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The use of LEDs has become commonplace for applications ranging from lighting, indicator lamps, and displays for mobile phones, tablet PCs, and TVs. LEDs offer high relative efficiency, lower energy consumption, high reliability, sharper colors, and smaller sizes, all important factors for these applications.
Numerical simulations are tedious since LEDs are inherently incoherent. Most traditional simulation techniques cannot easily manage incoherence since they are based on directly solving Maxwell's equations or some derived form such as the Wave equation. Moreover, the optical design for LEDs is further complicated due to factors like multiple interfaces, the use of novel materials and structures, dispersion, surface roughness, and the use of gratings to enhance efficiency, etc.
This application note uses FullWAVE and the LED utility, and describes the simulation of the 3D GaN-based LED structure shown in Fig. 1 and is based on Ref. 1. It has a hexagonal photonic crystal (PhC etched into the top).
Figure 1: Schematic of patterned LED structure:
b) photonic crystal (PhC), and
c) the structure drawn in the RSoft CAD.
This structure, as shown in Fig 1c, consists of a PhC object created using a dynamically-sized array, a mirror at the back fast (via a PEC boundary) and uses a built-in material library for GaN material properties.
First two simulations were run using a CW excitation at a single wavelength, one with the PhC and one without (flat). The far-field results are shown in Fig. 2.
Figure 2: Computed far-field for a) PhC case, and b) Flat case.
Next, two pulsed simulations were run over a range of wavelengths. The far-field results are shown in Fig. 3 and the extraction efficiencies are shown in Fig. 4.
Figure 3: Combined far-field plots from a pulsed simulation for a) PhC case, and b) Flat case.
Figure 4: Extraction Ratio Spectrum for a Pulsed simulation for PhC and Flat cases as a function of
a) frequency and
It is also possible to view the far-field profiles for individual frequencies as shown in Fig. 5.
Figure 5: Far-field patterns at three different frequencies (rows) obtained form a pulsed simulation.
Plots on the left are from the PhC case and plots on the right are from the flat case.
 Ch. Wiesmann, K. Bergenek, N. Linder, and U. T. Schwarz, Analysis of the emission characteristics of photonic crystal LEDs, Proc. SPIE 6989, Light Emission I, 69890L (2008).