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Effects of the refractive index of the encapsulant on the light-extraction efficiency of light-emitting diodes

Ming Ma, Frank W. Mont, Xing Yan, Jaehee Cho, E. Fred Schubert, Gi Bum Kim, and Cheolsoo Sone

Open Access Open Access

Abstract

We investigate the effects of the refractive index of the encapsulant on the light-extraction efficiency (LEE) of light-emitting diodes (LEDs) for GaN LEDs (n ≈ 2.5) and AlGaInP LEDs (n ≈ 3.0). For non-absorbing rectangular parallelepiped LED chips, as the refractive index of the encapsulant increases, the LEE first increases quasi-linearly, then increases sub-linearly, and finally a saturation is reached. Furthermore, LEDs with a dual-layer graded-refractive-index (GRIN) encapsulant (n encapsulant1 = 1.57 and n encapsulant2 = 1.41) is fabricated through a two-step curing process. We demonstrate that such an LED further enhances the LEE by reducing Fresnel reflection loss at the encapsulant/air interface by 35% compared with an LED encapsulated with a single-layer encapsulant (n encapsulant = 1.57).

©2011 Optical Society of America

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Figures (4)
Fig. 1
Fig. 1 Analytical calculation of the LEE as a function of the refractive index of the encapsulant for GaN LEDs and AlGaInP LEDs.

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Fig. 2
Fig. 2 (a) The numerically calculated LEE as a function of θ C at the semiconductor/encapsulant interface for a non-absorbing rectangular parallelepiped LED. (b) Numerical calculation results and the 3D ray-tracing simulation results of the LEE as a function of the refractive index of the encapsulant for GaN LEDs. (c) Numerical calculation results and the 3D ray-tracing simulation results of the LEE as a function of the refractive index of the encapsulant for AlGaInP LEDs.

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Fig. 3
Fig. 3 Comparison between the measured LOP and the 3D ray-tracing simulated LEE as a function of the refractive index of the encapsulant for GaN LEDs and AlGaInP LEDs.

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Fig. 4
Fig. 4 Measured LOP as a function of the refractive index of the encapsulant for unencapsulated AlGaInP LED chips, AlGaInP LEDs encapsulated with encapsulants having different refractive indices (n encapsulant = 1.41 and 1.57), and AlGaInP LEDs encapsulated with a dual-layer GRIN encapsulant (n encapsulant1 = 1.57 and n encapsulant2 = 1.41). The inset shows the schematic diagram of a fabricated AlGaInP LED encapsulated with a dual-layer GRIN encapsulant.

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Equations (1)

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η LEE(encapsulated) = 1 − cos θ C, encapsulant 1 − cos θ C, air η LEE(unencapsulated)   = 1 − cos ( arcsin n encapsulant n semiconductor ) 1 − cos ( arcsin 1 n semiconductor ) η LEE(unencapsulated)
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