Hollow nanosphere arrays with a high-index contrast for enhanced scintillating light output from β-Ga₂O₃ crystals

β-Ga₂O₃ is a new type of fast scintillator with potential applications in medical imaging and nuclear radiation detection with high count-rate situations. Because of the severe total internal reflection with its high refractive index, the light extraction efficiency of β-Ga₂O₃ crystals is rather low, which would limit the performance of detection systems. In this paper, we use hollow nanosphere arrays with a high-index contrast to enhance the light extraction efficiency of β-Ga₂O₃ crystals. We can increase the transmission diffraction efficiency and reduce the reflection diffraction efficiency through controlling the refractive index and the thickness of the shell of the hollow nanospheres, which can lead to a significant increase in the light extraction efficiency. The relationships between the light extraction efficiency and the refractive index and thickness of the shell of the hollow nanospheres are investigated by both numerical simulations and experiments. It is found that when the refractive index of the shell of the hollow nanospheres is higher than that of β-Ga₂O₃, the light extraction efficiency is mainly determined by the diffraction efficiency of light transmitted from the surface with the hollow nanosphere arrays. When the refractive index of the shell is less than that of β-Ga₂O₃, the light extraction efficiency is determined by the ratio of the diffraction efficiency of the light transmitted from the surface with the hollow nanosphere arrays to the diffraction efficiency of the light that can escape from the lateral surface.