Fig. 1. Cross sectional schematic of the simulated LED device structure employing microsphere arrays.

Fig. 2. Schematic of the microsphere LEDs (a) with hexagonal close-packed sphere array, (b) with square close-packed sphere array, (c) with submonolayer sphere array, and (d) with multilayer microsphere arrays.

Fig. 3. (a) Ratio of light extraction efficiency of microsphere LEDs with various sphere packing densities to that of the planar LED, (b) comparison of far-field intensity of microsphere LEDs with various packing densities at ϕ=0, (c) angle-dependent power distribution.

Fig. 4. Contour plots of far-field intensity of microsphere LED (b) with a submonolayer sphere array (dsphere/period=0.5), (c) with a monolayer sphere array (dsphere/period=1), and (d) with a multilayer sphere array (dsphere/period=2). The contour plot of the far-field radiation pattern of (a) the planar LED is included for reference.

Fig. 5. Far-field radiation patterns of LEDs with (a) hexagonal close-packed anatase-TiO2 sphere array and (b) square close-packed anatase-TiO2 sphere array; (c) schematic of hexagonal close-packed sphere array and (d) schematic of square close-packed sphere array.

Fig. 6. Contour plots of the far-field intensity of microsphere LEDs with microsphere arrays: (a) flat LED, (b) hexagonal close-packed sphere array with 7 spheres, (c) hexagonal close-packed sphere array with 19 spheres, (d) hexagonal close-packed sphere array with 37 spheres, (a′) one sphere in the center of the device, (b′) square close-packed sphere array with 9 spheres, (c′) square close-packed sphere array with 25 spheres, (d′) square close-packed sphere array with 36 spheres. The corresponding schematics of the sphere arrays are shown in the top and bottom rows.

Fig. 7. Ratio of the extraction efficiency for microsphere array LEDs with both hexagonal and square close-packed monolayer configurations with a varying number of spheres, similar to the ones presented in Fig. 6. The results are normalized to the extraction of planar LEDs.