## 4 Conclusions  
We performed a comprehensive thermal analysis of high-power LED modules to evaluate heat dissipation performance as a function of thermal via design, including the number of thermal vias, pitch, and misalignment. The temperatures of the LED and substrate exhibited saturation behavior as the number of thermal vias increased. The optimal via pitch for heat dissipation performance varied depending on the number of thermal vias, emphasizing the need for integrated consideration of pitch and via density. Misalignment of the thermal via array relative to the LED center also resulted in significant increases in both temperature and thermal nonuniformity, particularly for a smaller effective working area of the via array.  
We propose a cost-effective and fabrication-reliable design strategy for thermal vias, offering practical guidelines for the scalable design of high-power LED modules. In practical applications, the minimum via diameter and via-to-via spacing are often constrained by standard fabrication limits [49]. Our proposed thermal via design guidelines are fully compatible with these manufacturing constraints. Notably, they achieve effective thermal performance without requiring via configurations that approach the limits of process capabilities. Our results demonstrate that even with relaxed via configurations, substantial heat dissipation is possible due to the saturation behavior in thermal performance. Therefore, the proposed strategy provides a balanced solution between thermal efficiency and fabrication feasibility using conventional, cost-effective processes.  
Experimental validation of our proposed concept would be highly desirable for its practical application. Although this study primarily relies on numerical analysis, previous studies on similar thermal via implementations have reported good agreement between  
Figure 10: The trend of LED temperature with varying positions of thermal vias. \(T_{\text{LED}}\) and \(\Delta T_{\text{LED}}\) as a function of offset for **(a)** five thermal vias with a pitch of 0.3 mm and **(b)** nine thermal vias with a pitch of 0.2 mm.  
simulation and experimental measurements, typically within a 10% error margin when considering manufacturing tolerances [34; 35; 50].  
Importantly, the proposed via configuration strategy can be effectively applied to a wide range of heat dissipation modules, offering consistent thermal performance improvements across various device layouts. Our approach is applicable to a wide range of LED layouts and substrate configurations.  
Conceptualization, Y.J.H., K.W. and S.-U.K.; methodology, S.-C.P., K.W. and S.-U.K.; software, B.-Y.L. and S.-C.P.; validation, B.-Y.L. and S.-C.P.; investigation, M.J.K. and S.-C.P.; data curation, Y.J.H., M.J.K. and S.-C.P.; writing--original draft preparation, Y.J.H., B.-Y.L. and S.-U.K.; writing--review and editing, B.-Y.L., K.W. and S.-U.K.; visualization, Y.J.H., K.W. and S.-U.K.; supervision, K.W. and S.-U.K.; project administration, S.-U.K.; funding acquisition, S.-U.K., Y.J.H. and B.-Y.L. contributed equally to this study. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors upon request.  
This study was financially supported by Seoul National University of Science and Technology.  
The authors declare no conflicts of interest.