Temporal dynamics of deposit quality in aerosol jet printing using time-varying effects models

Aerosol Jet Printing (AJP) offers significant potential for additive manufacturing of miniaturized electronic devices, but challenges in quality monitoring during short-term print cycles hinder its reliability. Unpredictable line deposition characteristics lead to inconsistent line morphology, limiting further miniaturization. Current limitations include the absence of high-fidelity cameras to observe line formation in real-time and overly complex predictive models unsuitable for practical manufacturing environments. This study addresses these gaps by proposing an interpretable proxy for process stability, collected in real-time, and employing graphically understandable modeling methods to analyze important line morphology features. This research uses normalized system back pressure as a proxy for process stability. It considers this as a predictor variable and average line width, overspray area percentage, and their ratio as response metrics for process stability. Descriptive statistics revealed significant variability in back pressure (mean: 44.86%, SD: +/-37.56%), while average line width exhibited low variability (mean: 62.35 µm, SD: +/-1.68 µm), indicating a stable process. Overspray area percentage showed bimodal distribution (mean: 1.75%, SD: +/-0.66%), suggesting occasional deviations. Linear regression demonstrated a statistically significant but minor negative effect of back pressure on line width (coefficient: -0.0232, p < 0.05), while no significant relationship was found for overspray or its ratio to line width. Time-Varying Effect Models (TVEM) further revealed temporal trends. Type II TVEM outperformed linear regression for overspray area and its ratio with average line width (lower AIC values: 1123.36 and 3647.99, respectively), highlighting the importance of time-varying effects for these metrics. The findings underscore the need for tailored modeling approaches. Linear regression suffices for line width, while TVEM Type II better captures the temporal dynamics of overspray and its ratio with average line width. This study provides a framework for real-time monitoring for the quality of features printed with AJP, offering practical insights for improving process stability and advancing miniaturization in printed electronics.