Interfacial stress decoupling enables stable palladium-based hydrogen sensing

Domain: chemistry
Published: 2026-02-12
Editorial outcome: minor_revision

Abstract
Interfacial adhesion between the sensing layer and supporting substrate critically governs the long-term stability of electrical molecular sensors. However, achieving a robust heterointerface remains challenging due to the intrinsic lattice mismatch induces localized stress, which is further exacerbated by cyclic interactions between the sensing film and gas analytes. Here, we introduce a floating-structure palladium hydrogen (H2) sensor enabled by interfacial stress decoupling through a dithiol-based self-assembled monolayer (SAM). This interfacial layer acts as a molecular bridge between the palladium sensing layer and the substrate electrode, forming a dual-interface architecture that simultaneously mitigates the interfacial stress and suppresses the substrate clamping effects, thereby accelerating H2 absorption kinetics. The resulting sensor demonstrates a stable and cyclable H2 detection at concentrations up to 4 vol%, and an ultrasensitive detection limit of 1 ppm at room temperature. Moreover, we realize wafer-scale fabrication and integration of the sensor into a portable platform for real-time hydrogen leak detection. This interfacial stress-engineering approach provides a general route toward durable and high-performance molecular sensor.

Introduction
Robust heterogeneous interfaces are essential for integrating modern electronic devices1–4, particularly electrical molecular sensors, where strong adhesion between the sensing layer and substrate prevents delamination and ensures long-term acquisition of chemical information5–7. However, constructing durable heterointerfaces remains challenging because intrinsic lattice mismatches produce localized stress that is further exacerbated by gas–material interactions such as H2 adsorption. As a clean energy carrier with a high gravimetric energy density, H2 plays a pivotal role in the global transition toward carbon-neutral energy systems8,9. While its flammability and low ignition energy demand highly sensitive, rapid, and reliable detection methods for safety-critical applications10–12. Among the various strategies for hydrogen detection, electrical sensors based on Pd nanostructures have attracted considerable interest due to their exceptional H2-specific absorption properties and the resulting measurable changes in electronic conductivity13–15. Yet, despite their high sensitivity and selectivity, the long-term operational reliability of Pd-based sensors remains a grand challenge. This is primarily due to the inherent phase transition between Pd and PdHx during cyclic H2 absorption/desorption, which induces repetitive lattice expansion and contraction16,17. Over prolonged operation, this leads to microstructural degradation, including stress accumulation, dislocation generation, and grain boundary embrittlement, which ultimately lead to delamination or fracture18,19. This degradation in turn weakens the interfacial adhesion between the Pd layer and substrate, critically undermining device durability. To address this challenge, robust heterogeneous interfaces are strongly needed that can endure cyclic mechanical deformation while maintaining high sensitivity.

The central challenge in fabricating these gas sensor interfaces lies in achieving a combination of high interfacial strength to prevent delamination and adequate toughness to accommodate stress from H2-induced lattice transformations without brittle fracture. Conventional approaches to enhance interfacial adhesion include chemical functionalization20, adhesion-promoting polymer integration7, and substrate roughening21,22. These methods operate via mechanisms such as increasing interfacial surface energy, introducing chemical bonding sites, or enabling mechanical interlocking. For instance, titanium (Ti) buffer layers have been introduced to suppress Pd phase transitions23, while polymers like polydopamine have been shown to promote interfacial bonding24. Nevertheless, these strategies often exacerbate the substrate clamping effect, wherein rigid bonding inhibits hydrogen diffusion into the Pd layer23,25, thereby degrading response time and sensitivity. Moreover, interfacial stress accumulation arising from intrinsic material-molecule interactions still remains unsolved. To overcome these limitations, recent studies have employed flexible substrates, such as PDMS or other elastomers, to provide stress-buffering effects through their intrinsic stretchability17. By accommodating volumetric changes during H2 adsorption, these materials reduce interfacial delamination and prolong sensor lifespan. However, Pd layers deposited onto elastomers are typically bonded via weak van der Waals or electrostatic forces26,27, which are insufficient to ensure long-term mechanical stability under cyclic operations. Therefore, there is an urgent need for advanced heterointerfaces that not only enhance mechanical adhesion but also accommodate structural changes induced by H2 absorption. Such interfaces must regulate hydrogen transport kinetics while dissipating stress from lattice expansion, thereby enabling the development of durable, high-performance Pd-based H2 sensors.

Herein, we introduce a floating-structure H2 sensor that bridges the Pd sensing layer and the substrate electrode with the molecular dithiol SAM, forming a stress decoupling heterointerface. In contrast to conventional interfaces held together by weak van der Waals forces, our integrated heterointerface is reinforced by robust sulfur-metal coordination and a flexible carbon backbone, which significantly improves mechanical toughness and interface stability. This dual-interface design simultaneously mitigates interfacial stress and suppresses substrate clamping effects, thereby accelerating H2 absorption kinetics. As a result, the sensor exhibits a stable and cyclable H2 detection at concentrations up to 4 vol%, and an ultrasensitive detection limit of 1 ppm at room temperature. Furthermore, we realized wafer-scale fabrication of floating-structure H2 sensors and integrated them into a portable detection system for practical hydrogen leak detection. Collectively, this work establishes a design paradigm for molecular sensing interfaces, overcoming the trade-off between sensitivity and mechanical durability and providing a scalable foundation for next-generation chemical sensors with extended lifetimes and enhanced reliability.

Results
Design concept of dithiol SAM-engineered heterogeneous interfaces for H2 gas sensor integration
To ensure that the introduction of a SAM layer does not compromise the adsorption-absorption kinetics of the hydrogen molecules on Pd sensing layer during hydrogen detection, a floating-structure design of Pd-based H2 sensor is proposed here (Fig. 1a). The fabrication process consists of three key steps: (i) deposition of a stable gold (Au) bottom electrode film on the substrate, (ii) growth of a SAM interlayer to optimize interfacial bonding, and (iii) deposition of the Pd sensing layer onto the SAM surface to ensure H2 adsorption-desorption behavior unaffected by the interfacial layer during gas sensing. Regarding SAM molecule selection (Fig. 1c), we formed the SAM using dithiol-terminated molecules with either alkyl or π-conjugated benzene backbones (Supplementary Fig. 1). This molecular structure enables dual interfacial chemical bonding: on one side, the thiol (-SH) group forms a covalent Au-S bond with the gold electrode, while on the other, the terminal sulfur atom coordinates with the Pd sensing layer via Pd-S interactions, thereby enhancing interfacial adhesion and improving sensor stability. Furthermore, the innovative aspect of this structure lies in the mechanical buffering effect of the SAM layer (Fig. 1d). As is known, the sensing mechanism of the Pd-based hydrogen sensor primarily relies on the lattice expansion induced by hydrogen absorption16,28,29. As H2 molecules dissolve into the Pd lattice, the lattice parameter and unit cell volume increase proportionally, exhibiting a linear expansion trend (Fig. 1e). Simultaneously, as the H2 dissolution concentration varies, Pd undergoes a phase transition between α-PdHx and β-PdHx. Owing to the distinct electrical resistivity of Pd and PdHx, real-time monitoring of the electrical signal variations in the Pd sensing film enables quantitative detection of H2 concentration in the environment14,30. Additionally, the carbon backbone of the SAM imparts mechanical flexibility, allowing the layer to expand and contract in response to Pd lattice changes during H2 adsorption and absorption. This adaptability effectively buffers the mechanical stress, mitigating both lateral shear and longitudinal compressive strains induced by Pd lattice expansion and contraction (Fig. 1d). Such stress-buffering capacity is key to enhancing the long-term stability and operational reliability of the sensor. Meanwhile, theoretical calculations (Fig. 1f) reveal that the bonding energies of S-Pd (−2.85 eV) and S-Au (−1.92 eV) are substantially higher than that of Pd-Au (−1.15 eV), where Pd is directly deposited on the gold electrode. These results demonstrate that the introduction of dithiol SAM interlayer significantly enhances the adhesion between the Pd sensing layer and the Au electrode, thereby reducing interfacial delamination risk. Consequently, the floating-structure Pd-based H2 sensor, through synergistic optimization of interfacial engineering and micromechanical design, presents a robust solution to the persistent issues of interfacial failure and stress accumulation, thereby paving the way for highly stable and durable hydrogen sensing technologies.

SAM-engineered H2 sensor fabrication and performance
Figure 2a and Fig. 2b show a schematic illustration and corresponding optical images of the fabricated floating-structure sensor device integrated with a dithiol SAM layer. Detailed fabrication procedures are provided in the Experimental Section and schematically presented in Supplementary Fig. 2. In contrast to conventional planar sensor designs, where parallel-patterned electrodes on a substrate are subsequently coated by a sensing film (Supplementary Fig. 3), our device utilizes a vertically aligned crossbar architecture. In this design, two vertically stacked electrodes are separated by a dithiol SAM layer and a Pd sensing film, enabling full circumferential exposure to enhance hydrogen detection performance. To avoid electrical short-circuiting between the lower Au electrode and the upper Pt electrode, a SiO2 insulation layer was deposited over the Au electrode, leaving only a 200 μm circular window for selective SAM formation. A cross-sectional schematic of the sensor structure is provided in Fig. 2c. Considering that the thicknesses of the dithiol SAM and Pd sensing layer critically affect both mechanical stability and hydrogen detection sensitivity, these parameters were systematically optimized by tuning the SAM layer growth time and Pd film deposition thickness. The crystallographic orientation of the deposited Pd film was characterized by X-ray diffraction (XRD), confirming a cubic structure with a preferential (111) orientation (Fig. 2d). Scanning electron microscopy (SEM) imaging (inset of Fig. 2d and Supplementary Fig. 5) further demonstrates the formation of a uniform, densely packed Pd film with a thickness of approximately 80 nm.

To verify the incorporation of the dithiol self-assembled monolayer (SAM), cross-sectional high-resolution transmission electron microscopy (HRTEM) combined with energy-dispersive X-ray spectroscopy (EDX) mapping and line profiling was conducted on the Pd–SAM–Au junction within the sensor device (Fig. 2e–g). Here the incorporated dithiol SAM molecule is 1,10-decanedithiol (C10). HRTEM analysis reveals a uniform interfacial layer (~2 nm) in intimate contact with both Pd and Au, with a thickness consistent with the theoretical molecular length of C10 (Supplementary Fig. 1), confirming successful SAM integration in the floating structure. Notably, due to the use of RF sputtering for Au deposition, the resulting Au films exhibited a nanodot morphology (Supplementary Fig. 4), potentially allowing partial penetration of dithiol molecules into the Au layer. Such a structural configuration facilitates the formation of a continuous SAM across the nanodot surfaces, as evidenced by sulfur distribution in the EDX elemental mapping and line scan (Fig. 2f and 2g), which confirms sulfur presence throughout the Au region. Furthermore, the chemical interactions between the C10 and the Pd and Au were investigated using X-ray photoelectron spectroscopy (XPS) (Fig. 2h and Supplementary Fig. 6 and Fig. 7). The XPS analysis reveals distinct sulfur–metal binding peaks for both Pd (S–Pd: 2p3/2 = 164.0 eV, 2p1/2 = 162.7 eV)31,32 and Au (S–Au: 2p3/2 = 163.1 eV, 2p1/2 = 162.0 eV)33,34, confirming the chemisorption of thiol groups. Additionally, another set of sulfur satellite peaks which attributed to unbound –SH termini is observed in both the SAM-Pd (164.8 eV and 162.7 eV)35 and SAM-Au (164.7 eV and 162.7 eV)34 spectra, which further support the formation of a well-aligned, ordered SAM without disordered growth.

Furthermore, the electrical and hydrogen sensing performance of the SAM-engineered sensor devices was systematically investigated. Figure 2i presents the I-V characteristics of three different sensor architectures: conventional planar structure (Supplementary Fig. 8), a floating structure without a SAM layer, and a floating structure incorporating a C10 SAM layer. A detailed analysis of the conduction characteristics for floating-structured devices with different dithiol SAM is presented in Supplementary Fig. 8. The results indicate that the sputtered Pd film exhibit higher conductivity in the vertical direction compared to the lateral direction. Notably, a slight decrease in conductivity is observed upon the introduction of the dithiol SAM, suggesting that although the SAM introduces a heterointerface, efficient charge transport is still maintained. Subsequently, H2 sensing performance was further evaluated under 1000 ppm H2 at room temperature (Fig. 2j and Supplementary Fig. 9 and Fig. 10). It is seen that the planar structure device presents a very tiny sensing response (Supplementary Fig. 9), while the SAM-integrated floating structure demonstrated a gigantic sensing performance improvement over the planar and SAM-free floating structure. Moreover, the influences of SAM growth time and Pd film thickness on sensing sensitivity, response time, and recovery characteristics were also systematically assessed (Supplementary Fig. 11 and Fig. 12). Due to the SAM layer growth on metals surfaces proceeds via rapid initial diffusion-limited chemisorption, followed by slower two-dimensional nucleation and molecular reorganization into densely packed, ordered films36, the growth time critically influence the orientation characteristics and film qualities of SAM layer. Thus, the optimized SAM growth time for such a sensor architecture design was determined with 24 h. Under these conditions, a Pd film thickness of ~80 nm exhibited the highest H2 sensitivity and optimal response/recovery dynamics (Supplementary Fig. 12). Furthermore, the H2 sensing performance of floating-structured sensors incorporating various dithiol SAM was evaluated (Fig. 2k and Supplementary Fig. 10). The results reveal that aliphatic dithiol SAM composed of aliphatic dithiols, characterized by flexible alkyl chains, markedly enhance sensor sensitivity, with performance progressively increasing with chain length. In contrast, aromatic dithiol SAM produced a dendritic effect that adversely impacted the sensing response. This degradation is primarily caused by the rigid π-conjugated backbone of the aromatic molecules. This structural property first prevents tight molecular packing and then facilitates dendritic growth during film formation. Ultimately, these defects disrupt the interface uniformity37,38, hindering electron transport across the sensing junction. These findings highlight the pivotal role of interface engineering using aliphatic dithiol SAM layer in floating-structure designs for promoting H2 adsorption.

Sensing mechanisms of SAM-engineered H2 sensor
To elucidate the mechanism by which the C10 SAM layer enhances H2 sensing, we systematically investigate interfacial electron transport across the Pd-SAM-Au junction, which is regarded as a critical factor governing sensing performance. To this end, ultraviolet photoelectron spectroscopy (UPS) and current–voltage (I–V) measurements are employed to characterize the interfacial electronic structure and its correlation with H2-induced dynamic responses of the Pd layer.

Alkyl-chain thiol molecules, terminated with reactive –SH groups, readily form strong chemisorption bonds with noble metals such as Au and Pd, enabling the fabrication of robust and tunable molecule–electrode interfaces32,39. Their extended alkyl chains spontaneously organize into highly ordered SAM layer, allowing precise structural control in nanoscale electronic architectures. Owing to these characteristics, such molecules are widely employed in molecular-scale electronic devices, including switches and transistors40–42. In this study, we focus on C10, a saturated σ-bonded molecule exhibiting a wide HOMO–LUMO energy gap (Fig. 3a and Supplementary Fig. 18), which renders it electrically insulating in the absence of metal coupling. However, upon adsorption onto metal surfaces (Au or Pd), the end-group of thiol (-SH) usually form covalent S–metal bonds, inducing substantial interfacial electron coupling and energy-level realignment. This interaction leads to the formation of interfacial states near the Fermi level, indicative of Fermi-level pinning effects that modulate the local electronic structure and facilitate charge transport43–45. UPS measurements (Fig. 3b and 3c) reveal a pronounced decrease in work function following SAM adsorption, suggesting the formation of interfacial dipoles driven by S–metal bonding. The resulting energy-level reordering reduces the charge injection barrier, thereby enhancing electron transmission across the interface43,46. This phenomenon is further supported by first-principles calculations, which predict improved energy-level alignment and enhanced interfacial conductivity (Fig. 3e and Supplementary Fig. 19). Notably, coordination of the C10 molecule with Pd and Au induces the emergence of new electronic states near the Fermi level in the Pd–SAM–Au system, indicating strong interfacial electronic coupling that facilitates charge transport across the heterojunction47–49. To further assess the electron transport capability of the SAM layer during H2 response process, we simulated density of states (DOS) variations in the Pd–SAM–Au system under applied uniaxial strains ranging from 1% to 10% (Fig. 3e and Supplementary Fig. 20). The results show a progressive increase in DOS for energy states above the Fermi level (E–EF > 0) with increasing strain, indicating electron transport at the interface is further enhanced under mechanical stress. In addition, the PDOS results reveal that the Pd-d and Au-d orbitals exhibit minimal variation under compressive strain (Supplementary Fig. 21 and Fig. 22). In contrast, the S-p states show notable redistribution, particularly near the Fermi level. This selective modulation suggests that strain primarily influence the electronic states localized at the Pd–SAM–Au interface, rather than altering the bulk electronic structure of the metal layers. The observed change in S-p PDOS under strain indicates a strain-induced modification in the orbital hybridization between S and the adjacent Pd and Au layers. As the interface undergoes mechanical compression (mimicking the effect of hydriding-induced lattice stress), the overlap between S-p and metal d-orbitals is enhanced, which in turn can facilitate improved charge transport across the interface. In this context, charge transport across the heterojunction can be understood as electron tunneling through a potential barrier. Additionally, complementary I–V measurements were performed to evaluate charge transport behavior experimentally (Fig. 3f). The corresponding Fowler–Nordheim (F–N) plot of ln(I/V²) versus 1/V shows linear behavior across a wide voltage range, suggesting ohmic conduction with no discernible transition voltage even under high bias. This observation is consistent with a stable off-resonant transport regime43,50. These results indicated that, despite the formation of new electronic states following thiol coordination with Pd and Au, the heterointerface still remains remarkable electron transport properties (Fig. 3g). Collectively, these findings highlight that the introduction of the thiol SAM not only preserves the intrinsic conductive properties of the heterojunction interface but also enhances electron transport via interfacial stress transfer induced by hydrogen adsorption in the Pd film.

Furthermore, the influence of the SAM layer on H2 adsorption kinetics during the sensing process was investigated. In metallic Pd, H2 adsorption proceeds via surface molecular adsorption and dissociation, followed by the diffusion of dissociated atomic hydrogen into the Pd bulk, where it occupies interstitial lattice sites to form palladium hydride51,52 (Fig. 3h). The extent of hydrogen absorption is quantitatively described by the bulk hydrogen-to-palladium atomic ratio (H/Pd, denoted as n), which governs the phase transition from metallic Pd to the hydride phase. However, in the sensor architecture presented here, where the Pd film is deposited on a substrate, hydrogen diffusion into the bulk is constrained by mechanical clamping from the substrate53–55. This restriction limits volumetric expansion and thereby suppresses further hydrogen absorption until an equilibrium is established between bulk expansion and substrate-induced confinement (Fig. 3h). Consequently, the hydriding process in thin Pd films follows a nonlinear kinetic regime, defined by a dynamic equilibrium between lattice Pd and absorbed hydrogen51. This regime also corresponds to the phase during which the sensor gradually reaches maximum performance in its dynamic electrical response (Fig. 2j). To quantify the real-time H/Pd ratio in bulk Pd, an essential parameter for evaluating the SAM layer’s role in tailoring H2 absorption, we analyzed the temporal evolution of the n(t) within the bulk diffusion regime (Fig. 3i). These values were extracted from dynamic hydrogen response curves (Fig. 2j). The time scale was adjusted so that t=0 s marks the onset of the nonlinear regime. Details of the calibration procedure are provided in the Supplementary (Section VI, H2 absorption modeling). The solid lines in Fig. 3i represent fits obtained using absorption-related kinetic models for the bulk diffusion regime51.

n(t) = C1 + C2 exp(C1(t-t0)) (1)

C1 = k0ab 1+p Kffi p ffis H ffiffi 2 ffiffi (2)
C2 = k0ab

where n(t) is the time dependent H/Pd ratio, k0ab is the rate constant for hydrogen absorption, Ks is the Sievert’s constant. The average hydrogen absorption rate k0ab, obtained by fitting Eq. (1) to the H atom uptake regime across all experiments, reveals a markedly enhanced absorption rate in the dithiol SAM-integrated floating H2 sensor, with an average value of k0ab = (4.6±1.1)×10−4 s−1. This is an order of magnitude higher than that of the sensor without the SAM layer (k0ab = (4.0±1.2)×10−5 s−1) (Supplementary Table S1), as shown in Fig. 3j. These results indicate that the embedded dithiol SAM effectively mitigate the substrate clamping effect, thereby facilitating hydrogen absorption. Furthermore, the inherent flexibility of dithiol molecules further promotes this process by reducing mechanical constraints at the Pd interface. As a result, the floating-structured Pd film sensor architecture design achieves significantly improved hydrogen absorption kinetics, leading to enhanced sensitivity and reduced response time during sensing operations.

Unveiling the enhanced durability of SAM-engineered H2 Sensors
Understanding the mechanical behavior of Pd-Au heterointerfaces under tensile loading is essential for elucidating their fracture characteristics and interfacial adhesion properties. To this end, density functional theory (DFT) calculations were performed to obtain the interface binding strength and fracture behaviors of the C10 molecule incorporated Pd-Au systems. Details of the simulation procedures are provided in the Supplementary Information. Interfacial models of Pd(111)-Au(111) (Pd-Au) and Pd(111)-C10F-Au(111) (Pd-SAM-Au) were constructed with energetically stable bonding configurations, as shown in Fig. 4a. The computed interfacial binding energies indicate that the Pd-SAM-Au structure possesses a significantly lower binding energy than the Pd-Au interface (Fig. 4b), suggesting a thermodynamically more stable configuration. This enhanced interfacial adhesion is attributed to strong molecular interactions introduced by the SAM layer, as evidenced by the more negative binding energy.

To probe the mechanical integrity of the interfaces, the Pd-Au and Pd-SAM-Au systems were strained uniaxially along the z-axis until cohesive failure occurred. (Supplementary Fig. 23). The resulting stress-strain profiles are shown in Fig. 4c and Supplementary Fig. 24. For the Pd–Au interface, stress increased steadily with strain, reaching a peak at ~17%, followed by an abrupt drop, indicative of brittle fracture without significant atomic rearrangement. In contrast, the Pd-SAM-Au interface exhibited a more complex deformation behavior. Stress increased up to ~14% strain, followed by a plateau region suggesting a yielding phase. Beyond ~18%, the stress resumed rising, reaching a second peak at ~26% before final failure. This ~50% increase in fracture strain highlights the toughening effect introduced by the SAM layer, which modulates interfacial mechanics via molecular-level restructuring. The enhancement in ductility is attributed to the straightening of the SAM’s initial zig-zag conformation under strain, which delays crack propagation and imparts greater mechanical resilience. As a result, the failure mode transitions from brittle to ductile upon SAM incorporation, emphasizing the pivotal role of molecular architecture in regulating interfacial fracture behavior.

To quantitatively assess the influence of the SAM buffer layer on sensor reliability, 50 repeated sensing cycles were performed under identical conditions to low (1000 ppm) and high concentration (4 vol%) of H2, and the corresponding response curves were analyzed (Fig. 4d, e). At 1000 ppm H2 exposure test, the sensor incorporating the SAM layer exhibited excellent repeatability, with a maximum error below 5% across all cycles. In contrast, devices lacking the SAM layer experienced a marked performance decline, showing more than 50% signal degradation after several test cycles. The difference was even more pronounced at 4 vol% H2. Under a higher (4 vol%) H2 concentration, some non-SAM devices failed immediately upon first exposure (Supplementary Fig. 14), highlighting their vulnerability. This contrasts with SAM-integrated devices, which showed no performance loss over 50 cycles in 1 vol% H2, underscoring the critical role of the SAM in preventing irreversible failure (Supplementary Fig. 13). These results demonstrate that embedding a dithiol SAM at the interface substantially improves long-term operational stability by mechanically buffering the Pd–substrate interface and suppressing substrate clamping, effects that are especially critical when Pd undergoes α→β phase transitions and large lattice expansion upon hydrogenation. In addition, the Au–SAM–Pd multilayer architecture appears to enhance H2 adsorption/desorption kinetics in the Pd sensing layer, yielding concomitant improvements in sensitivity and response speed. Together, the data provide compelling experimental evidence that the SAM both mitigates interfacial stress and promotes faster, more reliable hydrogen sensing under practical, demanding conditions.

Sensing performance of SAM-engineered H2 sensor
Next, the sensing performance of the floating-structured H2 sensor incorporating a C10 SAM layer was systematically evaluated. Figure 5a shows the dynamic response curves of the sensor to H2 concentrations ranging from 1 ppm to 4 vol% at room temperature. Notably, the sensor device achieves reliable detection of hydrogen at concentrations as low as 1 ppm and stable sensing response to high concentration of H2 (1 vol% and 4 vol%, Supplementary Fig. 14 and Supplementary Fig. 15). Figure 5b demonstrating its suitability for trace-level monitoring in leak detection scenarios. To assess humidity tolerance, the sensor’s response was measured under varying ambient RH levels at room temperature, as shown in Fig. 5c. Between 16% and 31% relative humidity (RH) the sensor exhibited a modest reduction in sensitivity and a slight slowing of response and recovery kinetics (Supplementary Fig. 16). Above 31% RH, however, both sensitivity and response/recovery times remained essentially unchanged (Fig. 5d and Supplementary Fig. 16), consistent with a saturation regime for H2O adsorption and indicating that the floating Pd architecture mitigates humidity interference. Moreover, humidity-dependent I–V measurements show a small increase in baseline resistance (R0) with rising RH (Supplementary Fig. 16d), suggesting weak physisorption of H2O on Pd rather than chemisorption. This behavior is supported by H2O adsorption-energy calculations from DFT (Supplementary Fig. 25). Additionally, cross-sensing tests confirmed the as-fabricated H2 sensor shows high selectivity to hydrogen gas compared with other analytes, including NO2 and H2S (Fig. 5e), highlighting its robustness and gas-specific response. Meanwhile, long-term stability was assessed at both low and high H2 concentrations (Fig. 5f and Supplementary Fig. 17). As shown in Fig. 5f, the sensor exhibited unnoticeable degradation in performance during a continuous testing period of over three months, maintaining consistent sensitivity and dynamic response characteristics. These results clearly demonstrate that the embedded SAM layer not only mitigates interfacial stress but also significantly enhances the operational lifetime of the device. Furthermore, the sensor device maintained stable signal output at an applied bias as low as 0.005 V, corresponding to a power consumption of ~5 μW (Fig. 5g). This ultra-low power operation renders the sensor particularly promising for large-scale integration in wireless sensor networks. Finally, a comprehensive comparison of key performance metrics, including operating temperature, detection limit, power consumption, and operational lifespan is summarized in Fig. 5h56–65. This comparable study demonstrated that the proposed floating-structured H2 sensor exhibits a superior overall performance compared to previously reported H2 sensors.

Wafer-scale fabrication of SAM-engineered H2 sensors and test platform integration
Finally, we realized the wafer-scale fabrication of the proposed H2 sensor and demonstrated its potential for real-time hydrogen leakage monitoring. Figure 6a shows an array of H2 sensor devices fabricated on a 4-inch Si/SiO2 wafer via standard photolithography processes. Each individual sensor chip was diced into 2×2 mm, with the C10 SAM layer selectively formed within circular regions of 200 μm diameter, over which the Pd sensing film was deposited. Detailed fabrication steps are provided in the Supplementary Information. To satisfy the requirements for practical deployment, wafer-scale fabrication of H2 sensors must achieve both high yield and performance uniformity. To assess these metrics, 25 sensor chips were randomly selected from various regions across the wafer and characterized using a semiconductor parameter analyzer in conjunction with a probe station (Fig. 6b). The baseline resistances of all tested devices remained within 4.2 Ω, and the sensing responses to 1000 ppm H2 exhibited minimal variation, ranging around 0.56%, thereby confirming the excellent yield and uniformity of the wafer-scale process. Furthermore, sensor chips were packaged using Au wire ball-bonding techniques, and the packaged devices retained nearly identical sensing responses compared to their unpackaged counterparts (Fig. 6c). This result confirm the compatibility of the proposed sensor design with standard microelectromechanical systems (MEMS) packaging processes and underscores its potential for scalable and practical applications.

Since the sensing signal generated during H2 detection typically manifests as a weak voltage variation (on the order of tens of millivolts), signal amplification and noise suppression are critical for the development of reliable H2 leakage monitoring platforms. To address this, a multifunctional detection module integrating a Wheatstone bridge and an operational amplifier circuit was designed and fabricated on a printed circuit board (PCB), as illustrated in Fig. 6d. Detailed circuit schematics are provided in the Supplementary Fig. 29. Data acquisition and communication were facilitated via an analog-to-digital converter (ADC) and a microcontroller unit (MCU), powered by a 5 V regulator with integrated ON/OFF switches and GPIO interfaces. The processed sensing data was wirelessly transmitted to a smart platform through Wi-Fi for real-time feedback of environmental hydrogen concentrations (Fig. 6d). Figure 6e depicts the fully assembled hydrogen (H2) leakage monitoring module, with its data output interfaced to a laptop for visualization. To evaluate the efficacy of the signal amplification design, we compared the sensing responses of the platform integrated with and without the Wheatstone bridge-amplifier circuit under 1000 ppm H2 (Fig. 6f). The results revealed a three-order-of-magnitude enhancement in voltage signal amplitude upon integration of the amplification module, while maintaining excellent signal stability. Furthermore, the platform demonstrated consistent signal enhancement across a wide range of H2 concentrations (1–1000 ppm), with a notably strong and stable response even at 1 ppm (Fig. 6g and Supplementary Fig. 30), confirming its high sensitivity and practical utility for real-time hydrogen monitoring. To extend its applicability, a handheld hydrogen leakage monitoring platform was developed by integrating the fabricated MEMS H2 sensor with commercial temperature and humidity sensors, as illustrated in Fig. 6h. Details of the sensing platform design are provided in the Supplementary Fig. 31. Owing to its compact form factor and portability, the platform enables versatile deployment in real-time H2 leak detection scenarios. To demonstrate a practical application, Fig. 6i shows the system operating within a hydrogen cylinder cabinet, a setting where reliable safety monitoring is needed. Leveraging an embedded H2 concentration recognition algorithm, the platform is capable of delivering real-time feedback of ambient H2 levels (Fig. 6j, k) and automatically triggering a leakage alarm when abnormal concentrations are detected. Furthermore, a comparative test using our integrated handheld detection platform and a commercially available Honeywell hydrogen detector (BWS1-R-Y) was performed (Supplementary Movie 1 and Movie 2). The results show that our sensor-integrated device was able to accurately detect and quantify the 1000 ppm H2 sample, yielding a response comparable to that of the commercial sensor. Furthermore, our system demonstrated a faster detection response, which we attribute to the integration of a miniaturized micro-pump within the handheld unit. This active sampling route allow more rapid intake of ambient gas, thereby improving response speed compared to passive diffusion-based commercial H2 detector. This demonstrates the practical feasibility, precision, and reliability of our system in real detection scenarios, particularly for low-concentration, pre-explosive hydrogen monitoring.

Methods
SAM-engineered sensor device fabrication
The fabrication process begins with the patterning of gold electrodes on a Si/SiO2 substrate, using photolithography (ABM/6/350/NUV/SFM/SA, Incorporated company, San Jose, CA, USA). Subsequently, Cr/Au electrodes are deposited via radio-frequency magnetron sputtering (RF, ASC-5-501C, ANSEI TECH., Japan). Next, the patterning of SiO2 insulation layer is carried out using photolithography, followed by the deposition of SiO2 layer using RF sputtering. Afterward, photolithography is used to define the palladium (Pd) sensitive layer pattern, and the wafer is then immersed in a precursor solution to grow SAM buffer layer, and followed by the deposition of Pd layer via RF sputtering. Finally, the Pt electrode pattern is defined on the Pd-sensitive layer using photolithography, and Ti/Pt layer are deposited via RF sputtering, completing the fabrication of the hydrogen sensor.

Microstructure characterizations
The microstructure of deposited Au and Pd films were obtained using a JEOL JSM-7610F microscope. After the sensor device fabricated, a Pd-SAM-Au samples were processed by the focused ion beam method to obtain an ultrathin section of the interface, and then mounted it on grids and characterized using Transmission Electron Microscopy (TEM) (JEM-ARM200F, JOEL), with Elemental Dispersive X-ray (EDX) mapping for elemental analysis. To evaluate the chemical bonding at the SAM@Au and SAM@Pd interfaces, X-ray Photoelectron Spectroscopy (XPS) (PHI-5000 VersaProbe III, ULVAC) equipped with an argon ion sputtering system was employed. The process for fabricating the ultraviolet photoelectron spectroscopy (UPS) samples was the same as that for XPS samples. UPS measurements were conducted under a base pressure of >2×10−9 Torr, using He I (hν=21.22 eV) as the excitation source. To acquire secondary electron cutoff (SEC) data, a −10 V bias was applied to the sample in a normal emission geometry. For all UPS spectra, the Fermi level was calibrated by determining the Fermi edge of a clean Au film sputtered onto the sample, and it was set as the zero binding energy.

H2 sensing measurement
Gas measurements were conducted by using a probe station (KT-0904T-RL, Ketan Instrument) combined with a semiconductor analyzer (4200A-SCS, Keithley). The total flow rate was maintained at a constant 1000 sccm. The test temperature was controlled at 25 °C and a ranged relative humidity from 16-85%. The mass flow controller (MFC, KT-D07-19B) was controlled via LabVIEW software, enabling precise adjustment of hydrogen concentration (1 ppm-4 vol%) by mixing hydrogen with nitrogen. Resistance of the sensor device under N2 was recorded as baseline (R0). The resistance upon exposure of H2 gas (Weichuang Standard Reference Gas, Shanghai) was noted as Rgas, and sensing response was defined as Response (%) = [(Rgas - R0)/R0]×100. The recovery time was defined as the time required for the recovery of the resistance to 90% of R0 for the desorption process. All the sensing tests were carried out under a DC bias voltage of 0.1 V.

DFT calculations
The energy diagrams and strain-dependent density of state (DOS) of C10 molecule and Pd-C10-Au systems are modeled and calculated via Density functional theory (DFT) simulation. the Au-Pd and Au-SAM-Pd structures. To further investigate the mechanical properties of the interfaces, DFT calculations were applied to simulate the interface binding strength and fracture behavior of Pd-Au and Pd-SAM-Au models. Details of the simulation procedures are provided in the Supplementary Information.

Wafer-size H2 gas sensor fabrication and package
The wafer-scale fabrication of floating-structure H2 gas sensor are followed with a standard photolithography technique on 4-inch SiO2/Si substrate. Specific fabrication processes are similar as the above SAM-engineered sensor device. After wafer-level fabrication, the 4-inch wafer was diced into multiple micro-nano hydrogen gas sensor chips. The sensor chips were fixed to their respective packaging using epoxy resin, and the electrodes on both end soft the chip were connected to the package pins via ball bonding. Finally, the sensor chip package was sealed using epoxy resin.

H2 test platform integration
In the fabrication of the detection system, the circuit and PCB design were carried out using JLCPCB EDA software (JLCPCB, China). The Wheatstone bridge circuit and low-power instrumentation amplifier (AD8421BRZ, Analog Devices, USA) convert the small resistance changes caused by environmental gas variations into measurable voltage changes. These signals are then amplified in two stages and filtered to detect hydrogen at different concentrations. The voltage is sampled using an ultra-low noise ADC (AD7193BRUZ, Analog Devices, USA), which features high resolution, precision, and extremely low offset voltage, enabling accurate signal acquisition after amplification and filtering. The USB-to-UART bridge chip (CP2102-GMR, Silicon Labs, USA) and its peripheral circuitry are used for programming and driver downloading. The main controller (ESP32-S3-WROOM-1U-N4 MCU module) communicates with the ADC chip via SPI, receiving the digitized signals. This MCU module is a versatile Wi-Fi and Bluetooth Low Energy (BLE) chip, capable of transmitting the sensor signals collected by the ADC to a PC or smartphone over Wi-Fi. For power management, the system is powered by a 7.4 V lithium-ion battery (18650, Tianke Tai, China) and uses multiple linear regulators for voltage stabilization (AMS1117-3.3V, MSKSEMI, Hong Kong; TPS7A7002DDAR, TI, USA), as well as a charge pump (TP7660H, TOPPWER, China) to generate negative voltage. These components ensure proper power supply and reference voltage for each module. Additionally, the system uses passive components (resistors, capacitors, ferrite beads, etc., in 0805 and 0603 packages), power button switches (XKB8585-Z-150, China), and sliding switches (Shouhan, MST22D18G2125, China).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "I have carefully reviewed the theoretical and modeling components of your manuscript. The integration of first-principles calculations, stress–strain analysis, and kinetic modelling with experimental data is conceptually strong and technically promising. Below I summarise the computational strengths well-documented in the SI, followed by specific areas where the theoretical section would benefit from additional clarification or methodological refinement.\n1. Strengths\nThe DFT methodology is fully disclosed in Section VI.1 and VI.2 of the SI. VASP, PAW pseudopotentials, PBE+D3 dispersion correction, 450–500 eV plane-wave cutoffs, and appropriate k-point meshes are clearly stated.\nHydrogen uptake kinetics are carefully modelled in Equations (4)–(8) of the SI, and Figures S19–S20 differentiate between absorption- and adsorption-limited regimes.\nInterface mechanical properties are analysed using stress–strain simulations, and Fig. S17 shows a ~50% increase in fracture strain for the Pd–SAM–Au system compared to Pd–Au.\nThese details considerably strengthen the credibility of the theoretical framework and support the experimental narrative.\n2. Major points\nSAM Coverage and Periodicity: Figure S16 appears to model a single dithiol molecule between Pd and Au slabs. Please clarify whether this setup is meant to approximate a full monolayer or represents a dilute configuration. If dilute, discuss how lateral interactions or molecular packing could affect the binding and mechanical response.\nBinding-Energy Convention: The main text states that a “lower binding energy indicates a more stable interface,” which could confuse readers. Please report the numerical values of the interface energies in the main text and SI, with proper units (e.g., eV nm⁻²).\nStress–Strain Protocol: The stress–strain calculations elongate the Pd–SAM–Au system along the out-of-plane (z) direction. It remains unclear whether the in-plane lattice vectors were relaxed or fixed. Please specify the boundary conditions, comment on the impact of performing static calculations at 0 K, and address any artefacts arising from the small cell size. A short ab initio molecular dynamics run or calculations on a larger supercell would be valuable, though optional.\nElectronic-Structure Interpretation: The SI includes DOS plots for compressive strain (0–10%), while the main text discusses tensile strain due to hydriding. Also, no projected DOS (PDOS) is shown. Please provide PDOS plots (Pd-d, S-p, Au-d) for both 0% and a relevant strain value to clearly illustrate orbital hybridisation and support the interpretation of enhanced charge transport.\nKinetic-Fit Transparency: The SI outlines the fitting procedure for extracting parameters, but no values, uncertainties, or fit quality metrics are provided. Please include a table listing the extracted rate constants (mean ± standard deviation) for devices with and without the SAM, as well as R² or χ² values for each fit.\n3. Minor and Editorial Suggestions\nIndicate whether the k-meshes and energy cutoffs were convergence tested (e.g., to within 5 meV atom⁻¹).\nConfirm that the final spin moments are negligible, especially for S–C–Pd/Au interfaces where slight spin polarisation may emerge.\nSpecify the smearing method and width used for DOS plots (e.g., Gaussian or Methfessel–Paxton).\nA nudged-elastic-band (NEB) calculation for hydrogen diffusion across the interface would enrich the mechanistic understanding, though this is not essential for publication.", "reviewer_2": "The manuscript presents an interesting strategy to decouple interfacial stress in Pd-based H2 sensors by inserting a dithiol self-assembled monolayer between the Pd sensing film and the Au electrode. The effect of dithiol-SAM is investigated by both experimental and theoretical results. Wafer-scale fabrication and system-level integration are also demonstrated. These results are important and will be of broad interest to the chemical-sensor community. Nevertheless, several critical issues need to be resolved before the manuscript can be considered for publication.\n1. It is well known that Pd forms α-phase PdHx upon exposure to low concentration H2 (<~1%). For α-phase hydride, the hydrogen-to-palladium atomic ratio x (or n in the manuscript) is less than 0.02 and the expansion of Pd’s lattice parameter is less than 0.13%. Significant lattice expansion only appears during the α to β phase transition (~1%-5% H2). In this phase transition, x increases abruptly to ~0.7 with the lattice expansion increasing to ~3.5%.\nIn this work, it is noticed that the highest H2 concentration used is only 1000 ppm (~0.1 %), i.e., only α-phase PdHx can be formed. Therefore, will the mechanical clamping from the substrate be significant? Similarly, will the instability induced by Pd expansion and contraction be that significant?\nIn Figure 3i, what is the saturated value of the hydrogen-to-palladium atomic ratio for Pd with and without SAM?\nIf the lattice expansion is tiny, the present experimental results will not be able to support the conclusion that SAMs mitigate interfacial stress and suppress substrate clamping effects. Cyclic and long-term stability tested under high H2 concentration (4% H2, for example) would be more convincing.\n2. For a Pd film, when it absorbs H2 and forms PdHx, its resistance will increase as a result of the scattering effect of H atoms. The higher of surrounding hydrogen concentration, the higher of the resistance. It is reported that the maximum resistance increase is ~0.7 times when Pd fully forms β-phase PdHx, corresponding to a response value of 0.7. I am wondering how a response value of 0.8 can be obtained when Pd-SAM-Au sensor is exposed to 0.1% H2. Is there any explanation for this result?\n3. The supporting information, line 251, could you please further explain equation 4?\n4. It is noticed that the sensing performance test was performed with N2 as carrier gas. However, a hydrogen sensor is more likely to be used in air (with the presence of O2) in practical applications. Is there any performance difference in these two conditions?\n5. As a room-temperature gas sensor, the influence of relative humidity should be investigated.\n6. Are disulfides stable enough in practical applications?\n7. What if 1,10-decanedithiol is replaced by dithiol with a longer chain length? Will the performance be enhanced or weakened?\n8. Conclusions should be based on experimental results. Lifespan exceeding 10 years is overstated.\n9. Line 190, please check the interfacial layer thickness. Is 2 Å correct or not?\nPlease also check the binding energy of -SH and -S-metal in line 200 to 205.\nLine 142, fig. 1e should be 1f? Line 405, (c) should be (d)?", "reviewer_3": "The author presented a floating-structure palladium hydrogen sensor enabled by interfacial stress decoupling through a dithiol-based self-assembled monolayer. Although this study has made some progress in the relevant field, it lacks sufficient novelty to meet the high standards of Nature Communications. We recommend submitting to another journal. Additional comments are provided below.\n1) Please summarize some novelties of the structure and the sensing performance for this floating-structure palladium hydrogen sensor compared to commercial sensors with long lifespan on the market.\n2) Because H2 is prone to explosion when its concentration exceeds 4% in the air, it is necessary to provide the sensor's response to higher concentration of H2 gas. That is, how much concentration of H2 can the sensor accurately detect?\n3) The latest H2 sensing performance standards released by the U.S. Department of Energy requires response time and recovery time of less than 60 seconds at 1% concentration of H2 gas. What is the sensor performance when 1% concentration of H2 gas is detected?\n4) How does the sensor respond to other interfering gases such as H2S or NO2 gas?\n5) Please evaluate the influence of different relative humidity on baseline resistances and response values. To discuss it, the adsorption energy of materials for H2, H2O and O2, and other interfering gases should be calculated and compared.\n6) The author speculates on the lifespan of the sensor for ten years based on one year of stability testing results, which has no scientific basis. More importantly, the XPS spectrum in Figure 2h shows thiol groups only partially coordinate with noble metals, and thiol groups without coordination are not very stable in air and cannot remain stable for ten years. It is recommended to deeply analyze the stability of the baseline resistance as well as the sensor response.\n7) The author integrated a handheld hydrogen leakage monitoring platform to detect H2 gas. If possible, it is recommended to compare it with existing commercial H2 sensors in the form of a video to exhibit its precision and accuracy."}, "author_response": "Responses to Reviewer #1’s Comments\nComments of Reviewer #1:\nI have carefully reviewed the theoretical and modeling components of your manuscript. The\nintegration of first-principles calculations, stress–strain analysis, and kinetic modelling with\nexperimental data is conceptually strong and technically promising. Below I summaries the\ncomputational strengths well-documented in the SI, followed by specific areas where the\ntheoretical section would benefit from additional clarification or methodological refinement.\nReply:\nWe thank the reviewer so much for appreciating our work. By absorbing the helpful suggestions\nand comments, the manuscript is improved after revision. The point-by-point responses as follow:\n1. Strengths\nThe DFT methodology is fully disclosed in Section VI.1 and VI.2 of the SI. VASP, PAW\npseudopotentials, PBE+D3 dispersion correction, 450–500 eV plane-wave cutoffs, and appropriate\nk-point meshes are clearly stated.\nReply:\nWe sincerely thank the reviewer for the positive comment, and we are glad that the description of\nthe DFT methodology was found to be clear and complete.\nInterface mechanical properties are analysed using stress–strain simulations, and Fig. S17 shows\na ~50% increase in fracture strain for the Pd–SAM–Au system compared to Pd–Au.\nReply:\nWe sincerely thank the reviewer for their insightful summary and appreciate the reviewer’s\npositive evaluation of this result.\nInterface mechanical properties are analysed using stress–strain simulations, and Fig. S17 shows\na ~50% increase in fracture strain for the Pd–SAM–Au system compared to Pd–Au.\nReply:\nWe sincerely thank the reviewer for their positive comment and are pleased that this aspect of the\nstudy was clear.\nThese details considerably strengthen the credibility of the theoretical framework and support the\nexperimental narrative.\nReply:\nWe sincerely thank the reviewer for their encouraging comment. We are pleased that the\ntheoretical framework was found to meaningfully support the experimental results and enhance\nthe overall credibility of the study.\n2. Major points\nSAM Coverage and Periodicity: Figure S16 appears to model a single dithiol molecule between\nPd and Au slabs. Please clarify whether this setup is meant to approximate a full monolayer or\nrepresents a dilute configuration. If dilute, discuss how lateral interactions or molecular packing\ncould affect the binding and mechanical response.\nReply:\nThank you for the constructive comment. The configuration shown in Figure S16 represents a\ndilute molecular arrangement, intended to approximate a sparsely packed SAM. Specifically, we\nemployed a 2×2 supercell, corresponding to an intermolecular spacing of approximately 5.6 Å,\nwhich significantly reduces lateral interactions between neighboring dithiol molecules. In addition,\na 15 Å vacuum layer was introduced along the z-direction to eliminate interlayer interactions under\nperiodic boundary conditions. This modeling strategy allows us to capture the behavior of an\nisolated dithiol molecule at the Pd–SAM–Au interface, effectively simulating a dilute limit of\nSAM coverage.\nWhile as dithiol molecules assembled in a densely packed SAM, lateral van der Waals\ninteractions and dipole–dipole coupling between the alkyl chains could potentially influence not\nonly the electronic environment but also the mechanical response of the interface. Specifically,\nwhen an external normal pressure is applied, such as from hydrogen-induced lattice expansion of\nthe Pd film, the intermolecular forces between adjacent dithiol molecules could provide in-plane\ncohesive resistance. This lateral coupling may partially counteract normal stress propagation,\ndepending on the degree of molecular ordering and packing density. However, according to prior\nmolecular dynamics and spectroscopy studies1, 2, the dominant lateral interactions between alkane\nchains in decanedithiol SAMs arise from weak van der Waals forces, with binding energies of\n1.838kcal/mol (0.077eV) per CH unit3. While such interactions contribute to monolayer ordering\n2\nand thermal stability, they are not sufficiently strong to offer meaningful resistance to out-of-plane\nstress induced by hydride phase transitions in Pd, which involve lattice expansions of several\npercent. Therefore, even in the case of a fully packed SAM, the mechanical buffering effect against\nPd expansion is expected to arise primarily from the vertical S–metal coordination bonds rather\nthan lateral interchain interactions. In our dilute model, where lateral interactions are minimized,\nthe focus remains on the chemical bonding and charge-transfer dynamics at the Pd–SAM–Au\njunction, which are critical for hydrogen sensing.\nWe have clarified this modeling assumption and added discussion of this potential mechanical\ninterplay in the revised Supplementary Information (Section VI.2) to enhance the transparency and\ncompleteness of our analysis.\nBinding-Energy Convention: The main text states that a “lower binding energy indicates a more\nstable interface,” which could confuse readers. Please report the numerical values of the interface\nenergies in the main text and SI, with proper units (e.g., eV nm⁻²).\nReply:\nThank you for the reviewer’s comment. We have updated the main text and SI to include the\nnumerical values of the computed interfacial binding energies with proper units.\n“The computed interfacial binding energies indicate that the Pd–SAM–Au structure possesses a\nsignificantly lower binding energy (–2.667 J/m2) than the Pd–Au interface (–2.000 J/m2) (Fig. 4b),\nsuggesting a thermodynamically more stable configuration. This enhanced interfacial adhesion is\nattributed to strong molecular interactions introduced by the SAM layer, as evidenced by the more\nnegative binding energy.”\nStress–Strain Protocol: The stress–strain calculations elongate the Pd–SAM–Au system along the\nout-of-plane (z) direction. It remains unclear whether the in-plane lattice vectors were relaxed or\nfixed. Please specify the boundary conditions, comment on the impact of performing static\ncalculations at 0 K, and address any artefacts arising from the small cell size. A short ab initio\nmolecular dynamics run or calculations on a larger supercell would be valuable, though optional.\nReply:\nThank you for the reviewer’s insightful comments.\nBoundary conditions: In the stress–strain calculations, strain was applied incrementally along the\nout-of-plane (z) direction. At each step, the in-plane lattice vectors were fixed, while all atomic\npositions were fully relaxed. This approach allows the system to reach the minimum energy\nconfiguration under the applied strain, ensuring an accurate description of the mechanical response\nalong z.\nStatic calculations at 0 K: All calculations were performed at 0 K, which is standard in first-\nprinciples simulations. Since our study focuses on ground-state mechanical properties rather than\ntemperature-dependent phenomena or phase transitions, this approximation is reasonable.\nSmall cell size and artefacts: We acknowledge that the small supercell may limit the description\nof long-range interactions or collective effects. However, given that the primary focus is on local\nbond response and intrinsic mechanical properties, the current cell size is sufficient to capture the\nessential physics.\nIn addition, we agree that ab initio molecular dynamics or larger supercell calculations could\nprovide additional insight. These could be considered in future work to verify the robustness of\nthe stress–strain behavior, although they are not expected to qualitatively alter the main\nconclusions.\nWe have clarified this calculation details and discussions in the revised Supplementary\nInformation (Section VI.2) to enhance the transparency and completeness of our analysis.\nElectronic-Structure Interpretation: The SI includes DOS plots for compressive strain (0–10%),\nwhile the main text discusses tensile strain due to hydriding. Also, no projected DOS (PDOS) is\nshown. Please provide PDOS plots (Pd-d, S-p, Au-d) for both 0% and a relevant strain value to\nclearly illustrate orbital hybridisation and support the interpretation of enhanced charge transport.\nReply:\nWe sincerely thank the reviewer for raising this important point regarding the electronic structure\ninterpretation under strain conditions. In response, we have extended our DFT analysis to include\nprojected density of states (PDOS) for the Pd-d, S-p, and Au-d orbitals in the Pd–SAM–Au system\nunder both 0% and compressive strain conditions (up to 10%), as shown in Figure R1. The PDOS\nresults reveal that the Pd-d and Au-d orbitals exhibit minimal variation under compressive strain.\nIn contrast, the S-p states show notable redistribution, particularly near the Fermi level. This\nFigure R1. Projected density of states (PDOS) for the Pd–SAM–Au system under varying\ncompressive strain (0–10%). (a) Pd-d state PDOS over the full energy range. (b) Magnified\nview near the Fermi level. (c), (d) S-p state PDOS (full range and near Fermi level,\nrespectively). (e), (f) Au-d state PDOS (full range and near Fermi level, respectively).\nselective modulation suggests that strain primarily influences the electronic states localized at the\nPd–SAM–Au interface, rather than altering the bulk electronic structure of the metal layers. The\nobserved change in S-p PDOS under strain indicates a strain-induced modification in the orbital\nhybridization between S and the adjacent Pd and Au layers. As the interface undergoes mechanical\ncompression (mimicking the effect of hydriding-induced lattice stress), the overlap between S-p\nand metal d-orbitals is enhanced, which in turn can facilitate improved charge transport across the\ninterface. This supports our interpretation that mechanical strain, whether compressive or tensile,\nmodulates the interfacial electronic coupling, thereby contributing to the enhanced sensing\nperformance observed experimentally.\nWe have added the PDOS plots and associated discussion to main manuscript and the\nSupplementary Information (Section VI., Supplementary Information Fig. 21 and Fig. 22) to\nclarify and strengthen the theoretical basis for strain-enhanced interfacial charge transport.\nKinetic-Fit Transparency: The SI outlines the fitting procedure for extracting parameters, but no\nvalues, uncertainties, or fit quality metrics are provided. Please include a table listing the extracted\nrate constants (mean ± standard deviation) for devices with and without the SAM, as well as R² or\nχ² values for each fit.\nReply:\nWe thank the reviewer for this important comment regarding the transparency of the kinetic fitting\nanalysis. In response, we have compiled a summary table (now included as Table S1 in the revised\nSupplementary Information) presenting the extracted rate constants along with their corresponding\nstandard deviations, as well as the coefficient of determination (R2) and chi-squared (χ²) values for\neach fit. These values were obtained from repeated measurements on devices with and without the\nSAM layer, ensuring statistical reliability and reproducibility of the extracted parameters. The\ntable provides a direct comparison of reaction kinetics and fitting quality, highlighting the\ninfluence of the SAM layer on hydrogen adsorption and desorption dynamics. All fitting\nprocedures follow the methodology described in Section VI.3 of the SI, and goodness-of-fit\nmetrics confirm that the model adequately captures the experimental response behavior.\nWe have added this table and clarified the related discussion in the revised Supplementary\nInformation (Section VI.3) to ensure greater transparency and completeness.\nTable S1 Fitting\nk\nand related constants according to absorption-related kinetic models.\nab\nFitting k Fitting value R-square Chi-square Mean value Standard\nab\nk (R 2 ) (χ²) k deviation\nab ab\n1000 ppm H\nstructured\nsensor 2 nd cycle 4.5784×10 -5 0.9945 1.0525×10 -10\nembedded 3.9728×10 -5 1.2382×10 -5\nw/o SAM 3 rd cycle 3.0522×10 -5 0.9934 1.2016×10 -10\n4\nth\ncycle 2.5703×10\n-5\n0.9902 1.4915×10\n-10\nFloating- 1 st cycle 6.0727×10 -4 0.9993 1.1622×10 -9\nstructured\nsensor 2 nd cycle 5.3460×10 -4 0.9996 4.7129×10 -9\nembedded 4.6311×10 -4 1.1103×10 -4\nw SAM 3\nrd\ncycle 3.6431×10\n-4\n0.9996 5.3110×10\n-9\nth -4 -10\n4 cycle 3.4625×10 0.9993 7.0365×10\n2. Minor and Editorial Suggestions\nIndicate whether the k-meshes and energy cutoffs were convergence tested (e.g., to within 5 meV\natom⁻¹).\nReply:\nWe thank this reviewer’s important suggestion. All k-point meshes and plane-wave energy cutoffs\nwere carefully tested for convergence. The selected parameters ensure that the total energy is\nconverged to within 5 meV per atom for all systems studied, providing reliable results for structural\nrelaxation and binding energy calculations.\nWe have added convergence details in the revised Supplementary Information (Section VI.2) to\nensure greater transparency and completeness.\nConfirm that the final spin moments are negligible, especially for S–C–Pd/Au interfaces where\nslight spin polarisation may emerge.\nReply:\nWe thank this reviewer’s important suggestion. Spin-polarized calculations were performed to\ncheck for possible magnetic contributions, especially at the S–C–Pd/Au interfaces. The final spin\nmoments were found to be negligible (<0.01 μB per atom), indicating that any spin polarization\nhas minimal impact on the calculated properties.\nWe have added this clarification to the Supplementary Information (Section VI.1) to clarify and\nstrengthen the theoretical basis for strain-enhanced interfacial charge transport.\nSpecify the smearing method and width used for DOS plots (e.g., Gaussian or Methfessel–Paxton).\nReply:\nWe appreciate the reviewer’s insightful comment on hybrid approaches and the suggestion to\nconsider photoacoustic sensors. The study used VASP to perform density functional theory\ncalculations with projector augmented wave4, 5. The electron spin-polarization was included in all\ncalculations. The Perdew-Burke-Ernzerhof functional was employed for exchange-correlation\neffects6, while DFT+D3 was used for handling weak interactions7. The cut-off energy for the\nplane-wave basis was 450 eV. K-points were 2×2×1 in the Brillouin zone. 15 Å of layer vacuum\nwas applied at Z-axis of slab models to avoid the Periodic effect. Energy and maximum stress were\nconverged to 10-5 eV and 0.02 eV/Å, respectively. The electronic density of states (DOS) was\ncalculated employing the Gaussian smearing technique with a smearing width of 0.05 eV.\nWe have added this clarification to the Supplementary Information (Section VI.1) to clarify and\nstrengthen the theoretical basis for strain-enhanced interfacial charge transport.\nA nudged-elastic-band (NEB) calculation for hydrogen diffusion across the interface would enrich\nthe mechanistic understanding, though this is not essential for publication.\nReply:\nThank you for the reviewer’s suggestion. In the present study, the first-principles calculations\nprimarily focus on the mechanical properties and adsorption behavior of the system, rather than\nreaction pathways or reaction intermediates. Therefore, we consider the current computational\napproach to be reasonable and sufficient for the objectives of this work. We note, however, that\nperforming nudged-elastic-band (NEB) calculations to investigate hydrogen diffusion across the\ninterface could provide additional mechanistic insight and may be considered in future studies\nResponses to Reviewer #2’s Comments\nComments of Reviewer #2:\nThe manuscript presents an interesting strategy to decouple interfacial stress in Pd-based H2\nsensors by inserting a dithiol self-assembled monolayer between the Pd sensing film and the Au\nelectrode. The effect of dithiol-SAM is investigated by both experimental and theoretical results.\nWafer-scale fabrication and system-level integration are also demonstrated. These results are\nimportant and will be of broad interest to the chemical-sensor community. Nevertheless, several\ncritical issues need to be resolved before the manuscript can be considered for publication.\nReply:\nFirst of all, we are grateful to the reviewer for the constructive feedback and for highlighting both\nthe strengths and areas requiring improvement in our work. The reviewer’s comments are highly\nvaluable for enhancing the quality of our manuscript. We have carefully considered each point\nraised and have conducted thorough revisions accordingly. In the following, we provide detailed\nresponses to all comments and describe the corresponding modifications made to the manuscript.\n1. It is well known that Pd forms α-phase PdH upon exposure to low concentration H (<~1%).\nx 2\nFor α-phase hydride, the hydrogen-to-palladium atomic ratio x (or n in the manuscript) is less than\n0.02 and the expansion of Pd’s lattice parameter is less than 0.13%. Significant lattice expansion\nonly appears during the α to β phase transition (~1%-5% H2). In this phase transition, x increases\nabruptly to ~0.7 with the lattice expansion increasing to ~3.5%.\nIn this work, it is noticed that the highest H concentration used is only 1000 ppm (~0.1 %), i.e.,\n2\nonly α-phase PdH can be formed. Therefore, will the mechanical clamping from the substrate be\nx\nsignificant? Similarly, will the instability induced by Pd expansion and contraction be that\nsignificant? In Figure 3i, what is the saturated value of the hydrogen-to-palladium atomic ratio for\nPd with and without SAM?\nIf the lattice expansion is tiny, the present experimental results will not be able to support the\nconclusion that SAMs mitigate interfacial stress and suppress substrate clamping effects. Cyclic\nand long-term stability tested under high H concentration (4 vol% H , for example) would be\n2 2\nmore convincing.\nReply:\nWe sincerely thank the reviewer for the insightful and important comments. We would like to\naddress the questions raised regarding the extent of lattice expansion at low hydrogen\nconcentrations and the associated mechanical effects under α-phase PdHx formation.\n Mechanical clamping under low concentration of H :\nx 2\nthe lattice expansion in this regime is typically minimal (~0.13% for x < 0.02). However, we\nrespectfully point out that even this small expansion can result in non-negligible mechanical stress\naccumulation, especially in thin film systems mechanically clamped to rigid substrates.\nWagner and Pundt8 developed a quasi-thermodynamic model that explicitly accounts for the\nimpact of substrate-induced elastic stress on Pd–H thin films. Their results show that even in the\nα-phase, where the volumetric expansion is small (<0.13%), the substrate constraint contributes\n2–5 kJ/mol to the hydrogen chemical potential, thereby significantly modifying the solubility and\nH\nphase stability. This provides strong theoretical support that substrate clamping effects can indeed\nbe relevant under our experimental conditions, and that the SAM interlayer plays a critical role in\nmitigating such stress effects. Furthermore, Kim et al9 have demonstrated that mechanical\nclamping effects significantly alter hydrogenation thermodynamics even in the α-phase regime,\nespecially for thin films with constrained geometries. Their capacitive-based measurements\nshowed that hydrogen-induced expansion of Pd can be nearly fully suppressed (on the order of\n0.01 vol%) under rigid substrate clamping, leading to non-negligible mechanical energy storage\nand plastic deformation even before the α→β transition.\nIn our study, although the H concentration remains in the α-phase region (≤1000 ppm), we\n2\nobserve a clear suppression of the substrate constraint and a marked enhancement in hydrogen\nabsorption kinetics upon SAM integration (Figure 3i, 3j). These observations support the\nconclusion that interfacial stress and substrate clamping effects are already relevant even at low\nhydrogen concentrations.\n Significance of interfacial stress at small expansion:\nAlthough the absolute lattice expansion in the α-phase is small, the interfacial stress induced by\nrepeated cyclic expansion and contraction in confined thin-film geometries can lead to\nmicrostructural degradation, plastic deformation, and interface delamination due to mechanical\nconstraint from the substrate. In such confined geometries, the inability of Pd to freely expand\nleads to residual stress accumulation, which becomes significant over time. This is further\namplified in multilayer systems and vertical architectures like ours, where out-of-plane mechanical\nmismatch plays a larger role. In our experiments, our cyclic stability tests (Fig. 4d) demonstrate\nthat performance degradation occurs even at 1000 ppm H in SAM-free devices-strongly\n2\nsuggesting that stress accumulation from repeated α-phase expansion/contraction cycles is non-\nnegligible. The SAM interlayer effectively buffers this stress, reducing interfacial failure and\npreserving device performance. Therefore, although the lattice expansion per cycle is small, the\naccumulated mechanical effects over many cycles are significant and must be addressed—\nparticularly for real-world applications that require long-term operational stability.\n Saturated H/Pd ratio with and without SAM (Response to Fig. 3i)\nAccording to Figure 3i and electrical resistivity (ρ) difference between Pd and PdH (α-phase),\nx\nthe saturated hydrogen-to-palladium atomic ratio for SAM-integrated device is ~0.0152 and\n~0.0018 for SAM-free sensor device. This about 12-times increase in hydrogen absorption cannot\nbe explained solely by electronic effects or surface chemistry, as the Pd film morphology is\notherwise identical. Rather, this enhancement is consistent with a stress-buffering mechanism,\nwhere the SAM interlayer partially decouples the Pd film from the substrate, thereby relieving\nmechanical constraint and enabling more complete hydrogen absorption.\n Cyclic and long-term stability tested under high H concentration\n2\nregarding stress-induced degradation. Thus here, we conducted additional experiments to evaluate\nthe sensor performance of floating-structured Pd sensor device embedded with and without C10\nSAM layer to 1 vol% and 4 vol% H at room temperature, and the results are summarized as shown\n2\nas follows.\nFrom Figure R2a, it is seen that the sensors embedded with C10 SAM layers exhibit stable and\nrepeatable sensing behavior at both 1 vol% and 4 vol% H concentrations. And as expected, the\n2\nresponse and recovery times increase with higher H concentration (Figure R2d), which can be\n2\nattributed to enhanced lattice expansion and slower desorption kinetics at elevated hydrogen\nloading. Meanwhile, the response curve shows minor signal drift under 4 vol% H . This may due\n2\nto greater PdH -induced volume expansion and prolonged hydrogen retention. However, the\nx\ndevice remains fully operational, with no signs of mechanical or functional degradation. In contrast,\ndevices without SAM layers show significantly unstable dynamic responses under high H\n2\nconcentrations (Figure R2b and R2c). Particularly at 4 vol% H , the sensor signal continuously\n2\nincreases during hydrogen exposure and fails to recover upon H removal, indicating structural\n2\ndegradation or delamination at the Pd–Au interface. This behavior strongly suggests that, in the\nFigure R2. Sensing performance of the floating-structured Pd sensor to 1 vol% and 4 vol% H . (a) and\n2\n(b) Dynamic response and recovery profiles of floating-structured sensor device embedded with and without\nC10 SAM layer to 1 vol% and 4 vol% H at room temperature. (c) and (d) Average response and recovery\n2\ntime extracted from (a) and (b).\nabsence of a compliant SAM layer, interfacial stress accumulates due to lattice expansion, leading\nto mechanical failure from clamping effects and loss of contact at the Pd–electrode interface.\nTo further validate the stress-mitigating role of SAMs, we performed 50 consecutive fast H\n2\nresponse cycles at both 1 vol% and 4 vol% H (Figures R3). The SAM-integrated sensors\n2\nmaintained consistent and recoverable response signals throughout all cycles, whereas the non-\nSAM-integrated devices exhibited progressive signal fluctuation and permanent failure within just\na few cycles—especially under 4 vol% H , where some devices failed during the first cycle. These\n2\nresults provide compelling experimental evidence that embedding a SAM layer not only enhances\nlong-term operational stability but also effectively mitigates interfacial stress and suppresses\nsubstrate clamping effects, particularly under conditions where α-to-β phase transition and\nsignificant lattice expansion of PdH occur. The SAM acts as a mechanical buffer, maintaining\nx\nstructural integrity at the Pd–substrate interface and ensuring reliable hydrogen sensing\nperformance under practical and demanding conditions.\nFigure R3. Experimental durability evaluation via 50 consecutive responses–recovery cycles of planar Pd–\nAu and floating-structured Pd–SAM–Au sensors exposed to (a)1 vol% and (b) 4 vol% H .\nPd sensor under high hydrogen concentration. As shown in Figure R4, the sensor exhibited no\nnoticeable degradation in performance during a continuous testing period of over three months,\nmaintaining consistent sensitivity and dynamic response characteristics. These results clearly\ndemonstrate that the embedded SAM layer not only mitigates interfacial stress but also\nsignificantly enhances the operational lifetime of the device. We believe such floating-structure\ndesign offers substantial advantages for the commercial viability of Pd-based hydrogen sensors,\nparticularly for applications requiring long-term reliability under real-world conditions. Due to\ninstitutional safety regulations related to the storage and handling of high-concentration hydrogen\ngases (especially above 4 vol%), the long-term tests were conducted using 1 vol% H , which is\n2\nalso within the operational range relevant for safety monitoring and early leak detection. However,\nbased on the consistent results observed in our short-term high-concentration cycling tests (1 vol%\nand 4 vol% H ), we anticipate that the SAM-integrated device would similarly retain long-term\n2\nstability at 4 vol% H , as the structural design effectively accommodates the associated PdH\n2 x\nlattice expansion and interfacial stress. These findings further support the claim that the SAM-\nbuffered architecture is critical for achieving robust, long-life hydrogen sensing performance,\nespecially under mechanically challenging and high-loading conditions.\nFigure R3. Long-term operational stability under continuous (a) 1000ppm and (b) 1 vol% H sensing.\n2\nconcentration in the revised main manuscript (Figure 4e, Figure 5f) and Supplementary\nInformation (Supplementary Fig. 13, Fig. 14 and Fig. 17) to enhance the transparency and\ncompleteness of our analysis.\n2. For a Pd film, when it absorbs H2 and forms PdHx, its resistance will increase as a result of the\nscattering effect of H atoms. The higher of surrounding hydrogen concentration, the higher of the\nresistance. It is reported that the maximum resistance increase is ~0.7 times when Pd fully forms\nβ-phase PdHx, corresponding to a response value of 0.7. I am wondering how a response value of\n0.8 can be obtained when Pd-SAM-Au sensor is exposed to 0.1% H2. Is there any explanation for\nthis result?\nReply:\nWe sincerely thank the reviewer for raising such important question. Indeed, as reported in the\nliterature, pure Pd films under room-temperature hydrogenation typically show a maximum\nresistance increase of about 0.7 times10-12. In our work, however, the Pd-SAM-Au sensor exhibits\na resistance change of 0.8% (not 0.8 times) when exposed to 1000 ppm (0.1 vol%) H at room\n2\ntemperature. And this value is within a reasonable range, as supported by relevant literature11.\nImportantly, by comparing with prior studies, we found that the response of our Pd-SAM-Au\ndevice at room temperature is among the best reported to date, which further highlights the\nadvantage of the proposed interfacial engineering strategy.\n3. The supporting information, line 251, could you please further explain equation 4?\nReply:\nWe sincerely thank the reviewer for this detailed question. We apologize for the confusion caused\nby the brevity of the original description, where some intermediate steps of the derivation were\nomitted. To make the modeling more rigorous and transparent, and to help readers clearly follow\nour assumptions and reasoning, we have revised the Supporting Information to include a more\ndetailed derivation of eq. (4). The added explanation is as follows:\n“To understanding the influence of the SAM interlayer on hydrogen absorption kinetics during gas\nsensing, we model the correlation between the real-time hydrogen-to-palladium ratio, n(t), in bulk\nPd and the sensor sensitivity. The equivalent circuit representing the hydrogen sensing mechanism\nin the SAM-integrated H sensor is illustrated in Fig. 18. As hydrogen uptake increases, portions\n2\nof pure Pd are converted to PdH , with the corresponding resistance, R (t), directly related to\nx PdHx\nn(t). Consequently, the electrical resistance of the sensor before (R ) and after (R (t)) hydrogen\nexposure can be expressed as follows:\nL\nR  R R  R (1)\nS\nL (t) L (t)\nR (t) R (t)R (t)R  PdHx  Pd R (2)\nH PdHx Pd SAMH PdHx Pd SAMH\nS S\nL L (t)L (t) (3)\nPdHx Pd\nHere, L and S denote the thickness and area of the Pd sensing film, respectively. R and R\nSAM SAM-H\nrepresent the resistance of the Pd–SAM–Au interlayer before and after H absorption. L (t) and\nL (t) represent the instantaneous thickness of hydride and unhydrogenated Pd layer within the Pd\nPd\nsensing film, respectively. layer during Owing to the excellent electrical conductivity of the Pd–\nSAM–Au interlayer, which remains stable even under strain, the resistance variation between R\nSAM\nand R is negligible compared to that of the Pd sensing film. Thus, R ≈ R can be\nSAM-H SAM SAM-H\nassumed. Then the correlation between L (t) and the time-dependent overall H/Pd ratio, n(t), is\nPdHx\nestablished through mass conservation within a one-dimensional two-phase slab model comprising\nPd and Pd hydride. In the initial state, prior to H exposure, the total number of Pd atoms (N ) in\nthe sensing film is defined as:\nN c SL (4)\nPd Pd\nHere, c denotes the atom density of Pd. Upon exposure of the Pd sensing film to H , a Pd hydride\nPd 2\nlayer progressively forms from the surface toward the bulk. The number of Pd atoms within this\nhydride layer can be expressed as:\nNHydride(t)c SL (t) (5)\nPd PdHx\nPd\nAccording to the definition of n(t), the Pd atom number within Pd hydride layer can alternatively\nbe written as:\nNHydride(t) N n(t) (6)\nPd\nPd\nBy combing with eq. (4), eq. (5) and eq. (6), the thickness of the resulting Pd hydride layer, L ,\nPdHx\ncan be directly related to the time-dependent H/Pd ratio, n(t), as:\nL n(t)L (7)\nPdHx\n…”\n4. It is noticed that the sensing performance test was performed with N2 as carrier gas. However,\na hydrogen sensor is more likely to be used in air (with the presence of O2) in practical applications.\nIs there any performance difference in these two conditions?\nReply:\nWe thank the reviewer for this insightful comment regarding the relevance of testing hydrogen\nsensor performance under practical air environments. In response, we conducted additional\ncomparative experiments to evaluate the sensing characteristics of the SAM-integrated sensor to 1\nvol% H under both high-purity N and ambient air conditions (RH ~16%, 25oC). As shown in\n2 2\nFigure R4, a notable decrease of nearly 50% in sensitivity (ΔR/R\n0\n) was observed when switching\nthe carrier gas from N to ambient air. This reduction is attributed to the competitive adsorption of\n2 2\ndissociative adsorption of H and its subsequent diffusion into the Pd lattice. This is further\n2\nsupported by molecular adsorption simulations on the Pd(111) surface (Figure R6), which indicate\nthat both O and H O exhibit favorable adsorption energies that allow them to interfere with\n2 2\nhydrogen uptake. Despite this reduction in sensitivity, I–V measurements (Figure R4c) show that\nthe baseline resistance (R ) of the Pd sensing film increases only slightly under air conditions. This\n0\nsuggests that O , H O and other ambient molecules undergo primarily undergo weak physisorption\n2 2\non the Pd surface, without significantly altering its electronic structure or bulk conductivity. Thus,\nwhile the background molecules influence adsorption dynamics, they do not significantly alter the\nelectronic structure or baseline conductivity of the sensing layer.\nImportantly, we also observed that the sensor exhibits faster response and recovery times in air\ncompared to N (Figure R4e). Regarding the response process, the reduced flux of H to the Pd\n2 2\nsurface under competitive adsorption conditions may accelerate adsorption–desorption kinetics\ndue to lower hydrogen loading13. Furthermore, the presence of O facilitates surface reactions with\n2\ndissociated hydrogen atoms (e.g., formation of H O), which in turn promotes faster hydrogen\n2\ndesorption and recovery14. Taken together, these findings indicate that although the presence of\nambient gases slightly reduces the sensitivity, they enhance the sensor’s dynamic response\ncharacteristics, and most importantly, the sensor remains fully functional and stable in ambient air\nFigure R4. Comparison of carrier gas effects (high-purity N versus dry air) on the H sensing\n2 2\nperformance of the floating-structured H sensor embedded with embedded C10 SAM layer to 1 vol%\n2\nconditions. This demonstrates the practical viability of the proposed SAM-integrated Pd sensor for\nreal-world hydrogen sensing applications.\nWe have added the comparison results in the revised Supplementary Information (Section V,\nSupplementary Fig. 15) to enhance the transparency and completeness of our analysis.\n5. As a room-temperature gas sensor, the influence of relative humidity should be investigated.\nReply:\nWe thank the reviewer for highlighting the importance of relative humidity (RH) in evaluating\nroom-temperature gas sensor performance. In response to this valuable comment, we conducted a\nseries of additional experiments to investigate the influence of ambient humidity on the sensing\ncharacteristics of the SAM-integrated floating Pd sensor.\nSpecifically, we measured the H (1 vol%) response of the proposed sensor device under\n2\ncontrolled RH level of 16%, 31%, 56%, 68%, and 86% via MFC gas distribution system, as shown\nin Figure R5a. At low to moderate humidity levels (16% to 31%), it is observed that a slight\ndecrease in H sensitivity (ΔR/R ) (Figure R5b) and a modest slowdown in the response and\n2 0\nrecovery times (Figure R5c). However, at higher RH levels (above 31%), the sensing response\nremained relatively stable, with no significant further degradation in either sensitivity or\nresponse/recovery time. These results suggest that the sensor reaches a saturation regime in water\nmolecule adsorption beyond a certain RH threshold, and that the floating Pd architecture\neffectively mitigates humidity interference. Moreover, humidity-dependent variations in the\nbaseline resistance (R ) were investigated through I–V measurements under different RH\n0\nconditions (Figure R5d and R5e). A slight increase in R was observed with increasing\n0\nenvironmental humidity, suggesting that H O molecules interact weakly with the Pd surface, likely\n2\nthrough physisorption rather than chemisorption.\nTo further understand the underlying mechanism of humidity-induced sensing degradation, we\ncarried out DFT calculations to evaluate the adsorption energies of H , H O, and other potential\n2 2\ninterfering gases on the Pd(111) surface. As shown in Figure R6, the H O molecules tend to adsorb\n2\non Pd surface, but their adsorption energy is significantly lower than that of H , indicating that\n2\nhydrogen bond15. The competitive adsorption of H O occupies active sites on the Pd surface,\n2\nthereby hindering the dissociative adsorption and subsequent absorption kinetics of hydrogen into\nthe Pd lattice.\nOverall, these findings confirm that the floating-structured H sensor device exhibits excellent\n2\nhumidity tolerance, with only minor performance variation across a wide RH range. The data\nconfirm that the proposed sensor maintains reliable operation under realistic environmental\nconditions, including high-humidity environments.\nWe have added the humidity-dependent H sensing performance in the revised main manuscript\n2\n(Figure 5c and 5d) and Supplementary Information (Section V, Supplementary Information Fig.\n16 and Section VI, Fig. 25) to enhance the transparency and completeness of our analysis.\n6. Are disulfides stable enough in practical applications?\nReply:\nWe thank the reviewer for raising this important point. While isolated disulfides may exhibit\nlimited stability, in the context of self-assembled monolayers on Au, the disulfide group serves as\na precursor that dissociates into two thiol groups, each binding strongly to Au through robust Au–\nS bonds. This results in a chemically stable and densely packed SAM. The stability of such\ndisulfide-derived SAMs has been demonstrated in numerous prior studies on molecular electronics,\nelectrochemistry, and biosensors2, 16. Consistent with these reports, our Pd–SAM–Au sensors show\nexcellent cycling durability, with stable response to repeated H exposure and no observable\n2\ninterfacial degradation. These results indicate that the disulfide-derived SAMs are sufficiently\nstable for practical sensor applications.\n7. What if 1,10-decanedithiol is replaced by dithiol with a longer chain length? Will the\nperformance be enhanced or weakened?\nReply:\nWe sincerely thank the reviewer for this insightful question regarding the influence of dithiol chain\nlength on sensor performance. As correctly pointed out, the length of the alkanedithiol molecule\ncritically affects both mechanical and electronic properties at the Pd–SAM–Au interface.\nSpecifically, increasing the chain length of the dithiol spacer modulates two competing effects: (1)\nMechanical decoupling: Longer alkyl chains possess greater flexibility and can better\naccommodate strain arising from PdHx lattice expansion, potentially enhancing the mechanical\nbuffering effect and suppressing interfacial stress propagation. (2) Electronic transport: However,\nlonger chains also increase the tunneling barrier for charge carriers across the SAM, resulting in\nreduced electronic coupling and higher interfacial resistance. Prior studies on alkanedithiol\nSAMshave shown that charge tunneling conductance decays exponentially with chain length,\ntypically decreasing by 1–2 orders of magnitude for every additional 2–3 methylene units (–\nCH –)17, 18. Therefore, excessive chain elongation would likely impair electrical performance.\nmolecule) through Sigma-Aldrich to experimentally validate this hypothesis. However, we were\ninformed that this compound is currently out of stock, with an estimated lead time of more than\nsix months. We will continue to explore this direction as part of our future work, and we appreciate\nthe reviewer’s suggestion as a valuable contribution to our ongoing optimization efforts.\n8. Conclusions should be based on experimental results. Lifespan exceeding 10 years is overstated.\nReply:\nWe sincerely thank the reviewer for this important comment regarding the sensor lifespan. In\nresponse, we have corrected the corresponding statement. Instead, we now report the actual long-\nterm data obtained under controlled conditions: under 1000 ppm H (Figure R3a), the SAM-\n2\nintegrated floating Pd sensor showed stable operation for over 12 months, with no observable\nperformance degradation, as evidenced by consistent sensing response and baseline resistance. To\nfurther validate the stability at higher hydrogen concentrations, we conducted a three-month\ncontinuous test under 1 vol% H (Figure R3b). The results show that the baseline resistance\n2\nremained consistently around 3.2 Ω (1000 ppm H ) and 3.8 Ω (1 vol% H ), without signs of\n2 2\nirreversible increase (as seen in Pd film degradation) or decrease (indicative of potential short-\ncircuiting). The sensor response also remained highly stable, with no significant sensitivity decay\nthroughout the test period.\nThese experimentally validated results have now replaced the previous extrapolated lifetime\nestimation in the revised manuscript (Figure 5f and Supplementary Information Fig. 17). We\nbelieve this updated description more accurately reflects the current measured stability and\nprovides a solid experimental basis for evaluating device longevity.\nFigure R3. Long-term operational stability under continuous (a) 1000ppm and (b) 1 vol% H sensing.\n2\n9. Line 190, please check the interfacial layer thickness. Is 2 Å correct or not?\nPlease also check the binding energy of -SH and -S-metal in line 200 to 205.\nLine 142, fig. 1e should be 1f? Line 405, (c) should be (d)?\nReply:\nWe sincerely thank the reviewer for the careful reading and for pointing out these important\nerrors and inconsistencies, and we have corrected them in response.\nLine 190, interfacial layer thickness 2 Å has been corrected as 2 nm.\nLine 200 to 205, the binding energy of -SH and -S-metal have been corrected based on the fitting\ndata in Figure 2h. “… The XPS analysis reveals distinct sulfur–metal binding peaks for both Pd\n(S–Pd: 2p = 164.0 eV, 2p = 162.7 eV)31, 32 and Au (S–Au: 2p = 163.1 eV, 2p = 162.0\n3/2 1/2 3/2 1/2\neV)33, 34, confirming the chemisorption of thiol groups. Additionally, another set of sulfur\nsatellite peaks which attributed to unbound –SH termini is observed in both the SAM-Pd\n(164.8eV and 162.7eV)35 and SAM-Au (164.7eV and 162.7eV)34 spectra, which…”\nLine 142, Fig. 1e has been corrected as Fig. 1f.\nLine 405, (c) has been corrected as (f).\nResponses to Reviewer #3’s Comments\nComments of Reviewer #3:\nThe author presented a floating-structure palladium hydrogen sensor enabled by interfacial stress\ndecoupling through a dithiol-based self-assembled monolayer. Although this study has made some\nprogress in the relevant field, it lacks sufficient novelty to meet the high standards of Nature\nCommunications. We recommend submitting to another journal. Additional comments are\nprovided below.\nReply:\nWe thank the reviewer #3 for providing such helpful comments and suggestions to improve this\nmanuscript. In this revision, all the concerns have been fully addressed. The point-by-point\nresponses as follows:\n1) Please summarize some novelties of the structure and the sensing performance for this floating-\nstructure palladium hydrogen sensor compared to commercial sensors with long lifespan on the\nmarket.\nReply:\nWe sincerely thank the reviewer for the critical evaluation and the opportunity to clarify the\nnovelty and significance of our work.\n Novelty on the Structural Design\nThe core innovation of this work lies in the rational interfacial engineering strategy\nenabled by a self-assembled monolayer (SAM)-mediated floating architecture in the Pd-\nbased hydrogen sensor. Our design diverges from conventional hydrogen sensors by introducing\na molecular decoupling layer, a 1,10-decanedithiol SAM, between the sensitive Pd film and the\nsubstrate. This approach addresses two critical issues: mechanical stress and interfacial instability.\nDuring hydrogen absorption, the flexible SAM buffers the lattice expansion of Pd, preventing the\ninterfacial delamination common in rigid heterostructures and thereby improving durability.\nAdditionally, the thiol-based SAM forms covalent S–metal bonds with both Pd and Au,\ncreating a chemically stable and cohesive interface. This dual bonding mechanism provides\nsuperior chemical durability compared to physically adhered or sputtered interfaces in\nstandard sensors. Such design enables the hydrogen sensor enhanced performance and durability\nwithout the need for external encapsulation, nanostructuring, or complex microfabrication.\nThe strategy proposed in this work is highly scalable. The approach of inserting a chemically\ntailored molecular buffer layer between two functional layers can be broadly applied to other gas\nsensors, particularly those where gas–solid interactions induce mechanical or electronic strain at\nthe interface. Moreover, the conceptual framework of molecular-level stress modulation and\ncharge transport tuning has far-reaching implications in the design of other heterointerface-based\nmolecular devices, including but not limited to: (1) Organic photovoltaics (OPVs), where\ninterfacial dipole alignment and mechanical strain affect charge separation; (2) Molecular switches\nor junctions, where electronic coupling across interfaces is critical; (3) Flexible electronics and\nstrain sensors, where interfacial fatigue limits device lifetime. We believe this work serves not\nonly as a proof-of-concept for H sensing, but also as a versatile platform for interface design in\n2\nfunctional thin-film systems.\n Comparison with Commercial H Sensors\n2\nelectrochemical types) operate at elevated temperatures, involve bulky packaging, and lack\nsensitivity in the ppm range. In contrast, our SAM-engineered sensor achieves: (1) Ultrasensitive\ndetection down to 1 ppm H at room temperature; (2) Excellent cycling stability even under 4 vol%\n2\n1000 ppm and 3 months at 1 vol% H ) enabled by stress-decoupled design; (4) Platform\n2\ncompatibility with flexible integration into portable detection systems, with successful comparison\nagainst a commercial Honeywell detector. Such performance is achieved through interfacial design,\nrather than complex fabrication, and suggests clear advantages in miniaturization, power efficiency,\nand portable deployment.\n2) Because H2 is prone to explosion when its concentration exceeds 4% in the air, it is necessary\nto provide the sensor's response to higher concentration of H2 gas. That is, how much\nconcentration of H2 can the sensor accurately detect?\nReply:\nWe thank the reviewer for raising this important point regarding the sensor’s performance at higher\nhydrogen concentrations. Indeed, the ability to detect hydrogen concentrations approaching or\nexceeding the lower explosive limit (LEL, ~4%) is essential for safety monitoring applications. To\naddress this, we have conducted additional experiments measuring the response of the SAM-\nintegrated sensor to 1 vol% and 4 vol% H in air. As shown in Figure R5, the sensor exhibits a\n2\nrobust and reproducible response at both concentrations, with a clear signal increase from 1 vol%\nFigure R5. Sensing performance of the floating-structured Pd sensor to 1 vol% and 4 vol% H . (a) and\n2\n(b) Dynamic response and recovery profiles of floating-structured sensor device embedded with and without\nC10 SAM layer to 1 vol% and 4 vol% H at room temperature. (c) and (d) Average response and recovery\n2\ntime extracted from (a) and (b).\nto 4 vol% H . No signal saturation was observed up to 4 vol%, and the response remained stable\n2\nover multiple cycles, indicating reliable detection at these levels. These results confirm that the\nproposed sensor is capable of accurately detecting hydrogen concentrations at and beyond the\nexplosive threshold, while also maintaining its high sensitivity at sub-ppm levels. This broad\ndetection range, from 1 ppm to at least 4 vol% H , demonstrates the practical applicability of our\n2\ndevice for both early-stage leak detection and explosive-level hazard monitoring.\nWe have added the high concentration H sensing performance in the revised main manuscript\n2\n(Figure 5a and 5b) and Supplementary Information (Section V, Supplementary Fig. 14) to enhance\nthe transparency and completeness of our analysis.\n3) The latest H sensing performance standards released by the U.S. Department of Energy requires\n2\nresponse time and recovery time of less than 60 seconds at 1% concentration of H2 gas. What is\nthe sensor performance when 1% concentration of H2 gas is detected?\nReply:\nWe thank the reviewer for highlighting the DOE performance standards for hydrogen sensors. The\nsensing performance of the floating sensor device integrated with SAMs was evaluated at 1 vol%\nH in air background, as shown in Figure R7. Based on the standard definitions of gas sensor\n2\nresponse and recovery times, the device exhibited an average response time of 91.0s and a recovery\ntime of 49.0s, as presented in Figure R7c. While the recovery time falls in the DOE’s target of 60s,\nwe acknowledge that the response time exceeds 50% of the specified threshold. Nevertheless, we\nwould like to respectfully point out that the current sensor design is optimized primarily for\nultrasensitive detection and long-term operational stability at low hydrogen concentrations (1–\n1000 ppm), a regime that is critical for early-stage leak detection and pre-explosive safety\nmonitoring. In this context, our sensor achieves a detection limit as low as 1 ppm and exhibits\nexcellent cycling stability with minimal performance degradation over repeated use.\nFigure R7. Sensing performance of the floating-structured H sensor embedded with embedded C10\n2 2\nroom temperature. (b) Typical sensing performance curve of the sensor to 1 vol% H extracted from (a).\n2\n(c) Average response and recovery time extracted from (a).\nOverall, we believe that the current device demonstrates strong potential for practical hydrogen\nsafety applications, especially in scenarios where ppm-level sensitivity, reliability, and durability\nare prioritized. Future design modifications are expected to further enhance response dynamics at\nhigher H concentrations, aligning more closely with DOE performance targets.\n2\n4) How does the sensor respond to other interfering gases such as H2S or NO2 gas?\nReply:\nWe thank the reviewer for raising this important question regarding the selectivity of the proposed\nhydrogen sensor. In response, we conducted additional experiments to evaluate the sensor’s\nperformance against potential interfering gases, specifically 1000 ppm NO and 1000 ppm H S,\n2 2\nunder ambient conditions at room temperature. The results show that the Pd–SAM–Au suspended\nstructure exhibits negligible responses to both NO and H S gases (as shown in Figure R8). These\n2 2\nfindings indicate that the sensor possesses excellent selectivity toward H , which was attribute to\n2\nthe specific dissociative adsorption and absorption behavior of hydrogen on the Pd surface. The\npresence of the SAM layer further stabilizes the interface and reduces non-specific interactions.\nWe have included these results and their discussion in the revised main manuscript (Figure 5e) to\nfurther support the practical applicability of the sensor in complex environments.\nFigure R8. Sensing selectivity test of the floating-structured H sensor embedded with embedded C10\n2 2 2\n(b) Selectivity evaluation under exposure to interfering analytes.\n5) Please evaluate the influence of different relative humidity on baseline resistances and response\nvalues. To discuss it, the adsorption energy of materials for H2, H2O and O2, and other interfering\ngases should be calculated and compared.\nReply:\nWe thank the reviewer for highlighting the importance of relative humidity (RH) in evaluating\nroom-temperature gas sensor performance. In response to this valuable comment, we conducted a\nseries of additional experiments to investigate the influence of ambient humidity on the sensing\ncharacteristics of the SAM-integrated floating Pd sensor.\nSpecifically, we measured the H (1 vol%) response of the proposed sensor device under\n2\ncontrolled RH level of 16%, 31%, 56%, 68%, and 86% via MFC gas distribution system, as shown\nin Figure R5a. At low to moderate humidity levels (16% to 31%), it is observed that a slight\ndecrease in H sensitivity (ΔR/R ) (Figure R5b) and a modest slowdown in the response and\n2 0\nrecovery times (Figure R5c). However, at higher RH levels (above 31%), the sensing response\nremained relatively stable, with no significant further degradation in either sensitivity or\nresponse/recovery time. These results suggest that the sensor reaches a saturation regime in water\nmolecule adsorption beyond a certain RH threshold, and that the floating Pd architecture\neffectively mitigates humidity interference. Moreover, humidity-dependent variations in the\nbaseline resistance (R ) were investigated through I–V measurements under different RH\n0\nconditions (Figure R5d and R5e). A slight increase in R was observed with increasing\n0\nenvironmental humidity, suggesting that H O molecules interact weakly with the Pd surface, likely\n2\nthrough physisorption rather than chemisorption.\nTo further understand the underlying mechanism of humidity-induced sensing degradation, we\ncarried out DFT calculations to evaluate the adsorption energies of H , H O, and other potential\n2 2\ninterfering gases on the Pd(111) surface. As shown in Figure R6, the H O molecules tend to adsorb\n2\non Pd surface, but their adsorption energy is significantly lower than that of H , indicating that\n2\nhydrogen bond19, 20. The competitive adsorption of H O occupies active sites on the Pd surface,\n2\nthereby hindering the dissociative adsorption and subsequent absorption kinetics of hydrogen into\nthe Pd lattice.\nOverall, these findings confirm that the floating-structured H sensor device exhibits excellent\n2\nhumidity tolerance, with only minor performance variation across a wide RH range. The data\nconfirm that the proposed sensor maintains reliable operation under realistic environmental\nconditions, including high-humidity environments.\nFigure R5. Effect of humidity on the sensing performance of the floating-structured H sensor\n2\nembedded with embedded C10 SAM layer to 1 vol% H . (a) Dynamic response and recovery profiles to\n2\n1 vol% H at different humidity environment, room temperature. (b) and (c) humidity-dependent H\n2 2\nsensitivity and response/recovery time extracted from (a). (d) Humidity-dependent I-V curve of floating-\nstructured sensor device. (e) Humidity-dependent baseline resistances extracted from (d).\nWe have added the humidity-dependent H sensing performance in the revised main manuscript\n2\n(Figure 5c and 5d) and Supplementary Information (Section V, Fig. 16 and Section VI, Fig. 25) to\nenhance the transparency and completeness of our analysis.\nFigure R6. Adsorption energies of various molecules on the Pd(111) surface calculated via DFT.\n6) The author speculates on the lifespan of the sensor for ten years based on one year of stability\ntesting results, which has no scientific basis. More importantly, the XPS spectrum in Figure 2h\nshows thiol groups only partially coordinate with noble metals, and thiol groups without\ncoordination are not very stable in air and cannot remain stable for ten years. It is recommended\nto deeply analyze the stability of the baseline resistance as well as the sensor response.\nReply:\nWe sincerely thank the reviewer for this important comment regarding the sensor lifespan. In\nresponse, we have corrected the corresponding statement. Instead, we now report the actual long-\nterm data obtained under controlled conditions: under 1000 ppm H (Figure R3a), the SAM-\n2\nintegrated floating Pd sensor showed stable operation for over 12 months, with no observable\nperformance degradation, as evidenced by consistent sensing response and baseline resistance. To\nfurther validate the stability at higher hydrogen concentrations, we conducted a three-month\ncontinuous test under 1 vol% H (Figure R3b). The results show that the baseline resistance\n2\nremained consistently around 3.2 Ω (1000 ppm H ) and 3.8 Ω (1 vol% H ), without signs of\n2 2\nirreversible increase (as seen in Pd film degradation) or decrease (indicative of potential short-\ncircuiting). The sensor response also remained highly stable, with no significant sensitivity decay\nthroughout the test period.\nRegarding the XPS, Figure 2h shows partial coordination of thiol groups, which was ascribed\nto the limitations of XPS spectroscopy. As XPS is surface-sensitive and just can penetrate several\nnanometers deep into the Pd layer, leading to the S–metal coordination buried under the ~ 80 nm\nPd layer cannot be detected. To better verify the coordination of thiol molecules, we prepared two\nreference samples by growing 1,10-decanedithiol SAMs on pure Au and pure Pd films,\nrespectively. The XPS spectra from both samples confirmed the formation of stable S–Au and S–\nPd chemical bonds, consistent with previously reported thiol-metal interactions. The presence of\nuncoordinated thiol groups in the XPS spectra arises because 1,10-decanedithiol molecules possess\ntwo terminal thiol groups. Upon self-assembly, one thiol binds to the metal surface (Au or Pd),\nwhile the opposite end remains free-standing. This accounts for the observed free –SH signal,\nrather than indicating incomplete bonding or instability. This bilaterally binding nature is crucial\nfor forming a stable Pd–SAM–Au trilayer structure, wherein each terminal –SH group forms a\ncovalent bond with a metal surface, providing a mechanically and chemically stable interface over\ntime.\nFigure R3. Long-term operational stability under continuous (a) 1000ppm and (b) 1 vol% H sensing.\nlayer within the Pd–SAM–Au junction, even during prolonged exposure to H environments. The\n2\nupdated long-term testing results of the sensor response as well as the baseline resistance have\nbeen added to the revised main manuscript (Figure 5f) and Supplementary Information Fig. 17,\nand the conclusions in the manuscript have been carefully updated to reflect only experimentally\nvalidated claims.\n7) The author integrated a handheld hydrogen leakage monitoring platform to detect H2 gas. If\npossible, it is recommended to compare it with existing commercial H2 sensors in the form of a\nvideo to exhibit its precision and accuracy.\nReply:\nWe sincerely thank the reviewer for the valuable suggestion to compare the integrated handheld\nhydrogen leakage monitoring platform with commercial hydrogen sensors to evaluate its accuracy\nand application potential. Due to strict hazardous gas handling regulations in our laboratory, it is\nnot currently permissible to simulate hydrogen leakage scenarios by directly releasing high-\nconcentration hydrogen from gas cylinder fittings, particularly for safety-critical concentrations\nabove 1 vol%. As an alternative, we prepared sealed sampling bags filled with 1000 ppm H , which\n2\nare representative of early-stage leak concentrations relevant for safety monitoring. We then\nperformed a comparative test using our integrated handheld detection platform and a commercially\navailable Honeywell hydrogen detector (BWS1-R-Y). The results show that our sensor-integrated\ndevice was able to accurately detect and quantify the 1000 ppm H sample, yielding a response\n2\ncomparable to that of the commercial sensor. Furthermore, our system demonstrated a faster\ndetection response, which we attribute to the integration of a miniaturized micro-pump within the\nhandheld unit. This active sampling route allows more rapid intake of ambient gas, thereby\nimproving response speed compared to passive diffusion-based commercial H detector. This\n2\ndemonstrates the practical feasibility, precision, and reliability of our system in real-world\ndetection scenarios, particularly for low-concentration, pre-explosive hydrogen monitoring.\nAlthough video demonstration under high-leakage scenarios is currently restricted by institutional\nsafety policies, we believe the comparative measurement results substantiate the application\npotential of the proposed platform.\nWe have added this test result and discussion to the revised Supplementary Information\n(Supplementary Video 1 and Video 2).\nReferences\n1. Ulman, A., Formation and structure of self-assembled monolayers. Chemical reviews 1996, 96 (4),\n1533-1554.\n2. Vericat, C.;Vela, M.;Benitez, G.;Carro, P.;Salvarezza, R., Self-assembled monolayers of thiols and\ndithiols on gold: new challenges for a well-known system. Chemical Society Reviews 2010, 39 (5), 1805-\n1834.\n3. Salem, L., Attractive forces between long saturated chains at short distances. The Journal of\nChemical Physics 1962, 37 (9), 2100-2113.\n4. Kresse, G.;Furthmüller, J., Efficient iterative schemes for ab initio total-energy calculations using\na plane-wave basis set. Physical Review B 1996, 54 (16), 11169-11186.\n5. Blöchl, P. E., Projector augmented-wave method. Physical Review B 1994, 50 (24), 17953-17979.\n6. Perdew, J. P.;Burke, K.;Ernzerhof, M., Generalized Gradient Approximation Made Simple.\nPhysical Review Letters 1996, 77 (18), 3865-3868.\n7. Grimme, S.;Antony, J.;Ehrlich, S.;Krieg, H., A consistent and accurate ab initio parametrization of\ndensity functional dispersion correction (DFT-D) for the 94 elements H-Pu. The Journal of chemical\nphysics 2010, 132 (15).\n8. Wagner, S.;Pundt, A., Quasi-thermodynamic model on hydride formation in palladium–hydrogen\nthin films: Impact of elastic and microstructural constraints. International journal of hydrogen energy 2016,\n41 (4), 2727-2738.\n9. Kim, G.;Lee, S.;Lee, S. k.;Yu, H. J.;Cho, H.;Chung, Y.;Park, T. E.;Lee, H. S.;Shim, W.;Lee, K. H.,\nRevealing the Substrate Constraint Effect on the Thermodynamic Behaviour of the Pd–H through\nCapacitive‐Based Hydrogen‐Sorption Measurement. Advanced Materials 2024, 36 (15), 2310333.\n10. Lewis, F., The hydrides of palladium and palladium alloys. Platinum Metals Review 1960, 4 (4),\n132-137.\n11. Barton, J. C.;Lewis, F. A.;Woodward, I., Hysteresis of the relationships between electrical\nresistance and the hydrogen content of palladium. Transactions of the Faraday Society 1963, 59, 1201-\n1207.\n12. Sakamoto, Y.;Takai, K.;Takashima, I.;Imada, M., Electrical resistance measurements as a function\nof composition of palladium-hydrogen (deuterium) systems by a gas phase method. Journal of Physics:\nCondensed Matter 1996, 8 (19), 3399.\n13. Andersson, C.;Zimmerman, J.;Fritzsche, J.;Rabkin, E.;Langhammer, C., Hydride formation\npressures and kinetics in individual Pd nanoparticles with systematically varied levels of plastic\ndeformation. Nature Communications 2025, 16 (1), 9242.\n14. Liu, Y.;Koo, K.;Mao, Z.;Fu, X.;Hu, X.;Dravid, V. P., Unraveling the adsorption-limited hydrogen\noxidation reaction at palladium surface via in situ electron microscopy. Proceedings of the National\nAcademy of Sciences 2024, 121 (40), e2408277121.\n15. Carrasco, J.;Hodgson, A.;Michaelides, A., A molecular perspective of water at metal interfaces.\nNature materials 2012, 11 (8), 667-674.\n16. Grönbeck, H.;Curioni, A.;Andreoni, W., Thiols and disulfides on the Au (111) surface: the\nheadgroup− gold interaction. Journal of the American Chemical Society 2000, 122 (16), 3839-3842.\n17. Venkataraman, L.;Klare, J. E.;Tam, I. W.;Nuckolls, C.;Hybertsen, M. S.;Steigerwald, M. L.,\nSingle-molecule circuits with well-defined molecular conductance. Nano letters 2006, 6 (3), 458-462.\n18. Curtiss, L. A.;Miller, J. R., Distance dependence of electronic coupling through trans alkyl chains:\neffects of electron correlation. The Journal of Physical Chemistry A 1998, 102 (1), 160-167.\n19. Cao, Y.;Chen, Z.-X., Slab model studies of water adsorption and decomposition on clean and X-\n(X= C, N and O) contaminated Pd (111) surfaces. Physical Chemistry Chemical Physics 2007, 9 (6), 739-\n746.\n20. Tatarkhanov, M.;Ogletree, D. F.;Rose, F.;Mitsui, T.;Fomin, E.;Maier, S.;Rose, M.;Cerdá, J.\nI.;Salmeron, M., Metal-and hydrogen-bonding competition during water adsorption on Pd (111) and Ru\n(0001). Journal of the American Chemical Society 2009, 131 (51), 18425-18434."}, {"round": 2, "reviewer_comments": {"reviewer_1": "No further comments.", "reviewer_2": "The authors have addressed most of my concerns. There is only one small problem. If the response value in Figure 2j is ~0.8%, I think the y-axis label should not be ✖100%. 100% equals 1.", "reviewer_3": "The manuscript has been well revised. Therefore, I recommend the manuscript be accepted for publication."}, "author_response": "Responses to Reviewer #1’s Comments\nComments of Reviewer #1:\nNo further comments.\nReply:\nWe sincerely appreciate the reviewer’s thorough evaluation and constructive comments\nthroughout the revision process.\nResponses to Reviewer #2’s Comments\nComments of Reviewer #2:\nThe authors have addressed most of my concerns. There is only one small problem. If the response\nvalue in Figure 2j is ~0.8%, I think the y-axis label should not be ✖100%. 100% equals 1.\nReply:\nWe sincerely thank the reviewer for their careful attention to the y‑axis labeling in sensing response\ncalculation and for pointing out the potential ambiguity. The sensing response in our work is\ncalculated using the following expression:\nR R R\nResponse(%)  H2 N2 100 100 (1)\nR  R \nN2\nHere, the calculated response was multiplied by 100 and expressed in percentage units. However,\nrecent y‑axis label “×100%” indeed could lead to confusion, as it may be misinterpreted as an\nadditional scaling factor. To avoid ambiguity, we have revised the y‑axis label to “Response (%)”,\nwhich explicitly indicates that the plotted values represent the percentage form of the normalized\nresistance change, and the specific response definition is illustrated in the “Methods” section. The\nfigures that content the sensing response and corresponding caption have been updated accordingly\nin the revised manuscript. We thank the reviewer again for this helpful suggestion, which has\nimproved the clarity and accuracy of the presentation.\nResponses to Reviewer #3’s Comments\nComments of Reviewer #3:\nThe manuscript has been well revised. Therefore, I recommend the manuscript be accepted for\npublication.\nReply:\nWe appreciate the reviewer’s the recommendation for publication and insightful comments that\nhelp greatly improve the quality of the manuscript."}]

Decision letter