Introduction

Aerosol jet (AJ) printing, as an emerging non-contact additive manufacturing technique, is capable of fabricating various conformal electronics including passive components1,2,3,4,5, sensors6,7,8,9,10, and high-performance interconnects11,12,13,14,15 over different substrates. Compared to other direct ink-writing printing methods16, such as syringe/extrusion and ink-jet printing, AJ printing offers several key advantages. For example, the aerosolized ink stream enables a nozzle-to-build plate standoff distance of 2–5 mm and print ink stream widths having diameters as small as 10–20 μm17. The large working distance provides a distinct advantage for printing on surfaces with significant roughness or topographical features, especially along sharp corners over a complex surface. Most studies6,12 declare that AJ printing has a resolution down to 10 μm. However, it remains a challenge when it comes to fabricating a pattern with multi-ultrafine lines and very small line gaps. Moreover, the heavy overspray and bulged line geometry largely hindered its application in conformal electronics18, especially under high-frequency operation and confined printing areas19. As a consequence, the proximity of the planned deposition parts may result in inadvertent contact due to overspray20, potentially resulting in short circuits and substantial impairment to their electrical capabilities19. In addition, overspray is critical to the electrical properties of a printed device, as an excess of overspray may lead to short circuits and increased resistance21. Concurrently, the presence of overspray reduces the density of a given trace, leading to the actual effective deposition being insufficient compared to the intended amount22. Furthermore, deficient focus during the deposition procedure poses obstacles to achieving the desirable densification, thereby restricting conductivity and giving rise to insufficient print strength and compromised electrical performance23. Many efforts have been made to improve the printing resolution and uniformity, as well as to explore effective ways to reduce overspray issues, mainly involving three aspects, including optimization of operating parameters21,24,25,26, nozzle geometry27,28,29, and ink properties30. The focusing ratio, defined as the ratio of sheath gas flow rate to carrier gas flow rate, was considered as a key parameter to determine the geometry of printed traces31, which has an optimal value corresponding to the highest resolution obtained. This optimal value was reported to depend on the level of turbulence in the flow field. Das et al. established a detailed and accurate three-dimensional computational fluid dynamics model for AJ printing to reveal the interplay between the monodisperse droplet size and gas flow20 and pointed out that higher print resolution requires a higher sheath gas velocity, however, overspray increases after decreasing to its minimum value with the increasing sheath gas velocity. The fundamental fluid mechanics principles that govern the deposition process in AJ printing were also explored32, which proposed that those aerosols deposited along the center of the line are distorted much more significantly than the edge aerosols. The ink composition variation and the interaction between drying induced by the sheath gas and impaction also have a dramatic influence on the line quality33,34, and it is also necessary to consider whether they meet the physicochemical conditions of AJ printing when formulating inks to improve printing quality and conductivity. The above multi-directional research has effectively explored the key factors of AJ printing and their influence on the output, providing sufficient theoretical guidance for optimization. Despite the advancements in AJ printing technology, the micro-electronic devices produced exhibit suboptimal electrical performance due to the inferior geometric characteristics of the printed lines35. Specifically, the low controllability of the printed line width may induce overlap of narrowly spaced circuits or unnecessary intertrack voids, which will hinder the wide application of AJ printing in the advanced electronic manufacturing industry36. Therefore, ensuring high precision and low overspray for high-density is essential for AJ printing, which urgently needs an effective, real-time, stable, and low-constrained optimization approach.

Due to excellent directionality37,38, strong penetration39,40, high sensitivity41,42, and stability43, acoustic focusing (AF) is another promising approach to kinds of micro-manipulate particles in a fluid, which has been extensively applied in many particles focusing research works as follows. Acoustically assisted direct write printing44,45 has successfully revealed the enormous potential of tunable ordering46,47 and alignment of various microscale particles48,49 using acoustic electrophoresis. Cicek et al. numerically proposed an acoustophoretic separation method of spherical solid particles in the air by means of an acoustic Fresnel lens50. Choi et al. demonstrated controlled printing of charged nanoparticles using a metal-coated stencil mask by applying an electric potential to engineer the electric field streamlines through the mask opening51. Pan et al. focused a stream of moving micron-sized aerosol particles in the air by the combined drag force and optical force that is generated by a double-layer co-axial nozzle and a focused doughnut-shaped hollow laser beam, respectively52. Huang et al. presented an electrodynamic concentration approach for submillimeter-sized conductive metal particles focusing on moving gas-powder streams to generate a tightly focused powder stream in powder-fed directed energy deposition (DED) additive manufacturing53. Smith et al. demonstrated a methodology allowing magnetic fields to dynamically manipulate processing conditions in powder-fed DED as an adaptive control technique in cases where greater control of track dimensions or enhanced material feed control is required54. Martinez-Marchese et al. used an ultrasound phased array to produce a small volume of high-intensity ultrasound to acoustically focus and deflect particle streams exiting from a nozzle analog55, as well as demonstrating acoustic focusing within a working powder-fed DED machine, to increase catchment efficiency56. Nonetheless, for aerosolized particles (APS) with smaller particle sizes (20 ~ 50 nm), faster jet speed (30 ~ 80 m/s), and the shape of the 3D flow field17 as well as the requirement of radial focusing from all angles, this is still a challenge. Moreover, the complicated solvent system of conductive ink and evaporation around the periphery of the sheath gas tend to add another degree of challenges in the AF during the AJ printing process.

Here, we report on the realization of AJ printed ultrafine patterns with minimal overspray by utilizing the AF method. This efficient, stable, non-invasive, and fully reversible focusing strategy enables AJ printing to fabricate high-precision conformal traces with minimal overspray and better packing density at the same time. A modified print nozzle geometry with two tapered focusing zones was proposed to fix the annular piezoelectric tube, in order to form an annular acoustic field that radially focuses the APS toward the center of the piezoelectric tube. Experimentally, an ultrafine-printed Ag ink stream with a line width (LW) of 5.71 μm and overspray of 0.08 μm was achieved under AF, the corresponding focusing and defocusing process were observed which indicates the focusing behavior is fully reversible and omnidirectional. The focusing mechanism of APS coupling with the flow field and the annular acoustic field was revealed through particle trajectory tracking in a three-phase field model. We show that within the AF, the LW of Ag ink streams is decreased to 60 ± 5% compared to that without AF. Meanwhile, the conductivity of the AF Ag ink stream exhibits an increase of 180 ± 5% compared to that without AF due to a better packing density of the nanoparticles. Using this focusing strategy,a serpentine array comprising 24 ultrafine traces (LW: 6 ± 0.3 μm, overspray: 0.3 ± 0.1 μm, line gap: 6 ± 0.3 μm) is demonstrated. Furthermore, a printing experiment with AF was performed over 8 h with little observed variation of printed traces to exhibit remarkable printing stability. The complete demonstration of AJ printing with the AF for fine features with ultrafine LW, minimal overspray, and better packing density powerfully shows the enormous potential of AJ printing for next-generation conformal electronics with higher integration and better performance.

Results and discussion

Mechanism of annular acoustic field assisted aerosol-jet printing

Figure 1a demonstrates the incorporation of an externally positioned piezoelectric tube within the AJ print nozzle. In this configuration, an electrical field is selectively applied to the tube utilizing a signal generator and power amplifier. An annular acoustic field was established inside the nozzle to accomplish the AF of APS attributed to the inverse piezoelectric effect. The APS, propelled by the carrier/sheath gas, undergo laminar flow dynamics20 characterized by a notable Stokes number18. This leads to the dominance of Stokes drag27, as the primary acceleration mechanism for the particle, propelling the APS through the nozzle as depicted in Fig. 1b. The corresponding transition area (Fig. 1c) is a distinct indicator of the APS behavior during the AF process inside the nozzle channel. The initial diameter of the ink flow, denoted as D0, was predominantly influenced by factors such as limited pneumatic focusing20,31 and environmental disturbances. However, under the effect of AF (Fig. 1c), the diameter of the ink flow can be further diminished, leading to a smaller dimension denoted as DA. The LW of the deposited ink stream can be modified by manipulating the acoustic field, enabling fast and precise control over its ON and OFF states. Moreover, the overspray caused by droplet drift and dispersion due to insufficient focusing can also be mitigated to a certain degree (Fig. 1d).

Fig. 1: Overall concept, design, and effects.
figure 1

a Schematic diagram of AJ printing assisted with acoustic focusing (AF). A piezoelectric tube is attached to the nozzle of the original AJ printing system, which is excited by a signal generator through a power amplifier. b The APS are transported into the printhead by the carrier gas, then focused and sprayed by the sheath gas, and further focused through the annular acoustic field generated by the piezoelectric tube. c Schematic drawing of focusing behavior for APS when passing through the acoustic field. Vflow is the velocity, D0 is the original diameter, and DA is the focused diameter, of the ink flow, respectively. d Schematic drawing of AJ printed trace during the AF process. e, f Top and cross-section view of the APS distribution under the radial radiation force in the nozzle channel. g Force distribution on APS during the jetting process. Vaxial and Vradial are the axial and radial particle velocity, respectively. Vjet is the particle jetting velocity.

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As illustrated in Fig. 1e, f, an annular acoustic field is formed using the annular piezoelectric tube, inducing a radial acoustic radiation force that acts upon the APS, propelling them towards the central axis. During the AJ printing process, the APS experiences a variety of forces due to the interaction between high-speed gas flow and an annular acoustic field. As shown in Fig. 1g, Stokes drag force is acting in the axial direction of the nozzle, while the acoustic radiation force is exerted in the radial direction of the nozzle. As a result, the axial movement of the APS in the nozzle channel is concurrent with its convergence towards the central axis. The LW of printed traces can be in-situ changed by the AF ON and OFF.

A piezoelectric tube generates vibration through the inverse piezoelectric effect, and the boundary acceleration generated by mechanical vibration serves as the boundary input of the acoustic field. The coupling equation of the acoustic-structure boundary57 is

$${{{\bf{n}}}}\left(\frac{\nabla {{{{\bf{p}}}}}_{{{{\bf{t}}}}}}{{\rho }_{0}}\right)={{{\bf{n}}}}a$$
(1)

where \({{{{\bf{p}}}}}_{{{{\bf{t}}}}}\) is the acoustic pressure at the boundary of the acoustic field, \({\rho }_{0}\) is the static density of the acoustic propagation medium, \(a\) is the vibration acceleration generated by the interface between the piezoelectric transducer and the acoustic field, \({{{\bf{n}}}}\) is the normal component of the boundary.

The boundary input acoustic pressure \({p}_{t}\) produces the acoustic waves in the acoustic medium. The acoustic pressure distribution in the entire acoustic space is obtained from the Helmholtz equation57, and the simplified equation is

$${\nabla }^{2}{{{\bf{p}}}}=-{{k}_{{eq}}}^{2}{{{\bf{p}}}}$$
(2)

where \({{{\bf{p}}}}\) is the acoustic pressure and \({k}_{{eq}}\) is the wave number.

The calculation method of \({k}_{{eq}}\) is diverse for different medium models. This study involves two kinds of pressure acoustic models, the acoustic attenuation model for the nozzle wall, as well as the thermally conducting and viscous model for the gas layer and ink solvent layer48. For the acoustic attenuation model,

$${{k}_{{eq}}}^{2}={\left(\frac{\omega }{c}-i\alpha \right)}^{2}$$
(3)

where ω is the angular frequency of the ultrasonic transducer, \(c\) is the acoustic velocity, and \(\alpha\) is the acoustic attenuation coefficient. For the thermally conducting and viscous model50,

$${{k}_{{eq}}}^{2}=\frac{\rho {\omega }^{2}}{\rho {c}^{2}+i\omega \left[\frac{4}{3}\mu+{\mu }_{B}+\left(\gamma -1\right)\frac{{k}_{{th}}}{{c}_{p}}\right]}$$
(4)

where \(\rho\) is the density, \(\mu\) is the dynamic viscosity, \({\mu }_{B}\) is the volume viscosity, \(\gamma\) is the specific heat capacity ratio, \({k}_{{th}}\) is the thermal conductivity, and \({c}_{p}\) is the specific heat capacity at constant pressure.

The acoustic radiation force \({{{{\bf{F}}}}}_{{{{\bf{rad}}}}}\) exerted on an individual particle within an acoustic field58 can be expressed as

$${{{{\bf{F}}}}}_{{{{\bf{rad}}}}}=-\pi r\nabla \left\{\frac{2{\kappa }_{f}}{3}{{\mathrm{Re}}}\left[\left(1-\frac{{\kappa }_{p}}{{\kappa }_{f}}\right){{{\bf{p}}}}\nabla {{{\bf{p}}}}\right]-{\rho }_{f}{{\mathrm{Re}}}\left[\left(\frac{2\left({\rho }_{p}-{\rho }_{f}\right)}{2{\rho }_{p}+{\rho }_{f}}\right){{{\bf{c}}}}{{{\boldsymbol{\nabla }}}}{{{\bf{c}}}}\right]\right\}$$
(5)

where \({{{\bf{p}}}}\) is the acoustic pressure at the location of the particle, \({{{\bf{c}}}}\) is the acoustic velocity of the particle’s environment, \(r\) is the radius of the particle, \({\kappa }_{p}\) and \({\kappa }_{f}\) are the isentropic compressibility coefficient of the particle and ink solvent, respectively. \({\rho }_{p}\) is the particle density, \({\rho }_{f}\) is the ink solvent density.

It is noted that the frequency of the applied excitation largely affects the focusing behavior, as it controls the characteristics of the resulting acoustic field. In this case, the acoustic velocity stays constant, allowing us to determine the input frequency based on the ultrasound wavelength in the ink. The focusing behavior of APS relies on the distribution of acoustic pressure nodes significantly. To align particles towards the central axis of the print nozzle, a single pressure node in the nozzle channel is essential59. Without this, APS may converge towards multiple nodal points, dispersing ink particles (Supplementary Fig. 1a). It is determined that if there is no more than one pressure node within the diameter range, it must comply with \({\lambda }_{{ink}}\ge {D}_{{ink}}\), and if there is no less than one pressure node within the diameter range, it must comply with \({\lambda }_{{ink}}\le 2{D}_{{ink}}\), where \({D}_{{ink}}\) represents the diameter of the ink flow. Therefore, to meet these requirements, the relationship between wavelength and channel radius can be determined as \({D}_{{ink}}\le {\lambda }_{{ink}}\le 2{D}_{{ink}}\). At this point, we simulated the acoustic field distribution within this wavelength range (Supplementary Fig. 1b) and selected the most suitable design of the piezoelectric acoustic field (Supplementary Fig. 2a, b). In addition, the velocity distribution of the turbulent flow field was calculated based on the stationary Reynolds-averaged Navier-Stokes (RANS) equations in combination with a k-ε model32, as shown in Supplementary Fig. 2c.

Once the flow field is calculated, the drag force on a single jetting particle at any position can be obtained58, which is expressed as

$${{{{\bf{F}}}}}_{{{{\bf{drag}}}}}=6\pi \mu r({{{{\bf{v}}}}}_{{{{\bf{f}}}}}-{{{{\bf{v}}}}}_{{{{\bf{p}}}}})$$
(6)

where \({{{{\bf{v}}}}}_{{{{\bf{f}}}}}\) is the ink solvent flow velocity, and \({{{{\bf{v}}}}}_{{{{\bf{p}}}}}\) is the particle velocity.

Finally, the motion of particles under the coupling of acoustic radiation force and fluid drag force is mainly determined based on the conservation of momentum, which is given by

$$\frac{{{{\rm{d}}}}\left({m}_{p}{{{{\bf{v}}}}}_{{{{\bf{p}}}}}\right)}{{{{\rm{d}}}}t}=\sum {{{\bf{F}}}},\frac{4}{3}\pi {r}^{3}{\rho }_{p}\frac{{{{\rm{d}}}}{{{{\bf{v}}}}}_{{{{\bf{p}}}}}}{{{{\rm{d}}}}t}={{{{\bf{F}}}}}_{{{{\bf{rad}}}}}+{{{{\bf{F}}}}}_{{{{\bf{drag}}}}}$$
(7)

where \({m}_{p}\) is the mass of the particle, and \({{{{\bf{v}}}}}_{{{{\bf{p}}}}}\) is the particle velocity vector of the particle.

Due to the AF effect on ink particles, equivalent to the radial displacement \({A}_{r}\), it requires time \({t}_{0}\) to accumulate, which is determined by its axial motion through the acoustic field. The following is the time function of its axial and radial motion:

$${L}_{0}={\int }_{\!\!\!0}^{{t}_{0}}{{{{\bf{v}}}}}_{{{{\bf{p}}}}}\cdot {{{{\bf{e}}}}}_{{{{\bf{a}}}}}{{{\rm{d}}}}t,{A}_{r}={\int }_{\!\!\!0}^{{t}_{0}}{{{{\bf{v}}}}}_{{{{\bf{p}}}}}\cdot {{{{\bf{e}}}}}_{{{{\bf{r}}}}}{{{\rm{d}}}}t$$
(8)

where \({L}_{0}\) is the length of the AF area, \({{{{\bf{e}}}}}_{{{{\bf{a}}}}}\) is axial unit vector, and \({{{{\bf{e}}}}}_{{{{\bf{r}}}}}\) is radial unit vector.

The focus rate can be determined by \(\varnothing=\left({R}_{0}-{A}_{r}\right)/{R}_{0}\), where \({R}_{o}\) is the original particle flow radius. Based on the performance and specifications of the current piezoelectric tubes, we simulated the calculations for AJ printing traditional aerosol Ag nanoparticle ink using the AF method. The simulation results (Supplementary Fig. 2e) showed that the diameter of the aerosol ink flow has been focused from D0 to DA, with a focusing rate of around 70%. By tracking the trajectory of ink particles in the acoustic-flow coupled physical field model, the spatial arrangement of particle clusters deposited on the substrate is obtained (Supplementary Fig. 2f). The particle concentration distribution, stated as normalized as shown in Supplementary Fig. 2g, was derived from statistical analysis of the position information of all particles at the substrate in the simulation. The longitudinal trend of its distribution is closer to the topography profile of actual printed lines. The distance between the two ends of the distribution can be approximately determined as LW. Remarkably, our calculations reveal that the utilization of simulated AF has resulted in a reduction of LW to approximately 70% of its original magnitude.

Aerosol-jet printing assisted with acoustic focusing

To realize the annular acoustic field-assisted AJ printing, the primary task is integrating the circular piezoelectric tube into the printing nozzle which is normally fabricated with a taper cylindrical geometry and maintaining the printing capability as well. A modified design for print nozzle is introduced, featuring two distinct aerodynamic focusing zones and a cylinder zone to accommodate the piezoelectric tube. The two aerodynamic focusing zones are based on the convergence design which has been widely used in AJ printing nozzle. Based on the conical design of the original nozzle for pneumatic focusing, combined with the standard tubular geometry of the piezoelectric tube for AF and considering its assembly stability, a standard tubular channel has been integrated into the conical nozzle’s structure for the AF mechanism in the AJ system, in order to ensure consistent radial transfer of acoustic radiation force. The modified nozzle structure is depicted in Supplementary Fig. 3a. Its inlet maintains the original structure and parameters, connected to the printer. There are also five parameters to constrain this structure, defined as upper focusing length (UFL), lower focusing length (LFL), acoustic channel sizes (length and diameter), and outlet diameter, which jointly determine the printing effect of the corresponding nozzle. To ensure the AF quality, the acoustic channel length is calculated to be 30 mm which is determined by the focusing time and velocity of the APS. Here, the velocity is approximately 30 m/s, as determined from the aerosol particle jetting simulation (Supplementary Fig. 2d), which falls within the normal ejection speed range6 of 10–100 m/s, and the focusing time is established to be 1 ms from the simulated result. The inner and outer diameters of the acoustic channel are determined by theoretical calculations using the available parameters of the piezoelectric tube. The outlet diameter is determined by the minimum aperture achievable through current processes. The other two parameters, namely UFL and LFL, jointly determine the pneumatic focusing printing effect without AF in this structure. A numerical combination method, as shown in Supplementary Fig. 3a, was used to optimize these two parameters without AF. As shown in Supplementary Fig. 3d, e, the investigation resulted in a LW of 10.13 μm and an overspray of 0.84 μm, which has completely broken through the limit printing accuracy and printing quality of the commercial nozzle with an outlet diameter of 260 μm (Supplementary Fig. 3f–h), meeting the high-resolution requirement of AJ printing manufacturers. Therefore, the nozzle of this type can be selected for AF-assisted AJ printing, as shown in Supplementary Fig. 3b, c, and whose structural parameters are shown in Supplementary Table 2.

The modified nozzle demonstrates an exemplary printing capability by achieving a remarkable printing resolution of ~10 μm with an overspray of ~0.7 μm when AF is turned off (Fig. 2a, c). Another essential parameter to consider is the optimal focusing frequency for AF, as it could significantly impact the focusing effect. A simulation result yields a theoretical value of 6 MHz, which may exhibit slight disparities compared to the actual value due to variations in material properties and acoustic field between the theoretical model and the real printing system. AJ printing experiments were conducted using AF ON in the frequency range from 5 to 7 MHz, with a precise step size of 0.2 MHz. The morphology variations of the AJ printed traces were recorded by an optical camera, as shown in Supplementary Fig. 5, which enabled us to identify the optimal focusing frequency. By measuring and comparing their LWs, it can be seen that the LW under frequency changes does not vary monotonically, and the instantaneous values of LW at some single frequencies clearly cannot be stably maintained. This phenomenon can be associated with the simulated outcomes of acoustic field distribution established under different frequency inputs (Supplementary Fig. 1b) and explained. When the acoustic pressure nodes are not at the neutral axis position, ink particles are not sufficiently focused to the central axis, so the ink flow is not constrained to be dense enough, resulting in a larger LW. When the distribution of pressure node is erratic, ink particles are driven to move in chaotic directions, causing noticeable unstable LW variations of the printed traces. Thereby, the optimal focusing frequency of Ag nanoparticle ink employed in this study has been determined to be 5.8 MHz. It is known that there are indeed disparities exist between the designated material properties for ink, gas components, nozzles, and piezoelectric tubes in simulation, and their corresponding actual material characteristics in experiments, especially the precise material properties of the piezoelectric tube are not completely understood, thereby resulting in a minor incongruity between the optimal frequencies derived from simulations and those deduced from practical experiments. Moreover, an intermediate component, referred to as a power amplifier, serves the purpose of amplifying the acoustic signal’s output power to a significant extent. This crucial amplification process facilitates the attainment of a more refined and precise focusing phenomenon.

Fig. 2: The impact of AF on the geometric morphology of AJ printed line.
figure 2

a Original geometric morphology of an AJ printed line before acoustic focusing (AF). b Geometric morphology of the line printed continuously under AF ON. The linewidth (LW) has been significantly reduced, and the overspray has been suppressed to a lesser extent. c Geometric morphology of the line printed continuously with (b) after turning off AF. Both the LW and the overspray have been restored to their original condition. d Overview of an AJ printed line undergoing three consecutive states: AF OFF, ON, and OFF. e, f Converging and diverging processes of the AJ printed line during intervention and evacuation of AF. Vp is the printing speed, and lp is the length of transition zone. This proves the effectiveness and sufficiency of AF.

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It is worth mentioning that this remains almost consistent for each type of ink. Based on that the acoustic frequency is directly determined by the wavelength, and the design of the wavelength is based on the nozzle geometry, which will be explained as follows, the optimal focusing frequency is specifically determined by the nozzle geometry. For the purpose of focusing the particles, it is required that the pressure node of the acoustic wave be set at this axis position. There exists an optimal wavelength that satisfies this distribution, which enables the entire acoustic field to form an optimal acoustic pressure distribution and achieve an optimal focusing effect for printing ink particles. This design is not about the ink. For different inks printed using a nozzle of the type n this study, their optimal focusing frequencies are consistent, however, due to differences in ink particle properties, there may be variations in achievable focusing degree at this optimum frequency. What’s more, although the nozzle geometry design in this study has achieved comparable printing results compared with ones using ordinary nozzle, there is still room for optimization in its geometry and corresponding printing effects. As a result, the corresponding optimum frequency will undergo corresponding changes accordingly when using a possible more excellent nozzle geometry.

As illustrated in Fig. 2d, a consecutive AJ printed trace with three different sections was obtained. Under the AF OFF state, an AJ printed trace (LW: 9.68 μm LW, overspray: 0.66 μm) was achieved with the aforementioned nozzle geometry (Fig. 2a). Upon system transition to the AF ON state, APS migrated towards the central axis of nozzle channel due to acoustic force. As illustrated in Fig. 2b, an ink stream with a LW of 5.71 μm and a minimal overspray of 0.08 μm was observed without altering any printing parameters. When the acoustic field is switched off, both the LW and its overspray revert to 9.77 μm and 0.72 μm, respectively. The focusing rate of LW is calculated to be 58% for this case. The overspray for the ~6 μm traces is estimated to be ~2%, which is lower than the reported 7% overspray when the AF is OFF to generate 10 μm traces. The enlarged images of the edge morphology of the continuous AJ printed line with/without AF are shown in Supplementary Fig. 6d–f, where the changes of overspray before and after AF can be clearly seen. Moreover, the entire track geometries of the trace printed before, during, and after a short-term AF process, incorporating both two-dimensional and three-dimensional measurements, are supplemented in Supplementary Fig. 6g, h. It is noted that the slight disparity observed in trace morphology before and after the AF process can be ascribed to the gas flow fluctuation and drift in the ink composition over time which is common issues during AJ printing, mainly because of (a) fluctuation of carrier gas and sheath gas volumes; (b) impurities accumulate inside the nozzle, due to prolonged and repetitive use, leading to dislocation of the aerosol ink during transport; (c) manufacturing defect of the outlet roundness and internal channel standardization degree of nozzles affecting the ink flow distribution. Furthermore, two transition zones associated with the converging and diverging process of APS are observed (Fig. 2e, f). These transition areas exhibit noteworthy patterns of focusing and defocusing in the aerosol ink flow which are hard to observe in the acoustic channel of nozzle due to the opacity and diminutive structure of the nozzle channels as well as the fast jet speed of the ink flow. To ascertain the focusing time \({t}_{1}\) and jet velocity \(\widetilde{{v}_{0}}\), the length of transition zone \({l}_{p}\) and printing speed \({v}_{p}\) were recorded as depicted in Fig. 2e, where t0 = lp/vp = 8.2 μm/9 mm·s−1 ≈ 0.9 ms. The average velocity within the nozzle is in the range of the conventional empirical data24,60. It is essential to highlight that the focusing time of APS in the nozzle channel should maintain the same value with \({t}_{0}\). So that the jet velocity can be obtained by \(\widetilde{{v}_{0}}={l}_{0}/{t}_{0}\) = 30 mm/0.9 ms ≈ 33.3 m·s−1, where \({l}_{0}\) is the length of the piezoelectric tube. The experimental results show that using AF technique for AJ printing is a highly reversible and efficient method for printing high-resolution traces with less overspray. A representative video of continuous AJ printing with AF switched on and off is shown in Supplementary Movie 1.

Multi-width, repeatability tests for AF assisted AJ printing

To ensure the widespread adoption of the AF strategy, it is imperative to attain consistent and dependable AJ printing performance, especially for industrial applications. The repeatability test of the AJ printing with AF was conducted for various LWs such as 10 μm, 30 μm, 50 μm and 80 μm which are commonly utilized in AJ printing. For this test, we adjusted the printing parameters including atomizer voltage, carrier gas flow, sheath gas flow, and printing speed to maintain the LW to the desired value, and the corresponding printing parameters are listed in Supplementary Table 3. It is worth mentioning that the AF remains in an OFF state during this adjustment and the LW should be maintained in a steady state before proceeding to the next step to eliminate any variations resulting from flow fluctuation and deposition rate deviation. We then activated the acoustic field and the AF behavior was observed immediately through the camera. The cross-sections of AJ printed lines with different LW with AF ON/OFF are constructed by atomic force microscopy (AFM), as depicted in Fig. 3a–d. Supplementary Table 4 specifically quantifies the geometric features of the deposition cross-section. Because of the Gaussian profile in the cross-section, the reported thickness is defined as the highest thickness along the cross-section. Through analysis, the change rates of LW, thickness, and cross-sectional area after the AF process are around 60%, 115%, and 80%, respectively. The almost consistent change rates of the different geometric characteristics of these multi-width AJ printing lines under AF prove the universality and sufficiency of AF. In addition, the surface RMS roughness of AJ printed traces before and after AF at different printing resolutions was quantified based on the AFM measurement results, as shown in Supplementary Fig. 12a–h. Overall, AF has a certain effect ( ≤ 10%) on reducing the surface roughness of depositions, as shown in Supplementary Fig. 12i.

Fig. 3: Verification of AJ printing assisted with acoustic focusing (AF) in terms of multi-width, stability, omni-direction, and feasibility.
figure 3

a–d Cross-section profile of AJ printed traces with different LW (a)~10 μm, (b) ~30 μm, (c) ~50 μm, (d) ~80 μm with AF ON/OFF. Source data are provided as a Source Data file. e Continuous AJ printing in a 2D orthogonal direction with AF switched intermittently, to verify the omnidirectional focusing of AF. Vp is the printing speed. f A high-density array (both LW and spacing ranging ~6 μm) printed by AF-assisted AJ. g LW of a continuously AJ printed trace with multiple AF ON/OFF varies in different directions.

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Another issue that needs to be considered for AF is repeatability which could significantly affect its practicality in real applications. A print path consisting of a rectangular ambulatory plane was developed, and the AF was turned on and off multiple times to test the repeatability during the printing process. As shown in Supplementary Fig. 3e, the LW had an instant change associated with the state of the AF, serving as compelling evidence of the repeatability of the AF method. It is noted that a slight variation in the LW of printed traces under the same AF circumstances, quantified in Fig. 3g, is primarily attributable to the fluctuation in gas flow within the AJ printing system. Furthermore, the necking behavior exhibited in both the X and Y directions strongly indicates the excellent isotropic printing capability under the annular acoustic field.

Moreover, with the aid of AF, the APS are moving towards the central axis of the nozzle and maintaining a dense ink stream during the deposition process. To demonstrate the excellent AJ printing capability with AF, an exemplary serpentine array with superior resolution and ultrahigh printing density was achieved, as shown in Fig. 3f. The array was composed of 24 lines and corresponding morphological characteristic values (LW: 5.9 ± 0.3 μm, overspray: 0.3 ± 0.1 μm, line gap: 6.0 ± 0.3 μm) were obtained separately based on the definition and measurement methods of LW and overspray in this study. The range and average value of them were obtained from the 24 sets of data. In terms of theoretical analysis, the sum of the maximum overspray width and half of the maximum LW was much smaller than the axial spacing between adjacent printed lines, i.e. \(2 \cdot {{{{\rm{OW}}}}}_{\max } < {{{\rm{spacing}}}}\). In addition, we measured all adjacent lines, and the results showed that there was indeed no electrical shorting in any adjacent printed lines. Supplementary Movie 2 shows the operation process of this AJ printed array. Due to disturbances in the flow field and environment, there may be slight fluctuations in the LW of the dense traces with tiny overspray. However, such an AJ-printed array has broken through the challenge of fabricating high-precision and high-density arrays by AJ printing.

Electrical conductivity characterization

As the key functional property of AJ printed conductive traces, the poor electrical conductivity is mainly from internal structure and porosity after the ink solvent evaporation. To evaluate the influence of electrical conductivity on AJ printed traces with AF, an Ag nanoparticle ink was employed to print a variety of traces while subjecting the AF to both active and inactive conditions. It is worth mentioning that all the traces were printed in a short timeframe under the same printing condition to ensure the deposition rate remains unchanged during the whole procedure. Based on the aforementioned findings, the cross-sectional area of the printed trace is observed to undergo an immediate reduction of approximately 20% upon activation of the AF, as shown in Fig. 3a–d, and Supplementary Table 4. However, in an ideal case, it should maintain proportionality under a constant packing density. This intriguing discovery raises the need for further investigation and comprehensive analysis.

To fully illustrate the effect of AF on conductivity, we maintained a consistent sintering process, and all printed samples were sintered using the same sintering program. The conductivity calculation formula is \(\sigma=L/\left(R\times S\right)\), where \(\sigma\) is the conductivity, \(R\) is the measured resistance, \(L\) is the length of printed trace, and \(S\) is the cross-sectional area. In Fig. 4a, the resistance of annealed traces is presented with the AF ON and OFF under the same AJ printing conditions for each particular LW. It is found that the resistance of the AJ printed traces of the same length exhibited a reduction of approximately 35 ± 5% under the same printing conditions when the acoustic field is activated, as shown in Fig. 4a. The measured resistance and the corresponding conductivities for each trace were also calculated from the equation, recorded in Supplementary Table 5. The AJ printed traces displayed a remarkable increase in conductivity of approximately 80 ± 10% with AF, as shown in Fig. 4b. This outcome implies that the AF approach is not solely successful in reducing the LW with minimal overspray, but also serves as an effective method for achieving higher conductivity. We characterized the microstructure and porosity of printed traces using scanning electron microscopy (SEM). The SEM images of the surface and cross-section of traces with AF ON and OFF states are displayed in Fig. 4c–h. It should be noted that the annealed particle size remains almost unchanged after undergoing the AF process, which indicates that the AF has no damage to the nanoparticles for AJ printing that requires sintering. As illustrated in Supplementary Fig. 8a, b, the particle size was determined using Scherrer formula after scanning the AJ printed deposition with an X-ray diffractometer (XRD). From the SEM image of Fig. 4g, it is obvious that the AJ-printed metal trace with AF ON was more densely packed with minimal voiding compared to that with AF OFF (Fig. 4f, h). By using pore analysis software, we analyzed the porosity of AJ printed cross-sections before and after AF. As shown in Supplementary Fig. 9, with AF ON, the porosity decreased from 22.6 ± 1.3% to 3.4 ± 0.8%, and when AF was turned off, it returned to 21.7 ± 0.9%. It is known that commercially available Ag inks typically comprise Ag nanoparticles and other solid materials that are suspended within organic or aqueous solvents. These voids or porous structures are expected to form due to solvent evaporation during sintering, affecting material conductivity61. The electrically conductive area of the AJ printed metal trace is diminished with a lower overall density. Notably, as the interface area decreases, it engenders a more convoluted electrical pathway, thus requiring electrons to traverse greater distances. Owing to the swift jet velocity and diminutive size of the particles, capturing the intricate motion process via a high-speed camera proves to be quite challenging. As the hypothesis schematic drawing shown in Fig. 4i, within the microdroplets, the Ag nanoparticles are initially polydisperse in the organic solvents covered by polyvinylpyrrolidone (PVP), under the effect of the acoustic radiation force, these particles are moving toward the central axis in the nozzle channel. The radical motion of the APS leads to a favorable resolution with less overspray and higher density traces. It is important to note that the excellent form-holding capability of the acoustic-focused ink stream after exiting the acoustic field. The reasons summarized here assume that the acoustic-focused APS maintain their dense geometry due to the robust intermolecular interactions between the PVP62, and the small distance between the nozzle exit and substrate also hindered the diverging tendency, especially under such a high jet speed.

Fig. 4: Electrical properties and internal structure of AJ printed deposition under acoustic focusing (AF) OFF1/ON/OFF2 state.
figure 4

a Resistance of AJ printed traces at the same length without/with AF. Error bars show s.d., n = 3. b Conductivity of AJ printed traces under different focusing states. Source data are provided as a Source Data file. Error bars show s.d., n = 3. c–e Comparison of surfaces of AJ printed traces under different focusing states. f–h Comparison of cross-sections of AJ printed traces under different focusing states. i Hypothesis schematic illustration showing the motion of the aerosolized particles (APS) during the AF process. PVP is the polyvinylpyrrolidone.

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Stability and application prospects

To assess AJ printing stability with AF, four printing stability tests were conducted under ambient conditions, which involved printing lines with the resolution of 6, 10, 20, and 50 μm respectively. Among these, the stability of 6 μm resolution lasted for approximately 4.5 h. This duration was notably shorter compared to the other three resolutions with 10 μm, 20 μm, and 50 μm, which all maintained stability for almost 8 h. The discrepancy can be attributed to the instability observed in the original optimal resolution of 10 μm without AF, but still has greatly improved stability under ultrahigh printing resolution. An optical image was captured every 20 min as shown in Supplementary Fig. 10, the LW, and thickness of the trace at various time points can be viewed in Fig. 5a, b. Although a small variation of LW was observed during the long-term printing, the average LW (6.0 ± 0.3 μm, 10.8 ± 1.2 μm, 20.6 ± 1.4 μm, 50.7 ± 1.4 μm) of the AF-assisted AJ printed traces indicates that the excellent printing stability compared to traditional AJ printing method. Compared to the stability shown by the LW approach, there was a significant fluctuation in trace thickness which suggests that the deposition rate varies during printing, a common occurrence in practical applications. Specifically, there is a variation in deposition volume with consistent width but noticeable difference in height. However, this highlights the optimizing impact of AF in AJ printing to maintain the quality and stability of printed LW despite fluctuations in deposition rate. It is worth mentioning that the resolution is principally determined by the diameter of the nozzle and the focusing ratio, which provide a simple baseline estimate independent of the ink. Benefit from the integration of two aerodynamic focusing zones, alongside the AF zone, offers the potential to use a wide nozzle to print fine features with minimal overspray and enable the attachment of the piezoelectric tube as well. As a result, it achieves an ultra-high resolution in AJ printing, up to 5.7 μm, while minimal overspray occurred to less than 0.1 μm, which completely breaks through the results of previous optimization studies, as shown in Fig. 5c. This comparison is based on the intuitive printing results mainly including the resolution and overspray ratio, which is defined as the ratio of overspray width to effective line width, attached with the excellent advanced research methods worth learning and thinking about respectively.

Fig. 5: Stability quantification and performance comparison of AF-assisted AJ printing.
figure 5

For 8 h continuous AJ printing with resolution ~6 μm, ~10 μm, ~20 μm, and ~50 μm, a LWs and (b) thickness were recorded at intervals of 20 min. c Comparison of different optimization methods on printing resolution and overspray of AJ printing with other reported results. Source data are provided as a Source Data file.

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It should be noted that the radially focusing behavior of AF is primarily influenced by the acoustic radiation force (Eq. 5) which is determined by the ink properties including the viscosity, particle size and solid concentration. For different types of ink, preliminary calculations can be conducted using simulation models developed in this study to evaluate the achievable focus ratio. Here, the primary determinant of acoustic enhancement effectiveness lies in the optimal focusing frequency, which is determined by the nozzle geometry. For optimal focusing effect in this study, the acoustic wave’s pressure node should be positioned at the neutral axis of nozzle. This positioning requires an optimal distribution of acoustic pressure that is independent of the material properties. However, the optimal frequency may experience adjustments as needed when connected to a potentially superior nozzle with a distinct channel configuration for different inks. To explore the influence of AF for the standoff distance, AF-assisted AJ printing experiments were conducted with different standoff distance ranging from 1 mm to 6.5 mm. As depicted in Supplementary Fig. 11, the LW demonstrates a trend of initial decline followed by an increase as the standoff distance increases for both situations with the AF ON and OFF. This pattern aligns with previous findings on the AJ printing performed without AF, indicating an optimal standoff distance of 2.5 mm that results in the minimal LW for both scenarios. It has been observed that the maximum standoff distance required to maintain effective print quality in AJ printing with AF is 6 mm, whereas without AF, it is limited to 5 mm. This variation is attributed to the superior radial particle concentration achieved by AF, which exhibits an enhanced shape-preserving capability after exiting the nozzle. Regarding to the printing parameters such as carrier gas flow, sheath gas flow, and printing speed, they are still following the established guidelines from our previous observations. In future studies, a more systematic and comprehensive work should be done to fully explore the relationship between printing parameters and LW with AF ON. Nevertheless, through utilizing AF, it is possible to achieve a reduction proportion ( < 1) for originally achievable LW and expand the range of achievable resolution in practice. In addition, we have verified the impact of AF on interfacial adhesion. The results in Supplementary Fig. 13 showed that AF still maintained the interfacial adhesion within the classification of 5B specified by the standard63.

In summary, we have reported the ultrahigh-precision AJ printing with minimal overspray using the annular acoustic field. The fast response, material agnostic, cost-effective, and stable AF strategy is proved to be an effective way to focus the APS omnidirectional. Subsequently, an ultrafine-printed Ag serpentine array (LW: 6 ± 0.3 μm, overspray: 0.3 ± 0.1 μm) was achieved under AF. In particular, the ultranarrow line gap (6 ± 0.3 μm) represents the state of direct printing using AJ printing, indicating the great potential of high packing density conformal electronics. The corresponding focusing time and velocity of aerosolized particles are calculated to be around 0.9 ms and 33.3 m/s in the print channel, respectively. It is noted that AJ Printing’s conformal printing technique is capable of adapting to various substrate shapes and materials, due to the utilization of AF on ink particles during the jetting process rather than on the substrate. This method is still applicable to all types of substrates. We show that within the AF, the LW of Ag ink streams decreased to 60 ± 5% compared to that without AF. Meanwhile, the conductivity of the acoustic-focused Ag ink stream has an increase to 180 ± 5% compared to that without AF due to the more densely packed nanoparticles. Furthermore, an AJ printing stability experiment with AF was performed over 8 h with little observed variation of printed traces to demonstrate long-term printing stability. This AF assisted AJ printing technology with ultrahigh resolution, minimal overspray, excellent stability, and enhanced conductivity can be exploited for fabricating conformal electronics with high integration density and greatly improved electrical performance.

Methods

Device design and nozzle manufacturing

The overall AF-assisted AJ printing system is shown in Supplementary Fig. 4. The AJ Printer adopts a commercial nano jet subsystem (IDS Nanojet, USA), consisting of a process control module and a print module, carried by a three-axis motion platform (Ruibang, China), and its atomization mode is ultrasonic atomization. The AF device comprises a signal generator, a power amplifier, and a piezoelectric tube connected to the power amplifier by welding the wires. The power amplifier adopts the model LZY-22+ (Mini-Circuits, USA), with an operating frequency range of 0.1–200 MHz and an output voltage of 24 V. The piezoelectric actuator adopts a piezoelectric tube (YIJIA, China), with the dimensions of 30 mm×5.6 mm×3.6 mm (length×outer diameter×inner diameter), operating frequency range of 5–8 MHz, operating voltage ≤ 1000 V. The nozzles were manufactured by laser cladding deposition 3D printing (Sonic Mini 8 K, Phrozen), as shown in Supplementary Fig. 3b, c. Then, the nozzles underwent a meticulous cleaning regimen involving both acetone and isopropanol within an ultrasonic bath. Subsequently, compressed air was employed to meticulously expunge any contaminants and excess resin from the intricate internal configurations of the nozzles. This rigorous purification process is critical to maintaining the integrity of the internal structure, thereby precluding any potential functional discrepancies attributable to structural imperfections in the nozzles.

Materials of aerosol ink and nozzle

To use AJ for printing conductive wires and arrays, we used Ag nanoparticle conductive ink (JS-A221AE, Novacentrix, USA). The average dispersed particle size is 35 nm, the ink viscosity was 10–20 cP, specially formulated for AJ printing using ultrasonic atomization, and the Ag particles loading in the ink is about 50 wt%. For the printed nozzles, we used red wax (Photosensitive resin 121, Funcrecol), selected for its superior rigidity and minimal deformation characteristics (3%), which contributed to exceptional mold precision and negligible discrepancies.

Particle motion in the coupled multi-physical field

Based on the above theory and design, COMSOL Multiphysics 6.0 was used to calculate the coupling of the multi-physical field and the motion changes of the particles in it. The model is composed of the piezoelectric tube wall, the nozzle wall, the airflow layer, the ink flow, and the particle ejection through them. The material properties used in the simulation are listed in Supplementary Table 1. The following physical field modules are involved: Pressure Acoustics module for ink flow, gas layer, and nozzle wall, Solid Mechanics module and Electrostatics module for piezoelectric tube wall, Turbulent Flow module and Particle Tracing module for ink flow. In the pressure acoustic boundary, the ink flow, gas layer, and nozzle wall are respectively defined with acoustic transmission form and discretized into quadratic Lagrangian elements. The electric potential \({V}_{0}\) of 20 V and the grounding are respectively applied to the outer and inner wall of the piezoelectric tube to produce a reverse piezoelectric effect, thereby forming a radial annular acoustic field. The stationary Reynolds-averaged Navier-Stokes (RANS) equations are used to determine the flow field in combination with a k-ε model to describe the turbulence ink flow. In the frequency domain study, we performed a parameterized scanning to select the optimal acoustic field for focusing the particles and then determined the appropriate AF parameters. Next, a particle beam is placed in the ink domain, and the acoustic radiation force (only set in AF-assisted AJ printing simulation) and drag force are applied to it for transient study. The quantity of particles emitted at the nozzle inlet is 100, positioned initially with a release distribution accuracy order of 5. The initial velocity aligns with the gas velocity distribution at the inlet based on the gas flow rate. Transient investigations were performed utilizing a time step set at 0.01 ms. Subsequently, the printed LW was defined as twice the maximum distance covered by the particles from the base surface to the model axis. The simulated focusing ratio is derived from the LW of the simulation with acoustic radiation force applied relative to one without such force.

Characterization of morphology, conductivity, and adhesion

An industrial array camera (Hikvision, China) was installed on a relatively static sliding rail bracket designed on the periphery of the AJ printer to observe the dynamic printing effect in real-time and to evaluate and record the change process of the AJ printed deposition assisted with AF. The widths of both effective trace and overspray of all AJ printed deposition were measured by a digital micro scope (HiROX, Japan), and a unified definition standard was adopted for all measured objects. Both the LW and the overspray in this work were defined through the utilization of the average LW. Along the printing direction, the maximum deposition width \({{{{{\rm{L}}}}}_{\max }}_{{{{\rm{i}}}}}\) was extracted on each pixel column in orthogonal directions. Next, the discontinuous pixel units along the printing direction were removed and a continuous deposition width \({{{{\rm{L}}}}}_{{{{\rm{i}}}}}\) along the printing direction was obtained. Finally, the LW of the AJ printed traces was denoted as \({{{\rm{LW}}}}=\frac{1}{{{{\rm{n}}}}}\sum {{{{\rm{L}}}}}_{{{{\rm{i}}}}}\). The maximum printing range was defined as \({{{\rm{PW}}}}=\frac{1}{{{{\rm{n}}}}}\sum {{{{{\rm{L}}}}}_{\max }}_{{{{\rm{i}}}}}\). The width of overspray was denoted as \({{{\rm{OW}}}}=\frac{1}{2}({{{\rm{PW}}}}-{{{\rm{LW}}}})\). Within the range of both edges of the printed trace, from one edge to the opposite edge in the orthogonal direction to the printing direction, the height \({{{{{\rm{H}}}}}_{{{{\rm{a}}}}}}_{{{{\rm{i}}}}}\) of each pixel row along the printing direction are collected and averaged. Finally, take the maximum value \({{{{{\rm{H}}}}}_{{{{\rm{a}}}}}}_{\max }\) of all obtained average heights as the thickness of this trace. The cross-section profiles of the AJ printed traces were measured using AFM (NX10, Park, Korea). Three sets of repeated experiments with four print resolutions respectively were conducted in this study, and three slice contour measurements for each part (before, during, and after AF) of the printed traces were conducted, as depicted in Supplementary Fig. 7, to get 108 data of cross-sections. For cross-sectional area calculating, the entire contour discrete data points are imported into XEI software and fitted by polynomial fitting. Then a trapezoidal discrete integration was applied to calculate the cross-sectional contour area. The three cross-sectional areas obtained from each part were averaged, then the three average areas of each type of printed part were averaged again. Finally, the values of the cross-sectional area at different stages under different print resolutions were determined. The densification of the surface and internal microstructure of the AJ printed deposition is measured with SEM (NovaTM Nano 450). The particle size was calculated using Scherrer formula after scanning the AJ printed sample with an XRD. The sintering process involved heating to 200 °C for 30 min, then holding for one hour, and finally cooling down to room temperature in the heating oven (OGH60-S, Thermo Scientific). The resistance of AJ printed deposition is measured through a four-point probe. The change rate for all physical quantities in this work is defined as the ratio of the changed value to the original value, mainly related to LW, thickness, cross-sectional area, resistance, and conductivity. According to the standard test methods for measuring adhesion by tape test63, both pads printed with/without AF were subjected to grid processing and tape peel test.

Software

For statistical presentation, SciDAVis 2.7 was used. For nozzle manufacturing, SolidWorks 2021 was used to create the structure, and CHITUBOX 1.9.4 was used to slice the model for LCD. KeyShot 11 was used to create the schematics of the system. The multi-physical field modeling and particle motion simulation was completed by COMSOL Multiphysics 6.0. The software associated with the AJ printer is SPiiPlus-ADK-Suite 3.11.01 for motion control and Flow Vision 1.3.38 for process control. For porosity analysis of sedimentary cross-sections, PCAS 2.3 was used. Auto CAD 2024 was used for developing the print path for the printed pattern.