding to shallow and deep wells, respectively. Compared with the undoped sample, both doped materials exhibit markedly higher current amplitudes, indicating a higher density of potential wells.

By adjusting the heteroatom-doping ratio, the nonlinear-conduction characteristics can be systematically tuned (Supplementary Figure 12). Unlike conventional barrier-type SADs, where the switching field and nonlinear coefficient are governed by the grain-boundary barriers of semiconductor fillers, potential well-type SADs enable flexible modulation of nonlinear electrical responses solely through heteroatom doping, without altering the composite framework. This strategy allows precise design of electrical properties to meet diverse insulation and packaging requirements, offering broad versatility for practical applications.

To clarify the performance differences between potential-well-type SADs and conventional barrier-type SADs from a mechanistic perspective, we performed a systematic comparison using recently reported SADs based on different wide-bandgap semiconductors, including ZnO, SiC, and BaTiO3 (Supplementary Figure 13 and Table 3). These reported systems mainly rely on interfacial Schottky barriers to achieve nonlinear conduction. Their key parameters, including the switching field (Es), nonlinear coefficient (α), and the corresponding filler content, were compared with those of the potential-well-type SAD developed in this work.

Because SADs are used in diverse applications, performance is not determined solely by achieving a high switching field. Instead, it is important to tune Es over a broad range while maintaining a sufficiently high nonlinear coefficient (α > 10). The comparison shows that potential-well-type SADs allow a wider adjustable range of Es than conventional barrier dominated SADs, and the tunable window can cover and extend the reported ranges of typical barrier-type systems. Analysis of α as a function of filler content further indicates that SiC based barrier-type SADs can show nonlinear conduction at relatively low filler loadings, but their α values are often limited. In contrast, ZnO varistor based SADs usually require higher filler contents (35 vol%) to reach α values close to 10, and their Es is relatively low with a narrow tuning range.

In our system, the potential-well strategy shifts the dominant mechanism from interfacial barrier control to bulk potential well regulation. This change reduces the dependence of α on filler content. As a result, α values comparable to those of ZnO based SADs can be achieved at very low filler loadings, while Es remains continuously tunable over a wide range. These results suggest that the potential well strategy provides an effective route to optimize SAD performance beyond conventional barrier-based approaches.

Nonlinear Conduction Mechanism of Potential Well Based SADs
Since the I-V characteristics of individual CN struts reveal that the introduced potential well levels are not fixed but exhibit a distributed nature, it is essential to establish a quantitative framework for analyzing the energy levels and density distribution of these wells within the material. The space charge limited current (SCLC) theory provides a well-established approach for probing trap states in dielectrics and semiconductors29. At low electric fields, the current is primarily limited by carrier capture in traps; as the field strength increases, the traps become progressively filled, leading to an exponential rise in current that ultimately transitions into the trap-free regime. By segmentally fitting the current density-voltage (J-V) curves, the characteristic energy levels and densities of potential wells corresponding to different voltage regions can be extracted (Supplementary Table 4)30.

The J-V relationships of the EP/CN, EP/CN-B, and EP/CN-P composites exhibit clear exponential characteristics across distinct regimes (Fig. 3, a to c). Because the applied electric field drives carrier release and hopping between localized states, the exponential factor in each regime correlates with the effective trap energy. As summarized in Fig. 3d, both the trap depth and density distributions differ markedly among the three systems: B doping produces a higher proportion of deep wells, resulting in larger exponential factors at comparable current densities. These deeper traps require higher excitation energies but, once carriers are released, impart higher kinetic energies, thereby enhancing conductivity under strong fields (Fig. 3e).

To further validate this conduction model, temperature is introduced as an auxiliary excitation source. Higher temperatures increase carrier energy and accelerate release from traps. Under combined thermal and electrical excitation, fully emptied wells weaken their influence on transport, resulting in a lower J-V slope. Experimental results (Fig. 3, f to h) confirm this behavior: elevated temperature significantly reduces the slope in the high-voltage regime, particularly for EP/CN-B, which contains abundant deep wells. This demonstrates that deep potential wells delay carrier release but generate higher-energy carriers once activated, enhancing charge-dissipation efficiency and increasing the nonlinear coefficient.

Theoretical Verification of Potential Well Modulation
To further substantiate the experimental observations and elucidate the microscopic origin of potential well modulation, density functional theory (DFT) calculations were conducted on pristine and heteroatom doped CN frameworks. The electron localization function (ELF) was first computed to visualize carrier confinement in real space (Supplementary Note 2) 31. ELF values close to 1 represent highly localized electrons, values near 0.5 correspond to delocalized metallic-like states, and values near 0 indicate negligible electron density. Hence, ELF mapping directly reflects the degree of electron confinement and delocalization within the system. As shown in Fig. 4 (a to c) and Supplementary Figure 14, B substitution markedly increases ELF intensity around the dopant sites, indicating stronger electron localization and reduced delocalization-consistent with the formation of deep potential wells that tightly bind carriers. In contrast, P doping decreases the local ELF value but broadens its spatial distribution, suggesting weaker confinement yet an expanded region of influence, consistent with shallow potential wells that facilitate carrier excitation and transport under relatively low electric fields.

Band structure and density of states (DOS) analyses further substantiate these observations. Pristine CN exhibits a bandgap of approximately 1.48 eV (Fig. 4d). It should be noted that the bandgap obtained from DFT calculations is significantly smaller than the experimentally measured optical bandgap of CN. This discrepancy is mainly attributed to the inherent limitations of the DFT methodology and the structural differences between the calculated model and the experimental material. First, the DFT calculations in this work were performed using a GGA exchange-correlation functional, which is known to systematically underestimate bandgaps due to the lack of quasiparticle self-energy corrections. For g-C3N4 systems, GGA based calculations typically yield bandgaps around 1.3-1.6 eV, which is consistent with our calculated result32, 33. Second, it should be noted that the experimentally synthesized CN obtained by high temperature polymerization does not exhibit a perfectly crystalline structure, as evidenced by the broadened XRD features (Supplementary Figure 5). In contrast, the DFT model is based on an idealized periodic CN framework without structural disorder, defects, or terminal groups. Such differences in structural order and local bonding environments can significantly influence the optical transition energies, leading to a larger experimentally observed optical bandgap. In addition, the experimental bandgap derived from UV-vis spectroscopy corresponds to the optical bandgap, which includes excitonic effects and electron–hole interactions, whereas the DFT value represents the intrinsic electronic bandgap of the idealized structure. Importantly, the purpose of the DFT calculations in this work is not to quantitatively reproduce the experimental bandgap, but to qualitatively analyze the electronic structure evolution and trap-state modulation induced by heteroatom doping.

B substitution drives the CN framework toward an acceptor-like electronic structure, manifested by an upward shift of the valence-band edge toward the Fermi level (Fig. 4e). The projected DOS further shows that B incorporation introduces localized in-gap states close to the Fermi level (Supplementary Figure 15), which function as deep potential wells capable of efficiently capturing low-energy carriers under low-to-moderate fields and delaying their release. This microscopic picture explains the experimentally observed higher switching field and the enhanced high-field charge-dissipation efficiency (larger nonlinear coefficient) in B-doped composites. Importantly, our calculations indicate that this deep-well trend is robust against the specific substitution site: when different carbon sites are selected for substitution within the CN structural unit, the overall evolution of the band edges and impurity-state positions remains qualitatively unchanged (Supplementary Figure 16), implying that the deep-trap formation is an intrinsic consequence of acceptor-type B doping rather than a site-specific artifact. In addition, the electronic response is strongly concentration dependent. At low dopant densities (e.g., 1 atom per 8 units), the dopant contribution appears as discrete, highly localized impurity levels within the bandgap, providing well-defined trapping centers (Supplementary Figure 17 and Figure 18). In the dilute regime relevant to our samples (B:C < 0.1), the global bandgap remains open and transport is still governed by field-assisted detrapping and hopping via localized states. However, when the dopant density is increased to an excessive level (e.g., 1 atom per 2 units), the impurity-related DOS rises sharply and becomes broadened, which can be rationalized by the reduced dopant-dopant spacing that promotes wavefunction overlap and drives discrete impurity levels to evolve toward an impurity band. Such band broadening weakens carrier localization and can shift the transport mechanism toward more delocalized conduction, thereby increasing low-field leakage. Consistent with this prediction, the experimentally over-doped EP/CN-B10 shows a pronounced rise in low-field conductivity, confirming that excessive doping can compromise the insulation margin by enabling the interconnection/percolation of impurity states.

Taken together, the ELF, band structure, and DOS analyses consistently demonstrate that B doping forms deep potential wells that enhance electron localization and high field conduction, whereas P doping creates shallow wells that promote efficient charge transport at lower fields. These theoretical results corroborate the experimentally observed trends in switching field modulation and nonlinear coefficient enhancement, confirming that heteroatom doping provides a viable electronic-structure design strategy for tuning nonlinear conduction in potential well based SADs.

Validation of Charge Dissipation Capability in Potential-Well-Based SADs
To experimentally validate the charge-dissipation capability of potential well based SADs, electrostatic discharge (ESD) tests were conducted on EP/CN, EP/CN-B, and EP/CN-P composites under low, medium, and high electric fields9. In these experiments, transient pulse voltages were applied to the sample surface using an ESD gun, and the resulting surface potential was monitored in real time with a high-voltage probe to quantify charge dissipation efficiency (Supplementary Figure 19). The results show that the electrical conductivity under different field strengths directly determines the rate of charge dissipation.

For EP/CN, field strengths of 1, 2, and 3 kV/mm correspond to the insulation, transition, and conduction regimes, respectively. The residual surface charge after the ESD event accounts for 86.8%, 79.1%, and 69.3% of the injected charge at these respective fields, indicating that the charge-dissipation rate increases markedly with conductivity (Fig. 5a). This behavior arises from selective carrier trapping by potential wells within the SADs. Because the duration of an ESD pulse (tens of nanoseconds to microseconds) is too short to induce appreciable Joule heating, the applied electric field serves as the dominant excitation source for carriers. At low fields, most injected carriers are captured in potential wells, and the material remains insulating, effectively isolating surface charge. As the local field increases due to charge accumulation, carrier energy rises proportionally. Once the carrier energy exceeds the confining potential, the material undergoes a field-induced insulation-to-conduction transition, releasing accumulated charge through the interconnected CN foam network toward the ground electrode. When the surface charge density decreases, the local field weakens and the material recovers its insulating state. This reversible process ensures efficient field-dependent charge dissipation and prevents overvoltage-induced insulation failure caused by continuous charge accumulation.

Heteroatom doping provides an effective means of tuning the nonlinear conductivity and, consequently, the charge-dissipation efficiency under identical external conditions. At 2 kV/mm, the B-doped composite, dominated by deep potential wells, remains largely insulating (Fig. 5b), whereas the P-doped composite, characterized by shallow wells, exhibits rapid charge dissipation even at lower fields (Fig. 5c). Such tunability enables the design of SADs tailored to specific operating environments, providing the flexibility required to meet the diverse demands of practical applications.

In addition to the fundamental charge dissipation characteristics discussed above, the application potential of the potential well based SADs was further evaluated in the context of power electronics packaging. In practical power modules, severe electric-field distortion commonly occurs at the metal-ceramic-polymer triple junction (Supplementary Figure 20), where charge accumulation can increase nonlinearly with operating voltage and trigger local insulation failure. An application-oriented simulations and simplified experimental validation demonstrate that the EP/CN-B composite effectively suppresses such abnormal charge accumulation and electric-field enhancement (Supplementary Figure 21). Benefiting from its rapid charge dissipation capability under high electric fields, the material prevents the nonlinear escalation of local electric field intensity at critical interfaces. These results indicate that the proposed SADS is promising for mitigating electric-field distortion and enhancing insulation reliability in power electronics packaging systems.

Stability of potential-well-based SADs under extreme operating conditions
To ensure the proper functioning of SADs, the breakdown strength (Eb) of the material should be significantly higher than the switching field (Es)34. In practice, Eb is generally required to exceed at least twice Es to avoid irreversible failure during nonlinear conduction. Supplementary Figure 22 presents the breakdown strength distributions and corresponding statistical results of the EP/CN, EP/CN-B, and EP/CN-P composites. The average breakdown strengths of these materials are 9.79 kV/mm, 20.18 kV/mm, and 5.39 kV/mm, respectively, all satisfying the basic operational requirement of Eb > 2Es. Among them, EP/CN-B exhibits the most pronounced breakdown margin, with an Eb/Es ratio exceeding 9, which is significantly higher than those of EP/CN and EP/CN-P, and surpasses previously reported typical Schottky barrier based SADs, for which the ratio usually does not exceed approximately 5 (Supplementary Table 5)34.

The improved breakdown performance arises not from suppressing high-field long-range carrier migration along the continuous CN framework, but from regulating the energy distribution and release behavior of carriers participating in transport. In EP/CN-B, B doping introduces deeper potential wells into the CN framework. In the low to moderate electric field regime, these deep wells preferentially capture low energy carriers, making them less likely to participate in long range migration and thereby maintaining a relatively low effective current density over a wide field range. As the applied electric field further increases, only high energy carriers that acquire sufficient energy can be released from the deep wells and contribute to transport along the continuous framework. Consequently, nonlinear conduction is dominated by a controlled population of high energy carriers, and the transition process is gradual and reversible, rather than rapidly evolving into uncontrolled carrier multiplication or local thermal instability prior to breakdown. This regulated long range migration introduces a wider stable operating window between nonlinear conduction and irreversible breakdown, which is the key reason for the significantly enhanced breakdown strength and larger Eb/Es margin observed in EP/CN-B.

In contrast, the shallow wells introduced by P doping in EP/CN-P reduce the energy barrier for carrier excitation and release, allowing the material to enter the nonlinear conduction regime at lower electric fields and thus resulting in a lower Es. However, the earlier onset of carrier release also implies that a higher fraction of carriers participates in transport over a broader electric field range, which makes local current concentration and electrically induced heat accumulation more likely under high field conditions, thereby limiting further improvement in breakdown strength. As a result, although EP/CN-P still satisfies the operational requirement of Eb > 2Es, its breakdown margin is relatively smaller. Overall, by introducing potential wells with different depths, it is possible to significantly widen the safety window between nonlinear conduction and irreversible breakdown while preserving effective long-range migration and self-adaptive conduction at high electric fields. Among these systems, deep potential well strategy exhibits advantages in breakdown margin, providing a broader design space for achieving highly reliable SADs.

To assess the performance of the potential well based SADs under high frequency and conditions, temperature-dependent dielectric properties of EP/CN, EP/CN-B, and EP/CN-P were measured over a broad frequency range. EP/CN-B shows no obvious change in dielectric constant compared with EP/CN, whereas EP/CN-P exhibits a clear increase (Supplementary Figure 23). This increase is mainly attributed to P doping, which introduces more polarizable states and shallow traps in the CN framework, enabling easier carrier displacement and polarization under an alternating field. Both B- and P-doped samples show higher dielectric loss than EP/CN, indicating additional relaxation and hopping dissipation introduced by heteroatom doping. Two loss peaks are observed in EP/CN-B and EP/CN-P at approximately 103 and 105 Hz. The lower-frequency peak is mainly related to trap assisted carrier relaxation, whereas the higher-frequency peak is attributed to a faster relaxation process associated with shallow traps and localized polarization within the P doped CN framework. The presence of two relaxation peaks indicates a multilevel distribution of potential wells, consistent with the depth regulation discussed above. At 100 °C, the slight increase in high-frequency permittivity accompanied by a shift of both loss peaks toward higher frequencies reflects thermally activated relaxation with reduced relaxation time. Importantly, the dielectric loss of all samples remains below 0.1 across the measured frequency range (50-106 Hz), confirming an overall low-loss dielectric behavior.

Furthermore, the durability of the adaptive response was assessed through rapid charge-discharge cycling tests. The EP/CN-B was subjected to 10000 voltage pulses with amplitudes exceeding their respective switching fields to simulate repeated operating stress. The field-dependent conductivity characteristics of EP/CN-B measured after cycling remain highly consistent with the initial state (Supplementary Figure 24). This exceptional stability confirms that the potential wells, originating from intrinsic doping, provide a robust charge-transport pathway that resists degradation, ensuring reliable long-term protection against surge stress.

In addition to electrical stability, the mechanical reliability of the SADs as packaging materials was systematically evaluated. Supplementary Figure 25 compares the tensile properties of the EP/CN-B composite with pure epoxy resin and a representative barrier-type SAD (epoxy composite filled with 25 vol% SiC). The EP/CN-B composite exhibits a tensile strength significantly superior to that of the SiC-filled composite. While the high filler loading required for traditional barrier-type SADs inevitably introduces severe stress concentration and brittleness, the nonlinear electrical response of our potential well type SAD originates from the interconnected bulk CN framework. This continuous structure allows the internal resin matrix to maintain considerable integrity without severe degradation of mechanical properties. Furthermore, to verify electrical stability after mechanical stress aging, the EP/CN-B composite was subjected to a static pressure of 15 MPa for 24 hours. The material retains its characteristic nonlinear dielectric response after enduring prolonged compressive stress (Supplementary Figure 26 and Table 6). Although a slight increase in conductivity was observed, likely attributed to minor microscopic aging at the foam-epoxy interface. The nonlinear electrical response behavior remains stable, confirming the robustness of the potential well-based system under mechanical loads.

Finally, considering the typical operating environments of power electronic devices, for instance, the junction temperature of wide-bandgap semiconductors (e.g., SiC) can reach up to 175 °C, requiring packaging materials to withstand continuous operation at 100–150 °C35. We systematically evaluated the long-term reliability under thermal stress. Thermal aging tests were conducted by exposing the EP/CN-B composite to 130 °C for 72 hours. Subsequently, the J-E characteristics of the aged samples were measured at room temperature (Supplementary Figure 27). Based on the nonlinear parameters fitted from the curves, the Es decreased by approximately 10%, while the α decreased slightly compared to the initial state. This variation is primarily attributed to interfacial aging and thermal-oxidative aging of the matrix, which may introduce shallow traps that facilitate carrier hopping. Nevertheless, the material retains robust nonlinear electrical response characteristics, confirming the chemical stability of the CN framework and potential well structures against irreversible thermal degradation. Regarding operational stability at elevated temperatures, the material exhibits a temperature-dependent evolution of nonlinear properties (as shown in Fig. 3f). The Es naturally decreases with increasing temperature due to enhanced thermal activation of charge carriers, which facilitates detrapping from the potential wells. While this is a fundamental physical characteristic of trap-controlled transport, it defines the operational boundaries of the material. Further limiting tests revealed that under simultaneous exposure to 150 °C and a high electric field of 5 kV/mm, the composite eventually succumbs to electrical ablation due to the coupling effect of Joule heating and ambient thermal stress. Therefore, while the potential-well-based SADs demonstrate excellent structural stability up to 130 °C, thermal management remains a critical design factor for operation under extreme high-temperature and high-field conditions.

Methods
Materials
All chemical reagents used in this study were of analytical grade and used as received without further purification. Commercial melamine foam, a common building material for sound insulation, served as the precursor for the carbon nitride (CN) framework. Ammonium dihydrogen phosphate (NH4H2PO4) and boric acid (H3BO3) were purchased from Sigma-Aldrich and used as the P and B dopant sources, respectively. The epoxy resin was a cycloaliphatic epoxy (S-06E, Synasia) with an epoxy equivalent weight of 130-135 g/eq and a viscosity of 220-250 mPa·s at 25 °C. The curing agent methylhexahydrophthalic anhydride (MHHPA) and the accelerator 2-ethyl-4-methylimidazole (EMI) were supplied by Macklin Biochemical Co., Ltd.

Synthesis and heteroatom doping of CN foams
CN foams were synthesized by one-step pyrolysis of melamine foams (C3H6N6) in a tubular furnace at 550 °C for 4 h under a nitrogen (N2) atmosphere. The pyrolysis process preserved the original three-dimensional interconnected structure of the foam (Supplementary Figure 1). The resulting CN foam exhibited a honeycomb-like porous architecture composed of slender, interconnected struts forming open and continuous pores. This highly porous and stable skeleton provided abundant sites for carrier migration and served as an ideal scaffold for constructing potential-well networks.

Heteroatom-doped CN foams were prepared by a solution impregnation assisted pyrolysis route using commercial melamine foams as the structural precursor. In a typical procedure, melamine foams were immersed in aqueous dopant-precursor solutions until complete wetting of the three-dimensionally interconnected skeleton was achieved. Boric acid (H3BO3, BA) and ammonium dihydrogen phosphate (NH4H2PO4, ADP) were used as the B and P sources, respectively. After impregnation, the foams were taken out and briefly allowed to drain to remove excess surface liquid. The impregnated foams were then dried in a vacuum oven at 80 °C. Vacuum drying accelerates solvent removal and shortens the lifetime of the liquid phase inside the porous skeleton, thereby suppressing long-range solute redistribution during evaporation and promoting uniform precursor deposition along the struts. The dried foams were subsequently pyrolyzed in a tubular furnace at 550 °C for 4 h under a nitrogen atmosphere to convert the melamine framework into a CN network. During pyrolysis, the dopant species are incorporated into the CN framework and form stable B-N or P-N bonding environments.

The dopant-precursor solutions were designed to (i) provide comparable precursor dosage for B and P doping in the baseline samples and (ii) enable a convenient, scalable tuning knob for doping level. Specifically, the baseline BA and ADP solutions were prepared at the same molar concentration (6.33 mM) so that the number of dopant atoms delivered per unit solution volume is comparable for B and P (each precursor molecule contains one B or one P atom, respectively). Beyond the baseline condition, the doping level can be systematically tuned by varying the precursor-solution concentration while keeping all subsequent steps (impregnation procedure, vacuum drying, pyrolysis conditions, and composite fabrication) identical.

For clarity, pristine CN foams obtained by direct pyrolysis are denoted as CN. B- and P-doped foams are denoted as CN-B and CN-P, respectively. The corresponding epoxy-impregnated self-adaptive dielectric composites are denoted as EP/CN, EP/CN-B, and EP/CN-P. For the B-doping concentration series, samples are labeled as EP/CN-B2, EP/CN-B4, EP/CN-B6, EP/CN-B8, and EP/CN-B10, where Bx indicates the BA precursor-solution concentration used for impregnation. In this work, B2/B4/B6/B8/B10 correspond to BA solution concentrations of 6.33, 12.66, 18.99, 25.32, and 31.65 mM, respectively (Supplementary Table 7). Unless otherwise specified, all processing parameters other than the precursor-solution concentration were kept the same to ensure that the observed differences in electrical behavior arise primarily from the dopant level.

Fabrication of Epoxy/CN Composites
Epoxy/Carbon Nitride (EP/CN) composites were fabricated via vacuum impregnation. The epoxy monomer, MHHPA curing agent, and EMI accelerator were mixed at a predetermined mass ratio to form a homogeneous resin precursor solution. CN, CN-B, and CN-P foams were immersed in the mixture and subjected to vacuum treatment until no visible air bubbles remained, ensuring complete infiltration of epoxy resin into the three-dimensional foam skeleton. The impregnated samples were cured in an oven at elevated temperature to obtain the final composites, denoted as EP/CN, EP/CN-B, and EP/CN-P, respectively.

The volume fraction of the CN filler in the epoxy composite was calculated based on the measured mass and density of each component. The mass of the pyrolyzed CN foam used for composite fabrication was 0.02 g, and its density was approximately 2.22 g cm-3, corresponding to a filler volume of approximately 0.0090 cm3. The total mass of the prepared composite was 1.95 g, with a measured density of 1.164 g cm-3, yielding a total composite volume of approximately 1.676 cm3. Accordingly, the volume fraction of the CN filler was calculated to be approximately 0.54 vol%.

Characterization
The microstructures of melamine foams and CN foams before and after doping were examined using scanning electron microscopy (SEM, Merlin, Zeiss, Germany). UV–visible absorption spectra were obtained using a Shimadzu UV-2501PC spectrometer equipped with an ISR-2200 integrating sphere to estimate optical bandgaps. Fourier transform infrared (FTIR) spectra were collected on a Nicolet 6700 spectrometer (Thermo Fisher Scientific, USA) in the range of 4000–500 cm-1. X-ray photoelectron spectroscopy (XPS, Axis Supra+, Kratos, UK) and X-ray diffraction (XRD, XPert Powder, PANalytical, Netherlands) were performed to analyze chemical composition and crystal structure, respectively. Trap characteristics of the composites were investigated using thermally stimulated depolarization current (TSDC) analysis with a Keithley 6517B electrometer and a Quatro-Cryosystem temperature controller. Each sample was first polarized at 100 °C under a DC electric field slightly above the switching field for 30 min to ensure full trap filling. The samples were then rapidly cooled to 30 °C while maintaining the field, held for 10 min, and subsequently short-circuited. The temperature was then increased to 250 °C at a rate of 3 °C/min, and the depolarization current was recorded as a function of temperature.

DFT Calculations
Density functional theory (DFT) calculations were carried out using the Vienna ab initio Simulation Package (VASP). The exchange–correlation interaction was treated within the generalized gradient approximation using the Perdew–Burke–Ernzerhof (PBE) functional, and core–valence interactions were described by the projector augmented-wave (PAW) method. A plane-wave energy cutoff of 500 eV was applied. All structures were fully relaxed until the Hellmann–Feynman forces on each atom were below 0.001 eV/Å and the total energy change was less than 1 × 10-5 eV. A vacuum layer of 15 Å was introduced normal to the sheet to avoid interactions between periodic images.Based on the optimized geometries, the electron localization function (ELF) was calculated within VASP using the same computational settings. ELF isosurfaces were visualized in VESTA, and the isovalue was chosen to highlight bonding and lone-pair regions.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This study utilizes a recycled melamine foam-derived carbon nitride framework as a platform to precisely regulate the depth and distribution of potential wells through heteroatom doping, thereby achieving tailored design of nonlinear conductivity and switching field strength. The work transitioning from traditional Schottky barrier interface engineering to potential well engineering, offering a novel solution to address interface defects and performance fluctuations. It can be considered for acceptance for publication in the journal after major revision.\n1. The Introduction requires further refinement, as the explanation of how the strategy proposed in this work addresses the limitations of conventional SADs lacks clarity.\n2. The paper emphasizes the advantages of the potential well strategy over traditional Schottky barrier SADs (such as avoiding interface defects). However, there is a lack of performance comparison with Schottky barrier SADs under identical testing conditions. It is recommended to add a direct comparison in the main text or supplementary information, highlighting the differences in key performance indicators such as the nonlinear coefficient (α) and the stability of the switching field (Es).\n3. For nonlinear conductive materials, the breakdown strength must exceed twice the switching field to ensure the proper functioning of SADs. The author should provide relevant data on the breakdown strength of the EP/CN, EP/CN-B, and EP/CN-P composites.\n4. Rapid charge-discharge cycling tests should be conducted to demonstrate that repeated exposure to charge pulses does not compromise its adaptive charge dissipation capability.\n5. Has the author considered the impact of the compressive deformation of foam materials on their relevant properties when using them as insulating packaging materials for electronic devices?\n6. The authors are recommended to update the recent references related to melamine foam material and polymer dielectrics. For example, Nano Lett., 2024, 24, 3369−3377; Adv. Funct. Mater., 2022, 32, 2209898; Nano Res. 2023, 16(2), 3240-3253; Nano Energy, 2025, 143, 111313.", "reviewer_2": "This manuscript presents a highly interesting and comprehensive study on the development of self-adaptive dielectric (SAD) composites based on potential well engineering in graphitic carbon nitride (g-C₃N₄) frameworks. The concept of replacing traditional Schottky barrier-based mechanisms with tunable potential wells is innovative and addresses a critical challenge of interfacial instability in conventional SADs. The work is systematic, combining sophisticated material synthesis, thorough electrical characterization, theoretical calculations (DFT), and application-oriented validation (ESD tests). The strategy of using waste melamine foam also adds an element of sustainability. It is suitable for Nature Communications. However, the following questions exist in the article.\nThe manuscript needs major revision noted below.\n1. It is suggested that the authors make a comparison between this work and the commonly used SAD systems, such as ZnO-based varistors or other polymer composites with nonlinear fillers. A summary table or figure comparing key parameters (e.g., switching field, nonlinear coefficient, leakage current, stability) would help to clearly position the novelty and advantages of the proposed potential-well strategy over existing technologies.\n2. For practical application in electronic packaging, the operational stability of the materials under continuous electrical and thermal stress is paramount. The current manuscript lacks data on long-term reliability. It is recommended to include aging tests, such as monitoring the evolution of the I-V characteristics and switching field after prolonged exposure to high temperatures (e.g., 100-150 °C) and high electric fields.\n3. This work focuses on DC and transient pulse properties. However, power electronics often operate at high frequencies. An investigation into the frequency-dependent conductivity and permittivity (e.g., from 1 Hz to 1 MHz) under various DC bias fields would be highly valuable to assess the performance of these SADs in AC or pulsed operating conditions. The author is suggested to supplement relevant tests.\n4. While the SCLC model is effectively used to extract trap distributions, a more quantitative link between the dopant concentration (from XPS quantification) and the resulting trap energy depth/density. Could a predictive relationship be established? Further DFT analysis on different doping configurations or concentrations could provide deeper insights.\n5. The discussion on the application remains somewhat conceptual. It is recommended to supplement the packaging schematic diagram or performance test results of composite materials in real power modules.\n6. The DFT-calculated bandgap for pristine CN (~1.48 eV, Page 9) is significantly smaller than the experimental optical bandgap (~2.65 eV, Fig. S7). Why is that?\n7. In page 16: the author described “c-e, I-V curves of 428 CN-B (c), pristine CN (d), and CN-P (e) foams…” in Fig. 2’s caption, but the order of the three in the figure is not like this. Similarly, the author described “For each material, subfigures (1–3) correspond to low…” in Fig. 5’s caption, but 1, 2, 3 is not marked in the figure.", "reviewer_3": "The authors report nonlinear conduction behavior in epoxy composites filled with g-C₃N₄ skeletons. Controlled heteroatom doping with different dopants or doping levels enables customizable potential wells with tunable depths and distributions, allowing the nonlinear conductivity and the insulation-conduction threshold field to be tailored. The scientific quality of the work is strengthened by the combination of experimental results with simulations of electric-field distortion and charge-conduction pathways, electronic structure analysis based on DFT calculations, and electron localization function simulations. This work shows promise as a useful reference for the development of self-adaptive insulating electronic packing and insulation materials. This manuscript is clearly written and easy to follow. The experimental section is sufficiently detailed, and the findings are thoroughly discussed with conclusions well supported by the data. This work is suitable for publication after clarification of the following points.\n1. The authors did not discuss how the choice of polymer matrix influences the nonlinear conduction. The rationale for selecting epoxy as the matrix should be clarified in the revised main text. Although charge transport occurs primarily through the g-C₃N₄ semiconductor skeleton network, charge accumulation occurs at the g-C₃N₄/epoxy interfaces under electric fields due to their differences in permittivity and conductivity. How do the buildup and release of these interfacial charges affect the electrical properties of the composites?\n2. Doping plays a crucial role in determining the insulation–conduction transition and the nonlinear conductivity. How is the doping level quantitatively controlled, and how is doping uniformity ensured? How was the reported doping level (B/P:C < 0.1) quantified? What range of doping levels can be achieved using the proposed method?\n3. Page 3, line 75: Grain-boundary barriers exist within semiconductor particles, not at semiconductor–polymer interfaces. The sentence is confusing and should be clarified.\n4. Page 6, line 154: It would be preferable to include Eq. (S2) directly in the main text for clarity and completeness.\n5. Page 6: The authors mention two application scenarios, but the required switching-field values for each are not specified. Providing these values would help readers assess whether the switching field of the g-C₃N₄/epoxy composites is sufficiently low for rapid electrostatic discharge and sufficiently high to maintain insulation under strong electric fields.\n6. The three-electrode configuration used for field-dependent conductivity measurements should be schematically illustrated, particularly the electrode arrangement.\n7. Typographical errors :\no Page 2, line 46: “insulation-conduction conversion”\no Supporting Information, page 10, line 257: Fig. S14"}, "author_response": "Dear Editor and Reviewers,\nWe sincerely thank the Editor and the Reviewers for their careful evaluation of our manuscript and for the constructive comments and suggestions. These comments have greatly helped us to improve the clarity, rigor, and completeness of the work. We have revised the manuscript accordingly, and all changes are highlighted in the revised version. Below we provide a detailed, point-by-point response to each comment.\nReviewer #1 (Remarks to the Author):\nThis study utilizes a recycled melamine foam-derived carbon nitride framework as a platform to precisely regulate the depth and distribution of potential wells through heteroatom doping, thereby achieving tailored design of nonlinear conductivity and switching field strength. The work transitioning from traditional Schottky barrier interface engineering to potential well engineering, offering a novel solution to address interface defects and performance fluctuations. It can be considered for acceptance for publication in the journal after major revision.\nResponse: We sincerely thank the reviewer for the positive evaluation of the novelty and significance of our work. We have carefully addressed all the comments and revised the manuscript accordingly to further improve its clarity and completeness.\n1. The Introduction requires further refinement, as the explanation of how the strategy proposed in this work addresses the limitations of conventional SADs lacks clarity.\nResponse: Thank you for this valuable suggestion. We agree that the Introduction required clearer articulation of how the proposed strategy fundamentally addresses the limitations of conventional SADs. In the revised manuscript, we have refined the discussion by explicitly contrasting the interface dominated Schottky barrier mechanism in traditional SADs with the bulk-controlled potential well mechanism proposed in this work. The revised text clarifies how potential well engineering reduces dependence on interfacial quality, mitigates interface related defects, and enables precise regulation of nonlinear electrical response through tunable trap depth and density.\nTo address this comment, we have added a statement cited as “From the perspective of the origin of nonlinear electrical response, the advantage of potential-well-based SADs lies in shifting the nonlinear regulation from barrier heights that depend on interfacial contact states to designable and controllable bulk trapping states. Under low electric fields, charge carriers are trapped in potential wells, suppressing leakage and maintaining insulation, whereas increasing field strength activates field-assisted detrapping and hopping 13, resulting in a rapid and reversible transition to conduction near the threshold. The energy constraint imposed on charge carriers is mainly determined by the depth of the potential wells, while the number and spatial distribution of the wells are governed by their density. Because heteroatom doping with neighboring-group elements can introduce controllable impurity levels or localized states into the semiconducting framework, such as deep wells near the Fermi level or shallow wells near the conduction or valence band edges, the depth and density of potential wells can be tuned in a predictable manner 14, 15, 16. Consequently, constructing potential wells through doping enables effective regulation of the switching field and nonlinear coefficient, such that the nonlinear response is no longer primarily dictated by uncontrollable randomness associated with particle contact states or grain-boundary microstructures, thereby improving performance stability and batch-to-batch reproducibility.” in the Page 3 of the revised manuscript.\n2. The paper emphasizes the advantages of the potential well strategy over traditional Schottky barrier SADs (such as avoiding interface defects). However, there is a lack of performance comparison with Schottky barrier SADs under identical testing conditions. It is recommended to add a direct comparison in the main text or supplementary information, highlighting the differences in key performance indicators such as the nonlinear coefficient (α) and the stability of the switching field (Es).\nResponse: Thank you for this valuable and constructive suggestion. We agree that a direct performance comparison with conventional Schottky barrier based SADs under comparable testing conditions would strengthen the manuscript and help more clearly demonstrate the advantages of the potential well strategy proposed in this work. We have added representative barrier-type SADs reported in recent research as reference systems and applied a screening procedure to improve comparability among different design strategies. Specifically, the selected barrier-type SADs are all based on insulating polymer matrices, where the nonlinear electrical response mainly originates from Schottky barriers formed at semiconductor filler particle contacts or grain boundaries. On this basis, we chose the achievable tuning range of the switching field (E ) and the relationship between the nonlinear coefficient (α) and filler content as the key comparison metrics, and the rationale for selecting these metrics has been clarified in the revised manuscript.\nThe comparison results indicate that, at a relatively low filler content of 0.5 vol%, potential well based SADs can achieve a higher nonlinear coefficient (α > 10) while exhibiting a substantially broader tunable range of switching field, reflecting greater flexibility in parameter design. From the perspectives of performance and tunability, this comparative analysis further supports the potential advantages of the proposed potential well regulation strategy for material design and application adaptation.\nTo address this comment, we have added a statement cited as “To clarify the performance differences between potential-well-type SADs and conventional barrier-type SADs from a mechanistic perspective, we performed a systematic comparison using recently reported SADs based on different wide-bandgap semiconductors, including ZnO, SiC, and BaTiO (Fig. S13 and Table S3). 3 These reported systems mainly rely on interfacial Schottky barriers to achieve nonlinear conduction. Their key parameters, including the switching field (E ), nonlinear coefficient (α), and the corresponding filler content, were compared with those of the potential-well-type SAD developed in this work.\nBecause SADs are used in diverse applications, performance is not determined solely by achieving a high switching field. Instead, it is important to tune E over a broad range while maintaining a sufficiently high nonlinear coefficient (α > 10). The comparison shows that potential-well-type SADs allow a wider adjustable range of E than conventional barrier dominated SADs, and the tunable window can cover and extend the reported ranges of typical barrier-type systems. Analysis of α as a function of filler content further indicates that SiC based barrier-type SADs can show nonlinear conduction at relatively low filler loadings, but their α values are often limited. In contrast, ZnO varistor based SADs usually require higher filler contents (35 vol%) to reach α values close to 10, and their E is relatively low with a narrow tuning range.\nIn our system, the potential-well strategy shifts the dominant mechanism from interfacial barrier control to bulk potential well regulation. This change reduces the dependence of α on filler content. As a result, α values comparable to those of ZnO based SADs can be achieved at very low filler loadings, while E remains continuously tunable over a wide range. These results suggest that the potential well strategy provides an effective route to optimize SAD performance beyond conventional barrier-based approaches.” in the Page 9 of the revised manuscript.\nFig. S13. Comparison of nonlinear electrical performance between potential-well-based SADs and representative Schottky-barrier-based SADs reported in recent literature1, 2, 3, 4, 5, 6, 7, 8, 9. (a) Switching electric field E of various SAD systems reported in the literature (Ref. S1-S9) and in this work. The shaded bars represent the reported ranges of switching fields. The red star highlights the performance of the EP/CN-based composite developed in this work. (b) Nonlinear coefficient α as a function of filler volume fraction for different SADs. Data points are extracted from the corresponding references and compared with the present work (marked by the red star).\nTable S3. Comparison of potential-well-based SADs with representative nonlinear conductive systems reported in the literature.\nSwitching field range Nonlinear coefficient Filler content at\nSample E (kV/mm) α maximum α\ns\nfrom to (vol %)\nEP/CN 1.05 3 11.26 0.5\nSE/SiC-AlN 0.93 1.75 6.12 8.7\nEP/BT-TiO 1.9 2.75 3.08 7.87\nnano\nSR/SiC 0.9 3 0.97 9.48\nEP/SiC-Alginate 0.61 1.57 7.5 1.57\nEPDM/ZnO 0.725 0.925 9 37\nEP/ZnO-fiber 0.3 1.07 9.7 35\nSR/ZnO 1.106 1.725 8.4 42\nSR/ZnO-s 1.314 2.14 13.9 35\n3. For nonlinear conductive materials, the breakdown strength must exceed twice the switching field to ensure the proper functioning of SADs. The author should provide relevant data on the breakdown strength of the EP/CN, EP/CN-B, and EP/CN-P composites.\nResponse: Thank you for this important comment. In response, we have added systematic breakdown strength measurements for the EP/CN, EP/CN-B, and EP/CN-P composites in the revised manuscript. As shown in the revised text and Fig. S22, the average breakdown strengths of EP/CN, EP/CN-B, and EP/CN-P are 9.79 kV mm-1, 20.18 kV mm-1, and 5.39 kV mm-1, respectively, all satisfying the commonly accepted operational criterion of E > 2E . Notably, EP/CN-B exhibits a particularly large breakdown margin, with an E /E ratio exceeding 9, which is significantly higher than those of EP/CN and EP/CN-P and exceeds values reported for typical Schottky-barrier-based SADs in the literature.\nWe further clarified in the manuscript that the enhanced breakdown margin is closely related to the regulation of the energy distribution and release behavior of charge carriers by potential wells. Specifically, the deep wells introduced by B doping capture low-energy carriers over a wide electric field range and allow only sufficiently energized carriers to participate in long range transport at high fields. This regulated and reversible transport process widens the stable operating window between nonlinear conduction switching and irreversible breakdown. In contrast, the shallow wells introduced by P doping, while reducing the energy threshold for carrier release, are more prone to inducing local current concentration and electrically induced heat accumulation under high field, thereby limiting further improvement in breakdown margin. These additional data and discussions have been incorporated into the revised manuscript to demonstrate that potential-well-based SADs can maintain effective nonlinear conduction while also providing sufficient insulation margin for practical applications.\nTo address this comment, we have added a statement cited as “To ensure the proper functioning of SADs, the breakdown strength (E ) of the material should be significantly higher than the switching field (E )34. In practice, E is generally required to exceed at least twice Es to avoid irreversible failure during nonlinear conduction. Fig. S22 presents the breakdown strength distributions and corresponding statistical results of the EP/CN, EP/CN-B, and EP/CN-P composites. The average breakdown strengths of these materials are 9.79 kV mm-1, 20.18 kV mm-1, and 5.39 kV mm-1, respectively, all satisfying the basic operational requirement of E > 2E . Among them, EP/CN-B exhibits the most pronounced breakdown margin, with an E /E ratio exceeding 9, which is significantly higher than those of EP/CN and EP/CN-P, and surpasses previously reported typical Schottky barrier based SADs, for which the ratio usually does not exceed approximately 5 (Supplementary Information Table S5)34.\nThe improved breakdown performance arises not from suppressing high-field long-range carrier migration along the continuous CN framework, but from regulating the energy distribution and release behavior of carriers participating in transport. In EP/CN-B, B doping introduces deeper potential wells into the CN framework. In the low to moderate electric field regime, these deep wells preferentially capture low energy carriers, making them less likely to participate in long range migration and thereby maintaining a relatively low effective current density over a wide field range. As the applied electric field further increases, only high energy carriers that acquire sufficient energy can be released from the deep wells and contribute to transport along the continuous framework. Consequently, nonlinear conduction is dominated by a controlled population of high energy carriers, and the transition process is gradual and reversible, rather than rapidly evolving into uncontrolled carrier multiplication or local thermal instability prior to breakdown. This regulated long range migration introduces a wider stable operating window between nonlinear conduction and irreversible breakdown, which is the key reason for the significantly enhanced breakdown strength and larger E /E margin observed in EP/CN-B.\nIn contrast, the shallow wells introduced by P doping in EP/CN-P reduce the energy barrier for carrier excitation and release, allowing the material to enter the nonlinear conduction regime at lower electric fields and thus resulting in a lower E . However, the earlier onset of carrier release also implies that a higher fraction of carriers participates in transport over a broader electric field range, which makes local current concentration and electrically induced heat accumulation more likely under high field conditions, thereby limiting further improvement in breakdown strength. As a result, although EP/CN-P still satisfies the operational requirement of E > 2E , its breakdown margin is relatively smaller. Overall, by introducing potential wells with different depths, it is possible to significantly widen the safety window between nonlinear conduction and irreversible breakdown while preserving effective long-range migration and self adaptive conduction at high electric fields. Among these systems, deep potential well strategy exhibits advantages in breakdown margin, providing a broader design space for achieving highly reliable SADs.” in Page 15 of the revised manuscript.\nFig. S22. Weibull distributions of breakdown strength (E ) for EP/CN, EP/CN-B, and EP/CN-P composites measured under identical testing conditions. The solid lines represent Weibull fitting of the experimental data. The extracted average breakdown strengths are 9.79 kV mm-1 for EP/CN, 20.18 kV mm-1 for EP/CN-B, and 5.39 kV mm-1 for EP/CN-P. All samples satisfy the operational requirement of E > 2E , while EP/CN-B exhibits a larger breakdown margin. For each composite, the Weibull distribution was constructed from 16 breakdown events (n = 16 data points) measured at different locations on the same specimen under identical conditions. Each data point corresponds to an independent breakdown event, and the lines are Weibull fits to the experimental data.\nTable S5. Comparison of switching field, breakdown field, and filler content for potential-well-based SADs in this work and representative barrier-type SAD systems reported in the literature.\nSwitching field Breakdown field Filler content E /E\nb s\nSample\nE (kV/mm) E (kV/mm) (vol %) value\ns b\nEP/CN-B 2.21 20.18 0.5 9.13\nEP/CN 1.25 9.79 0.5 7.83\nEP/CN-P 1.05 5.39 0.5 5.13\nEP/SiC-Ag 3 1.5 7.7 25 5.13\nnano\nSR/Al O -GQD10, 11 10 36.49 6.5 3.65\n2 3\nEPDM/BN-PPY 11.4 52.65 2.1 4.61\n4. Rapid charge-discharge cycling tests should be conducted to demonstrate that repeated exposure to charge pulses does not compromise its adaptive charge dissipation capability.\nResponse: Thank you for this crucial suggestion. We fully agree that the stability of the adaptive charge dissipation capability under repeated electrical stress is a prerequisite for practical applications. To address this, we subjected the potential well-type SADs (EP/CN-B) to a rigorous rapid charge-discharge cycling test involving 10000 voltage pulses. The amplitude of the applied voltage pulses was set to exceed the switching field (E ) to ensure that the material repeatedly underwent the insulation-to-conduction transition.\nAs shown in the newly added Fig. S24, we compared the field-dependent conductivity characteristics of the SAD before and after the 10000 cycles. The results demonstrate that the nonlinear conductivity curves remain virtually unchanged, with no degradation in either the switching field or the nonlinear coefficient. This exceptional stability is attributed to the robustness of the potential wells constructed within the CN framework, which are less susceptible to degradation than the interfaces in traditional barrier-type SADs.\nTo address this comment, we have added a statement cited as “Furthermore, the durability of the adaptive response was assessed through rapid charge-discharge cycling tests. The EP/CN-B was subjected to 10000 voltage pulses with amplitudes exceeding their respective switching fields to simulate repeated operating stress. As shown in Fig. S24, the field-dependent conductivity characteristics of EP/CN-B measured after cycling remain highly consistent with the initial state. This exceptional stability confirms that the potential wells, originating from intrinsic doping, provide a robust charge-transport pathway that resists degradation, ensuring reliable long-term protection against surge stress.” in the Page 17 of the revised manuscript.\nWe have also added the experimental details in the revised Supplementary Information: “Cyclic Charge-Discharge Stability Test: To evaluate the long-term reliability of the SADs, the sample was subjected to a rapid cycling test using a high voltage pulse generator. A total of 10000 voltage pulses were applied to the samples. The pulse amplitude was set to generate an electric field strength of 3 kV/mm (significantly higher than the E of EP/CN-B) to ensure the SAD entered the nonlinear conduction regime during each cycle. After the cycling process, the nonlinear conductivity of the samples was re-measured using the three-electrode system to assess any performance degradation.”.\nFig. S24. Field-dependent conductivity of the EP/CN-B composite measured before and after 10000 rapid charge-discharge cycles. The amplitude of the voltage pulses was set to 3 kV/mm. The before/after curves were obtained from measurements on the same specimen.\n5. Has the author considered the impact of the compressive deformation of foam materials on their relevant properties when using them as insulating packaging materials for electronic devices?\nResponse: Thank you for raising this critical point regarding the stability of foam-based composites under mechanical stress. We fully agree that characterizing the electrical performance under compressive deformation is vital for evaluating their reliability as packaging materials. Ideally, simultaneous monitoring of nonlinear conductivity under varying compressive loads would most directly reveal this issue. However, we regret to mention that due to safety risks associated with applying high-voltage (kV-level) electrical stress under high mechanical pressure, and limited by equipment constraints, we adopted an alternative strategy to verify the material's reliability. Our focus was on assessing whether the material can structurally withstand mechanical loads and whether it retains its electrical functionality after enduring stress.\nFirst, we assessed the tensile performance of the potential-well-based SAD (EP/CN-B) via tensile testing and benchmarked it against pure epoxy resin and a typical barrier-type SAD (epoxy composite filled with 25 vol% SiC). As shown in Fig. S25, the tensile strength of the EP/CN-B composite is significantly superior to that of the SiC-filled composite. The high filler loading required for traditional barrier-type SADs introduces severe stress concentration and brittleness. In contrast, the nonlinear electrical response of the potential-well-type SAD originates from the interconnected bulk CN framework within the material, which allows the internal resin matrix to maintain considerable integrity without severe degradation of mechanical properties. Second, to verify the electrical stability of potential-well-based SADs after mechanical stress aging, we subjected the EP/CN-B composite to a static pressure of 15 MPa for 24 hours (Pressure aging test). The results presented in Fig. S26 demonstrate that after enduring compressive stress, the material retains its characteristic nonlinear dielectric response. We observed a slight increase in conductivity, which may be attributed to minor microscopic aging at the foam-epoxy interface, but its nonlinear electrical response behavior remains stable.\nTo address this comment, we have added a statement cited as “In addition to electrical stability, the mechanical reliability of the SADs as packaging materials was systematically evaluated. Fig. S25 compares the tensile properties of the EP/CN-B composite with pure epoxy resin and a representative barrier-type SAD (epoxy composite filled with 25 vol% SiC). The EP/CN-B composite exhibits a tensile strength significantly superior to that of the SiC-filled composite. While the high filler loading required for traditional barrier-type SADs inevitably introduces severe stress concentration and brittleness, the nonlinear electrical response of our potential well type SAD originates from the interconnected bulk CN framework. This continuous structure allows the internal resin matrix to maintain considerable integrity without severe degradation of mechanical properties. Furthermore, to verify electrical stability after mechanical stress aging, the EP/CN-B composite was subjected to a static pressure of 15 MPa for 24 hours. As shown in Fig. S26, the material retains its characteristic nonlinear dielectric response after enduring prolonged compressive stress (Supplementary Information Table S6). Although a slight increase in conductivity was observed, likely attributed to minor microscopic aging at the foam-epoxy interface. The nonlinear electrical response behavior remains stable, confirming the robustness of the potential well-based system under mechanical loads.” in the Page 17 of the revised manuscript.\nFig. S25. Tensile stress–strain curves of neat epoxy resin, EP/CN-B composite, and EP/SiC (25 vol%) composite measured. Epoxy resin exhibits the highest tensile strength (65.04 MPa) with an elongation at break of 3.4%, showing typical brittle fracture behavior. The EP/CN-B composite shows a reduced tensile strength (50.93 MPa); however, compared with the EP/SiC composite (39.27 MPa), it demonstrates clear advantages in both tensile strength and elongation at break.\nFig. S26. Field-dependent conductivity of the EP/CN-B composite measured before and after pressure aging (15 MPa static pressure for 24 hours). Before/after measurements were performed on the same specimen, which had previously undergone 10000 pulsed charge-discharge cycles (Fig. S24).\nTable S6. Stability of nonlinear electrical parameters of the EP/CN-B composite under various stress conditions, including charge-discharge cycling, mechanical stress aging, and thermal aging.\nSample Nonlinear coefficient α Switching field E (kV/mm)\ns\nEP/CN-B 11.26 2.25\nAfter 10,000 pulse cycles 10.92 2.23\nAfter mechanical stress aging 10.07 2.20\n6. The authors are recommended to update the recent references related to melamine foam material and polymer dielectrics. For example, Nano Lett., 2024, 24, 3369−3377; Adv. Funct. Mater., 2022, 32, 2209898; Nano Res. 2023, 16(2), 3240-3253; Nano Energy, 2025, 143, 111313.\nResponse: We thank the reviewer for this helpful suggestion. In the revised manuscript, we have updated and expanded the references related to melamine foam–based materials and polymer dielectrics by incorporating several recent and representative studies. These newly added references provide important context regarding the structural design, dielectric regulation strategies, and electrical performance of polymer-based dielectric systems, thereby strengthening the background and highlighting the distinctions between previously reported approaches and the potential well-type SADS mechanism proposed in this work.\n18. Wu L, et al. Microwave-Absorbing Foams with Adjustable Absorption Frequency and Structural Coloration. Nano Letters 24, 3369-3377 (2024).\n19. Zhao L, et al. Thermal-insulating carbon foam for efficient electromagnetic energy absorption and conversion. Nano Energy 143, 111313 (2025).\n21. Yan Y-Z, et al. “One stone, two birds” solvent system to fabricate microcrystalline cellulose-Ti3C2Tx nanocomposite film as a flexible dielectric and thermally conductive material. Nano Research 16, 3240-3253 (2023).\n22. Wu L, et al. Carbon Nanocoils/Carbon Foam as the Dynamically Frequency-Tunable Microwave Absorbers with an Ultrawide Tuning Range and Absorption Bandwidth. Advanced Functional Materials 32, 2209898 (2022).\nReviewer #2 (Remarks to the Author):\nThis manuscript presents a highly interesting and comprehensive study on the development of self-adaptive dielectric (SAD) composites based on potential well engineering in graphitic carbon nitride (g-C₃N₄) frameworks. The concept of replacing traditional Schottky barrier-based mechanisms with tunable potential wells is innovative and addresses a critical challenge of interfacial instability in conventional SADs. The work is systematic, combining sophisticated material synthesis, thorough electrical characterization, theoretical calculations (DFT), and application-oriented validation (ESD tests). The strategy of using waste melamine foam also adds an element of sustainability. It is suitable for Nature Communications. However, the following questions exist in the article.\nResponse: We sincerely thank the reviewer for the positive evaluation of our work. We have carefully addressed the specific comments and questions below.\nThe manuscript needs major revision noted below.\n1. It is suggested that the authors make a comparison between this work and the commonly used SAD systems, such as ZnO-based varistors or other polymer composites with nonlinear fillers. A summary table or figure comparing key parameters (e.g., switching field, nonlinear coefficient, leakage current, stability) would help to clearly position the novelty and advantages of the proposed potential-well strategy over existing technologies.\nResponse: Thank you for this valuable suggestion. We agree that a comparison with commonly used nonlinear conductive systems is helpful for more clearly positioning the novelty and advantages of the potential-well regulation strategy proposed in this work. In response, we have added a comparative analysis with representative SAD systems in the revised manuscript, including ZnO-based varistor systems and barrier-type polymer composites, and further clarified the differences between bulk potential-well-regulated SADs and conventional Schottky-barrier-based SADs in terms of key performance parameters and design concepts.\nRegarding the selection of comparison metrics, we adopted the achievable switching-field range, the maximum nonlinear coefficient, and the filler content required to reach the maximum nonlinear response as the primary parameters to characterize the nonlinear bulk conduction behavior governed by different mechanisms. These parameters reflect the essential differences among various systems in terms of regulation mechanism, material efficiency, and design flexibility. In addition, the breakdown strength (Eb) and its ratio to the switching field (Eb/Es) were introduced as supplementary comparison metrics to describe the electric-field safety window between reversible nonlinear switching behavior and irreversible electrical breakdown, thereby providing insight into the potential operational stability of the SADs.\nThe comparison results indicate that conventional ZnO-based varistor systems and barrier-type polymer composites typically require relatively high filler loadings to achieve pronounced nonlinear responses. In contrast, the potential-well-based SADs developed in this work can realize relatively high nonlinear coefficients at substantially reduced filler contents, while simultaneously offering a wider and tunable switching-field range and a larger breakdown margin. From a comparative perspective, these results suggest that the potential-well regulation strategy provides certain advantages in polymer-based SAD systems, particularly in terms of low filler requirement, good parameter tunability, and potential stability benefits.\nTo address this comment, we have added a statement cited as “To clarify the performance differences between potential-well-type SADs and conventional barrier-type SADs from a mechanistic perspective, we performed a systematic comparison using recently reported SADs based on different wide-bandgap semiconductors, including ZnO, SiC, and BaTiO (Fig. S13, Table S3). 3 These reported systems mainly rely on interfacial Schottky barriers to achieve nonlinear conduction. Their key parameters, including the switching field (E ), nonlinear coefficient (α), and the corresponding filler content, were compared with those of the potential-well-type SAD developed in this work.\nBecause SADs are used in diverse applications, performance is not determined solely by achieving a high switching field. Instead, it is important to tune E over a broad range while maintaining a sufficiently high nonlinear coefficient (α > 10). The comparison shows that potential-well-type SADs allow a wider adjustable range of E than conventional barrier dominated SADs, and the tunable window can cover and extend the reported ranges of typical barrier-type systems. Analysis of α as a function of filler content further indicates that SiC based barrier-type SADs can show nonlinear conduction at relatively low filler loadings, but their α values are often limited. In contrast, ZnO varistor based SADs usually require higher filler contents (35 vol%) to reach α values close to 10, and their E is relatively low with a narrow tuning range.\nIn our system, the potential-well strategy shifts the dominant mechanism from interfacial barrier control to bulk potential well regulation. This change reduces the dependence of α on filler content. As a result, α values comparable to those of ZnO based SADs can be achieved at very low filler loadings, while E remains continuously tunable over a wide range. These results suggest that the potential well strategy provides an effective route to optimize SAD performance beyond conventional barrier-based approaches.” in the Page 9 of the revised manuscript, “To ensure the proper functioning of SADs, the breakdown strength (E ) of the material should be significantly higher than the switching field (E )34. In practice, E is generally required to exceed at least twice Es to avoid irreversible failure during nonlinear conduction. Fig. S22 presents the breakdown strength distributions and corresponding statistical results of the EP/CN, EP/CN-B, and EP/CN-P composites. The average breakdown strengths of these materials are 9.79 kV mm-1, 20.18 kV mm-1, and 5.39 kV mm-1, respectively, all satisfying the basic operational requirement of E > 2E . Among them, EP/CN-B exhibits the most pronounced breakdown margin, with an E /E ratio exceeding 9, which is significantly higher than those of EP/CN and EP/CN-P, and surpasses previously reported typical Schottky barrier based SADs, for which the ratio usually does not exceed approximately 5 (Supplementary Information Table S5)34.\nThe improved breakdown performance arises not from suppressing high-field long-range carrier migration along the continuous CN framework, but from regulating the energy distribution and release behavior of carriers participating in transport. In EP/CN-B, B doping introduces deeper potential wells into the CN framework. In the low to moderate electric field regime, these deep wells preferentially capture low energy carriers, making them less likely to participate in long range migration and thereby maintaining a relatively low effective current density over a wide field range. As the applied electric field further increases, only high energy carriers that acquire sufficient energy can be released from the deep wells and contribute to transport along the continuous framework. Consequently, nonlinear conduction is dominated by a controlled population of high energy carriers, and the transition process is gradual and reversible, rather than rapidly evolving into uncontrolled carrier multiplication or local thermal instability prior to breakdown. This regulated long range migration introduces a wider stable operating window between nonlinear conduction and irreversible breakdown, which is the key reason for the significantly enhanced breakdown strength and larger E /E margin observed in EP/CN-B.\nIn contrast, the shallow wells introduced by P doping in EP/CN-P reduce the energy barrier for carrier excitation and release, allowing the material to enter the nonlinear conduction regime at lower electric fields and thus resulting in a lower E . However, the earlier onset of carrier release also implies that a higher fraction of carriers participates in transport over a broader electric field range, which makes local current concentration and electrically induced heat accumulation more likely under high field conditions, thereby limiting further improvement in breakdown strength. As a result, although EP/CN-P still satisfies the operational requirement of E > 2E , its breakdown margin is relatively smaller. Overall, by introducing potential wells with different depths, it is possible to significantly widen the safety window between nonlinear conduction and irreversible breakdown while preserving effective long-range migration and self adaptive conduction at high electric fields. Among these systems, deep potential well strategy exhibits advantages in breakdown margin, providing a broader design space for achieving highly reliable SADs.” in the Page 15 of the revised manuscript.\nFig. S13. Comparison of nonlinear electrical performance between potential-well-based SADs and representative Schottky-barrier-based SADs reported in recent literature1, 2, 3, 4, 5, 6, 7, 8, 9. (a) Switching electric field E of various SAD systems reported in the literature (Refs. S1–S9) and in this work. The shaded bars represent the reported ranges of switching fields. The red star highlights the performance of the EP/CN-based composite developed in this work. (b) Nonlinear coefficient α as a function of filler volume fraction for different SADs. Data points are extracted from the corresponding references and compared with the present work (marked by the red star).\nFig. S22. Weibull distributions of breakdown strength (E ) for EP/CN, EP/CN-B, and EP/CN-P composites measured under identical testing conditions. The solid lines represent Weibull fitting of the experimental data. The extracted average breakdown strengths are 9.79 kV mm-1 for EP/CN, 20.18 kV mm-1 for EP/CN-B, and 5.39 kV mm-1 for EP/CN-P. All samples satisfy the operational requirement of E > 2E , while EP/CN-B exhibits a larger breakdown margin. For each composite, the Weibull distribution was constructed from 16 breakdown events (n = 16 data points) measured at different locations on the same specimen under identical conditions. Each data point corresponds to an independent breakdown event, and the lines are Weibull fits to the experimental data.\nTable S3. Comparison of potential-well-based SADs with representative nonlinear conductive systems reported in the literature.\nSwitching field range Nonlinear coefficient Filler content at\nSample E (kV/mm) α maximum α\ns\nfrom to (vol %)\nEP/CN 1.05 3 11.26 0.5\nSE/SiC-AlN 0.93 1.75 6.12 8.7\nEP/BT-TiO 1.9 2.75 3.08 7.87\nnano\nSR/SiC 0.9 3 0.97 9.48\nEP/SiC-Alginate 0.61 1.57 7.5 1.57\nEPDM/ZnO 0.725 0.925 9 37\nEP/ZnO-fiber 0.3 1.07 9.7 35\nSR/ZnO 1.106 1.725 8.4 42\nSR/ZnO-s 1.314 2.14 13.9 35\nTable S5. Comparison of switching field, breakdown field, and filler content for potential-well-based SADs in this work and representative barrier-type SAD systems reported in the literature.\nSwitching field Breakdown field Filler content E /E\nb s\nSample\nE (kV/mm) E (kV/mm) (vol %) value\ns b\nEP/CN-B 2.21 20.18 0.5 9.13\nEP/CN 1.25 9.79 0.5 7.83\nEP/CN-P 1.05 5.39 0.5 5.13\nEP/SiC-Ag 3 1.5 7.7 25 5.13\nnano\nSR/Al O -GQD10, 11 10 36.49 6.5 3.65\n2 3\nEPDM/BN-PPY 11.4 52.65 2.1 4.61\n.\n2. For practical application in electronic packaging, the operational stability of the materials under continuous electrical and thermal stress is paramount. The current manuscript lacks data on long-term reliability. It is recommended to include aging tests, such as monitoring the evolution of the I-V characteristics and switching field after prolonged exposure to high temperatures (e.g., 100-150 °C) and high electric fields.\nResponse: We appreciate this constructive suggestion. We agree that long-term operational stability under continuous electrical and thermal stress is a prerequisite for the practical application of electronic packaging materials. We first subjected EP/CN-B to a rigorous rapid charge–discharge cycling test consisting of 10,000 voltage pulses with amplitudes exceeding the switching field (E ), ensuring repeated insulation-to-conduction transitions. As shown in the newly added Fig. S24, the field-dependent conductivity curves before and after cycling are nearly identical, exhibiting no observable degradation in either the switching field or the nonlinear coefficient. This excellent cycling stability is attributed to the robustness of the potential-well-dominated conduction mechanism within the CN framework, which is inherently less vulnerable to degradation than interfacial barrier structures in conventional SADs.\nTo validate the reliability of the material under high temperatures, we conducted thermal aging tests by exposing the samples to 130 °C for 72 hours. As illustrated in the newly added Fig. S27, the room temperature J-E characteristics measured after aging show around 10% decrease in the switching field (E ) and a slight decrease in the nonlinear coefficient compared to the initial state. This is primarily attributed to interfacial aging and thermal-oxidative aging of the matrix; additionally, high-temperature aging may introduce uncontrolled shallow traps that facilitate carrier hopping. Nevertheless, the material retains nonlinear electrical response characteristics. This confirms the stability of the chemical structure of the CN framework and the potential wells, indicating that no significant thermal decomposition or irreversible chemical degradation occurred under these conditions.\nFurthermore, it should be noted that the switching field (E ) decreases and the high-field conductivity increases with rising temperature (Fig. 3f). This behavior is governed by the intrinsic physics of the potential well mechanism: as thermal energy increases, the probability of carrier thermal detrapping from the wells rises, resulting in a reduction of the threshold energy for the nonlinear switching. This is an inherent characteristic of potential-well-based materials and represents a key focus area for our future research aimed at broadening the practical application of SADs. To define the safe operating boundaries, we conducted limit tests under extreme conditions (150 °C, 5 kV/mm). The results indicate that the material eventually underwent electrical ablation after the system reached a steady state. This suggests that although the material is chemically stable at 150 °C, the coupling effect of high ambient temperature and Joule heating generated by the high electric field can trigger thermal runaway if heat accumulation exceeds the dissipation capacity. Therefore, thermal management must be carefully considered in practical application designs.\nTo address this comment, we have added a statement cited as“Furthermore, the durability of the adaptive response was assessed through rapid charge-discharge cycling tests. The EP/CN-B was subjected to 10000 voltage pulses with amplitudes exceeding their respective switching fields to simulate repeated operating stress. As shown in Fig. S24, the field-dependent conductivity characteristics of EP/CN-B measured after cycling remain highly consistent with the initial state. This exceptional stability confirms that the potential wells, originating from intrinsic doping, provide a robust charge-transport pathway that resists degradation, ensuring reliable long-term protection against surge stress.” in the Page 17, and “Finally, considering the typical operating environments of power electronic devices, for instance, the junction temperature of wide-bandgap semiconductors (e.g., SiC) can reach up to 175 °C, requiring packaging materials to withstand continuous operation at 100–150 °C35. We systematically evaluated the long-term reliability under thermal stress. Thermal aging tests were conducted by exposing the EP/CN-B composite to 130 °C for 72 hours. Subsequently, the J-E characteristics of the aged samples were measured at room temperature (Fig. S27). Based on the nonlinear parameters fitted from the curves, the E decreased by approximately 10%, while the α decreased slightly compared to the initial state. This variation is primarily attributed to interfacial aging and thermal-oxidative aging of the matrix, which may introduce shallow traps that facilitate carrier hopping. Nevertheless, the material retains robust nonlinear electrical response characteristics, confirming the chemical stability of the CN framework and potential well structures against irreversible thermal degradation. Regarding operational stability at elevated temperatures, the material exhibits a temperature-dependent evolution of nonlinear properties (as shown in Fig. 3f). The E naturally decreases with increasing temperature due to enhanced thermal activation of charge carriers, which facilitates detrapping from the potential wells. While this is a fundamental physical characteristic of trap-controlled transport, it defines the operational boundaries of the material. Further limiting tests revealed that under simultaneous exposure to 150 °C and a high electric field of 5 kV/mm, the composite eventually succumbs to electrical ablation due to the coupling effect of Joule heating and ambient thermal stress. Therefore, while the potential-well-based SADs demonstrate excellent structural stability up to 130 °C, thermal management remains a critical design factor for operation under extreme high-temperature and high-field conditions.” in the Page 18 of the revised manuscript.\nFig. S24. Field-dependent conductivity of the EP/CN-B composite measured before and after 10000 rapid charge-discharge cycles. The amplitude of the voltage pulses was set to 3 kV/mm. The before/after curves were obtained from measurements on the same specimen.\nFig. S27. Effect of thermal aging on the nonlinear electrical behavior of EP/CN-B composites. (a) J-E characteristics of EP/CN-B before and after thermal aging at 130 °C for 72 h. (b) Corresponding σ-E curves extracted from the J-E data. The E and α are indicated for both the pristine and aged samples. The results show that EP/CN-B retains its characteristic nonlinear conduction behavior after thermal aging, with a slight reduction in E and α. The before/after measurements were performed on the same specimen (pre- and post-aging), and similar trends were confirmed on independent specimens (n = 3).\n3. This work focuses on DC and transient pulse properties. However, power electronics often operate at high frequencies. An investigation into the frequency-dependent conductivity and permittivity (e.g., from 1 Hz to 1 MHz) under various DC bias fields would be highly valuable to assess the performance of these SADs in AC or pulsed operating conditions. The author is suggested to supplement relevant tests.\nResponse: Thank you for this valuable suggestion. We agree that frequency-dependent dielectric behavior is important for evaluating the applicability of SADs under AC operating conditions. Due to limitations of the available testing setup, we have supplemented the revised manuscript with temperature-dependent (20-100 °C,) dielectric permittivity and dielectric loss measurements of EP/CN, EP/CN-B, and EP/CN-P over the frequency range of 50-106 Hz to characterize their AC dielectric response (Fig. S23). The results show that EP/CN-B exhibits a dielectric permittivity comparable to that of EP/CN, whereas EP/CN-P shows a pronounced increase in permittivity, which can be attributed to the introduction of additional polarizable states and shallow trap levels by P doping. Compared with EP/CN, both doped samples display slightly increased dielectric loss and two relaxation peaks located near 103 and 105 Hz, which can be assigned to trap assisted carrier relaxation and a faster relaxation process associated with shallow traps, respectively. Importantly, the dielectric loss of all samples remains below 0.1 across the entire measured frequency range, indicating that the materials maintain an overall low loss dielectric behavior under AC conditions.\nTo address this comment, we have added a statement cited as “To assess the performance of the potential well based SADs under high frequency and conditions, temperature-dependent dielectric properties of EP/CN, EP/CN-B, and EP/CN-P were measured over a broad frequency range. As shown in Fig. S23, EP/CN-B shows no obvious change in dielectric constant compared with EP/CN, whereas EP/CN-P exhibits a clear increase. This increase is mainly attributed to P doping, which introduces more polarizable states and shallow traps in the CN framework, enabling easier carrier displacement and polarization under an alternating field. Both B- and P-doped samples show higher dielectric loss than EP/CN, indicating additional relaxation and hopping dissipation introduced by heteroatom doping. Two loss peaks are observed in EP/CN-B and EP/CN-P at approximately 103 and 105 Hz. The lower-frequency peak is mainly related to trap assisted carrier relaxation, whereas the higher-frequency peak is attributed to a faster relaxation process associated with shallow traps and localized polarization within the P doped CN framework. The presence of two relaxation peaks indicates a multilevel distribution of potential wells, consistent with the depth regulation discussed above. At 100 °C, the slight increase in high-frequency permittivity accompanied by a shift of both loss peaks toward higher frequencies reflects thermally activated relaxation with reduced relaxation time. Importantly, the dielectric loss of all samples remains below 0.1 across the measured frequency range (50-106 Hz), confirming an overall low-loss dielectric behavior.” in the Page 16 of the revised manuscript.\nFig. S23. Frequency-dependent dielectric properties of the EP/CN, EP/CN-B, and EP/CN-P composites. (a) Dielectric constant and (b) dielectric loss tangent measured across a frequency range of 50 Hz to 106Hz. Measurements were performed on independently prepared specimens (n = 3 per material), and representative results are shown.\n4. While the SCLC model is effectively used to extract trap distributions, a more quantitative link between the dopant concentration (from XPS quantification) and the resulting trap energy depth/density. Could a predictive relationship be established? Further DFT analysis on different doping configurations or concentrations could provide deeper insights.\nResponse: We sincerely thank the reviewer for this insightful suggestion. We have added XPS quantification of the dopant content in the Supporting Information. Taking B-doped CN as an example, the XPS surface analysis indicates a boron content of ~4.6 at. % in CN-B, corresponding to a B/C atomic ratio below 0.1. At this doping level, EP/CN-B exhibits pronounced deep-potential-well-dominated nonlinear conduction with a relatively high switching field.\nWe apologize that, at the current stage, we are still unable to establish a strictly quantitative and predictive relationship between dopant concentration and the resulting well depth/density. This is mainly because the CN frameworks are produced by pyrolysis of melamine foams pre-impregnated with heteroatom containing solutions, and the resulting CN is not a perfectly crystalline phase. A certain fraction of carbon-rich/amorphous carbon domains is inevitably present, which is also reflected in the XPS elemental composition. Consequently, the well states in our materials are better described by a distribution of well depths and densities rather than a single, sharply defined energy level. Therefore, in this work we rely on the combined analysis from SCLC/TSDC and related characterizations to evaluate the depth and density distribution of potential wells. We acknowledge this as a limitation of the current study and have explicitly highlighted it in the Conclusion as a key direction for future work.\nMotivated by your suggestion, to better understand how doping concentration affects potential well characteristics, we further performed DFT calculations for different substitution sites and doping levels, including band structures, total DOS, and dopant-projected DOS. At a relatively low dopant concentration (1 atom/8 units), highly localized and discrete impurity levels emerge within the bandgap. These localized states serve as effective charge-capture centers (potential wells), providing the basis for the nonlinear electrical response. In contrast, when the dopant concentration increases to a high level (1 atom/2 units), the impurity-related DOS peaks become significantly stronger and broadened. This can be attributed to the reduced impurity spacing at high doping density, which promotes spatial overlap of impurity wavefunctions. As a result, discrete impurity levels evolve into an impurity band and may even drive an insulator-to-metal transition; correspondingly, the charge transport mode tends to shift from localized trapping/hopping-dominated transport toward delocalized conduction.\nTo verify the above interpretation, we synthesized a series of B-doped samples with different doping levels (denoted as “EP/CN-B2/4/6/8/10”). As shown in the newly added Fig. S17 and Fig. S18, over-doped samples exhibit a pronounced increase in low-field conductivity, indicating that excessive doping facilitates the percolation of impurity states and results in significant leakage current. These results provide experimental support for the DFT-based interpretation and also highlight that precise control of dopant concentration is essential in SAD design to balance a high density of potential wells (for adaptive dissipation) and a sufficient insulation margin (to suppress low-field leakage).\nTo address this comment, we have revised and rewritten the section in the main text that discusses the DFT results, cited as “Boron substitution drives the carbon nitride framework toward an acceptor-like electronic structure, manifested by an upward shift of the valence-band edge toward the Fermi level (Fig. 4e). The projected DOS further shows that B incorporation introduces localized in-gap states close to the Fermi level (Fig. S15), which function as deep potential wells capable of efficiently capturing low-energy carriers under low-to-moderate fields and delaying their release. This microscopic picture explains the experimentally observed higher switching field and the enhanced high-field charge-dissipation efficiency (larger nonlinear coefficient) in B-doped composites. Importantly, our calculations indicate that this deep-well trend is robust against the specific substitution site: when different carbon sites are selected for substitution within the CN structural unit, the overall evolution of the band edges and impurity-state positions remains qualitatively unchanged (Fig. S16), implying that the deep-trap formation is an intrinsic consequence of acceptor-type B doping rather than a site-specific artifact. In addition, the electronic response is strongly concentration dependent. At low dopant densities (e.g., 1 atom per 8 units), the dopant contribution appears as discrete, highly localized impurity levels within the bandgap, providing well-defined trapping centers (Fig. S17 and Fig. S18). In the dilute regime relevant to our samples (B:C < 0.1), the global bandgap remains open and transport is still governed by field-assisted detrapping and hopping via localized states. However, when the dopant density is increased to an excessive level (e.g., 1 atom per 2 units), the impurity-related DOS rises sharply and becomes broadened, which can be rationalized by the reduced dopant-dopant spacing that promotes wavefunction overlap and drives discrete impurity levels to evolve toward an impurity band. Such band broadening weakens carrier localization and can shift the transport mechanism toward more delocalized conduction, thereby increasing low-field leakage. Consistent with this prediction, the experimentally over-doped EP/CN-B10 shows a pronounced rise in low-field conductivity, confirming that excessive doping can compromise the insulation margin by enabling the interconnection/percolation of impurity states.” in the Page 12, “It should be noted that, due to the non-ideal crystallinity and intrinsic structural heterogeneity of the carbon nitride frameworks derived from melamine foams, the potential wells in these materials are better described by a distribution of depths and densities rather than a single, sharply defined energy level. As a result, a strictly quantitative and predictive relationship between dopant concentration and potential well characteristics cannot yet be fully established. Nevertheless, our DFT analysis reveals that increasing dopant concentration promotes the overlap of impurity states, leading to a transition from discrete localized levels to broadened impurity bands. This theoretical trend is further supported by experimental observations on over-doped systems, where excessive dopant loading induces increased low-field leakage conductivity. These findings highlight the importance of dopant concentration control in balancing adaptive charge dissipation and insulation reliability and point to a clear direction for future efforts toward predictive design of SADs.” in the Page 19 of the revised manuscript, and “\nTo further elucidate the influence of dopant concentration on potential-well characteristics in carbon nitride frameworks, a combined analysis based on XPS quantification, electrical measurements, and DFT calculations was conducted.\nXPS surface analysis indicates that the boron-doped carbon nitride (CN-B) framework contains approximately 4.6 at.% boron, corresponding to a B/C atomic ratio below 0.1. At this doping level, the EP/CN-B composite exhibits pronounced nonlinear electrical conductivity with a relatively high switching field, which is consistent with charge transport dominated by deep potential wells. These experimental observations suggest that moderate dopant concentrations effectively introduce localized trapping states without compromising the insulating character of the composite.\nIt should be noted that a strictly quantitative, one-to-one correspondence between dopant concentration and a single trap energy level cannot be readily established in this system. The carbon nitride frameworks are derived from the pyrolysis of melamine foams pre-impregnated with heteroatom-containing solutions and therefore do not form a perfectly crystalline structure. Instead, a certain fraction of carbon-rich or amorphous carbon domains is inevitably present, as also reflected in the XPS elemental composition. As a consequence, the trapping states are more appropriately described by a distribution of potential-well depths and densities rather than discrete, uniform energy levels. In this work, well characteristics are therefore evaluated in terms of their depth–density distribution using a combination of SCLC fitting and TSDC analysis.\nTo gain deeper insight into how dopant concentration governs the electronic structure and potential-well formation, DFT calculations were performed for different substitution sites and doping levels (Fig. S16-S18). At a relatively low dopant concentration (1 dopant atom per 8 heptazine units), highly localized and discrete impurity states emerge within the bandgap. These states act as effective charge-capture centers, forming well-defined potential wells that provide the microscopic origin of the observed nonlinear electrical response. Importantly, the overall bandgap remains open under this doping condition, preserving the semiconducting nature of the carbon nitride framework.\nIn contrast, when the dopant concentration increases to a higher level (1 dopant atom per 2 units), the impurity-related density of states increases markedly and exhibits significant broadening. This behavior originates from the reduced spatial separation between dopants at high concentrations, which promotes overlap of impurity wavefunctions. As a result, the initially discrete impurity levels gradually evolve into an impurity band, leading to partial delocalization of charge carriers and a pronounced increase in electronic conductivity. Such an evolution indicates a transition in the charge-transport mechanism from localized, well-controlled conduction toward more delocalized, band-like transport, potentially approaching an insulator-to-metal-like transition.\nTo experimentally verify the concentration-dependent trend predicted by DFT, a series of B-doped carbon nitride samples with different doping levels (denoted as CN-B2/4/6/8/10) were synthesized and systematically compared. As shown in Fig. S21, samples with excessive doping exhibit a sharp increase in low-field conductivity, providing direct experimental evidence that high dopant concentrations facilitate the percolation and interconnection of impurity states, thereby introducing significant leakage currents. These results corroborate the DFT predictions and demonstrate that while moderate doping enhances potential-well density and nonlinear response, excessive doping undermines the insulating margin.\nOverall, these results highlight that dopant concentration is a critical parameter governing the balance between potential-well density and electrical insulation in potential-well-based self-adaptive dielectrics. Precise control of dopant concentration is therefore essential to achieve robust nonlinear electrical behavior while maintaining sufficient insulation reliability.” in the revised Supplementary Information.\nFig. S12. Field-dependent conductivity of excessive B doping. The field-dependent conductivity of EP/CN-B composites prepared with varying doping levels (denoted as EP/CN-B2 to EP/CN-B10). Samples with excessive doping (EP/CN-B10) exhibit a sharp increase in low-field conductivity and a loss of nonlinear switching capability, which is consistent with the transition to quasi-metallic behavior predicted by DFT calculations. For each doping level, the field-dependent conductivity was measured on independently prepared composite specimens (n = 3 specimens per condition), and representative curves are shown.\nFig. S16. DFT analysis of site dependence for B/P substitution in CN (a,d) Optimized atomic structures of carbon nitride with (a) B and (d) P substitution at carbon sites (1 dopant per 4 heptazine units). (b,e) Corresponding band structures along the Γ–M–K–Γ path and total/element-resolved density of states (TDOS/PDOS) for (b) B-doped and (e) P-doped models. (c,f) Dopant-projected DOS highlighting the impurity-state contribution of (c) B and (f) P. The Fermi level is set to 0 eV.\nFig. S17. Dopant-concentration-dependent electronic structure of B-doped CN (a,c) Calculated band structures and total/element-resolved DOS for B-doped carbon nitride at (a) high concentration (1 B per 2 heptazine units) and (c) low concentration (1 B per 8 units). (b,d) Dopant-projected DOS of B for (b) high and (d) low concentrations.\nFig. S18. Dopant-concentration-dependent electronic structure of P-doped CN. (a,c) Calculated band structures and total/element-resolved DOS for P-doped carbon nitride at (a) high concentration (1 P per 2 heptazine units) and (c) low concentration (1 P per 8 units). (b,d) Dopant-projected DOS of P for (b) high and (d) low concentrations.\n5. The discussion on the application remains somewhat conceptual. It is recommended to supplement the packaging schematic diagram or performance test results of composite materials in real power modules.\nResponse: We thank the reviewer for this valuable suggestion. We have supplemented both application-oriented finite element simulations based on a representative power electronics packaging structure and a simplified experimental validation mimicking the critical triple-junction region in real modules. Specifically, we first added a schematic of a bonded wire type power electronics packaging structure, in which the triple junction formed by metal, ceramic substrate, and encapsulation polymer is well known as the most severe electric-field distortion region. A corresponding finite element model was established to analyze the electric-field and charge distribution evolution at the triple junction with increasing device voltage. The simulation results demonstrate that, when conventional epoxy is used as the encapsulation material, charge accumulation at the triple junction increases nonlinearly with voltage, leading to a sharp rise in local electric field. In contrast, after replacing the encapsulation material parameters with the EP/CN-B developed in this work, the abnormal electric-field enhancement is effectively suppressed due to rapid charge dissipation under high-field conditions.\nFurthermore, a simplified experimental configuration was designed to emulate the encapsulation-metal-ceramic triple-junction environment. The residual surface potential of the metal electrode after DC polarization was measured to evaluate charge accumulation behavior. The results show that, when the SADS-based composite is used as the encapsulation layer, the residual potential of the metal electrode is reduced by approximately 65% compared with that of pure epoxy, indicating significantly suppressed charge accumulation at the triple junction.\nTo address this comment, we have added a statement cited as “In addition to the fundamental charge dissipation characteristics discussed above, the application potential of the potential well based SADs was further evaluated in the context of power electronics packaging. In practical power modules, severe electric-field distortion commonly occurs at the metal-ceramic-polymer triple junction (Fig. S20), where charge accumulation can increase nonlinearly with operating voltage and trigger local insulation failure. An application-oriented simulations and simplified experimental validation demonstrate that the EP/CN-B composite effectively suppresses such abnormal charge accumulation and electric-field enhancement (Fig. S21). Benefiting from its rapid charge dissipation capability under high electric fields, the material prevents the nonlinear escalation of local electric field intensity at critical interfaces. These results indicate that the proposed SADS is promising for mitigating electric-field distortion and enhancing insulation reliability in power electronics packaging systems.” in the Page 14 of the revised manuscript and “\nFig. S20a illustrates a typical bonded-wire-type power electronics packaging structure, in which the encapsulation polymer, metal conductor, and ceramic substrate form a triple-junction region. Due to the abrupt change in dielectric permittivity and conductivity, this region is widely recognized as the most vulnerable location for electric-field distortion and premature insulation failure in high-voltage power modules.\nBased on this structure, a finite element model was established, as shown in Fig. S20b. The electric potential corresponding to different device voltage levels was applied to the metal conductor, while the ceramic substrate was grounded. The encapsulation material properties were first set as those of conventional epoxy resin. The simulated electric-field distribution (Fig. S20c) reveals pronounced field enhancement localized at the triple junction. Further analysis of charge accumulation and local electric field as a function of applied voltage (Fig. S20d) indicates a nonlinear surge in charge density at the triple junction with increasing voltage, which directly leads to abnormal electric-field amplification. To evaluate the effectiveness of the proposed material system, the encapsulation material parameters in the model were then replaced with those of the EP/CN-B composite developed in this work. Notably, the nonlinear increase in charge accumulation at high electric fields was effectively mitigated, and the corresponding electric-field enhancement at the triple junction was significantly suppressed.\nTo further verify the simulation results experimentally, a simplified triple-junction test structure was designed (Fig. S21). The structure consists of an encapsulation layer, a metal plate, and a ceramic substrate bonded sequentially. The bottom surface of the ceramic substrate was electrically grounded. A DC voltage was applied to the metal plate for 10 minutes to induce charge accumulation, after which the voltage was removed. The surface potential of the metal plate was subsequently measured using a high-impedance, non-contact electrostatic potential probe positioned at a fixed distance above the metal surface, minimizing charge leakage during measurement. As shown in Fig. S21b, when pure epoxy resin was used as the encapsulation material, a high residual surface potential was observed, indicating significant charge accumulation at the triple junction. In contrast, when the SADs was employed, the residual surface potential of the metal plate decreased by approximately 65%, demonstrating that charge accumulation at the triple junction was effectively suppressed. These results are consistent with the simulation outcomes and confirm the application potential of the proposed material in power electronics packaging.” in the revised Supplementary Information.\nFig. S20. Simulation of electric field distortion in power electronics packaging (a) Schematic illustration of a bonded-wire-type power electronics packaging structure, highlighting the metal-ceramic-encapsulation polymer triple-junction region where severe electric-field distortion typically occurs. (b) Finite element simulation model corresponding to the packaging structure shown in (a). (c) Simulated electric field distribution under DC voltage, showing pronounced field enhancement localized at the triple junction. (d, e) Variation of electric field and charge accumulation at the triple junction when pure epoxy resin and EP/CN-B serve as encapsulation materials, as a function of device voltage level.\nFig. S21. Experimental validation of charge accumulation suppression at a triple-junction-like structure (a) Schematic of a simplified experimental configuration mimicking the encapsulation-metal-ceramic triple-junction structure in power electronics packaging. (b) Residual surface potential of the metal plate after DC polarization and voltage removal for different encapsulation materials. The residual surface potential measurements in (b) were performed on independently specimens (n = 3 specimens per material), and representative results are presented.\n6. The DFT-calculated bandgap for pristine CN (~1.48 eV, Page 9) is significantly smaller than the experimental optical bandgap (~2.65 eV, Fig. S7). Why is that?\nResponse: Thank you for pointing out this important issue. We acknowledge that the GGA-DFT bandgap of pristine CN (~1.48 eV) is smaller than the experimental optical bandgap (~2.65 eV). This difference is expected for three main reasons: (i) GGA-level DFT is well known to systematically underestimate bandgaps due to the absence of quasiparticle self-energy corrections, and similar values (~1.3-1.6 eV) have been reported for g-C N in prior GGA calculations (Applied Catalysis B: 3 4 Environmental 224 (2018) 983–999, Catalysis Letters (2025) 155:99); (ii) the experimentally synthesized CN is not perfectly crystalline, as evidenced by the broadened XRD features (Fig. S5), whereas the DFT model assumes an ideal periodic structure without disorder, defects, or terminal groups; and (iii) the UV-vis derived value corresponds to the optical bandgap that includes excitonic effects, while DFT yields the intrinsic electronic bandgap. Importantly, our DFT calculations are intended to capture relative electronic-structure changes and trap-state modulation upon doping rather than to reproduce absolute experimental bandgap values. We have clarified this point in the revised manuscript.\nTo address this comment, we have added a statement cited as “It should be noted that the bandgap obtained from DFT calculations is significantly smaller than the experimentally measured optical bandgap of CN. This discrepancy is mainly attributed to the inherent limitations of the DFT methodology and the structural differences between the calculated model and the experimental material. First, the DFT calculations in this work were performed using a GGA exchange-correlation functional, which is known to systematically underestimate bandgaps due to the lack of quasiparticle self-energy corrections. For g-C N systems, GGA based calculations typically yield bandgaps 3 4 around 1.3-1.6 eV, which is consistent with our calculated result32, 33. Second, it should be noted that the experimentally synthesized CN obtained by high temperature polymerization does not exhibit a perfectly crystalline structure, as evidenced by the broadened XRD features (Supplementary Information Fig. S5). In contrast, the DFT model is based on an idealized periodic CN framework without structural disorder, defects, or terminal groups. Such differences in structural order and local bonding environments can significantly influence the optical transition energies, leading to a larger experimentally observed optical bandgap. In addition, the experimental bandgap derived from UV-vis spectroscopy corresponds to the optical bandgap, which includes excitonic effects and electron–hole interactions, whereas the DFT value represents the intrinsic electronic bandgap of the idealized structure. Importantly, the purpose of the DFT calculations in this work is not to quantitatively reproduce the experimental bandgap, but to qualitatively analyze the electronic structure evolution and trap-state modulation induced by heteroatom doping.” in the Page 11 of the revised manuscript.\n7. In page 16: the author described “c-e, I-V curves of 428 CN-B (c), pristine CN (d), and CN-P (e) foams…” in Fig. 2’s caption, but the order of the three in the figure is not like this. Similarly, the author described “For each material, subfigures (1–3) correspond to low…” in Fig. 5’s caption, but 1, 2, 3 is not marked in the figure.\nResponse: We sincerely apologize for this oversight and thank the reviewer for their careful observation. We have carefully re-examined all figures and captions in the revised manuscript to ensure consistency.\nTo address this comment, we have made the following modifications:\nFor Fig. 2: We have corrected the caption to strictly match the actual arrangement of the subfigures (i.e., specifying the correct order of pristine CN (c), CN-B (d), and CN-P (e)).\nFor Fig. 5: We have added the corresponding labels (1, 2, 3) to the subfigures as described in the caption to clearly distinguish the different magnifications. The corrected figures and captions are now consistent in the revised manuscript.\nFig. 5 Charge dissipation performance of potential-well-based SAD composites under different electric field regimes. J–E characteristics of EP/CN (a), EP/CN-B (b), and EP/CN-P (c), respectively. For each material, subfigures (1–3) correspond to low, medium, and high electric fields, showing the J–E characteristics together with the surface charge dissipation behavior after ESD pulse. For each material, subfigures (1–3) were measured sequentially on the same specimen, and the results were confirmed on independent specimens (n = 3 per material)\nReviewer #3 (Remarks to the Author):\nThe authors report nonlinear conduction behavior in epoxy composites filled with g-C₃N₄ skeletons. Controlled heteroatom doping with different dopants or doping levels enables customizable potential wells with tunable depths and distributions, allowing the nonlinear conductivity and the insulation-conduction threshold field to be tailored. The scientific quality of the work is strengthened by the combination of experimental results with simulations of electric-field distortion and charge-conduction pathways, electronic structure analysis based on DFT calculations, and electron localization function simulations. This work shows promise as a useful reference for the development of self-adaptive insulating electronic packing and insulation materials. This manuscript is clearly written and easy to follow. The experimental section is sufficiently detailed, and the findings are thoroughly discussed with conclusions well supported by the data. This work is suitable for publication after clarification of the following points.\nResponse: We sincerely thank the reviewer for the positive and encouraging evaluation of our work, and we have carefully addressed all the points raised below to further clarify and strengthen the manuscript accordingly.\n1. The authors did not discuss how the choice of polymer matrix influences the nonlinear conduction. The rationale for selecting epoxy as the matrix should be clarified in the revised main text. Although charge transport occurs primarily through the g-C₃N₄ semiconductor skeleton network, charge accumulation occurs at the g-C₃N₄/epoxy interfaces under electric fields due to their differences in permittivity and conductivity. How do the buildup and release of these interfacial charges affect the electrical properties of the composites?\nResponse: Thank you for the valuable comments. We agree that the choice of polymer matrix and the accumulation behavior of interfacial charges are important for understanding the electrical properties of the composites. We have further clarified the rationale for selecting epoxy as the matrix. In this work, epoxy resin was chosen mainly because of its high dielectric strength, low intrinsic electrical conductivity, and good processability, which are beneficial for constructing a stable CN semiconducting framework in the composite system while maintaining sufficient insulation margin.\nIn addition, finite element simulations have been supplemented to investigate how the mismatch in permittivity and conductivity between CN and epoxy affects the electric field distribution and interfacial charge behavior.\nThe simulation results show that when CN and epoxy are arranged in a series configuration along the electric field direction, the difference in permittivity and conductivity leads to enhanced electric fields in the vicinity of the CN framework, promoting charge accumulation. When a continuous CN framework forms a conductive pathway between the electrodes, charge transport is mainly governed by the CN skeleton, and interfacial charge accumulation is significantly reduced. These results indicate that the polymer matrix mainly influences the electric field distribution and provides insulation support, whereas the nonlinear conduction behavior of the composites is still primarily controlled by bulk potential well states within the CN framework.\nTo address this comment, we have added a statement cited as:\nEpoxy resin was selected as the polymer matrix in this work mainly due to its high dielectric strength, low intrinsic electrical conductivity, and good processability, which are beneficial for constructing a stable CN semiconducting framework while maintaining sufficient insulation margin in the composite system. It should be noted, however, that the pronounced differences in permittivity and conductivity between CN and epoxy can still influence the local electric-field distribution and interfacial charge behavior. To clarify this effect, finite-element simulations were performed using COMSOL Multiphysics to analyze the electric-field and charge distributions arising from the dielectric and conductive mismatch at the CN/epoxy interface. The geometric configurations and boundary conditions are illustrated in Fig. S28.\nFor the configuration in which CN and epoxy are effectively connected in series along the direction of the applied electric field (layered EP/CN/EP structure, Fig. S28a), the external voltage drop is mainly concentrated in the epoxy region due to its much lower conductivity. As a result, the local electric field in epoxy is significantly higher than that in the CN region (Fig. S28c). Meanwhile, pronounced charge accumulation appears at the CN/epoxy interfaces, with opposite polarities at the upper and lower interfaces, reflecting interfacial polarization induced by the mismatch in permittivity and conductivity. Such interfacial charges primarily modulate the local electric-field distribution and affect carrier injection and transport in the vicinity of the interfaces, thereby playing an auxiliary role in regulating the electrical response. Nevertheless, their contribution is mainly associated with field redistribution and polarization effects, rather than serving as the dominant source of nonlinear conduction.\nIn contrast, when the CN phase forms a continuous conductive pathway between the electrodes (a configuration in which the CN framework bridges the top and bottom electrodes, Fig. S28b), charges injected from the electrodes preferentially migrate along the CN framework and are collected at the counter electrode, leading to a substantial reduction in charge accumulation at the CN/epoxy interfaces (Fig. S28d). In this case, charges are mainly concentrated near regions of electric-field distortion close to the electrodes, rather than being distributed along the entire CN/epoxy interface. These results indicate that once a continuous CN framework is established, the macroscopic current pathway is governed by the CN skeleton, while the polymer matrix primarily functions as an insulating support and field-distribution medium. Consequently, the nonlinear conductive behavior of the composites investigated in this work remains predominantly controlled by bulk potential-well states within the CN framework. in the revised Supplementary Information.\nFig. S28. Finite-element simulation analysis of the electric-field and charge distributions at the interface between epoxy resin and CN. (a, b) Geometric configurations and boundary conditions for the simulation models, representing (a) the layered EP/CN/EP structure (b) the continuous CN bridging structure. (c, d) The corresponding simulation results illustrating the distributions of electric potential, electric field, and space charge density.\n2. Doping plays a crucial role in determining the insulation–conduction transition and the nonlinear conductivity. How is the doping level quantitatively controlled, and how is doping uniformity ensured? How was the reported doping level (B/P:C < 0.1) quantified? What range of doping levels can be achieved using the proposed method?\nResponse: We thank the reviewer for raising this important point. In the revised Supporting Information, we have clarified how the dopant level is quantitatively controlled, how doping uniformity is ensured, and how the reported B/P:C < 0.1 was quantified. Briefly, the doping level is primarily controlled by the molar concentration of the dopant-precursor solution (BA for B and ADP for P) used in the impregnation step, while keeping all subsequent processing parameters (impregnation procedure, vacuum drying, pyrolysis conditions, and composite fabrication) identical. This provides a straightforward parameter to tune the dopant level.\nRegarding doping uniformity, we emphasize that uniform distribution is verified experimentally. As shown by SEM-EDS elemental mapping, both the dopant precursors are homogeneously distributed on the foam skeleton after impregnation/drying and remain spatially uniform after pyrolysis (Fig. S2-S3 and Fig. 2a). These results confirm that the impregnation-vacuum drying-pyrolysis route yields a uniform dopant distribution throughout the three dimensionally interconnected skeleton.\nThe reported “B/P:C < 0.1” was quantified from XPS elemental atomic percentages (Supporting Information Table S7). In addition, we designed the baseline BA and ADP solutions at the same molar concentration (6.33 mM), ensuring comparable dopant-precursor dosage for B and P (one precursor molecule provides one B or one P atom), which makes the donor/acceptor doping comparison more rigorous. Finally, the achievable range of doping levels using this method is determined by the precursor-solution concentration. To demonstrate tunability, we prepared a B-doping concentration series (EP/CN-B2, B4, B6, B8, B10) by increasing BA concentration from 6.33 to 31.65 mM (Table S7). Importantly, excessive doping is not necessarily beneficial for self-adaptive dielectrics: at high precursor concentration, low-field conductivity increases markedly (Fig. S12), indicating increased leakage associated with the enhanced percolation of impurity-related states. Therefore, we consider the moderate-doping regime (≤ EP/CN-B8 in this work) as a practical upper bound to balance high potential-well density and sufficient insulation margin.\nTo address this comment, we have added a statement cited as: Heteroatom-doped carbon nitride (CN) foams were prepared by a solution impregnation assisted pyrolysis route using commercial melamine foams as the structural precursor. In a typical procedure, melamine foams were immersed in aqueous dopant-precursor solutions until complete wetting of the three-dimensionally interconnected skeleton was achieved. Boric acid (H BO BA) and ammonium dihydrogen 3 3, phosphate (NH H PO , ADP) were used as the boron and phosphorus sources, respectively. After 4 2 4 impregnation, the foams were taken out and briefly allowed to drain to remove excess surface liquid. The impregnated foams were then dried in a vacuum oven at 80 °C. Vacuum drying accelerates solvent removal and shortens the lifetime of the liquid phase inside the porous skeleton, thereby suppressing long-range solute redistribution during evaporation and promoting uniform precursor deposition along the struts. The dried foams were subsequently pyrolyzed in a tubular furnace at 550 °C for 4 h under a nitrogen atmosphere to convert the melamine framework into a CN network. During pyrolysis, the dopant species are incorporated into the CN framework and form stable B-N or P-N bonding environments. The uniformity of dopant distribution was verified by SEM–EDS elemental mapping, which shows homogeneous B/P signals throughout the foam skeleton after pyrolysis (Fig. 2a and Figs. S2-S3), confirming the reliability of this impregnation-drying-pyrolysis strategy for achieving spatially uniform doping.\nThe dopant-precursor solutions were designed to (i) provide comparable precursor dosage for B and P doping in the baseline samples and (ii) enable a convenient, scalable tuning knob for doping level. Specifically, the baseline BA and ADP solutions were prepared at the same molar concentration (6.33 mM) so that the number of dopant atoms delivered per unit solution volume is comparable for B and P (each precursor molecule contains one B or one P atom, respectively). Beyond the baseline condition, the doping level can be systematically tuned by varying the precursor-solution concentration while keeping all subsequent steps (impregnation procedure, vacuum drying, pyrolysis conditions, and composite fabrication) identical.\nFor clarity, pristine CN foams obtained by direct pyrolysis are denoted as CN. Boron- and phosphorus-doped foams are denoted as CN-B and CN-P, respectively. The corresponding epoxy-impregnated self-adaptive dielectric composites are denoted as EP/CN, EP/CN-B, and EP/CN-P. For the B-doping concentration series, samples are labeled as EP/CN-B2, EP/CN-B4, EP/CN-B6, EP/CN-B8, and EP/CN-B10, where “B𝑥” indicates the BA precursor-solution concentration used for impregnation. In this work, B2/B4/B6/B8/B10 correspond to BA solution concentrations of 6.33, 12.66, 18.99, 25.32, and 31.65 mM, respectively (Table S7). Unless otherwise specified, all processing parameters other than the precursor-solution concentration were kept the same to ensure that the observed differences in electrical behavior arise primarily from the dopant level.in the revised supplementary information.\nTable S7. Dopant-precursor solutions used for preparing heteroatom-doped CN foams and the corresponding SAD composites.\nSample Precursor Dopant precursor concentration Fabricate SADs\nCN-P NH H PO 6.33 mM EP/CN-P\n4 2 4\nCN-B H BO 6.33 mM EP/CN-B2\n3 3\nCN-B H BO 12.66 mM EP/CN-B4\n3 3\nCN-B H BO 18.99 mM EP/CN-B6\n3 3\nCN-B H BO 25.32 mM EP/CN-B8\n3 3\nCN-B H BO 31.65 mM EP/CN-B10\n3 3\nFig. S2. SEM image and EDS elemental mapping of melamine foam after impregnation with boric acid (a) or ammonium dihydrogen phosphate (b) solution. The dopant precursors are uniformly adsorbed on the surface of the foam skeleton, ensuring homogeneous B and P distribution for subsequent pyrolysis.\nFig. S3. SEM image and EDS elemental mapping of phosphorus-doped carbon nitride foam (CN-P), showing a well-preserved porous structure and uniform phosphorus distribution throughout the framework.\nFig. S12. Field-dependent conductivity of excessive B doping. The field-dependent conductivity of EP/CN-B composites prepared with varying doping levels (denoted as EP/CN-B2 to EP/CN-B10). Samples with excessive doping (EP/CN-B10) exhibit a sharp increase in low-field conductivity and a loss of nonlinear switching capability, which is consistent with the transition to quasi-metallic behavior predicted by DFT calculations. For each doping level, the field-dependent conductivity was measured on independently prepared composite specimens (n = 3 specimens per condition), and representative curves are shown.\n3. Page 3, line 75: Grain-boundary barriers exist within semiconductor particles, not at semiconductor–polymer interfaces. The sentence is confusing and should be clarified.\nResponse: We apologize for the imprecise terminology in the original manuscript. We agree that grain-boundary barriers exist within the semiconductor particles, distinct from the barriers at the composite interface. We have corrected this sentence in the revised manuscript to accurately reflect the physical mechanism\nTo address this comment, we have added a statement cited as: “Conventional self-adaptive dielectrics (SADs) typically achieve nonlinear conductivity through grain-boundary barriers within wide-bandgap semiconductor fillers or Schottky barriers at inter-particle interfaces, which rely on continuous filler pathways for charge migration17.” in the Page 4 of the revised manuscript.\n4. Page 6, line 154: It would be preferable to include Eq. (S2) directly in the main text for clarity and completeness.\nResponse: We fully agree with the reviewer’s suggestion. Including the defining equation for the nonlinear coefficient and switching field directly in the main text improves the clarity and self-containment of the manuscript.\nTo address this comment, we have moved Eq. (S2) from the Supporting Information to the main text on Page 7. The subsequent equation numbers in the main text and Supporting Information have been adjusted accordingly.\n5. Page 6: The authors mention two application scenarios, but the required switching-field values for each are not specified. Providing these values would help readers assess whether the switching field of the g-C₃N₄/epoxy composites is sufficiently low for rapid electrostatic discharge and sufficiently high to maintain insulation under strong electric fields.\nResponse: We thank the reviewer for this insightful comment. We agree that specifying representative switching-field ranges is important for assessing the suitability of the proposed composites for different application scenarios. In the revised manuscript, we have clarified the typical electric-field requirements for the two application cases discussed. For electrostatic discharge (ESD)-sensitive devices such as integrated circuits and optoelectronic components, rapid charge dissipation is generally required at relatively low electric fields (0.1-1 kV mm-1), to prevent damage to ultrathin insulating layers. In contrast, high-voltage insulation and overvoltage protection applications demand much higher switching fields, generally exceeding 5-10 kV mm-1, to ensure low leakage current under normal operating conditions and to activate conductive pathways only under abnormal electrical stress.\nTo address this comment, we have added a statement cited as: “Devices such as integrated circuits and optoelectronic components typically contain ultrathin insulating layers with low breakdown thresholds and are therefore highly susceptible to electrostatic discharge. In these systems, rapid charge dissipation is required at relatively low electric-field strengths (0.1-1 kV mm-1), to prevent irreversible damage induced by charge accumulation26. In contrast, high-voltage insulation and overvoltage protection systems, such as those used in power electronics, must maintain extremely low leakage current under normal operating conditions and are therefore required to exhibit much higher switching fields, generally exceeding 5-10 kV mm-1 2. In these applications, conductive pathways should only be activated under abnormal electrical stress, such as overvoltage or transient surge events. Consequently, materials intended for adaptive dielectric regulation must balance low-field charge dissipation capability with high-field insulation stability, depending on the targeted application scenario.” in the Page 7 of the revised manuscript.\n6. The three-electrode configuration used for field-dependent conductivity measurements should be schematically illustrated, particularly the electrode arrangement.\nResponse: We thank the reviewer for pointing this out. To clarify the experimental configuration used for the field-dependent conductivity measurements, a schematic illustration of the three-electrode system has now been added to the revised manuscript. The schematic explicitly shows the arrangement of the high-voltage electrode, the guarded electrode, and the grounded electrode, as well as their electrical connections during measurement. This configuration ensures a uniform electric field within the bulk material while effectively suppressing surface leakage currents, thereby allowing reliable evaluation of bulk conductivity under high electric fields. The corresponding schematic has been included as Fig. S8 in the revised Supporting Information, and the description has been updated accordingly.\nFig. S8. Schematic illustration of the three-electrode configuration used for field-dependent conductivity measurements. The top electrode is connected to a high-voltage DC source, while the bottom electrode is grounded. A guarded electrode is employed to suppress surface leakage currents, ensuring that the measured current reflects bulk charge transport through the sample under an applied electric field.\n7. Typographical errors :\no Page 2, line 46: “insulation-conduction conversion”\no Supporting Information, page 10, line 257: Fig. S14\nResponse: We thank the reviewer for carefully identifying these typographical issues. The suggested corrections have been implemented in the revised manuscript and Supporting Information. Specifically, the wording on Page 2, line 46 has been corrected, and the figure reference on Supporting Information, Page 10, line 257 has been revised to ensure consistency with the actual figure numbering."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The author has made appropriate revisions to the manuscript, and so it can be published on Nature Communications.", "reviewer_2": "After reviewing the revised version, I find that the authors have comprehensively responded to all ，my comments. The manuscript has been significantly improved in methodology and presentation, and I recommend its acceptance in its current form.", "reviewer_3": "The authors fully addressed the reviewers'concerns and now the revised manuscript can be published."}, "author_response": ""}]

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