Thermal design of rectangular microscale inorganic light-emitting diodes

The recently developed microscale inorganic light-emitting diodes (μ-ILEDs) have attracted much attention due to their potential use in biointegrated applications such as optogenetics. It is critical to understand the thermal properties of μ-ILEDs since excessive heating may reduce the performance significantly. A three-dimensional analytical model based on the Fourier Cosine transform is developed to study the thermal properties of rectangular μ-ILEDs in this paper. The analytical prediction agrees well with finite element analysis. A scaling law for the normalized temperature increase of a single μ-ILED is established in terms of four non-dimensional parameters: the normalized shape factor γ=b/a, the normalized μ-ILED thickness H¯LED=HLED/a, and χ1=kmHm/(ksa) and χ2=ksHB/(kBa), where a and b are the half-lengths of the μ-ILED, k and H are the thermal conductivity and the thickness with the subscripts LED, m, B and s for the μ-ILED, metal layer, encapsulation layer and substrate, respectively. The influences of these non-dimensional parameters on the normalized temperature increase are systematically investigated. The temperature increase for rectangular μ-ILED array is then obtained analytically by the method of superposition. These results provide design guidelines to minimize the adverse thermal response of rectangular μ-ILEDs.