Introduction

The rapid advancement of science and technology has driven the miniaturization and intelligent automation of various electronic devices. Among them, Flexible force sensors have attached significant attention due to their unique mechanical properties and extensive applications in microelectronics, medical devices, and robotics1,2. The pursuit for the miniaturization of flexible force sensors is particularly critical in medical applications, including catheters, interventional surgical devices, and implantable monitoring systems, where achieving high sensitivity, stability, and biocompatibility at the micro- and nano-scale are essential3,4.

To design flexible force sensors that simultaneously meet high-performance requirements while maintaining mechanical robustness and electrical performance, researchers have explored various fabrication strategies. One widely used approach involves integrating specialized geometric structures, such as wavy, spiral, or buckled configurations, within elastic polymer substrates to enhance force sensitivity5. Another approach utilizes novel conductive nanomaterials, such as carbon nanotubes (CNTs), MXene (Ti3C2Tx), and graphene, to develop flexible conductive composites capable of converting mechanical stimuli into electrical signals6,7,8. While these methods have demonstrated notable progress, conventional layer-by-layer fabrication techniques, such as mask-based lithography, digital light processing (DLP), and extrusion-based 3D printing, impose limitations on resolution, geometric complexity, and material integration. These constraints hinder the fabrication of high-resolution, complex 3D microstructures with advanced conductive nanomaterials, limiting their potential for high-precision medical applications. Two-photon polymerization (TPP) has emerged as a promising microfabrication technique for manufacturing high-resolution 3D structures at the micro- and nano-scale9,10,11,12,13. Unlike conventional additive manufacturing techniques, TPP utilizes nonlinear light absorption to achieve sub-diffraction-limit resolution, enabling the fabrication of highly precise, intricate structures14. Despite these advantages, traditional photosensitive resins are generally insulating, and their compatibility with TPP is often limited to structural applications rather than functional electronic devices. Additionally, post-processing techniques such as selective coating with conductive conjugated polymers introduce fabrication complexity and result in non-uniform conductivity across the printed structures15. The integration of functional conductive nanomaterials into TPP-compatible resins represents a critical step toward developing flexible electronic devices.

Efforts to functionalize photosensitive resins have primarily involved the incorporation of conductive nanomaterials to impart electrical conductivity. While CNTs have been widely studied, their high modulus limits the ability to enhance the sensitivity of force sensors through internal structural modifications. In contrast, MXene, a novel 2D carbon-based nanomaterial, has exhibited outstanding performance due to its excellent electrical conductivity, mechanical flexibility, and surface chemistry16. MXene has been extensively explored for its applications in energy storage17, supercapacitors18,19, and sensors technologies20. Its capability to facilitate interlayer electron movement plays a crucial role in enhancing the performance of flexible force sensors. Additionally, the abundant hydrophilic functional groups on the surface of MXene significantly enhance the interactions with hydrophilic network, improving mechanical properties. Unlike graphene oxide nanosheets, MXene exhibits a balanced combination of high conductivity and dispersibility, ensuring uniform distribution in hydrogels or resin matrices without aggregation, thereby forming stable conductive pathways. These properties make MXene highly sensitive to external stimuli, rendering it a promising candidate for flexible force sensors. Recent studies have demonstrated MXene-based force sensors with outstanding performance. Ma et al. reported the application of MXene in force sensors, achieving GF values ranging from 180.1 to 94.8 within the sensitivity range, demonstrating excellent performance21. Zhang et al. show that MXene achieved strong sensitivity over a longer compression range and enabled bidirectional sensing of stretching and compression22. Furthermore, Hui et al. improved MXene materials to develop force sensors capable of operating at low temperatures (−40 °C)23. Despite these advantages, integrating MXene into photosensitive resins for TPP-based fabrication remains challenging. The addition of Improper incorporation of MXene fillers can disrupt the polymerization process by inducing agglomeration and light scattering, which may result in polymerization defects, non-uniform dispersion, reduced structural fidelity, and degraded printing resolution and mechanical properties. These challenges underscore the need for an optimized conductive resin formulation that ensures uniform MXene dispersion while maintaining high-resolution printability and mechanical stability for advanced microfabrication applications.

This paper proposes the development of a conductive photosensitive resin formulation optimized for TPP, facilitating the fabrication of high-precision micro-scale force sensors with enhanced electrical and mechanical properties. A micro-spring force sensor (MSFS) was designed and fabricated using the optimized MXene-doped resin. To optimize the fabrication process, molding data were collected under varying TPP laser parameters and material compositions, and a Support Vector Machine (SVM) model was developed to predict the moldability of different conditions. The mechanical and electrical properties of the MSFS were systematically analyzed to understand the influence of MXene concentration on sensor performance. Furthermore, Finite Element Analysis (FEA) was employed to evaluate the mechanical and electrical characteristics across different structural configurations, guiding the optimization of structural parameters for enhanced sensitivity and stability. Finally, a comprehensive validation integrating numerical simulations and experimental measurements was performed to assess the feasibility and performance of the MSFS, paving the way for future applications in biomedical devices, soft robotics, and next-generation flexible electronics.

Results and discussions

Conductive photosensitive material

The photosensitive resin formulation was consisted of 71 wt% SR348OP and 29 wt% Bis-GMA. To improve mechanical properties and facilitate the dispersion of conductive nanomaterials, PEGDMA was added as a crosslinking agent. A 2 wt% concentration of the photoinitiator IC819 was incorporated to enable effective light absorption and initiate polymerization. The mixture was stirred using a magnetic stirrer for 6 h to ensure homogeneity. Subsequently, conductive nanomaterials, such as silver nanoparticles (AgNPs), CNTs, and MXene, were individually added to the mixture and further stirred at 1000 r/min for 12 h to achieve uniform dispersion within the resin matrix.

The dispersibility of AgNPs, CNTs, and MXene, in the photosensitive resin was systematically evaluated. Macroscopic observations indicated that the AgNPs (Fig. 1a) exhibit poor dispersion, as evidenced by the presence of uneven distribution and visible agglomerates. This leads to non-uniform integration within the resin, which can negatively affect the overall performance of the resin. In contrast, CNTs (Fig. 1b) and MXene (Fig. 1c) demonstrated significantly better dispersibility. During the TPP process, photosensitive resin samples mixed CNTs exhibited partial structural polymerization (Fig. 1d). However, as the laser scanned through the photosensitive resin, appear larger CNTs clusters (appearing as black dots under the microscope) absorbed excessive laser energy, leading to the two major issues: (1) localized thermal expansion induced structural damage at the polymerized boundaries; (2) strong van der Waals interactions among CNTs promoted aggregation, hindering uniform dispersion. Additionally, the linear optical absorption of CNTs significantly limited their maximum mixing concentration under nonlinear TPP conditions. Notably, MXene (Fig. 1c) showed the most promising dispersion characteristics. To further improve the dispersibility of MXene in the photosensitive resin, a 0.5 mg/mL modified MXene ethanol solution was added to the formulation, as shown in Fig. 1e. The enhanced compatibility of MXene with the resin, aided by ethanol, contributed to its superior dispersion and subsequently improved the molding quality during the TPP process.

Fig. 1: Overview of dispersibility and printability of photosensitive resins doped with different conductive nanomaterials.
Fig. 1: Overview of dispersibility and printability of photosensitive resins doped with different conductive nanomaterials.
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The status of photosensitive resin doped with AgNPs (a), CNT(b), and MXene (c), respectively. The printing process of photosensitive resin sample mixed with CNT (d), and MXene (e), respectively. Scale bar: 100 µm

Fabrication of micro spring force sensors and data collection

The fabrication of MSFS was performed using a TPP system. The design of the micro-scale structures was created using SolidWorks and imported into the TPP printer’s control system for precise execution. Each model slice was set to a thickness of 1 µm to achieve high-resolution printing. A drop of the composite resin was carefully deposited onto single-side polished silicon wafers, ensuring uniform material distribution on the polished surface. Printing was performed using a 25× microscope objective lens in dill mode, optimizing focus and exposure control. To guarantee high precision and structural integrity, the fabrication process was fine-tuned by systematically adjusting laser power and scan speed, ensuring optimal polymerization and minimizing defects in the printed MSFS structures.

To ensure broader applicability of the resulting fabrication parameters, a spiral microstructure was selected as the target structure, with dimensions of 200 µm in length, 100 µm in width, 12.5 µm in helix diameter, and 50 µm in pitch. The fabrication process involved four key variable parameters: two material-related parameters—the ratio of the crosslinking agent PEGDMA and the concentration of the conductive material MXene—as listed in Table 1, and two printing parameters—laser scan speed and laser power. The laser scan speed was varied from 500 µm/s to 50000 µm/s, while the laser power ranged from 10 to 95% of the system’s maximum 50 mW output, where 100% represents full power and all experimental values were expressed as percentages relative to this maximum.

Table 1 Composition ratios of conductive material and photosensitive resin used in training
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Due to the extensive number of possible parameter combinations, testing every combination of the four variables would have been impractical. Instead, data collection was conducted systematically by modifying one variable at a time to determine its influence on printability. The transition boundary between printable and non-printable regions was identified by gradually adjusting laser power and scan speed. For each sample that was successfully printed, experiments were extended in both upward and downward directions along the variable range until the transition to non-printable conditions was reached. The data collection process was terminated when three consecutive non-printable results were obtained due to either insufficient polymerization due to insufficient power or overexposure-related defects due to excessive power.

The fabrication of laser parameters MSFS under varying laser parameters resulted in three distinct outcomes: uncured, cured, and damaged, as shown in Fig. 2a. When the laser power was too low, polymerization was either incomplete or entirely unsuccessful, resulting in uncured samples with insufficient structural integrity. Conversely, If the laser power was too high, thermal effects caused structural damage, such as bubble formation or aggregation of the conductive medium. Only when the laser parameters fell within an optimal range did the structures exhibit successful polymerization without defects. To streamline data classification, both uncured and damaged samples were grouped into a single category, while fully polymerized, defect-free structures were classified separately, forming a binary labeling system. During data collection, the printing duration varied from a few minutes to over twenty minutes, depending on the laser scan speed. The entire printing process was continuously monitored, with particular attention given to the polymerization state at each layer. If none or partial polymerization was observed, the sample was categorized as uncured. Damaged samples were identified when bubbles appeared, excessive heating occurred, or conductive nanoparticles aggregated, even if no visible defects were immediately apparent post-printing. Cured samples required a clear polymerized structure with no visible printing defects throughout the fabrication process. Representative image examples of these two classifications across the three scenarios are provided in Fig. 5a. For training a machine learning classification model, a total of 222 data samples were collected. Among them, 80% were used as training and validation sets, while the remaining 20% were reserved as the testing, ensuring robust cross-validation and model generalization.

Fig. 2: SVM-based prediction workflow and model performance evaluation for MSFS cured.
Fig. 2: SVM-based prediction workflow and model performance evaluation for MSFS cured.
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a Representative optical images of MSFS structures under different curing outcomes: uncured, cured, and damaged. b Workflow of the SVM-based prediction process for printability evaluation. c Confusion matrices of SVM classifiers using different kernel functions (Linear, Rbf, Poly, Sigmoid), showing prediction performance on test datasets. Scale bar: 100 µm

SVM model development

To improve the efficiency of determining optimal polymerization parameters, a SVM classification model was developed, which performs well on small sample sizes. The model was trained to classify whether a given resin formulation with conductive materials could successfully polymerize under specific laser parameters. A schematic diagram illustrating the model construction and training process is presented in Fig. 2b.

For data processing, the labels were assigned as “0” for cured sample and first “1” for uncured sample. All input features were normalized before training to ensure numerical stability and prevent features with large magnitudes from disproportionately influencing the model. In the model construction phase, the Scikit-learn machine learning library was utilized to implement and train the SVM classification model. The penalty parameter (C), which regulates the trade-off between maximizing the margin and minimizing classification errors, was initially set to its default value of 1. A larger C results in a narrower margin, prioritizing accuracy but increasing sensitivity to noise, whereas a lower C value allows for a wider margin, enhancing generalization at the cost of potential misclassifications. In this study, C was set to 2 to optimize the balance between model robustness and classification accuracy. For loss calculation, the hinge loss function, defined as \(L(z)=\max (\mathrm{0,1}-z)\), was employed to measure the classification error based on the position of samples relative to the decision boundary. The SVM model was trained using four different kernel functions, including linear, gaussian radial basis function, polynomial, and sigmoid kernels, to evaluate their performance in classifying successful polymerization under various laser conditions and resin formulations. Model accuracy was assessed based on its prediction capability across different polymerization scenarios, ensuring reliable classification of printability outcomes.

To improve model reliability and prevent overfitting, K-fold cross-validation (K-CV) was applied. The 180 training and validation samples were divided into five subsets, with five cross-validation performed for each kernel function. In this study, each subset was used as a validation set once, while the remaining four subsets were used for training, ensuring that all samples contributed to the learning process. This method helped reduce bias, mitigate underfitting and overfitting, and enhance both accuracy and model stability.

The model training and evaluation were performed on a system equipped with an AMD Ryzen5 4600 u 2.1 GHz processor, 16 GB of RAM, and a Windows 10 ×64 operating system. The development environment was set up using Python 3.8.8.

SVM models for predicting MFSF polymerizability

The SVM classification model developed for predicting the polymerizability of MFSF under varying laser print parameters demonstrated strong performance. After training, the best-performing classification model for each kernel function was selected for testing, with their performance comparison presented in Table 2. The results indicate that the radial basis function (Rbf) kernel achieved the highest test set accuracy of 92.66% and a validation accuracy of 95.56%, indicating excellent generalization capability. The polynomial (Poly) and linear kernels also performed well, with test accuracies of 92.09% and 85.88%, respectively. However, the sigmoid kernel showed poor performance, with test accuracy dropping to 54.80%, likely due to overfitting and non-linear separability issues inherent in the dataset.

Table 2 Training results of different kernel functions
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The confusion matrices of the four kernel-based models are shown in Fig. 2c, indicating that while the linear and Poly kernel models perform reasonably well, the Rbf kernel achieved the best balance between sensitivity and specificity. Notably, the majority of misclassifications occurred when polymerizable samples were incorrectly identified as non-polymerizable, particularly in models using the linear and polynomial kernels, where all misclassifications fell into this category. Therefore, when assessing the feasibility of printing parameters, this model demonstrates high reliability in identifying polymerizable outcomes, making it useful for the preliminary prediction of structure formation potential. Its application can effectively reduce the time required for print parameter adjustments and lower the cost associated with material formulation trials. Furthermore, the features used for classification, including laser parameters and material composition, are physically meaningful and generalizable. This makes the model highly adaptable to other material systems or resin formulations, provided that appropriate retraining is conducted. Thus, the SVM-based framework offers a scalable and transferable methodology for accelerating the parameter optimization process in two-photon polymerization of functional materials, ensuring efficiency and robustness in a wide range of applications.

Mechanical characterization

The PEGDMA content in the photosensitive resin was gradually increases from 0 wt%. When PEGDMA exceeded 80 wt%, photo-polymerization became increasingly difficult, and the resin samples exhibited a high tendency to fracture or crumble. The stress-strain curves of samples with PEGDMA concentrations ranging from 0 wt% to 80 wt% are shown in Fig. 3a. The results indicate that the sample with the highest elongation rate achieved a 38% length increase. The variation trends of Young’s modulus initially a slight increasing and then gradual decreasing with the continuous increase in PEGDMA content, the maximum Young’s modulus is 470 MPa, indicating flexibility, as shown in Fig. 3b. The variation trend of maximum stress followed a similar pattern, with the maximum fracture stress reaching 57.62 MPa, as shown in Fig. 3c. It was observed that when PEGDMA content exceeded 20 wt%, the stress slightly decreased after reaching its peak, leading to fracture, which can be classified as brittle failure. Initially, the introduction of PEGDMA increased the cross-linked network density while reducing the relative monomer mass fraction, causing stress to become more localized during tensile loading. This structural change made the material stiffer and more prone to fracture. However, as PEGDMA content further increased, the monomer concentration decreased, leading to a reduction in active groups available for photopolymerization. Consequently, the material became softer due to increased dilution, and Young’s modulus decreased to approximately 49 MPa at 80 wt% PEGDMA. At this stage, the photopolymerized network was insufficiently dense, further increasing the fracture susceptibility. These findings suggest that an optimal PEGDMA concentration must be maintained to balance mechanical strength and deformability, preventing excessive brittleness while ensuring sufficient structural integrity.

Fig. 3: Mechanical and electrical characterization of MSFS.
Fig. 3: Mechanical and electrical characterization of MSFS.
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a–c Mechanical properties at different PEGDMA mass fractions: (a) stress–strain curves; (b) Young’s modulus; (c) maximum stress. d–f Mechanical and structural responses at different MXene mass fractions: (d) stress–strain curves; (e) Young’s modulus. f Schematic of a monolayer MXene sheet. g Geometry of the nanocomposite unit cell with randomly doped MXene; (h) Geometry of the nanocomposite unit cell considering the tunneling effect. i Schematic of effective electrical conductivity calculation in the nanocomposite. j Curve of effective conductivity versus height variation percentage of the unit cell. k Electrical conductivity at different MXene mass fractions. l Schematic diagram of MSFS geometry and structural parameters

The mechanical properties of the polymerized resin were evaluated by examining the influence of varying MXene concentrations on the stress-strain behavior and Young’s modulus, as illustrated in Fig. 3d, e. The results demonstrate that increasing MXene content led to a proportional increase in the Young’s modulus of the polymer, indicating a strong reinforcement effect. As shown in Fig. 3f, the stress-strain curves indicate that with higher MXene concentrations, the material exhibits greater fracture stress and enhanced mechanical strength. The sample with 1 wt% MXene achieved the highest fracture stress and strain, whereas the 0.5 wt% and 0 wt% MXene samples showed progressively lower mechanical performance. This trend suggests that MXene significantly enhances mechanical resilience by improving load-bearing capacity. Additionally, as depicted in Fig. 3e, Young’s modulus increased proportionally with MXene concentration, rising from 380 MPa (0 wt% MXene) to 530 MPa (1 wt% MXene). This increase can be attributed to the formation of continuous conductive pathways within the resin, establishing an electron transport network. This network not only enhances the electrical conductivity of the material but also reinforces its structural integrity, making the polymer matrix denser and more ordered. Such structural modifications are crucial for improving the mechanical durability of MSFS under operational conditions.

Electrical Characterization

MXene within the nanocomposite exists in the form of square-shaped sheets (Fig. 3f). Accordingly, the geometry of the nanocomposite unit cell was designed to reflect this morphology, with square MXene sheets randomly distributed throughout the photosensitive resin matrix (Fig. 3g). The distribution process was implemented using a loop function, allowing for the iterative placement of individual MXene sheets. The resulting unit cell structure incorporates the inter-sheet spacing necessary to capture quantum tunneling effect (Fig. 3h). A constant current terminal was applied to the upper surface of the unit cell, while the lower surface was grounded (Fig. 3i). The overall conductivity of the unit cell was determined through finite element calculations (Fig. 3j). As the height \(h\) of the unit cell gradually decreased, new geometric models were constructed using random placement and shortest distance search algorithms to calculate the total conductivity. The reduction in height decreased the distance between MXene sheets, enhancing the quantum tunneling effect, which resulted in an increase in overall conductivity.

The overall conductivity and relative height (\(\Delta h/h\)) exhibited an exponential relationship, as shown in Fig. 3j. The fitting equation can be expressed as:

$$\sigma ={k}_{1}{\sigma }_{0}\,\cdot \,{exp} \left({k}_{2}\frac{\Delta h}{h}\right)$$
(1)

Where \({k}_{1}\) = 1, \({k}_{2}\) = 3.82, \({\sigma }_{0}\) = 1.6 × 10−4, and the fitting coefficient R2 = 0.95.

The MSFS material was formulated by first mixing 20 wt% bis-GMA, 33.3 wt% SR348OP, 46.7 wt% PEGDMA. Then, 2 wt% photoinitiator IC819 was added, followed by the final addition of 0.05–0.15 wt% MXene. The electrical conductivity test results of MSFS, as shown in Fig. 3k, indicate that as the mass fraction of conductive particles increases, the conductivity of the resin also rises. However, the rate of increase gradually slows at higher concentrations. At low concentrations, the addition of conductive materials introduces isolated conductive particles within the resin, improving its electrical conductivity. As the concentration increases, these isolated particles progressively merge, forming continuous conductive pathways, which further enhance conductivity. However, beyond a certain threshold, the interaction forces between conductive particles intensify, leading to particle aggregation. This aggregation reduces the formation of additional effective conductive paths, leading to a saturation in conductivity, where further increases in concentration result in only marginal improvements in conductivity. The electrical conductivity of the conductive formulation falls within the range of 10−6 to 10−3 S/m, indicating that MSFS functions as a semiconductor with sufficient conductivity to meet the requirements for flexible sensor applications.

Structural design

The MSFS designed in this study features a spring-like structure, with thin layers attached to both the upper and lower ends of the spring, as shown in Fig. 3l. The key structural parameters include the outside of diameter (\(R\)), wire diameter (\(r\)), and axial pitch (\(L\)), and the number of turns in all structures was fixed at 3.5 turns. Through simulation analysis of the developed MSFS model, the critical relationship between the structural parameters and mechanical and electrical performance was investigated. By varying the outside of diameter (\(R\)), wire diameter (\(r\)), and axial pitch (\(L\)) of the spring structure, the mechanical response and electrical performance of the MSFS was characterized.

The wire diameter (\(r\)) of the MSFS was varied at 0.01 mm, 0.015 mm, and 0.02 mm, while keeping \(R\) = 0.08 mm, and \(L\) = 0.06 mm constant, as shown in Fig. 4a. The corresponding mechanical and electrical responses were evaluated using the MSFS model. The force-displacement curves indicate that all three radii exhibit strong linear mechanical performance under applied force, as illustrated in Fig. 4b. However, as \(r\) decreases, the slope of the force-displacement curve increases, indicating that MSFS structure with smaller radius experience greater deformation under the same external force. Specifically, the \(r\) = 0.01 mm structure exhibits the steepest slope, suggesting the highest deformability, while the \(r\) = 0.02 mm structure shows the lowest displacement under equivalent loading conditions. This trend highlights that reducing the wire diameter enhances the mechanical flexibility of MSFS but may also lead to lower structural stability under high loads. The force-resistance curves follow a negative exponential trend, where resistance decreases with increasing external force, but the rate of decrease decreases gradually stabilizes, as shown in Fig. 4c. At low applied forces, MSFS structures with smaller \(r\) exhibit significantly higher initial resistance, suggesting that their conductive pathways are more isolated in the unstressed state. As the force increases, these pathways merge more rapidly, leading to a steep decline in resistance. Conversely, MSFS structures with larger \(r\) exhibit a lower initial resistance and a more gradual resistance drop, indicating that they have more continuous conductive networks even before external loading is applied. This behavior suggests that MSFS with smaller \(r\) are more sensitive to external forces, making them suitable for high-sensitivity applications, whereas MSFS with larger \(r\) offer a broader measurement range but lower sensitivity to small force variations.

Fig. 4: Structural parameter variations and their influence on the electromechanical response of MSFS.
Fig. 4: Structural parameter variations and their influence on the electromechanical response of MSFS.
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a–c Geometry of the MSFS with wire diameter \(r\) = 0.01 mm, 0.015 mm, and 0.02 mm (a), as well as their force-displacement curve (b) and force-resistance curve (c), where (c) includes both linear plot and logarithmic subplot. d–f Geometry of the MSFS with outside of diameter \(R\) = 0.08 mm, 0.016 mm, and 0.24 mm (d), as well as their force-displacement curve (e) and force–resistance curve (f), where (f) includes both linear plot and logarithmic subplot. g–i Geometry of the MSFS with axial pitch \(L\) = 0.06 mm, 0.09 mm, and 0.23 mm (g), as well as their force–displacement curve (h) and force-resistance curve (i), where (i) includes both linear plot and logarithmic subplot

The outside of diameter of the MSFS is varied with \(R\) = 0.08, 0.16, and 0.24 mm, while maintaining \(r\) = 0.02 mm and \(L\) = 0.06 mm, as shown in Fig. 4d. The force-displacement curves in Fig. 4e indicate that as \(R\) increases, the displacement under a given force also increases, suggesting that larger-radius MSFS structures experience greater deformation due to their reduced stiffness. This implies that MSFS with larger \(R\) are structurally more compliant and better suited for applications requiring higher flexibility. As illustrated in Fig. 4f, the force-resistance curves exhibit a negative exponential trend, where resistance decreases with increasing force and then stabilizes. Notably, larger-radius MSFS demonstrate a greater overall resistance change, making them more responsive to applied force variations. However, they also exhibit a lower upper force limit, indicating that while they are more sensitive to external forces, their operational range is narrower compared to structures with smaller \(R\).

The axial pitch (\(L\)) of the MSFS was varied at to 0.06 mm, 0.09 mm, and 0.23 mm, while keeping the \(r\) = 0.02 mm and \(R\) = 0.08 mm constant, as shown in Fig. 4g. The force-displacement curves in Fig. 3h reveal that variations in axial pitch have minimal impact on mechanical deformation, as all structures exhibit similar slopes, indicating comparable stiffness. This suggests that changes in \(L\) do not significantly affect the structure’s ability to deform under force. As depicted in Fig. 4i, the force-resistance curves maintain a negative exponential trend, where resistance decreases as force increases. However, variations in L have little impact on overall sensitivity, as the resistance curves remain nearly identical across different axial pitches. Larger \(L\) values allow for a greater force tolerance and exhibit a slight increase in initial conductivity, potentially due to improved conductive path formation.

Based on the simulation results, an optimized MSFS structure was selected to ensure testing accuracy and minimize resistance. A wire diameter (\(r\)) of 0.02 mm was chosen to maintain structural integrity while achieving a balanced mechanical response. To keep the device’s projected area manageable, an outside of diameter (\(R\)) of 0.15 mm was selected. For structural stability, an axial pitch (\(L\)) of 90 µm was adopted. For fabrication, the MSFS element was manufactured using a photosensitive resin formulation with a mass ratio of bis-GMA:SR348OR = 3:7:5, a photoinitiator (IC819) concentration of 2 wt% and a conductive material MXene of 1 wt‰.

Performance characterization of the MSFS

The MSFS was fabricated using an optimized photosensitive resin formulation and TPP parameters. The mechanical behavior of the fabricated MSFS structure was first analyzed by comparing simulation and experimental results under gradual compression, as shown in Fig. 5a–l. The color figures (Fig. 5a, c, e, g, i, k) presents simulation results, while the black figures (Fig. 5b, d, f, h, j, l) displays corresponding experimental images, illustrating the stepwise deformation of the MSFS under applied force. The close agreement between simulation and experiment confirms the predictive accuracy of the numerical model and the structural reliability of the fabricated sensor. The gradual and consistent deformation patterns observed further validate the mechanical stability and repeatability of the MSFS.

Fig. 5: Electromechanical performance and structural validation of the MSFS.
Fig. 5: Electromechanical performance and structural validation of the MSFS.
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a–l Progressive deformation of the MSFS under applied force: (a, c, e, g, i, k) simulation results and (b, d, f, h, j, l) corresponding optical microscopy images captured at applied forces of 0, 50, 100, 150, 200, 250, and 300 \({\rm{\mu }}{\rm{N}}\), respectively. m Simulation and experimental displacement-resistance curves. n Force-resistance response curves of MSFSs with and without MXene, highlighting the critical role of MXene in conductivity enhancement. o Force-resistance response of the MSFS at 1, 15, and 30 days. p Relative resistance changes versus strain curve. q 3D surface morphology map of the MSFS. Scale bar: 100 µm

To quantify the mechanical response of the MSFS, atomic force microscopy (AFM) was used to measure the displacement of the upper surface under a series of controlled force loads. The resulting force–displacement curve, shown in Fig. 5m, demonstrates strong agreement between experimental and simulation data, with corresponding slopes of 0.096 and 0.087 \(\mu {\rm{m}}\)/\({\rm{\mu }}{\rm{N}}\), respectively. This minimal deviation confirms that the fabricated MSFS closely follows the expected mechanical behavior, validating both the accuracy of the numerical model and the precision of the fabrication process. The force-resistance response of the MSFS was analyzed to assess its electrical performance. The experimentally measured resistance closely aligns with simulation predictions, following a negative exponential trend, as shown in Fig. 5n. The results indicate that at low forces, resistance undergoes a rapid decrease, while at higher forces, the change stabilizes. This behavior suggests that the MSFS is highly sensitive to small force variations, making it a promising candidate for high-precision force sensing applications. In addition to high sensitivity, the MSFS demonstrates fast response behavior due to its resistive sensing mechanism. Although time-domain measurements were not the focus of this study, the device exhibits immediate resistance changes upon applied load with no observable delay, indicating sub-millisecond-level response and recovery times. The absence of noticeable hysteresis during repeated loading also confirms excellent reversibility and real-time tracking capability, which are essential for dynamic or wearable sensing applications. This rapid response is attributed to the tunneling-dominated conduction mechanism between MXene nanosheets, which allows instantaneous modulation of resistance upon mechanical deformation. To further validate the role of MXene and the presence of quantum tunneling conduction, a control experiment was performed using an MSFS fabricated without MXene, as shown in Fig. 5n. The control sensor exhibited a consistently high resistance that remained nearly constant under varying forces, indicating negligible electromechanical responsiveness. In contrast, the MXene-doped MSFS showed a distinct exponential reduction in resistance with increasing force. This stark contrast demonstrates that the resistance variation in the doped sensor is not merely due to structural deformation but arises from the force-dependent tunneling effect between adjacent MXene sheets. As compressive force reduces the interlayer spacing, electron tunneling is enhanced, resulting in a significant increase in conductivity. Furthermore, the experimental measurements closely follow the simulated resistance curve derived from a tunneling-based conduction model, providing compelling indirect evidence of quantum tunneling as the dominant mechanism. These findings confirm MXene’s critical role in enabling real-time, force-responsive electrical modulation and reinforce the feasibility of using MXene-based composites for high-performance, micro-scale force sensing applications.

To evaluate the long-term reliability of the MSFS, stability tests were conducted over a period of 30 days. Resistance–force measurements were performed at 1, 15, and 30 days after fabrication under identical conditions. As shown in Fig. 5o, the resistance–force response curves show excellent overlap across the three time points. While slight variations are observed at lower forces (0–50 μN), primarily due to environmental noise and initial surface oxidation, the overall trends remain highly consistent. The standard deviation of resistance measurements remains within 8%, indicating minimal signal drift and excellent structural integrity over time. Although a slight increase in baseline resistance was observed under zero load—potentially due to surface oxidation or humidity effects—the overall sensor behavior remained stable, with no noticeable degradation in sensitivity or measurement repeatability. These results demonstrate the excellent long-term stability of the MXene-doped MSFS, reinforcing its potential for continuous use in practical applications such as biomedical monitoring and soft robotic interfaces.

The strain-dependent electrical behavior of the MSFS is presented in Fig. 5p, which plots the normalized resistance change (ΔR/R0) as a function of applied strain. The response exhibits a nonlinear yet monotonic increase, with the most pronounced resistance variation observed in the low-strain regime (0–11%). Within this range, the maximum gauge factor (GF) reaches 5.65, reflecting the sensor’s high sensitivity at small deformations (see detailed information in Supplementary Section S1). This sharp response is attributed to the enhanced quantum tunneling effect, as the distance between adjacent MXene nanosheets decreases under compressive strain, facilitating electron transport. As the strain exceeds 22%, the resistance change begins to saturate, suggesting a transition from a quantum tunneling-dominated regime to a more stable conduction phase, where conductive pathways have already formed and further compression yields diminishing changes in resistance. To further evaluate the fabrication accuracy, AFM was used to analyze the surface morphology of the MSFS, as shown in Fig. 5q. The results indicate that the surface roughness is within ±50 nm, reflecting the high precision achievable through the TPP process under optimized conditions. The 3D surface profile further confirms the excellent fidelity between the printed structure and the original design, with well-defined microscale features preserved. It is worth noting that potential sources of error in the fabrication process may include the homogeneity of the photosensitive resin mixture and the dispersion quality of MXene nanosheets. Inhomogeneous mixing can introduce local refractive index variations, affecting laser focusing during polymerization. Similarly, agglomerated MXene particles may lead to uneven light absorption or scattering, resulting in incomplete curing or localized structural deviations. Although these effects were minimized in our process, they remain critical parameters that influence the reproducibility and consistency of microscale printing outcomes. The fabricated MSFS exhibits exceptional mechanical and electrical performance, with high structural accuracy, measurement sensitivity, and fabrication precision. The strong agreement between experimental and simulation results validates the reliability of the MSFS design and manufacturing process, reinforcing its potential for micro-scale force sensing applications.

Materials and methods

Formulation of Conductive Photosensitive Resin

To develop a nanocomposite photosensitive resin with enhanced conductive properties for TPP, this study investigated a combination of three resin components and three conductive nanomaterials. The resin formulation consists of BisGMA (glycidyl methacrylate, Sartomer, France) and SR348OP (Ethoxylated Bisphenol A Dimethacrylate, Sartomer, France), and PEGDMA (600) (Poly (ethylene glycol) dimethacrylate, Sartomer, France), each selected for its specific role in optimizing the mechanical and processing properties of the resin. BisGMA contains hydroxyl groups that enhance intermolecular interactions, significantly increasing the viscosity of the monomer mixture. This elevated viscosity enhances the reactivity of the system, leading to polymerized structures with superior mechanical strength and durability. SR348OP is incorporated due to its rapid curing capability, high boiling point, and thermal stability. Additionally, its low volatility and strong chemical resistance ensure the formation of a stable and resilient polymer network under TPP conditions. PEGDMA is a UV-reactive difunctional methacrylate monomer with high photoreactivity and diffusion-controlled free radical cross-linking polymerization. By serving as a cross-linking agent, PEGDMA modulates the mechanical flexibility of the final printed structures, effectively balancing the rigidity of BisGMA and SR348OP. By adjusting the concentration and molecular weight of PEGDMA, the elasticity and mechanical performance of the resulting polymer can be precisely controlled. To initiate the photopolymerization process, IC-819 (Sigma, Germany) was employed as the photo initiator, ensuring efficient light absorption and activation under TPP exposure.

To enhance the electrical properties of the polymerized structures, three conductive nanomaterials were incorporated: AgNPs, CNTs, and MXene. The AgNPs with an average size of 20 nm, were selected due to their excellent electrical conductivity and ease of dispersion within the polymer matrix. CNTs, with a length ranging from 15 to 30 nm and a diameter of 3 to 15 nm, were incorporated to provide a high aspect ratio, which contributes not only to electrical conductivity but also to mechanical reinforcement. MXene, a novel 2D material with a particle size of approximately 100 nm, was dispersed in ethanol at a concentration of 0.5 mg/ml. Its unique layered structure and tunable surface chemistry facilitate improved dispersion and interaction with the resin, further enhancing the electrical performance of the final printed structures.

SVM model development

For data processing, the labels were assigned as “0” for cured sample and first “1” for uncured sample. All input features were normalized before training to ensure numerical stability and prevent features with large magnitudes from disproportionately influencing the model. In the model construction phase, the Scikit-learn machine learning library was utilized to implement and train the SVM classification model. The penalty parameter (C), which regulates the trade-off between maximizing the margin and minimizing classification errors, was initially set to its default value of 1. A larger C results in a narrower margin, prioritizing accuracy but increasing sensitivity to noise, whereas a lower C value allows for a wider margin, enhancing generalization at the cost of potential misclassifications. In this study, C was set to 2 to optimize the balance between model robustness and classification accuracy. For loss calculation, the hinge loss function, defined as \(L(z)=\max (\mathrm{0,1}-z)\), was employed to measure the classification error based on the position of samples relative to the decision boundary. The SVM model was trained using four different kernel functions, including linear, gaussian radial basis function, polynomial, and sigmoid kernels, to evaluate their performance in classifying successful polymerization under various laser conditions and resin formulations. Model accuracy was assessed based on its prediction capability across different polymerization scenarios, ensuring reliable classification of printability outcomes.

To improve model reliability and prevent overfitting, K-fold cross-validation (K-CV) was applied. The 180 training and validation samples were divided into five subsets, with five cross-validation performed for each kernel function. In this study, each subset was used as a validation set once, while the remaining four subsets were used for training, ensuring that all samples contributed to the learning process. This method helped reduce bias, mitigate underfitting and overfitting, and enhance both accuracy and model stability.

The model training and evaluation were performed on a system equipped with an AMD Ryzen5 4600 u 2.1 GHz processor, 16 GB of RAM, and a Windows 10 × 64 operating system. The development environment was set up using Python 3.8.8.

Mechanical and electrical characterization

During the TPP process process, the MSFS was printed layer by layer, ensuring uniform dispersion of MXene within the photosensitive resin matrix, which significantly enhanced its conductivity—a key factor influencing MSFS performance. ITO conductive glass was used as the printing substrate, enabling fabrication on a conductive surface for streamlined testing. For electrical characterization, a source meter (SMU, Keithley 2450) was employed. One electrode was connected to the ITO glass, while the other was attached to a metal probe, which was precisely positioned using a three-axis translation stage to complete the test circuit. Conductivity was measured as a function of MXene concentration, with additional tests performed under compressive forces to simulate the MSFS’s electromechanical response.

Nanocomposite unit model of sensor

Due to the small size of the MSFS designed in this study, its electrical properties change under compressive deformation as a result of the quantum tunneling effect. To accurately describes the relationship between the applied force to the MSFS and its electrical properties, it is essential to consider quantum tunneling effects. A detailed analysis of a nanocomposite unit containing MXene was conducted, focusing on its electrical characterization. The nanocomposite unit model was constructed using COMSOL finite element software, and a custom algorithm for generating the nanocomposite unit was developed using the COMSOL App Builder tool.

The geometric parameters of the nanocomposite unit were determined based on a volume-to-mass ratio of 1 mL of photosensitive resin to 1 mg of MXene. Assuming each MXene sheet measures 100 nm × 100 nm × 10 nm, approximately 35 MXene sheets were randomly distributed within a 1000 nm × 1000 nm × 1000 nm resin matrix. To define the spatial arrangement of MXene, each square sheet was assigned a spatial position coordinate (x, y, z) and an orientation coordinate (n1, n2, n3), both generated using random numbers. Since quantum tunneling primarily occurs at the shortest distance between two conductors, a shortest-distance search algorithm was first applied to identify the closest MXene square sheets. The spatial coordinates of the closest points were then determined, and a cylindrical tunneling region with length \(d\) and cross-sectional area \(A\) was estabilshed, introducing a conductivity increment ∆σ due duo the tunneling effect. This process was iterated for each MXene sheet using a loop function, ultimately forming a nanocomposite unit cell that accounts for the quantum tunneling effect. The final nanocomposite unit consists of a rectangular resin matrix embedded with randomly dispersed MXene flakes, with cylindrical tunneling regions serving as the quantum tunneling conduction paths. The electrical conductivity parameters for each component are summarized in Table 3.

Table 3 Electrical conductivity parameters of nanocomposite unit components
Full size table

When the MSFS undergoes compressive deformation due to an applied external force, the nanocomposite unit contracts at the microscopic level. However, since the number of MXene sheets remains constant, the distance between adjacent MXene sheets decreases, enhancing the quantum tunneling effect and increasing overall electrical conductivity. To analyze this behavior, the nanocomposite unit model was simulated under compressive strain to determine its impact on electrical conductivity. For finite element analysis, a constant current was applied to the top surface of the nanocomposite unit, while the bottom surface was grounded. The overall electrical conductivity of the unit was then computed through finite element simulations, allowing for a quantitative assessment of how compressive strain enhances tunneling conductivity.

Micro spring force sensor model

To simulate the deformation process of the MSFS under an externally applied force, a computational model was constructed using the Solid Mechanics module in COMSOL. The force-deformation process of the MSFS is governed by three control equations: the equilibrium equation—Ensures force balance throughout the structure., the constitutive equation—Defines the relationship between stress and strain based on the material’s mechanical properties, and the kinematic equation—establishes the correlation between displacement and strain, describing how the structure deforms under load. These governing equations were integrated into the FEA framework, allowing for a comprehensive simulation of MSFS deformation under mechanical stress. By solving these equations, the model accurately predicts stress distribution, strain evolution, and displacement fields, providing insights into the MSFS’s mechanical response under operational conditions (see detailed information in Supplementary Section S2).

Mesh convergence analysis

A mesh convergence analysis was performed on the MSFS model to ensure the accuracy and stability of the numerical simulations. The deformation displacement of the top surface was selected as the convergence criterion, with the mesh gradually refined until the displacement values stabilized. The relationship between the number of mesh elements and the corresponding displacement values is presented in Fig. 6. The results indicate that a mesh consisting of 188,391 achieves high computational accuracy while minimizing computational cost, ensuring an optimal balance between precision and efficiency.

Fig. 6: Mesh convergence analysis of the MSFS model.
Fig. 6: Mesh convergence analysis of the MSFS model.
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Top displacement of the MNSF structure as a function of the number of mesh elements

Characterization methods of micro spring force sensor

The electrical resistance of the MSFS element was characterized under various compression conditions to analyze its response to applied force. This test measured the resistance of the MSFS at different compression displacements, evaluating its electromechanical behavior. For resistance measurements, the source meter (SMU, Keithley 2450) was configured in current source mode, with its terminals connected to the printed substrate and the metal probe, as shown in Fig. 6f. Since the printed substrate exhibits negligible conductivity, its influence on resistance calculations was considered insignificant. The metal probe, mounted on a three-axis translation stage, enabled precise control over the compression displacement applied to the MSFS. The measurement principle involved applying a small current, and the resistance was determined by measuring the voltage drop across the two terminals. To investigate the mechanical response of the MSFS, AFM was used to obtain force–displacement curves, providing insight into the relationship between applied force and deformation. Additionally, AFM surface characterization was performed on the central top region of the MSFS, allowing for an assessment of manufacturing precision and structural fidelity.

Conclusion

This study developed and characterized a novel conductive photosensitive resin formulation optimized for TPP to fabricate MSFS. By incorporating MXene as a conductive nanomaterial within the photosensitive resin matrix, we successfully addressed the challenges of balancing mechanical stability and enhanced conductivity at the micro- and nano-scale. To optimize TPP parameters, a machine learning approach was implemented using a SVM classification model, achieving 92.66% accuracy with a Gaussian radial basis kernel function. This approach significantly reduced the time and effort needed for extensive experimental trials, improving fabrication efficiency and reproducibility. The developed methodology provides a scalable optimization framework, applicable to other resin systems and functional nanomaterials. Comprehensive mechanical and electrical characterization demonstrated a strong correlation between MXene concentration and Young’s modulus, while electrical conductivity increased with higher MXene content due to the quantum tunneling effect, particularly under compressive stress. These electromechanical behaviors were further validated through experimental testing, confirming the feasibility of MXene-doped resins for high-performance MSFS fabrication. Using the optimized MXene-doped resin, we designed and fabricated an innovative 3D MSFS. FEA simulations provided insights into the relationship between structural parameters and sensor performance, guiding the design and optimization process. The fabricated MSFS exhibited high sensitivity, with a sensitivity coefficient of 5.65, and high-precision manufacturing, achieving a fabrication accuracy of ±50 nm.

Compared to previously reported 3D-printed flexible sensors, such as the CNT-coated by Li et al.24, which demonstrated a force–displacement sensitivity of 56.8 \({\rm{\mu }}{\rm{N}}/{\rm{\mu }}{\rm{m}}\) with a structure height of 300 \({\rm{\mu }}{\rm{m}}\), our MSFS achieves superior electromechanical performance at a significantly reduced scale ( ~ 90 μm height). While the CNT-coated sensor relies on contact-based conduction, the MXene-integrated MSFS operates through a quantum tunneling conduction mechanism, enabling continuous and stable resistance modulation under compressive strain. Furthermore, the MXene-doped MSFS exhibits reliable long-term stability, maintaining consistent electrical performance over 30 days, which addresses a critical performance dimension not covered in previous studies. Collectively, these features offer substantial advantages over many previously reported TPP-printed flexible sensors, particularly in terms of sensitivity, miniaturization, and functional durability. This research integrates advanced materials, machine learning, and high-precision fabrication techniques, positioning it at the forefront of flexible electronics and functional microdevices. The synergy between nanomaterial engineering, machine learning process optimization, and high-resolution fabrication establishes a scalable and efficient strategy for developing next-generation microscale sensors. This breakthrough paves the way for high-performance biomedical force sensors, soft robotics, and flexible electronic systems, driving innovation in intelligent microscale sensing technologies.