I. Abstract of the Paper’s Core Research

This study focuses on silver nanoparticle ink and an ultrasonic aerosol‑printing system, establishing an integrated machine‑learning optimization framework encompassing “image classification – feature extraction – electrical‑property prediction.” The system completes dataset construction, model comparison, process‑window calibration, and multi‑ink validation. The key findings are as follows:

Construction of a Standardized Image Dataset for Aerosol Pathways

Latin hypercube sampling was employed to explore the entire parameter space of carrier gas flow, sheath gas flow, and printing speed, acquiring 4,500 sets of microscopic images of printed circuits. These images were then categorized into eight defect types—such as broken traces, sparse patterns, material overflow, and standard defects—enabling the construction of a comprehensive image‑annotation database.

Optimal Morphological Recognition Scheme for ResNet Convolutional Neural Networks

Compared with the three major CNN architectures—AlexNet, VGGNet, and ResNet—ResNet achieves an accuracy of 91.3% thanks to its residual structure, enabling it to automatically extract key geometric features such as line width, edge roughness, voids, and overflow, thereby defining a stable three-dimensional process operating window.

Comparison of Resistivity Prediction Among Three Types of Nonparametric Regression Models

Random Forest (RF), Support Vector Regression (SVR), and Gaussian Process Regression (GPR) were simultaneously employed for modeling. GPR exhibited the best overall performance, achieving an \(R^2\) of 0.872 on the test set and minimizing the mean error, while also providing a predictive uncertainty interval in a single output.

Morphology–Electrical Quantitative Correlation Mechanism

Voids and open circuits can cause a sharp increase in resistivity, while excessive over‑molding leads to non‑uniform resistance. Within the three‑dimensional window, the standard line resistivity is stably maintained in the 1.2–3.5 μΩ·cm range, making it well suited for high‑precision micro‑interconnect devices.

Generalized Modeling Framework

Two sets of tests using silver inks from different brands confirmed that the model‑fitting trends are consistent, and the approach is not limited to a single material; it can be extended to optimize processes for carbon‑, metal‑, and other composite aerosol‑based conductive inks.

II. Machine Learning–Assisted Complete Aerosol Experimental Workflow

1. Experimental variable settings: carrier gas flow rate 5–50 sccm, sheath gas flow rate 10–100 sccm, printing speed 1–9 mm/s; nozzle diameter fixed at 150 μm, substrate: polyimide (PI), sintering temperature: 200°C.
2. Batch printing of standard test lines, followed by the acquisition of 4,500 sets of micro-optical images and pixel-based image processing.
3. Image algorithm quantification metrics: average line width, edge roughness, overflow volume, and void defect density.
4. CNN training: A comparative analysis of three network architectures, with ResNet selected for defect classification and microscopic feature extraction.
5. Feature extraction and process parameters are used as inputs to construct RF, SVR, and GPR models for resistivity prediction, respectively.
6. The three-dimensional parameter space was delineated, and the electrical performance of ink samples within and outside the defined range was compared to validate the model’s reliability.
7. Generalization testing on multiple batches of unfamiliar ink datasets to validate the model’s general-purpose adaptability.

III. Five Key Process Advantages of Aerosol Manufacturing Empowered by Machine Learning

Eliminate manual, trial-and-error experimentation and significantly reduce experimental consumables and turnaround time.

AI automatically explores the parameter space, eliminating the need for hundreds of manual trial samples and reducing the ink and process development cycle by more than 70%.

Non-destructive, rapid image quality inspection—no four-point probe contact measurement required.

Optical imaging enables pre‑emptive assessment of electrical conductivity, preventing probe‑induced damage to flexible films and supporting in‑line visual inspection on the production line.

Precisely define the stable mass-production window and standardize process specifications.

Three-dimensional airflow—quantitative output across the velocity operating range, enabling standardized parameters to be reused across different devices and operators.

Simultaneous Analysis of the Microstructural Morphology and Its Electrical Coupling Relationship

Differentiate the adverse effects of voids, flash, and surface roughness on electrical resistance, and provide targeted guidance for equipment parameter adjustments.

The model boasts material versatility and is compatible with all types of conductive inks.

Silver, carbon nanotubes, and composite conductive pastes can all be integrated into this CNN-plus-regression modeling framework, forming a unified algorithmic R&D platform.

IV. Five Core Technological Innovations of This Study

Innovation 1: A novel modeling approach that integrates CNN-based morphological feature extraction with electrical regression.

By integrating deep-learning-based image recognition with nonparametric machine learning, we enable end-to-end quantitative prediction across the entire workflow—process–morphology–resistivity.

Innovation 2: An Optimal Aerosol Defect Classification Framework Based on ResNet

Compared with mainstream convolutional networks, residual networks have been shown to achieve the highest accuracy in detecting fine micro‑lines, minute voids, and edge defects.

Innovation 3: Gaussian Process Regression for Resistivity Prediction with Confidence Intervals

Unlike conventional fitting models, GPR can output a range of prediction uncertainty, providing a quantitative basis for setting yield thresholds in mass production.

Innovative Quantitative Calibration of a Three-Dimensional Parameter-Stable Process Window

Based on the classification results of a massive dataset, standard operating ranges for no wire breakage, low material spillage, and low resistance have been defined, enabling direct deployment on the production line.

Innovation 5: A cross-ink, universally applicable, standardized AI‑optimized workflow.

Unconstrained by any single conductive material, it enables the development of a universal, data-driven process for aerosol printing.

V. Current Industry Challenges and Corresponding Solutions

Challenge 1: The system features multiple gas paths and complex coupling among velocity parameters, making it possible to achieve only a local optimum through manual tuning.

✅ Machine learning–based full‑domain sampling modeling globally locks in a stable process window, preventing on‑wafer defect detection.

Challenge 2: The electrical conductivity must be measured with a probe after printing, making it impossible to predict in advance, resulting in significant scrap.

✅ Non-destructive optical imaging for resistivity prediction, enabling online visual quality inspection to proactively screen out non-conforming samples.

Challenge 3: Microscopic defects such as line voids and flash cannot be quantitatively distinguished in terms of their impact on resistance.

✅CNN automatically extracts various morphological features and quantifies the extent of resistive degradation caused by each type of defect.

Challenge 4: There is no unified optimization approach for different inks, equipment, and processes, leading to high costs associated with repeated experimentation.

✅ A universal AI modeling framework that allows you to switch conductive materials without redesigning the experimental logic.

Challenge 5: Traditional linear fitting models exhibit low predictive accuracy, making it difficult to capture complex nonlinear printing patterns.

✅ Nonparametric Gaussian regression is employed to capture the nonlinear deposition dynamics of aerosol fluids, resulting in a substantial improvement in prediction accuracy.

VI. Future Diversified Industrial Application Scenarios

1 Quality Control for Mass Production of Microelectrodes in Flexible Display Pixels

An AI model integrated with the production line’s visual inspection system provides real-time predictions of line resistance, thereby reducing the defect rate of finished displays.

2 MEMS Sensor Interdigital Electrode R&D Platform

Rapidly iterate ink formulations and printing parameters to achieve batch‑level optimization of low‑resistance, highly uniform sensing circuits.

3 RF Millimeter-Wave Micro-Interconnect Lines

Precise control of low-loss conductive microstrips ensures compliance with the low-resistance consistency requirements of high-frequency devices.

4 Flexible Circuits for Wearable Physiological Sensing

Non-destructive online detection to prevent probe damage to the ultra-thin PI‑based sensing electrode.

5 High-Throughput Research and Development of New Materials in the Laboratory

Rapid screening of carbon, metal, and composite inks, with automated generation of optimal printing parameters.

Image and Text Guide

• The quality of the printing line is quantified by five geometric features: Average line width w̄ 、 Average edge roughness Rₘ 、 Line Splash Oₛₚ 、 Average line density L̄ _rho 、 Line Discontinuity L _disc 。
• Rₘ is characterized by the root-mean-square deviation of the upper and lower edges from the mean line; Oₛₚ is characterized by the average distance of the upper and lower spatter from the mean line (Equations 1–5).
• Based on these features, a dataset of 4,500 wire‑sample images was constructed for CNN‑based classification and resistivity modeling.

• The resistivity is calculated according to Ohm’s law: R = ρ·L/S. The resistance R is measured using the four‑terminal Kelvin method, and the cross‑sectional area S is determined with a confocal microscope.
• For each 1.5 cm wire sample, the cross-sectional area was measured three times and the average was calculated; the sample’s width ranged from 20.6 to 65.9 μm (mean 40.9 μm), with a thickness of approximately 8 μm.
• At each design point, three wire samples are arranged, and their average is used for subsequent modeling.

• The wire samples were classified into eight categories based on quality metrics: (a) I—broken wires (low CGFR, insufficient ink delivery), (b) II—sparse lines, (c) III—insufficient thickness, (d) IV—high spatter, (e) V—high edge roughness, (f) VI—low focus, (g) VII—high spread, and (h) VIII—normal lines.
• The wire roughness ranges from 0.58 to 4.29 μm, and the overspray ranges from 0.15 to 6.56 μm.
• Open circuits are prone to occur with broken or sparse traces, while excessive spattering and wide spreading can easily lead to short circuits—thus, a balance must be struck among SHGFR, CGFR, and printing speed.

• Type I open-circuit faults all exhibit an infinite (∞) resistance; Type II sparse-line faults show elevated resistivity.
• Type VII exhibits lower resistivity (0.9–2.6) due to excessive CGFR enlargement, but this is accompanied by high non-uniformity; Type VIII shows the best overall electrical and morphological performance (1.2–3.5 μΩ·cm).
• The two inks (Clariant ink1 / Metalon ink2) exhibit a consistent morphology–resistivity correlation.

• The optimal CNN classifier is   ResNet (Testing accuracy: 91.3%, outperforming AlexNet and VGGNet), used to extract representative geometric features.
• Shallow convolution layers preserve the overall morphology; as the network depth increases, they progressively identify features strongly correlated with resistivity, such as intra‑line cavities/indentations, overspray, and spreading.
• The extracted features, together with the process parameters (printing speed, CGFR, and SHGFR), serve as inputs to the resistivity model.

• A three-dimensional decision boundary is used to distinguish inferior line morphologies (Types I–II, IV, and VII) from the remaining ones, thereby defining the three-dimensional optimal window for SHGFR–CGFR–printing speed.
• Within the chamber, aerodynamic balance between SHGFR and CGFR must be maintained, and the material deposition rate should be kept at an appropriate level.
• Complex geometries (such as helices and intersecting lines) may deform due to stress distribution, necessitating further refinement of the window.

• The dataset is split into training and testing sets at an 80%:20% ratio (with the test set proportion optimized to 20% by R).
• GPR optimal : On the test set, R = 0.935 and R² = 0.872, outperforming RF (0.909/0.821) and SVR (0.913/0.843).
• The probabilistic outputs of GPR, combined with its high flexibility, enable it to better capture the nonlinearity introduced by an increasing CGFR.

• The four metrics (R, R², RMSE, MAE) consistently indicate that GPR outperforms all others: training RMSE of 0.046 and test RMSE of 0.075.
• An additional 90 new samples validate the generalization of GPR: R = 0.923, R² = 0.859, RMSE = 0.079, MAE = 0.229.
• This data-driven approach is transferable to other inks, providing a foundation for online, non-destructive resistivity prediction in AJP-printed electronics.