I. Abstract of the Paper’s Core Research

This study employs silver and zinc oxide nanoparticle inks as printing materials to systematically investigate how corner angles (15°, 30°, 45°, 90°, and 180°) and fillet radii influence the deposition patterns of material on the inner and outer surfaces of aerosol‑based deposits. A geometric prediction model based on mass conservation is established, a path‑optimization scheme tailored to micro‑walls with arbitrary curvatures is developed, and validation of complex, non‑standard geometries is completed. The key findings are as follows:

Revealing the underlying mechanisms of corner defects

On the inner side of the curve, the path is shorter and material deposition is more pronounced, leading to protrusions; on the outer side, the longer path results in insufficient material, creating voids. For substrate acceleration and deceleration during start‑stop operations, as well as shutter delay, the impact on linear features ≥100 μm in length is negligible. The key variables are the corner angle and the radius of curvature.

Angle‑dependent standardized fillet threshold (based on a line width of 20 μm)

15° Extremely sharp angle: Simple rounded corners cannot eliminate defects; the feature must be split into separate line segments for printing.

30° angle: Rounded corners with a radius ≥ the line width (20 μm) can completely suppress buildup.

45° angle: rounded corners ≥ half the line width (10 μm) with no noticeable height difference;

90° and large-angle right angles: No additional fillets are required, and deposition is uniform with no defects.

Sedimentary Geometric Model + Self-leveling correction

Pure geometric models significantly overestimate the build height; a 70°C substrate induces an ink self‑leveling effect, which mitigates the height difference between the interior and exterior and serves as a key factor in defect mitigation, providing a basis for correcting process simulations.

Two Major Path Optimization Core Strategies

① Segmentally reserve minute shutter gaps along the closed contour to eliminate overlapping and accumulation at the start and end points.

② Alternate and offset the printing gap positions layer by layer to prevent the accumulation of multi-layer defects; it is compatible with a variety of functional inks, including silver and zinc oxide.

Complete verification of complex structures

Eight-pointed star‑shaped microstructures and a CMU‑shaped cartoon logo were fabricated via three‑dimensional micro‑wall printing. After path optimization, the corners exhibit no protrusions or voids, and the layer height remains uniform, with model predictions closely matching the experimental morphology.

II. Aerosols Standard Fabrication Process for 3D Microstructures

1) Silver/zinc oxide nano‑ink is diluted with deionized water and ultrasonically dispersed to stabilize the colloid.

2) Plasma cleaning of alumina polishing substrates, with the equipment substrate maintained at a constant temperature of 70°C.

3) Use CAD to draw the basic outline, match the corresponding fillets according to the included angles, and design the shutter gap in layers.

4) Optomec AJ equipment employs ultrasonic atomization, nitrogen sheath gas focusing, and a constant printing speed of 1 mm/s.

5) Three-dimensional micro-walls are fabricated by layer-by-layer stacking; upon completion, their corner morphologies are characterized using an optical profiler and SEM.

6) Compare the height differences and defect distribution patterns between the original and optimized path samples.

III. Core Advantages of the Three- and Five‑Photon Aerosol‑Based Processing Technology (Compared with Direct Writing and Two‑Photon Techniques)

Only the printing path is optimized; no hardware or ink formulation modifications are required.

Without replacing the nozzle, heat source, or ink, defect suppression can be achieved directly from CAD drawings, resulting in extremely low R&D and modification costs.

Micron-level support-free 3D printing, balancing precision and height.

Single‑line features as narrow as 20 μm can be achieved, and multilayer stacking enables the fabrication of freestanding micro‑walls on the order of hundreds of micrometers, without the need for a sacrificial support layer.

Multi-material General-Purpose Optimization System

Both silver conductive ink and zinc oxide functional ceramic ink can be applied using the same rounded‑corner path standard, making them suitable for electronic and catalytic devices.

Digital rapid iteration of irregular, complex patterns

For star-shaped and irregular curved-surface logos, adjust path parameters with a single click—no need to repeatedly tweak and optimize process temperature and airflow.

Rapid validation with small batch sizes significantly reduces consumable waste.

There is no need to conduct extensive sample‑based trials to optimize temperature and airflow conditions; instead, yield can be improved simply by refining the design, thereby reducing the consumption of nano‑precious‑metal inks.

IV. Five Core Technological Innovations of This Study

Innovation 1: Angle–Corner Radius Quantitative Matching Standard System

By specifying minimum fillet thresholds for various corner types, we establish a readily reusable design guideline, thereby addressing the gap in 3D microstructural design for aerosols.

Innovation 2: Self-Leveling Correction of Ink Deposition Geometric Model

Distinguish between the pure geometric path‑accumulation effect and the substrate’s thermal leveling effect, correct deviations in theoretical predictions, and accurately forecast corner height differences.

Innovative Three-Layer Shutter Gap Offset Path Strategy

A tiny gap is left at the closed contour, and the transition positions between layers are carefully staggered to completely eliminate the massive protrusions caused by repeated deposition at the start and end points.

Innovation: A Universal Defect Suppression Methodology for Multiple Materials

The optimized logic is independent of any specific ink, making it fully compatible with metal and ceramic aerosol slurries and highly versatile.

Innovative Integrated Manufacturing Solution for Complex, Irregular Microstructures

Breaking free from the limitations of simple lattice structures and pillars, it enables high‑precision 3D micro‑wall printing with multiple curvatures and sharp angles, thereby expanding the design freedom of devices.

V. Current Industry Challenges and Corresponding Solutions

Challenge 1: In aerosol‑printing, material distribution is uneven at curve corners, with significant protrusions or voids arising from multilayer stacking.

✅ Standardized rounded corners are matched according to the included angle; corners of 30° or greater can eliminate deposition imbalance, and extremely sharp angles are split into multiple line segments for printing.

Challenge 2: In closed‑shape printing, the start and end points overlap, leading to massive stacking defects.

✅ A minimal shutter gap is reserved at the contour of each layer, with the gap positions staggered across layers to prevent the cumulative amplification of multi-layer defects.

Challenge 3: Lack of quantitative design guidelines; corner radii are increased solely based on experience, at the expense of the device’s effective area.

✅ Provides a minimum fillet radius threshold corresponding to the line width, eliminating the need to excessively widen curves while balancing precision and build quality.

Challenge 4: The lack of a theoretical model for defect causation makes it impossible to predict print outcomes in advance.

✅ A mass-conservation deposition model is established, and corner height differences are predicted through simulation by incorporating corrections for the substrate’s self-leveling effect.

Challenge 5: The optimization scheme is tailored to a single ink; switching materials requires re‑evaluating the process.

✅The path‑optimization logic is independent of the filler; functional inks such as silver and zinc oxide are directly applied using the standard procedure.

VI. Future Diversified Industrial Application Scenarios

1 Brain–computer interface high-density 3D microelectrode array

High-precision, defect-free three-dimensional conductive micro‑walls enhance brain tissue conformability and signal acquisition accuracy.

2 Microelectrochemical Biosensing Chip

Three-dimensional mesh catalytic electrode with a uniform, defect-free structure enhances molecular capture efficiency and shortens detection time.

3 Micro-scale Three-dimensional Current Collector for Energy Storage

A non‑protruding porous metallic micro‑lattice increases the loading of active materials, thereby enhancing the areal capacity of lithium batteries.

4 RF Miniature Antennas and Microelectronic Packaging

High-precision 3D interconnect traces, with uniformly reduced signal loss at bends, are compatible with miniaturized chip integration.

5. University-level R&D Platform for 3D Microfabrication of Aerosols

Standardized path‑design specifications enable rapid development of microstructures of arbitrary complexity, reducing experimental trial-and-error costs.

Image and Text Guide

Figure 1. Principle of the AJP process and typical defects at sharp corners

Figure 1(a) shows the ultrasonic atomizer aerosolizing silver nanoparticle ink; carrier gas N₂ is delivered to the print head, while sheath gas at the nozzle further focuses the microdroplets, which then land on a heated alumina substrate and dry rapidly. The z/x–y stage enables precise positioning. Figure 1(b) presents an eight-pointed star CAD design. Figure 1(c) provides an enlarged view of the toolpath contour at the sharp corners. Figure 1(d) shows the actual morphology obtained by directly printing at the sharp corners, as revealed by SEM: underfill at the outer corners creates voids, whereas overfill at the inner corners results in protrusions—this constitutes the central issue addressed in this paper.

Figure 3. Single-pass volume/height data for different bend angles θ (15°/30°/45°) and various fillet radii r.

Figure 3(a) defines the tool‑path bend angle θ, the inner‑corner radius r, the ROI path length from A to B, and the line height h; eight values of r are shown (0, 7.5, 15, 30, 50, 100, 500 μm, and 1 mm). Figures 3(b–d) show ROI length versus ROI volume: for all conditions, the relationship is linear, indicating a constant deposition rate per unit length. Figures 3(e–g) present the percentage of total deposited volume contributed by the inner corner: as r decreases (resulting in sharper corners) and the ROI becomes shorter, inner‑corner buildup becomes more pronounced (from 38% to 48%); at r = 1 mm, the value approaches the theoretical uniformity threshold of 50%. Figures 3(h–j) reveal an average line height of approximately 14–15 μm, which is nearly independent of r and θ. Figures 3(k–m) illustrate the height difference between the inner and outer corners: when r = 0, the inner side of the sharp corner protrudes more than 2 μm above the outer side, but this difference rapidly converges to ±0.5 μm as r increases.

Figure 4. Comparison between exponential decay fitting and the pure geometric model

Figure 4(a) shows the geometric model with defined variables: R, the radius of the large circular arc; r, the fillet at the inner corner; l, the equidistant scanning vector; and Δ, the effective path length. Figures 4(b–d) present experimental data (diamond‑shaped points) together with an exponential decay curve fit (solid line): the height difference between the inner and outer corners decays exponentially to near zero as the ROI length increases, with the time constant dependent on r and θ. Figures 4(e–g) display dashed lines representing predictions from a purely geometric model that neglects self‑leveling; these values are one order of magnitude larger than the experimental results, demonstrating that during drying, the capillary self‑leveling effect of the ink droplet on the substrate substantially compensates for over‑ or under‑filling at sharp corners, indicating that geometric considerations alone are insufficient.

Figure 5. High-fidelity 3D eight-pointed star achieved using a fillet toolpath.

Figure 5(a–c) compares three toolpaths: r = 0 (original sharp corner), outer corner R20/inner corner R10 μm, and outer corner R30/inner corner R20 μm; with a diameter of 2 mm, 32 layers, layer thickness ~20 μm, and the shutter on/off gap shifted to different positions to eliminate seam artifacts. Figures 5(d–f) show SEM images of 3D eight-pointed stars corresponding to the three paths: at r = 0, the corner tip exhibits a pronounced protrusion; at r = 20/30 μm, the outer corners are smoothly rounded, with good contour fidelity. Figures 5(g–i) present local SEM views of the outer corner tips: at r = 0, there is material buildup and protrusion, whereas at r = 20/30 μm, the edges are neat and well-defined. Figures 5(j–l) display 3D topography obtained using white-light interferometry: at r = 0, the corner peak height reaches an abnormal 300 μm, while at r = 20/30 μm, the wall height is uniformly around 200 μm. Figure 5(m) provides quantitative data: at r = 0, the corner height exceeds the wall height by approximately 100 μm, whereas at r = 20/30 μm, the difference between corner and wall heights is less than 20 μm.

Figure 6. Verification of printing a complex contour of the 32-layer Scotty Dog (CMU mascot)

Figure 6(a–b): Two toolpaths, with r = 0 and r = 20 μm; seven internal/external corners along the contour, ranging from 26° to 65°, with shutter gaps adjusted at layer‑switching locations to avoid visible seams. Figure 6(c): Printing results for r = 0—noticeable material buildup and warping at the sharp corners, highlighted by red, blue, and green boxes. Figure 6(d): Printing results for r = 20 μm—sharp corners are rounded, wall thickness is 20 μm, and the contours are well defined. Figures 6(e–l): High‑magnification SEM comparisons of the corresponding sharp corners: for r = 0, internal corners collapse and external corners exhibit burrs; for r = 20 μm, edges are neat and sidewalls are dense. Conclusion: Adding a 20‑μm fillet (approximately equal to the line width) to the toolpath enables high‑fidelity printing of arbitrary 3D microstructures without introducing additional process steps.