Polarization-insensitive GaN metalenses at visible wavelengths

Abstract

The growth of wide-bandgap materials on patterned substrates has revolutionized the means with which we can improve the light output power of gallium nitride (GaN) light-emitting diodes (LEDs). Conventional patterned structure inspection usually relies on an expensive vacuum-system-required scanning electron microscope (SEM) or optical microscope (OM) with bulky objectives. On the other hand, ultra-thin metasurfaces have been widely used in widespread applications, especially for converging lenses. In this study, we propose newly developed, highly efficient hexagon-resonated elements (HREs) combined with gingerly selected subwavelength periods of the elements for the construction of polarization-insensitive metalenses of high performance. Also, the well-developed fabrication techniques have been employed to realize the high-aspect-ratio metalenses working at three distinct wavelengths of 405, 532, and 633 nm with respective diffraction-limited focusing efficiencies of 93%, 86%, and 92%. The 1951 United States Air Force (USAF) test chart has been chosen to characterize the imaging capability. All of the images formed by the 405-nm-designed metalens show exceptional clear line features, and the smallest resolvable features are lines with widths of 870 nm. To perform the inspection capacity for patterned substrates, for the proof of concept, a commercially available patterned sapphire substrate (PSS) for the growth of the GaN LEDs has been opted and carefully examined by the high-resolution SEM system. With the appropriately chosen metalenses at the desired wavelength, the summits of structures in the PSS can be clearly observed in the images. The PSS imaging qualities taken by the ultra-thin and light-weight metalenses with a numerical aperture (NA) of 0.3 are comparable to those seen by an objective with the NA of 0.4. This work can pioneer semiconductor manufacturing to choose the polarization-insensitive GaN metalenses to inspect the patterned structures instead of using the SEM or the bulky and heavy conventional objectives.

Figure 1

Design and simulation of the building block for metalenses. (A) Schematic of a dielectric metalens operating in a transmissive mode. (B, C) Schematics of the tilt-view and top-view of the building block for the metalens composed of the HREs. (D, E) Simulated electric and magnetic field intensity distribution. (F, G) The x–y cross-sections of simulated electric field intensity distribution at z = 500 and 200 µm, individually. (H, I) The x–y cross-sections of simulated magnetic field intensity distribution corresponding to (F, G). Scale bar, 50 nm in (F–I). (J–L) Diagrams showing the range of phase modulation for the building block periods of 200, 260, and 320 nm on the combinations of wavelength and radius profiles for the metalenses designed at wavelengths of 405, 532, and 633 nm, respectively. (M–O) Simulated efficiencies of the metalenses designed at the wavelengths of 405, 532, and 633 nm, respectively. The black dashed lines represent the implemented radius range for the metalens.

Figure 2

Micrographs of the metalenses. (A–C) Optical images of the fabricated metalenses designed at wavelengths of (A) 405, (B) 532, and (C) 633 nm. Scale bar: 10 μm. (D–I) The top-view SEM images shown in (D, G), (E, H), and (F, I) corresponding to the highlighted regions in (A–C). Scale bar, 2 μm in (D–I). (J–L) The tilt-view SEM images shown in (J–L) corresponding to the highlighted regions in (A–C). Scale bar, 1 μm in (J–L).

Figure 3

Characterization of the metalenses. (A–C) Phase profiles for the metalenses designed at wavelengths of (A) 405, (B) 532, and (C) 633 nm. Solid lines depict optimized phase profiles, and hollow circles indicate implemented phase profiles. (D) Measurement setup for metalenses characterization. (E–G) The intensity profiles along the axial planes for the metalenses designed at wavelengths of (E) 405, (F) 532, and (G) 633 nm. (H–J) Measured focal spots of the metalenses designed at wavelengths of (H) 405, (I) 532, and (J) 633 nm. Scale bar: 6 μm. (K–M) Corresponding horizontal cuts of focal spots with the dashed lines referring to normalized ideal Airy function.

Figure 4

Imaging with the metalenses. (A) Fabrication of the 1951 USAF resolution test chart. (B–J) Images of the 1951 USAF resolution test chart formed by the metalenses at the laser wavelength of 405 nm. The smallest features are (B) line widths of 3.91 µm and center-to-center distances of 7.82 µm, (C) line widths of 3.1 µm and center-to-center distances of 6.2 µm, (D) line widths of 2.19 µm and center-to-center distances of 4.38 µm, (E) line widths of 1.95 µm and center-to-center distances of 3.9 µm, (F) line widths of 1.55 µm and center-to-center distances of 3.1 µm, (G) line widths of 1.23 µm and center-to-center distances of 2.46 µm, (H) line widths of 1.1 µm and center-to-center distances of 2.2 µm, (I) line widths of 0.98 µm and center-to-center distances of 1.96 µm, and (J) line widths of 0.87 µm and center-to-center distances of 1.74 µm. Scale bar, 20 μm in (B, C). Scale bar, 10 μm in (D–F). Scale bar, 3 μm in (G–J).

Figure 5

Imaging with the native PSS and the blue LED on the PSS. (A) Schematic of patterned structures inspected by the metalens. (B) The top-view SEM micrograph of the native PSS. Scale bar: 2 μm. (C) The tilt-view SEM micrograph of the PSS. Scale bar: 1 μm. (D)The epitaxial structures of the blue LED. (E) Photoluminescence spectrum. Images of the PSS formed by the objective lens (NA = 0.4) with the incidences of (F) the halogen lamp and (G) the 405-nm laser light. (H) PSS Image formed by the 405-nm-designed metalens (NA = 0.3) at the laser wavelength of 405 nm. Scale bar, 3 μm in (F–H). (I) The tilt-view SEM micrograph of the fabricated metalens designed at the wavelength of 450 nm. Scale bar: 500 nm. Images of the PSS on which the blue LED taken by (J) the objective lens (NA = 0.4) at the laser wavelength of 450 nm, and (K) the 450-nm-designed metalens (NA = 0.3) at the laser wavelength of 450 nm. Scale bar, 3 μm in (J, K).