I. Abstract of the Paper’s Core Research

This study compares the aerosol‑printing fabrication, microstructure, AC and DC electrical properties, and RF transmission performance of commercial silver nanoparticle inks with those of particle‑free reactive MOD silver inks. It establishes a dual‑coupling conductive prediction model incorporating porosity and grain boundaries, quantifying the two key pathways for enhancing conductivity. The main findings are as follows:

Two Types of Ink: Formation Mechanisms and Vast Microscopic Differences

Nanoparticle ink: The droplets contain solid silver nanoparticles, which form a loosely packed structure upon printing; the solid-phase fraction is only 40%, with an average grain size of 21 nm and numerous pores and grain boundaries.

Reactive MOD ink: Contains only silver‑organic molecular precursors; at 80°C, the substrate undergoes instantaneous thermal decomposition, in situ forming a continuous, large‑grain silver layer with a solid‑phase density of 93% and characteristic grain sizes of 120 nm, leaving no organic impurity residues.

Ultra-high electrical conductivity at low temperatures

No high‑temperature, long‑duration sintering is required; at 80°C, the in‑situ‑formed conductive traces exhibit a conductivity of 61% that of pure silver. After a brief annealing at 300°C, this improves to 73%, approaching the industry‑standard practical conductivity ceiling of 75%—equivalent to copper plating (approximately 85% of bulk silver). By contrast, conventional nano‑silver achieves only 24% of the conductivity of bulk silver.

Wideband RF Stable Transmission Characteristics

Microstrip transmission line measurements in the 0.1–20 GHz frequency range show that silver‑plated lines exhibit return loss and insertion loss characteristics comparable to those of conventionally electroplated metals; however, the nanoporous silver structure completely fails to support high‑frequency signals and is therefore unsuitable for RF components.

Multiphysics Electrical Conductivity Prediction Model

By integrating Maxwell’s effective medium theory with the Matthiessen scattering rule and accounting for both pore tortuosity and grain-boundary electron scattering losses, this approach enables accurate prediction of thin-film conductivity, providing a quantitative tool for optimizing inks and processing parameters.

Process Versatility Verification

Aerosol‑based pneumatic atomization enables the deposition of reactive inks with controllable multilayer stacking thicknesses; it is compatible with substrates such as silicon wafers and polyimide, allowing precise control over feature linewidths and facilitating the large‑scale fabrication of four‑probe test structures and RF microstrip antennas.

II. Complete Preparation Procedure for Reactive Silver Ink Aerosol

Prepare a particle-free silver‑organic MOD precursor ink, free of solid silver nanoparticles and surfactants.

The Optomec AJ300 system employs a pneumatic atomization mode, features a 100-μm nozzle, and incorporates standardized matching of carrier‑gas and sheath‑gas flow rates.

The printing platform maintains a stable temperature of 80°C, enabling the droplets to undergo an instantaneous thermal decomposition reaction upon deposition and in situ generate continuous metallic silver.

The single-layer thickness is 0.35 μm, and the total thickness of the multilayer stack can be tuned by adjusting the layer configuration; for as‑grown samples, a short‑duration anneal at 300 °C can be employed to further enhance densification.

Four-probe DC conductivity, RF network analyzer, and SEM/TEM characterization of microstructure, porosity, and grain morphology—comprehensive suite of analyses.

III. Five Core Process Advantages (Nano-Silver Ink Aerosol vs. Photolithography Sputtering)

Ultra-low-temperature molding, compatible with all thermally sensitive flexible substrates.

The reaction is carried out in situ at only 80°C, eliminating the need for high‑temperature sintering above 200°C; PI, PET, and various polymeric flexible substrates do not undergo thermal deformation or carbonization.

The thin film exhibits high density and large grain size, resulting in a dual leap in both AC and DC performance.

With a solid-phase density of 93% and a grain size far exceeding the electron mean free path, pore‑induced and grain‑boundary electron scattering are significantly reduced, enabling simultaneous optimization of low‑frequency conductivity and high‑frequency RF loss.

No organic residues, resulting in enhanced long-term device stability.

The MOD molecule undergoes complete thermal decomposition, and the resulting thin film is free of PVP and high-boiling solvent impurities, exhibiting excellent resistance to oxidation and migration, making it well suited for high-reliability aerospace devices.

Digital maskless direct writing, compatible with 3D Three-dimensional microstructure

CAD‑customized RF antennas and interdigitated electrodes, conformal printing on curved and irregular substrates; vacuum sputtering is limited to planar wafers.

Long-term mass production offers lower costs, and the ink eliminates the risk of nozzle clogging due to nano‑agglomeration.

It contains no solid particles, so the print head does not clog during printing, and its continuous‑production stability surpasses that of nano‑suspension inks.

IV. Five Core Technological Innovations of This Study

Innovation 1: Aerosol-compatible, particle-free MOD reaction silver ink complete system

The system demonstrates that reactive‑molecule inks can be employed across the entire aerosol‑jet printing manufacturing chain, overcoming the two inherent drawbacks of particulate inks—high porosity and elevated sintering temperatures.

Innovative Two-Dimensional Conductivity Prediction Model Coupling Pores and Grain Boundaries

By integrating effective medium theory with the principles of electron scattering, we quantify the attenuation of electrical conductivity caused by pore tortuosity and grain size, enabling early‑stage simulation and prediction of the performance of printed silver traces.

Innovation: A One-Step Low-Temperature (80°C) Fabrication of Conductive Silver Films Approaching Industrial Limits

No high-temperature post‑treatment is required; the as‑deposited material exhibits a bulk electrical conductivity of 61%, which increases to 73% after annealing, reaching the practical metallic conductivity threshold for the microelectronics industry.

Innovation 4: A High-Performance RF Printing Solution Covering the Full Frequency Range of 0.1–20 GHz

Addressing the pain point of high-frequency failures in nano-silver, aerosol‑direct‑write RF transmission lines and antennas can replace conventional electroplating and vapor deposition processes.

Innovative 5: A Microstructure-Controllable Additive Manufacturing Paradigm

By controlling the number of printing layers to tune the film thickness and employing an annealing process to precisely regulate grain size and density, we achieve targeted improvements in the performance of both conductive and RF devices.

V. Current Industry Challenges and Corresponding Solutions

Challenge 1: Conventional nano-silver inks require high-temperature sintering above 200°C, which can damage flexible, heat-sensitive substrates.

✅MOD reactive ink decomposes in situ on the substrate at 80°C, maintaining low temperatures throughout the process, while preserving the full mechanical properties of PI and flexible films.

Challenge 2: The nano-silver film has a porosity of 60%, with densely packed grain boundaries, resulting in an electrical conductivity that is only one-quarter that of bulk silver.

✅ Molecular in-situ growth of a continuous, large-grained silver layer increases the solid-phase density to 93% and boosts electrical conductivity by more than 2.5 times.

Challenge 3: Porous nano-silver interconnects exhibit extremely high RF losses at high frequencies, rendering them unsuitable for microwave devices.

✅ A dense, pore-free reactive silver thin film with extremely low skin-effect losses, ensuring stable signal transmission up to 20 GHz.

Challenge 4: Nanoparticle-based inks tend to agglomerate over long-term printing, clogging the nozzles and leading to frequent production line shutdowns.

✅ In a molecular‑free particle system, atomization eliminates solid‑phase agglomeration, significantly enhancing continuous printing stability.

Challenge 5: Lack of quantitative modeling to guide ink and process iterations, with optimization relying entirely on trial-and-error.

✅ A coupled conductive theory of porosity and grain boundaries has been established, enabling prediction of electrical properties from input microstructural features and reducing experimental costs.

VI. Future Diversified Industrial Application Scenarios

1 Aerospace High-Frequency RF Components

Onboard miniature antennas, microwave transmission lines, and low-temperature‑printed, lightweight, high‑reliability RF structures that replace costly vacuum‑plating processes.

2 Flexible Wearable Wireless Sensor Circuit

Low-temperature direct-write conductive traces on PET/PI substrates, high-conductivity, low-loss flexible RF tags, and physiological monitoring devices.

3 MEMS Micro-Sensing High-Precision Interconnects

High-temperature‑compatible dense metal leads, with highly stable electrical signal output, compatible with industrial high‑temperature miniature sensors.

4 Rapid Prototyping of High-End Miniature RF Modules

During the R&D phase, there is no need to fabricate photolithographic masks; aerosol-based rapid iteration of antenna and filter structures helps shorten the development cycle.

5 University RF and Microelectronics R&D Platform

Low-cost aerosol-based equipment for fabricating high-performance metallic interconnects, used in microwave and conductive-material mechanism studies.

Image and Text Guide

Figure 1. Schematic illustration of the printing process, microstructure, and DC/RF testing for AJP nanoparticle ink (a) and reactive silver ink (b).

Left‑column nanoparticle ink: The pL‑scale droplets contain a ~20 nm silver‑sphere suspension, deposited on a 25 °C substrate with a packing density of only 40%—as shown in (c), the cross‑sectional line width is 14–23 μm; in (d), SEM reveals a loose particle network; and in (g,h), plan‑view SEM/TEM images indicate that particles contact only at their edges. Right‑column reactive‑ink: The droplets hold a molecular‑level silver precursor (Tollens’ reagent), which undergoes instantaneous liquid‑phase decomposition on an 80 °C substrate to form dense silver—with a packing density of 93% and line widths of 48–121 μm (Fig. e); cross‑sectional SEM (f) shows virtually no porosity, while TEM (i,j) reveals large, plate‑like grains on the order of 120 nm. Fig. (k) presents DC four‑probe measurements of high‑aspect‑ratio lines on Si/SiO₂; Fig. (l) shows RF microstrip‑line testing (140 μm polyimide with Cu tape ground, S‑parameters measured via PNA).

Figure 2. (a) Summary of electrical conductivity for AJP nanoparticle inks versus reactive silver inks; (b, c) RF S-parameters of reactive microstrip lines.

Figure 2(a): Vertical axis—longitudinal resistance; horizontal axis—aspect ratio L/A (double logarithmic scale). The theoretical curve for pure silver, with σ_Ag = 6.3 × 10⁷ S/m, is shown as a thick black line. The orange squares represent Ag nanoparticles, whose electrical conductivity reaches only 24% of that of bulk silver (consistent with recent literature: Efimov 2018, Stewart 2017, Smith 2017, Laurent 2018). The light-blue circles correspond to as‑printed reactive Ag, achieving 61%; the green dots indicate 73% after annealing at 300 °C for 1 hour; and the yellow diamonds denote electroplated copper (industry standard: 0.85 σ_Ag, i.e., 85%) used as a reference. The reactive ink approaches the performance of industrial electroplated copper in a single step. Figure 2(b): S11 return loss remains below −10 dB across 20 GHz, with a bandwidth Δf = 3.6 GHz corresponding to a trace length of 2.3 cm. Figure 2(c): S21 insertion loss decreases gradually with frequency, exhibiting the characteristic behavior of a dense metallic microstrip line.

Table 1. Characteristic length λ_LoS measured by TEM versus the estimated average grain diameter

AJP nanoparticles: λ_LoS = 21 nm; based on the 4r/π relationship, the average grain diameter is estimated to be 33 nm, which is consistent with the Scherrer formula value of 24 nm. For the AJP reaction: λ_LoS = 120 nm, with an average grain size of 190 nm; for the DoD reaction (industrial comparison): λ_LoS = 460 nm, with an average grain size of 720 nm. The grain size in the AJP reaction is nearly six times larger than that of the nanoparticles and approximately four times smaller than that of the DoD reaction.

Figure 3. (a) Predicted effective conductivity–characteristic length model versus measured data points; (b) Histograms of the λ_LoS distributions for three types of ink.

Figure 3(a): The vertical axis shows the normalized conductivity σ/σ_Ag, and the horizontal axis represents the characteristic length λ_LoS. The red curve corresponds to the Maxwell–EMT limit (considering only porosity), while the solid blue and green lines depict EMT predictions augmented by grain-boundary size effects. The three measured data points are as follows: the red square indicates AJP‑fabricated nanoparticles (ρ = 40%), located at 24%; the blue circle denotes AJP‑processed material (ρ = 93%), positioned at 61%; and the green triangle represents DoD‑processed material (ρ = 95%), situated at 85%. Moving along the “increase densification” arrow brings the system closer to the EMT upper bound, whereas shifting toward “enlarge grains” further reduces grain-boundary scattering, ultimately approaching the practical limit of approximately 75% of pure silver’s conductivity. Figure 3(b) presents three histograms: AJP‑fabricated nanoparticles are distributed in the sub‑100 nm range, AJP‑processed material spans 150–450 nm, and DoD‑processed material covers 300–900 nm; the inset shows the volume‑weighted average grain size.

Table 2. Density, EMT theoretical limit, model-predicted and measured electrical conductivity of three types of inks

AJP nanoparticles: Φ_metal = 0.40 (60% void), EMT limit 31%, model prediction 10%, measured 24%—indicating that the EMT assumption does not hold at low densities and that the model underestimates. AJP formulation: Φ_metal = 0.93 (7% void), EMT limit 90%, model prediction 63%, measured 61%—with the model and measurement differing by only 3%. DoD formulation: Φ_metal = 0.95, EMT limit 93%, prediction 83%, measured 82%. The measured values for these formulations are already very close to the theoretical upper limits, while nanoparticle inks remain constrained by a 60% porosity threshold and cannot exceed it.