Iterative printing of bulk metal and polymer for additive manufacturing of multi-layer electronic circuits

It is crucial to enhance existing research efforts to advance additive manufacturing (AM) beyond its current status and solidify its place in mainstream manufacturing¹, and dispel the notion of it being merely a market “gimmick”². Multi-material additive manufacturing (MM-AM) offers a promising solution, combining the efficiency and flexibility of 3D printing with the ability to incorporate diverse material properties and complex geometries for added functionalities^3,4,5. MM-AM enables the creation of customized 3D electronics with multiple functions, addressing sustainability concerns by reducing waste in the electronics industry and enabling the downsizing of electronic devices^6,7,8. The most common MM-AM of 3D-printed electronics or 3D electronics is to combine a direct ink write (DIW) setup that prints electrically conductive material with a dielectric printing technology. To this end, DIW of electrically conductive material has been combined with different dielectric printing technologies, which include fused filament fabrication(FFF) technology^{9,10,11,12,13}, stereolithography (SLA) technology^14,15, digital light processing (DLP) technology¹⁶, or with DIW using photo cure and epoxy cure monomers¹⁷. DIW is an extrusion-based AM technique using a syringe needle tip primarily based on using viscoelastic ink¹⁸ as printable or electrically conductive ink¹⁹. The majority of electrically conductive inks are silver-based inks that are readily available in the commercial market and consist of silver nanoparticles, flakes, or other solid particles dispersed within organic or aqueous solvents^{20,21,22,23,24}. These conductive ink formulations rely on suspensions for physical delivery onto the dielectric substrate surface²⁵. In addition, they demand robust sintering and potential post-processing steps to remove the carrier liquids and fuse the densely packed particles into a continuous agglomerate²⁶. It is important to note that the effectiveness of the sintering process is highly dependent on the sintering temperature²⁷. Unoptimized sintering temperature could lead to undesired effects, including trapped solvent, porosity²⁸, low density, tortuosity, and numerous high-resistance interfaces that collectively result in low electrical conductivity (<25% of bulk metal)^29,30. Methods for post-processing, such as high-temperature baking (>200 °C), photonic curing³¹, or pulsed laser sintering³², can gradually enhance electrical conductivity³³ to nearly half that of bulk silver (({sigma }_{{{{rm{Ag}}}}}=6.3times 1{0}^{7}{{{rm{S}}}}/{{{rm{m}}}}))²⁹. However, it is worth noting that these post-processing techniques surpass the degradation temperature of the majority of AM dielectric substrates^34,35 and, therefore, would not be an ideal candidate for MM-AM in terms of material selection. It was also observed that the performance of conductive inks is affected by printing conditions and substrate properties. Therefore, it presented a need for a pre-processing substrate such as primer-coated polymer for enhancing the adhesion³⁶.

Roach et al. reported material bonding as one of the challenges in designing inks for MM-AM¹³. They also highlighted that the solutions in conductive inks could percolate between printed polymer layers and cause short circuits. Grouchko et al.³⁷ reported a “self-sintered” metal dispersion-based conductive ink in which changes in the concentration of chloride ions trigger sintering. This approach leads to very high conductivities, up to 41% conductivity of the bulk silver. To our knowledge, its use in MM-AM of 3D electronics has yet to be demonstrated. Weeks et al.³⁸ presented an intriguing methodology utilizing graph theory for embedded 3D printing. Their approach optimizes path planning, streamlining the printing process while preventing potential damage by avoiding nozzle overlap. However, they employ post-processing, involving overnight curing, extending fabrication time. In addition, their study does not explore incorporating conductive materials or inks for applications like printed electronics. Other MM-AM combination work showcased non-contact jetting of conductive inks on different material extrusion technique-based printed polymer³⁹. They showed low-temperature Ag-particulate conductive ink on substrates such as Acrylonitrile Butadiene Styrene (ABS) and polyamide (PA). They also demonstrated the reliability of conductive inks for MM-AM electronic devices, promising improved performance when coupled with in-situ LASER sintering³⁹. However, other limitations present with conductive inks mentioned above remain a challenge. Moving away from the use of pure conductive inks as conductive material, other researchers worked on the enhancement of properties of conductive material, where silver flakes in combination with liquid metals (LM) were used to print multilayer electronics⁴⁰. It was noticed that although LM wets many substrates due to Ga₂O₃ layer, its wetting properties depend on the substrate material and surface roughness. In the same research, particle-filled LMs were introduced to modify the rheological properties of the LM. However, it was found that these mixtures suffered from low mechanical integrity and surface roughness. The above findings show that conductive inks or metal-dispersed conductive inks could be suitable for the electronics industry by using sintering or additives, which come with limitations or restrictions, as discussed above. Moreover, achieving good adhesion necessitates chemically treated substrates, contributing to the increasing disposal of chemical waste into the environment²⁴. Li et al.⁴¹ employed LM gallium alloy for soft and stretchable electronics, presenting a novel method for creating 3D circuits without microchannels. However, the process entails long substrate resin curing times and necessitates additional interconnects for multilayer circuitry. Furthermore, limited data was provided on the reliability of printed traces under different temperatures or their interaction with the substrate. Another method for manufacturing functional 3D electronics is through 3D-MID, enabling the creation of complex 3D-shaped electronic devices without conventional wiring and substrates used in traditional rigid PCBs. Li et al.⁴² utilized a hybrid AM approach, combining dual-material FDM 3D printing with selective electroless plating. Surface etching with a strong oxidizing solution was employed to enhance the adhesion of electroless plating catalysts to the plastic surface. However, this process resulted in chemical waste, and the thickness and adhesion of plated metal structures depended heavily on etching time and uniformity. Structural electronic devices can also be obtained through injection molding of a thermoplastic integrated with electronics⁴³. Kololuoma et al.⁴⁴ demonstrated the manufacturing of personal activity meters with roll-to-roll printing, discrete component assembly, laser processing, and injection molding technologies. However, simulation is required to study whether the printed circuitry and discrete components (SMD) can sustain the thermoforming conditions. Encapsulation of circuitry and ICs is needed to withstand the injection molding process. Researchers have explored alternative approaches to create MM-AM of 3D electronics. Oliver Ozioko et al. presented a 3D-printed tilt sensor utilizing FFF technology to print conductive and dielectric parts⁴⁵. The model included grooves for printing conductive composites, contact pads on different layers connected with vertical conductive via, and a housing printed layer-by-layer vertically upwards. However, the study did not provide resistance values or reliability results of the printed conductors or their adhesion with the dielectric part. In other works, dielectric substrates were combined with electroplated copper conductors^46,47,48. Hong et al. demonstrated printed traces on vacuum-formed 3D-printed sheets⁴⁶, while Wang et al. combined 3D printing with laser-activated electroless plating to fabricate fully functional ceramic electronic products⁴⁷. Li et al. demonstrated 3D electronics with electroplated copper conductors using laser-activated stereolithography⁴⁸. However, these studies did not demonstrate multilayer embedded 3D electronics. Yu et al. injected liquid metal into hollow channels, demonstrating functional electronic circuits⁴⁹, but faced limitations such as leakage and non-wettability with channel walls. Chrisey et al. fabricated embedded electrically conductive traces by injecting silver paste into 3D-printed channels, achieving about 70% infilling in a 600 μm wide channel⁵⁰.

There is a growing interest in using low-temperature solders or metal alloys to address challenges in MM-AM of 3D electronics, such as out-of-plane printing and embedding electrically conductive traces in dielectric material while achieving compatibility with untreated dielectric. Ota et al. employed Galinstan as a conductive material to demonstrate sensing, actuation, and signal processing capabilities of printed electronics, integrating liquid-state printed components with silicon IC chips in three dimensions and multiple layers⁵¹. However, challenges arise due to the deposition of conductive material in a liquid state at room temperature, affecting the fidelity of printed trace shapes and the uncertain reliability of liquid metal traces under temperature variations, limiting their application in high-temperature-resistant scenarios.

Low-temperature solders, typically comprising tin (Sn) with silver (Ag), bismuth (Bi), or indium (In), are favored for their compatibility with thermoplastic materials printed at temperatures up to 250 °C or with glass transition temperatures (Tg) of up to 200 °C^34,52,53. Bartlomiej Podsiadly et al. demonstrated an approach involving polymer substrates prepared with standard FFF combined with electrically conductive traces using a modified FFF technique. They tested two solder alloys (Sn₆₀Pb₄₀ and Sn₉₉Ag_0.3Cu_0.7) with ABS polymer substrate, showcasing exceptional electrical conductivity and highlighting the potential of leveraging MM-AM of low-melting molten metals combined with thermoplastics in 3D electronics⁵⁴. Meanwhile, Dou et al. printed SAC305 (Sn_96.5Ag_3.0Cu_0.5) on various substrates, assessing their compatibility regarding wettability and adhesion⁵⁵. Though they demonstrated the use of low-melting point solders for creating electronic circuits, MM-AM of 3D electronics was not showcased. Nevertheless, they underscored the potential of SAC305 as a promising candidate for electronic circuits. Furthermore, empty spaces around the partially embedded electrically conductive traces could increase their susceptibility to corrosion at elevated temperatures and humidity. Wang et al. observed the formation of oxide film on SAC305 due to Sn oxidation, with corrosion increasing with higher temperature and humidity⁵⁶. Hence, a more robust strategy was required to eliminate these empty spaces, such as the conformal placement of electrically conductive traces within the polymer channels.

Consequently, we utilized the low-melting point solder alloy, SAC305, to produce multilayer embedded 3D electronics. This was achieved by developing Synkròtima-a novel one-stop hybrid printing platform integrating polymer and metal printing on a single setup. Notably, Synkròtima enabled uninterrupted MM-AM of electronic circuits, eliminating the need for post-processing steps such as sintering or manual hand-soldering of electronic components, as demonstrated in previous work⁵⁷. The development, integration, characterization, and capabilities of Synkròtima for printing single-layer functional electronic circuits have been extensively described in prior research. Zeba et al. achieved electrically conductive traces with a width of (230 ± 7) μm from SAC305 molten metal microdroplets (diameter = 285 ± 15 μm) on PETG polymer (printed from FFF technology). The printing height of the StarJet printhead was fixed at 4 mm from the top polymer surface. Side-by-side deposition of molten metal microdroplets enabled the generation of electrically conductive traces. These traces were printed with a droplet spacing of (100 ± 7) μm at a print speed of 1.8 mm s⁻¹, as calculated using Eq. (1). In addition, electrically conductive traces were deposited in polymer channels with a width of (700 ± 60) μm and depth of (1000 ± 55) μm. However, the width of the polymer channels was more than double that of the electrically conductive traces, resulting in only partial embedding. The bonding between the polymer (PETG) and electrically conductive traces exhibited adequate adhesion, as measured by a shear-off force of (11 ± 5) N. This bonding strength is comparable to that observed for displacing reflow-soldered Surface Mount Devices (SMD), recorded between 15 and 17 N⁵⁸. Notably, the reflow-soldering of SMD involved reflowing SAC305 solder paste at 100 °C for 24 h. Zeba et al. also demonstrated the direct soldering of SMD on a single-layer electronic circuit. However, this approach relied on pure computer-aided modeling (CAD) since no straightforward method, to our knowledge, was available for converting electrical schematics to G-code (commonly used 3D printer operation file format).

In this study, we introduce three significant advancements in the streamlined manufacturing of multilayer fully embedded electronic rigid circuits using bulk metal printing in conjunction with polymer on our hybrid printer, Synkròtima. First, we demonstrate the printing of electrically conductive traces from molten metal microdroplets directly onto untreated polymer surfaces, effectively embedding them within a 3D polymer body. Second, we expand the capabilities of MM-AM to construct multilayer embedded 3D electronics by integrating vertical electrically conductive pathways (vertical bulk metal via) layer-by-layer, reaching heights of up to 10 mm within the embedded electronic circuits. Third, we establish a seamless and uninterrupted workflow for printing such multilayer embedded 3D electronics. Our approach aligns with lean AM principles, eliminating overprocessing and reducing waste production. The continuous workflow ensures uninterrupted printing, with only manual placement of electronic components required. Furthermore, we address optimizing process parameters for polymer and conductive trace printing. We investigate their interdependencies and propose various methodologies to overcome associated bottlenecks in printing both materials simultaneously on a single setup. Finally, through exemplary models, we showcase the robustness of our approach for MM-AM of 3D multilayer electronics, demonstrating scalability and customization in the printed circuit shapes.

Workflow and design guidelines

To explain the workflow for MM-AM of multilayer 3D electronics, we used a free-form bunny model of dimensions (28 mm × 58 mm × 3 mm); see Fig. 1a, left. We created multilayer embedded 3D electronics by distributing electrically conductive traces in two different planes (referred to as Conductive layer-1 and Conductive layer-2 to denote layers in the 3D object), interconnecting them with vertical bulk metal via and covering each conductive layer with a polymer layer (Polymer layer-1, Polymer layer-2, and Polymer layer-3), see Fig. 1a, right.

a Final CAD model of Bunny (28 mm × 58 mm × 3 mm) with a universal serial bus (USB) power plug-in connector prepared on Fusion360 (left). The exploded view shows two layers of electrically conductive traces (conductive layer-1 and conductive layer-2) interconnected with two vertical via (yellow via) (right). b Schematic of the 555-timer astable electrical circuit. c PCB layout illustrates the electrical circuit with conductive traces (depicted in orange) arranged on a dielectric board shaped like a bunny (illustrated in green), including SMD footprints. In the design, R1, R2, and R3 represent resistors, while C1 represents the capacitor. In addition, D1 denotes the LED, and IC1 denotes the 555-timer. d 2D image of the one selected layer of the bunny model showcases the 3D nozzle tracks for both polymer and metal printing during MM-AM. Polymer nozzle tracks are depicted in green, while metal nozzle tracks are depicted in orange. e Electrically conductive traces created in MCAD format. f 3D CAD model depiction of polymer body features within a section of the hybrid bunny model (black square). Highlighted slots denote areas for SMDs, vertical vias, and conductive traces.

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The first step in creating this multilayer embedded 3D electronics is the generation of an electrical schematic. This work employed a fixed 555-timer astable oscillator circuit across all our 3D electronic circuits. The Astable oscillator mode of the 555-timer circuit is a resistive-capacitive-based circuit with a built-in trigger to oscillate between its high and low states⁵⁹. We connected a light-emitting diode (LED) to blink at the oscillations of the astable mode for the demonstration of multilayer embedded 3D electronics.

Fusion360 modeling software (Autodesk) was used to prepare the electrical schematic of the multilayer circuit; see Fig. 1b. The three-dimensional PCB variant of the 555-timer circuit in a bunny-shaped dielectric substrate was designed for conformal placement of electrically conductive traces to the shape (Fig. 1c) interconnected with two vertical vias. The electrically conductive traces were converted to a mechanical computer-aided model (MCAD) as conductive layers (shown as separate designed layers); see Fig. 1e. Layer-by-layer printing methodology, leveraging the MM-AM approach, was selected to print both polymer and conductive layers. In Fig. 1f, a portion of the hybrid bunny model was utilized to visually represent the features of the polymer body via a CAD model. Specifically, it highlights the slots designated for embedding SMDs, vertical vias, and conductive traces within the polymer body. Importantly, it should be noted that no additional slots or holes are incorporated through CNC (computer numeric control) machining or any supplementary process. This was validated by the presence of these design features in the sliced part, affirming a purely MM-AM printing process. The polymer layers and conductive layers were converted from CAD to distinct Standard Tessellation Language (STL) format files. Next, the STL files are added to the slicer project (see SI, Section 1) in the order they should appear in the final multilayer embedded 3D electronics. Subsequently, the slicer model (see Fig. 1d) undergoes slicing to generate a single G-code. According to Eq. (1), we assigned distinct print speeds for printing electrically conductive traces and vertical via in slicer project.

Here, s = print speed in mms⁻¹, d = droplet spacing (dot spacing) in mm, and f = Droplet print frequency in Hz. Different print speeds, droplet spacing and print frequencies used for electrically conductive traces and vertical via are discussed later in this work. Before the printing step of conductive layers, a special priming step was added to prepare the StarJet printer for printing molten metal microdroplets (see SI, Section 1). For integrating electronic components in the circuit, first, the electronic components are placed in their respective position (see SMD slot in Fig. 1d) on the polymer layer, and then the conductive layer is printed. A pause code was added for 12,000 ms in the slicer project before the conductive layer to place the components in the circuit (in this case, Conductive layer-2). Once the top layer of the polymer was printed by Synkròtima, the MM-AM of multilayer embedded 3D electronics end and a functional device were obtained. This straightforward workflow would allow any multilayer electrical schematic layout to be converted into multilayer embedded 3D electronics using a single G-code without overprocessing.

Strategies for depositing electrically conductive traces in polymer channels

Conformal deposition of electrically conductive traces in polymer channels is said to exist when the electrically conductive trace conforms to the shape of the polymer channel⁶⁰. In this work, the print height of the StarJet printhead = 4 mm, droplet spacing = 100 μm, and print speed = 1.8 mm s⁻¹ are fixed parameters for the printing of electrically conductive traces, if not denoted otherwise. Optimal parameter configurations were determined for these values through meticulous optimization efforts detailed in a prior investigation⁵⁷.

The first step in conformal printing was to evaluate the width of the polymer channel that could be printed by FFF technology for conformal deposition of molten metal microdroplets. To this end, the behavior of PETG polymer was investigated by varying channel widths. The design width of the polymer channel was varied from 200 to 450 μm. The measured values from the printed polymer channels showed deviations from the design width values or target dimensions (see SI, Supplementary Fig. S1 and Supplementary Table S1). Therefore, a linear regression fit was performed to predict the dimensional errors based on the significance of coefficients (see SI, Supplementary Fig. S2). A prediction formula was derived from target and printed dimensions; see Eq. (2).

where, x = dependent variable, target dimension or design channel width in μm, and y = independent variable, measured or printed channel width in μm.

Ideal channel width for conformal deposition of electrically conductive traces = 265 μm, width of electrically conductive trace (see SI, Supplementary Fig. S3 and Supplementary Table S2). We get the target dimension or design channel width = 250 μm from the prediction formula. While the design depth of the polymer (PETG, if not denoted otherwise) channel was fixed to 400 μm. The design depth equals two sliced layers of polymer for nozzle diameter = 100 μm; see “Methods”. This is based on the results from ref. ⁵⁷, where the electrically conductive traces were printed with an aspect ratio (height/width) = 0.8, which means that the height of the electrically conductive traces = 0.8 × width electrically conductive trace = (212 ± 7) μm.

In the following step, we introduce two process techniques designed for the conformal deposition of electrically conductive traces within polymer channels, now with fixed dimensions of a channel width of 250 μm and a channel depth of 400 μm. The first technique is described as the polymer–polymer–metal (PPM) technique, where the conventional method involves creating the channel first and then depositing the electrically conductive traces⁶¹. On the other hand, the second technique, described as the polymer-metal–polymer (PMP) technique, follows the ideal layer-by-layer MM-AM approach by printing polymer and electrically conductive trace layers consecutively. The PPM technique bears similarities to a method introduced by Roach et al.¹³, involving the printing of conductive silver ink in grooves using FFF technology, allowing us to underscore the significance of the innovative PMP technique presented in this study for the MM-AM of 3D electronics, utilizing molten metal microdroplets with polymer. Figure 2a, c illustrates the processing steps involved in PPM and PMP, respectively. PPM technique enables FFF printhead for printing two layers of polymer, each of layer height = 200 μm, consecutively. An arrow on the image shows the consecutive steps, while a hollow green box highlights the active printhead. The polymer layers (shown in blue) are illustrated without irregularity or gaps and may not represent reality. If otherwise stated, metal structures (electrically conductive trace) are illustrated in yellow. Metal structures are shown to infill up the entire channel space in the final step. This depiction also illustrates the deposition of metal and may not depict reality. PMP technique enables FFF printhead to print a single layer of polymer channel, 200 μm. In the next step, metal was deposited via the StarJet printhead. Figure 2a shows the metal structure oozing out of the 200-μm printed polymer layer since it was smaller than the height of the metal, (220 ± 7) μm. The final step for both PPM and PMP techniques (not shown in Fig. 2a, c) was the complete embedding of electrically conductive traces by printing a polymer layer on top. In the following work, we use the words “metal” and “electrically conductive traces” interchangeably to highlight either a specific part (metal) or the entire electrically conductive trace.

a–c Illustration of PPM and PMP methodology, respectively, for printing conductive traces in polymer channels. b–d Microscopic images of the sample at the cross-section planes of a sample printed with PPM and PMP methodology, respectively, with empty spaces covered by epoxy highlighted in light green. e, f Comparison of metal infill percentages in polymer channels for PPM and PMP methodologies. The central line inside the “violin” indicates the mean, while the width of the “violin” represents the kernel density estimate of the data. Error bars extending from each data point indicate the variability around the mean, with the length of the error bars corresponding to one standard deviation from the mean. g, h Microscopic images of conductive trace embedded in polymer viewed after cross-section grinding highlighting conformal printing and metal fusion, respectively. i Infill percentage for PMP-printed samples before and after the thermal cycling procedure. The central point inside the “violin” indicates the mean, while the width of the “violin” represents the kernel density estimate of the data. The error bars correspond to the standard deviation from the mean. j Resistance measured on embedded conductive traces for PMP-printed samples before and after the thermal cycling procedure. The central line inside the “violin” indicates the mean, while the width of the “violin” represents the kernel density estimate of the data. The error bars correspond to the standard deviation from the mean.

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Both PPM and PMP techniques are used to fabricate completely embedded samples. Therefore, for optical examination of samples, we exposed the surface containing both metal structure and polymer, see Fig. 2b, d, employing cross-sectional grinding using epoxy resin. Cross-section grinding using epoxy resin preserves material integrity by preserving features and reducing distortion⁶². Optical inspection aimed to assess the effect of SAC305 electrically conductive traces (metal) deposition on PETG polymer. Conformal deposition of an electrically conductive trace was visible for both the techniques, PPM and PMP, seen in Fig. 2b, d. At a glance, Fig. 2b shows a higher degree of conformity at the base and sides of the metal–polymer interface. Figure 2d shows a higher degree of conformity at the covering layer of the polymer-metal interface (top part in the image). Samples from PPM and PMP techniques were used to evaluate and assess the infill percentage of metal in polymer channels and the morphology of the metal–polymer interface, respectively. We have defined the infill percentage of metal in the polymer channel in Eq. (3).

The area unfilled by metal was covered by epoxy resin during sample preparation for cross-section grinding. For this assessment, 60 measurements were performed on four samples (40 mm × 25 mm × 2 mm) each for PPM and PMP techniques. Each sample was ground five times to expose five different metal–polymer interface layers for investigation. Layer-1 marks the starting part in the direction of metal deposition in the polymer channel. In order to control the depth of grinding, only defined values of grinding papers were used with a defined number of grinding rotations (see “Methods”). Both techniques facilitated the creation of conformal and fully embedded electrically conductive traces within polymer channels. However, a simple visual examination of the PPM and PMP techniques, as depicted in Fig. 2b, d, reveals more significant unfilled spaces in the PPM technique in comparison to the PMP technique. The empty spaces are highlighted in green and are labeled as epoxy. Infill percentage obtained for PPM technique was (84 ± 16)%, see Fig. 2e. The elongated shape of the violin for PPM shows distributed data density across different samples, thereby implying that the infill percentage of metal in PPM is skewed towards a lower-than-mean infill percentage value. Roach et al.¹³ did not quantify the infill percentage of metal in FFF channels but highlighted the limitation of using conductive inks for creating PPM-embedded circuits. They observed that multiple layers of conductive ink were needed to be deposited to ensure trace conductivity since the ink fell into cracks in FFF-printed channels. The novel PMP technique achieved an exemplary infill percentage of (92 ± 5)% for metal deposition. The shape of the Violin for PMP in Fig. 2e clearly shows a high concentration of data at 92% infill percentage. Moreover, it was observed that the novel PMP approach provided better infilling because it smoothened any irregularity in the polymer printing by FFF technology. This was possible because metal took the shape of the polymer channel (single layer of polymer channel at this stage) and allowed even placement of the following polymer layer to complete the channel fabrication. In the next step, we also investigated the effect of the solidification rate of the metal droplets on the two printing techniques by varying the droplet printing frequency, see Fig. 2f. Increasing the frequency reduces the deposition time between two sessile droplets; see Eq. (1). With increased frequency, a more stable and uniform infill percentage was obtained for both techniques. However, the deviation in PPM was observed to be 21%, while that for PMP was only 7%. A decreasing trend was observed towards Layer 5 (see SI, Supplementary Table S3). This could be due to the difference in thermal energies between the two printing materials as the amount of metal increases, possibly increasing the cohesion between metals. Therefore, it does not touch the polymer surface, see prior work Supplementary Information⁵⁷. Further investigation is needed to understand the behavior of metal embedded in different polymers. Notably, both approaches facilitated the fabrication of conformal and fully embedded electrically conductive traces within polymer channels in a single run, achieving a high infill percentage contrasting the results observed in ref. ⁵⁰ and could be accounted to using bulk molten metal microdroplets to create the conductive traces. Nevertheless, the PMP approach presents a more reliable, fully MM-AM approach selected as the preferred printing technique in the following work. Furthermore, PMP could be investigated in conductive materials other than bulk molten metal microdroplets.

Cross-section grinding of the conductive traces printed via PMP was done along the length of the channel, revealing exemplary conformity of metal with the polymer channel, see Fig. 2g. It was also noteworthy to see no air entrapment in the metal structures as in the polymer layer; see Fig. 2h. Furthermore, we estimated the infill percentage for the PMP technique against thermally cycled samples using similar sample sizes and measurements as described above. The samples were subjected to a thermal cycle between −40 and 60 °C for 60 min length of a cycle. After 100 cycles, there was almost no deviation observed in the infill percentage at different layers (Fig. 2i) or the resistance measured for each conductive trace prior to cross-section grinding (Fig. 2j). This is an exemplary result despite the difference in coefficient of thermal expansion (CTE) of metal and polymer; see Tables 1 and 2.

Drop-on-demand printing of bulk-metal vertical via

To our knowledge, the achievement of MM-AM for multilayer embedded 3D electronics, incorporating integrated vertical conductive pathways (vertical bulk-metal via) on a single setup without subsequent post-processing, has yet to be reported. This work introduces a layer-by-layer printing approach for vertical bulk metal via reaching up to 10 mm with a cross-section of 0.28 mm². The printing of metal microdroplets was maintained at a constant frequency of 18 Hz and a droplet diameter of (285 ± 15) μm. In contrast, printing polymer via holes using FFF relies on nozzle diameter, design parameters, and the printing process. The nozzle diameter and FFF process parameters are kept constant to streamline the investigation and reduce dependent parameters; see Table 3. Instead, the polymer via hole diameter was varied to understand the dependency of printed diameter (hereafter referred to as polymer via hole diameter) on the design parameters. Consequently, the diameter of the bulk-metal via is influenced by the polymer via hole diameter. The following paragraph presents optimization in achieving minimum polymer via hole diameter, optimum parameters for metal via holes, and characterization of 10 mm long vertical bulk-metal via. The polymer via hole was designed with a fixed cross-section, circular, and cylindrical body configuration. The choice of a circular cross-section was deliberate as it aligns well with the circular shape of the metal droplets deposited during the printing process. This configuration aims to minimize empty spaces and optimize the infill percentage in the printed samples, thereby enhancing the quality of the multilayer embedded 3D electronics produced via MM-AM. To explore the optimum dimensions for polymer via holes, we fabricated samples with variations in polymer via hole diameter and height. Four different configurations were prepared, altering either the target diameter (“CAD diameter” term denotes the design diameter) from 1 to 2.2 mm (see Fig. 3a, b) with a step size of 200 μm or the target height (“CAD height” term denotes design height) from 1 mm to 15 mm with a step size of 2500 μm, while keeping the other parameter constant (see SI, Section 4). We estimated the dimensional error in the polymer via hole diameter compared to CAD diameter to estimate the minimum printable via hole diameter. To ensure that metal via diameter consistently fits within the polymer via hole, we define metal via diameter = minimum printable via hole diameter. The polymer via hole diameter showed a nonlinear relationship for CAD diameter <1.6 mm (Fig. 3a). While the polymer via hole diameter showed a linear relationship for CAD diameter >1.6 mm (Fig. 3b). However, irregular behavior was observed for the entire range of CAD diameter starting from 1 to 2.2 mm. Therefore, the average polymer via hole diameter was calculated to estimate the dimensional error.

a, b Binary images of circular via hole printed with various CAD diameters from 1 to 2.2 mm with a step size of 200 μm. c Influence of via height on polymer via hole diameter. Each data point in the scatter plot represents individual observations. In addition, a line is plotted to visually represent the trend observed in the data. The error bars indicate the standard deviations. d Linear regression fit (red) to estimate the variation in polymer via hole diameter from CAD via hole diameter. The dotted line in green is obtained metal via diameter, and the dotted line in blue is obtained polymer via hole diameter. The error bars correspond to the standard deviation from the mean. e Influence of print speed on measured metal via diameter and height when CAD via diameter = 600 μm and CAD via height = 250 μm. The vertical dotted line is the obtained print speed. The error bars correspond to the standard deviation from the mean. f Cross-section image of bulk-metal via of height 10 mm covered in epoxy resin, (inset top) microscopic image of out-of-plane printed metal droplets with empty spaces covered in epoxy (highlighted in green), (inset bottom) magnified microscopic image showing the boundary of two layers of bulk-metal via.

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Calculated average measured polymer via hole diameter values were used in a linear regression model to create a linear fit, see Fig. 3d, and an equation for calculating dimensional error is obtained, see Eq. (4).

Where, x is CAD diameter in μm; y is polymer via hole diameter in μm.

The dimensional error calculated was (183 μm). Further validation tests for the dimensional error are done on different designs (see SI, Supplementary Table S5). Using Eq. (4), we determine the CAD diameter needed for optimum polymer via hole by adding the initial CAD diameter (minimum printable polymer via hole was obtained for this CAD diameter) of 1200 μm and the dimensional error (183 μm), see Fig. 3d blue line with label “polymer via hole”. Minimum printable via hole was obtained at 1200 μm. Therefore, the selected metal via diameter (Fig. 3d, green line with label “Metal via”) = 600 μm. Next, we determine the print speed for printing metal via. For this we employ Eq. (1), and vary the dot spacing between 75 and 250 μm with a step size of 25 μm (see SI, Section 6). Samples are prepared by keeping a fixed CAD via height = 250 μm, and CAD via diameter = 600 μm. Since we employ the MM-AM process, CAD via height = polymer layer height. Figure 3e shows the optimum print speed obtained = 3.15 mm s⁻¹ for a dot spacing of 175 μm.

Therefore, by systematic evaluation of process parameters for polymer via hole diameter and metal via diameter, we obtained the CAD diameter needed for optimum polymer via hole = 1400 μm and CAD metal diameter = 600 μm. The obtained CAD diameter for polymer was specific to FFF printed via hole and can be reduced to make smaller vias depending on the polymer technology. The desired dot spacing for printing fixed metal via configuration was obtained as 175 μm for metal microdroplet diameter of (285 ± 15) μm. Figure 3f shows a cross-section image of a 10 mm high via printed in polymer via hole. The inset (top) shows the microscopic view of metal and some epoxy present after sample preparation. The bulk-metal via was seen with round edges towards the side exposed to air, while the conformal placement of bulk-metal via was seen on the edge in contact with polymer. A magnification image in the inset (bottom) shows fusion or bonding between different layers of bulk metal via deposit. Despite the MM-AM process with significant residence time between consecutive metal layers, the fusion indicates lower oxidation of exposed tin (Sn in the SAC305 metal droplets). However, further investigation is needed to quantify the reliability of the MM-AM printed bulk metal via. Measured via diameter and measured via height (printed via diameter and height), see Fig. 3e showed variation in varying the dot spacing.

Analyzing the interaction between SAC305 molten metal microdroplets and polymer substrates

Yi et al.⁶³ presented a detailed report on the morphological evolution of molten metal droplets impacting different substrates. They presented different deposition morphologies of single-metal droplets impacting non-horizontal substrates such as ridges and grooves, to name a few. In this section, we investigated the behavior of molten metal microdroplets (also called metal droplets) of SAC305 on a polymer substrate (PETG). We found results aligning with the theory presented by Yi et al. polymer substrates printed using FFF technology often display non-horizontal surfaces due to roughness and suboptimal surface morphology⁶⁴. Consequently, these substrates typically undergo surface modification when integrated with printed electronics, as discussed by Roach et al. Since the metal droplet diameter (285 ± 15) μm is smaller than polymer road width extruded 450 ± 15 μm from FFF nozzle (see Supplementary Table 3), the metal droplet may fall either on the ridge of the polymer road or the flat surface during the printing process.

Metal droplets from SAC305 were examined using scanning electron microscopy (SEM), revealing variations in their contact with the PETG substrate based on the deposition point, see Fig. 4a–e. The morphological behavior of metal droplets on ridges, grooves, etc., was similar to that explained in ref. ⁶³. In higher magnification SEM images, it was intriguing to observe that, irrespective of the contact (angle) with the substrate, the metal droplets exhibited fusion or bonding with the PETG substrate, see Fig. 4b, d, f. This fusion structure resembled a wedge-shaped ridge, a phenomenon explained in ref. ⁵⁵, attributed to the kinetic energy loss of the metal droplet upon contact with the PETG substrate. Moreover, Dou et al. reported poor adhesion of SAC305 droplets on the pre-printed thermoplastic substrate. In contrast, the conductive traces printed on Synkròtima showcased exemplary trace width shape fidelity and high adhesion (ref. ⁵⁷). Zeba et al.’s notable enhancement in adhesion may be attributed to the fusion/bonding with the thermoplastic substrate (polymer/PETG) caused by MM-AM of bulk metal and polymer on a single setup. To delve further into this phenomenon, we conducted an investigation involving peeling the metal structures from the polymer substrates (Fig. 4g, h). Remarkably, the base of the peeled-off metal (Fig. 4i) and its contact area on the polymer substrate (Fig. 4j) exhibited an interference pattern, providing additional evidence for bonding through material bonding.

a, c, e SEM images of metal droplets deposited on non-horizontal polymer surfaces. b, d, f Magnified SEM images of droplets in (a, c, e), highlighting the interface of metal droplets at polymer surfaces, respectively. g Polymer surface without conductive trace highlighting the continuous ridge formed from conductive trace (removed in this image). h SEM image of conductive trace before it was ripped off from (h). i Patterns visible on the bottom surface of the conductive trace where it was in contact with the polymer substrate. j Surface of polymer with “negative” patterns visible after conductive trace (j) was ripped off. k–n Molten metal microdroplets deposited at various droplet spacing (higher to lower from left to right) to form bulk-metal via.

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In this stage of our investigation of MM-AM of metal droplets on thermoplastic substrates, the disparity in bonding between our samples (SAC305 on a thermoplastic substrate) printed using MM-AM and that reported by Dou et al., where SAC305 was printed on a pre-printed thermoplastic substrate, suggests that MM-AM may contribute to the improved bonding achieved. PETG has low thermal conductivity and low Tg (measured using differential scanning calorimetry (DSC)) of 57 °C (see SI, Supplementary Fig. S6) Therefore, its limited heat dissipation capability may have made the polymer rubbery when metal droplets were deposited. Notable (Fig. 4h) shows exemplary fusion on molten metal microdroplets to form conductive traces that do not exhibit distinct boundaries of individual droplets. This observation reveals that the sessile molten metal droplet remained molten when the next metal droplet was deposited with a dot spacing three times smaller than the droplet diameter (ref. ⁵⁷). In addition, the conductive traces demonstrated the melting or smoothening of the polymer substrate, see Figure (Fig. 4g). The ridge from the PETG substrate was visible protruding in the SEM image outside the area where the metal was peeled off. A distinct variation was observed on this ridge from the area on which metal was previously present. The area where metal was present can be easily distinguished from the continuous “wedge” formed on the polymer surface and is visible as bright lines. The smoothening or melting of the polymer substrate possibly facilitated better shape fidelity in the conductive traces formed from metal droplets.

In contrast to the side-by-side deposition of metal droplets to form conductive traces, metal droplets must be deposited out-of-plane to form a vertical column, which acts as a vertical via. As discussed above, the droplet spacing was varied between 75 and 250 μm with a step size of 25 μm to determine the optimum droplet spacing for which the target bulk metal via configuration could be achieved. The number of droplets printed per layer was calculated based on the print speed (see Eq. (1)) and the metal via diameter (discussed above) using Eq. (5).

Where D (mm) = Metal via circumference in mm obtained from the metal via diameter.

Equation (5) reveals that droplet spacing is inversely proportional to the number of droplets, implying that for increasing droplet spacing, fewer droplets are deposited. Figure 4k–n shows bulk metal via printing with increasing dot spacing from left to right. This agrees with the least number of droplets deposited in Fig. 4n. Nevertheless, the growth of the bulk-metal via with an increasing number of droplets appears relatively uniform, indicating that the difference in thermal properties of bulk metal (SAC305) and PETG present during the MM-AM process assisted in uniform morphological growth of the bulk-metal via.

MM-AM-printed multilayer demonstrators with embedded electronics

Employing the developed workflow for MM-AM of embedded 3D electronics, a 555-timer circuit with blinking LED (two metal layers sandwiched between three polymer layers) are printed in a single run as two different demonstrators, the Squid and Bunny demonstrator. These demonstrators validate the results obtained above, highlight the flexibility of the developed workflow, and showcase easy scalability in MM-AM process. The Squid demonstrator of dimension (105 mm × 55 mm × 3 mm) was printed as multilayer embedded 3D electronics 92 min (Fig. 5a). The total length of conductive traces distributed as two metal layers was 460 mm. The longest traces was 135 mm (Fig. 5b). In contrast, employing the ink-based technology to print only the gold antennas of length 175 mm on a substrate, Mohammed Alhendi et al.⁶⁵, needed 100 min. Two bulk-metal via of height 1 mm were integrated at a distance 43 mm (Fig. 5b, as red cylindrical block). The conductive traces consisted of features such as 90-degree sharp bends and 45-degree bends. In a single print run, the entire model was printed in transparent PETG (Fig. 5c) without any missing droplet on the longest trace. The longest trace required consecutive and precise deposition of 730 molten metal microdroplets. The neat deposition of conductive traces at the pins of the 555 microcontroller can be seen in Fig. 5d, A. While direct soldering of the embedded SMD resistor (Fig. 5d, b) was enabled by molten metal microdroplets of SAC305 (a common soldering metal⁶⁶).

a Exploded CAD model view showing the different conductive layers (yellow) and polymer layers (green). b Isolated view of the longest metal trace of length, 134 mm, and two metal via (red) of the height of 1 mm. c Printed result of the squid-shaped demonstrator showing both embedded conductive layers (right) and highlighted single conductive trace (placed against light source) (left). d Top view of electrical connections to 555-timer pins (A). Directly soldered SMD placed in a polymer slot with conductive traces printed on contact pads (B).

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The Bunny demonstrator with dimension (58 mm × 28 mm × 3 mm), half the size of the first demonstrator, was printed in 45 min, highlighting the scalability of print time based on object dimension. The total length of conductive traces distributed as two metal layers was 260 mm. This demonstrator highlights further aspects of scalability possible in terms of variation in features of conductive traces with respect to a smaller radius of curvature, closer via placements, and denser distribution of conductive traces (Fig. 6a). MM-AM printed Bunny was also stopped before the completion of the final print to highlight the features of conductive traces formed from molten metal microdroplets on PETG (Fig. 6b). Figure (Fig. 6b, inset) shows an exemplary printed bulk-metal via neatly embedded in polymer and interconnected to the subsequent conductive trace. Although the SMDs used for these demonstrators were directly soldered from the molten metal microdroplets of SAC305, they exhibited a uniform placement on SMD contact pads and conformal interface with polymer layer (Fig. 6c). Furthermore, for SMDs with legs (such as the 555-timer IC), microdroplets exhibited a conformal interface around the pins (legs) of the IC. Refer to SI Section 9 for further details. For both demonstrators, all SMD components were manually placed in their respective slots. Two different approaches were employed for placing SMDs with legs (such as the 555-timer IC, similar to the approach in ref. ⁶⁷) and SMDs without legs (such as LEDs and resistors), as detailed in the Supplementary Information (SI), Section 7. To ensure the reproducibility of results regarding the placement of SMD components in the FFF-printed slots and their subsequent interconnection with the next layer of conductive traces, the FFF-printed slots underwent calibration using a sample size of 60, as outlined in SI, Section 8. Single setup, single G-code based, fully embedded MM-AM of molten metal microdroplets and the polymer were successfully demonstrated with the 555-timer electronic circuit and its blinking LED (Fig. 6d).

a Isolated view of free-form metal traces highlighting multiple variation in the features of conductive traces. b Top conductive layer before embedding it with the polymer cover, (inset) exemplary image of an interconnected bulk-metal via. c Microscopic image of a cross-sectioned embedded LED showing electrical connections. d Successful scale down of 555-timer circuit showing the blinking LED in ON state.

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We demonstrated the single-run printing of two free-form shaped demonstrators with distinct features using MM-AM for multilayer embedded 3D electronics on Synkròtima. This process involves the on-demand deposition of molten metal microdroplets to create electrically conductive traces and vertical bulk-metal vias. Using embedded electronic circuits with bulk metal introduces a promising technology to reduce surface modifications on polymer substrates. This reduction helps alleviate environmental impact by minimizing waste production and decreasing the overall production time for the final device. Various techniques for embedding electronics likely apply to other printed electronics technologies with similar printing resolutions. Embedding electronic circuits offers longevity by reducing empty air and humidity-filled spaces, mitigating degradation and corrosion in low-resistance metal-based conductive traces. MM-AM for multilayer embedded 3D electronics using molten metal microdroplets addresses deformities and limitations presented by polymer technology through conformal interaction observed at the interface of the two materials. The investigation of the metal–polymer interface reveals a bonding between the two materials through interlocking features and a wedge-shaped peripheral ridge of polymer around the metal. Sequential integration of vertical via in MM-AM for multilayer circuits enhances the scalability of 3D electronics. Observations indicate a uniform growth of bulk metal via with an increase in the number of deposited metal droplets. The configuration of bulk-metal via can be customized according to polymer technology requirements. The presented straightforward workflow facilitates the conversion of various multilayer electrical schematics into a unified G-code for multilayer embedded 3D electronics. This approach holds the potential for diverse combinations of polymer and conductive material printing technologies. The straightforward workflow, bulk-metal embedded electronics, easy integration, and adaptable sizing of bulk-metal via within the multilayer 3D electronic circuits create possibilities for tailored user-specific and free-form 3D electronics. Our process offers significant advantages, including low resistance, cost-effectiveness, and efficient fabrication, while providing unparalleled design freedom and precise deposition through non-contact printing of molten metal microdroplets. Notably, this approach eliminates the need for sintering or additional processing steps, streamlining our fabrication method. However, challenges persist in long-term reliability testing, integrating sensing and other functionalities into 3D-printed devices, and exploring diverse substrate materials for widespread applications in the electronics industry.

The future scope encompasses several exciting possibilities in AM for electronics. First, there is an opportunity to enhance the versatility of 3D-printed devices by integrating a range of sensing and actuation modalities, expanding beyond simple electronic circuits. This could involve leveraging existing PCB sensing technologies for seamless integration into 3D-printed structures⁶⁸. Moreover, advancements in 3D electronics could involve incorporating display systems to enable more user-interactive features⁶⁹. In addition, integrating computational capabilities through microcontrollers holds promise for enhancing the functionality of 3D-printed electronics. Inspired by recent research on self-assembly techniques for microcontrollers and electronic components in 3D electronics⁷⁰, further exploration in this area could lead to more efficient and streamlined fabrication processes. Exploring alternative materials such as metamaterials⁷¹ could minimize reliance on traditional rigid semiconductor electronics, offering enhanced reliability and contributing to the concept of decentralized fabrication units. Extending these advancements to free-form structure printing opens up new AM innovation avenues. Previous research by Ostmann et al.⁷² showcased the development of 3D electronics within free-form 3D structures by thermoforming deformable electronics embedded in a thermoplastic matrix. Similarly, in the work by Paulsen et al.⁷³, non-contact deposition of metal nanoparticle inks was achieved using Aerosol Jet printing. This study successfully demonstrated the deposition of metallic traces on curved surfaces (both convex and concave) as well as within trenches and via holes. Expanding on their contributions, we aim to enhance the versatility of electrical and mechanical designs for 3D electronics. This includes the ability to print on non-planar surfaces such as hemispheres, trenches, curves or irregular free-form 3D object surfaces. This could enable the fabrication of complex, organic shapes with integrated electronics, pushing the boundaries of what is achievable in 3D printing for electronics.

Synkròtima: the hybrid printing setup

Utilizing the MM-AM approach for 3D electronics, our method, depicted in Fig. 7b, employs two printheads on a linear x axis. Each printhead is designated for the printing of polymer and metal, respectively. Synkròtima serves as the enabling platform for MM-AM, allowing for the sequential deposition of polymer filament and molten metal microdroplets on an open-source desktop printer, specifically the Original Prusa i3 MK3 from Prusa Research a.s., Czech Republic, as highlighted in Fig. 7a. Critically, this process is uninterrupted, requiring no pre- or post-processing steps for polymer or metal The complete information on the construction, integration, and optimization of different printheads is explained in prior work.

a CAD model (top view) of Synkrótima with the StarJet printhead integrated next to the FFF printhead for MM-AM of embedded 3D electronics. b Illustration of sequential printing by FFF and StarJet printhead.

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The Fused Filament Fabrication (FFF) technology prints polymers utilizing the Prusa extruder(direct drive, bondtech gears, V6 hotend). The molten thermoplastic filament is deposited layer-by-layer onto a heated print bed, following a pre-defined tool path file known as G-code prepared on Prusa Slicer (Edition v2.4.2 software, Prusa Research, Czech Republic). This G-code is employed generically for any 3D printer. Metal is deposited through the StarJet technology, the University of Freiburg patented technology. Prior art published on the StarJet technology^74,75,76,77 comprehensively explains the technology and its relevant parameters. Molten metal microdroplets are generated by the Drop-on-Demand (DoD) operation mode of the StarJet technology, whereby pneumatic actuation through a solenoid valve allows droplet generation. This work operates the StarJet printhead at a constant melt temperature through a closed control loop. Furthermore, the StarJet printhead utilizes nitrogen gas to prevent oxidation and induce the break-off of droplets.

Printing materials

Two variations of Polyethylene Terephthalate Glycol Copolymer (PETG) filament are used to print the polymer parts. The first variation of PETG filament is Prusament PETG Prusa Orange, 1 kg (obtained from Prusa Polymers a.s., Prague, Czech Republic). The second variation of PETG filament is Fillamentum PETG Pink Lollipop Transparent, 1 kg (obtained from 3djake, Austria). Both filaments are transparent filaments to observe the embedded electronic components. Some essential physical and thermal properties for both the filaments^78,79 are listed in Table 1. Molten metal microdroplets are printed from flux-free SAC305 solder alloy, TAMURA ELSOLD – LEAD-FREE SOLID WIRE, D=1MM, Sn_96.5Ag_3.0Cu_0.5, 1KG, (obtained from TAMURA ELSOLD, Ilsenburg, Germany), see Table 2^80,81.

Fixed parameters for polymer and metal deposition

The printing parameters used for polymer extrusion and droplet deposition during the sample preparation are displayed in Table 3. The polymer filaments were stored at room temperature for printing. The filaments did not undergo any active or passive drying processes. There was no heated printing chamber for polymer printing. The StarJet printhead was kept at a 75% fill level relative to the total volume of the reservoir, which had a volume of 20,000 mm³.

Characterization methods

Imaging and image processing are done using LEICA M165C Optical microscope and ImageJ software, respectively. For resistance measurements, we meticulously conducted a four-point measurement using gold pad probes. Precautions were taken to ensure the probes remained free of any oil or dust particles. All measurements were performed under similar environmental conditions within a well-isolated laboratory setting. The four-wire resistance measurement was executed utilizing the KEITHLEY 1100 V SourceMeter with KickStart software in the current sweep mode. Throughout this process, the current was incrementally increased from 0 to 1 A, while recording the corresponding voltage drop. One hundred data points were collected per measurement. Subsequently, the resistance of the printed metal structures was calculated based on the resulting I–V curve. Metal structures enclosed in polymer undergo cross-section analysis by embedding the samples in two-component epoxy to maintain structural integrity. After hardening the epoxy in a pressurized (2 bar) container to remove air gaps, the cross-section plane of the samples is reached using wet grinding with grit sandpapers of decreasing roughness (180, 320, 600, 1200, 2500, and 4000) with a Struers Knuth Rotor wet-grinder. The procedure includes optical microscope checks to ensure the desired cross-section plane is reached. Subsequently, the samples are polished with 9-, 6-, and 3-μm suspensions (SiC), respectively, followed by image capture using a Zeiss Axioplan microscope with a ProgRes C12 camera. Thermal cycling tests were performed in the VOETSCH temperature test chamber (Voetsch Industrietechnik, Germany) by varying the temperature from −40 to 60 °C. Each temperature extreme was sustained for a duration of 30 min within the test chamber, forming a cycle. Resistance of the samples was passively measured before and after thermal cycling using a four-wire resistance measurement.

Statistical analysis

The measurement values and relationship between parameters are represented using graphs. The correlation between the two parameters is depicted using a scatter plot. It illustrates the relationship between data points on the x axis and y axis. Each point represents a unique data observation and pattern when the data are taken as a whole. The error bars depict the standard deviation. Violin plots are used to make a comparison of distributions between multiple sets of data. The violin plot displays the distribution of a continuous variable (on the y axis) across different categories or groups (on the x axis). It is used to visualize the distribution of the data. The width of each “violin” represents the data density at different values along the y axis. The box-and-whisker plot provides information on quartiles and mean within a specific range (commonly 1.5 times the interquartile range). The whiskers depict the standard deviation, while the outliers are represented with dots.