## 1 Introduction  
Light-emitting diodes (LEDs) have largely replaced traditional light sources due to their high energy efficiency and long lifetime. Thermal management in high-power applications is crucial as the majority of input energy--typically 70-85%--is dissipated as heat [1, 2]. Inadequate heat dissipation leads to a self-reinforcing temperature rise, significantly degrading LED performance and reliability [3, 4, 5, 6, 7, 8]. As high-density LED devices have emerged, the importance of thermal management has become increasingly evident [9, 10]. For instance, micro-LED array panels generate continuous heat within confined regions, which can severely impact device performance. In flexible LEDs, the inherently low thermal conductivity of substrate materials imposes additional constraints on thermal management. LEDs integrated on polyimide substrates often lack sufficient thermal conduction layers, resulting in substantial reductions in optical output and overall device performance [11]. The design of high-density LED arrays, including the output power of individual chips, the number of LEDs, and their spatial arrangement, plays a crucial role in achieving effective heat distribution, thereby reducing the overall thermal resistance of the system [12]. Various approaches have been explored to enhance heat dissipation, including the use of high thermal conductivity packaging materials [8, 13, 14] and external thermal man agement components such as heat sinks [15; 16; 17; 18], heat pipes [18; 19], and active cooling systems [14; 20; 21]. The heat dissipation performance of these methods strongly depends on power output and device form factor. Heat sinks, typically composed of highly thermally conductive materials (e.g., aluminum or copper), dissipate heat by increasing the effective surface area exposed to the surrounding air. Radial heat sinks, which feature symmetrically arranged fins around a central axis, have been widely adopted, with key design parameters such as base thickness and fin geometry optimized to enhance thermal dissipation efficiency [15; 16; 17; 18]. In addition, various fin designs, such as staggered, elliptic, or twisted geometries, have been developed to further facilitate effective natural convection cooling [22; 23]. Heat pipes enable efficient heat transfer to remote cooling surfaces through the phase change of a working fluid involving evaporation and condensation. In LED devices, they have demonstrated significant reductions in thermal resistance, particularly in compact or enclosed environments. Beyond the conventional cylindrical shape, loop-type or flat-type heat pipes with micro-grooves have been proposed for high-power LEDs [24; 25; 26]. Moreover, transient modeling of heat pipe behavior has enabled accurate prediction of thermal hysteresis and dryout recovery dynamics [27]. Active cooling systems, such as miniature fans or thermoelectric modules, are commonly employed to dissipate heat using external power. While they offer fast response and localized cooling capability, they are often hindered by relatively low energy efficiency. For example, the coefficient of performance of thermoelectric modules remains significantly below that of traditional refrigeration systems, limiting their use in high-precision applications [28]. Moreover, although hybrid designs integrating phase-change materials or immersion cooling techniques have been proposed, their compact, scalable integration in miniaturized LED systems is elusive [29; 30]. In another approach, thermal vias are embedded in substrates to provide efficient heat dissipation pathways. These sub-millimeter-scale vertical holes, fully filled or coated with highly thermally conductive materials, facilitate heat transfer from LEDs to underlying heat management components [31; 32]. Thermal vias reduce the thermal resistance of devices by providing direct, high-conductivity pathways from the LED junction to the underlying heat-spreading layers.