Light extraction limits in textured GaN-InGaN light-emitting diodes: Radiative transfer analysis

Abstract

We present a study on the light extraction properties of thin film light-emitting diodes (LEDs) based on the radiative transfer theory. We show that the well known ergodic limit for absorptivity in textured solar cells also applies to emissivity in LEDs accordance with the Kirchhoff’s radiation law. This limit for the emission enhancement by surface texturing in LEDs is fundamental and cannot be exceeded even with index-matched optics. We further carry out numerical calculations accounting for realistic absorption in typical GaN-InGaN LEDs to compare their performance with the ergodic limit for non-absorbing structures. The results show that the optical power of InGaN-GaN LED designs can be improved by a substantial factor of 2–4 with textured surfaces and engineering of the emission pattern and provide a guideline for more efficient LED designs.

Effect of plasmonic losses on light emission enhancement in quantum-wells coupled to metallic gratings

“…The theoretical upper limit of the enhancement for lossless ergodic structures 30,31 is 2 (i.e., approximately 15 for GaN based structures), but the intrinsic losses due to the thin QW typically reduce the enhancement to only 2-3. 31 This is comparable to the values observed here as well although the ergodic limit does not directly apply to strongly resonant plasmonic structures where a much larger enhancement is expected to be possible. Despite the large values, the enhancement does not necessarily translate into large values of the internal quantum efficiency (IQE) and does not imply that the IQE could exceed unity (100%).…”

“…This definition corresponds to the earlier definitions of luminescence and absorption enhancements. 15,[30][31][32] The maximal enhancement factor is in this example as high as 2.8, 2.3, and 1.5 for a QW located 1 nm, 10 nm, and 20 nm below the grating, respectively, for a wavelength k $ 540 nm. However, Fig.…”

Enhanced light extraction from InGaN/GaN quantum wells with silver gratings

“…This is comparable with an enhancement that could be expected from a perfectly diffusive surface. 19 Figure 2 transverse magnetic (TM) polarization, where a smaller ratio was obtained: 1.6. This figure demonstrates first that a significant luminescence enhancement can be obtained with metallic gratings covered with PVA, and second that the enhancement is higher in the TE than in the TM polarization.…”

Improving Light Extraction From GaN Light-Emitting Diodes by Buried Nano-Gratings

“…In the studied configuration, we only focus on the TE polarization [1] but our model is also fully applicable to TM polarization, which may exhibit larger losses when the QW is located sufficiently near (typically at most a few tens of nanometers) to the metal surface supporting surface plasmon polaritons. Outside the near field, however, the emission enhancement is only due to scattering and cannot exceed the ergodic limit for enhancement, given by 2 [22], [24], [25] (where is the effective permittivity of the emitter region, e.g. GaN in this case) for ideal lossless structures and dropping quickly to around 2-3 for more realistic structures [1], [25].…”

“…Outside the near field, however, the emission enhancement is only due to scattering and cannot exceed the ergodic limit for enhancement, given by 2 [22], [24], [25] (where is the effective permittivity of the emitter region, e.g. GaN in this case) for ideal lossless structures and dropping quickly to around 2-3 for more realistic structures [1], [25].…”