Effect of The Temperature-Dependent Anisotropic Refractive Index on The Spectral Resonances of β-Ga₂O₃:Cr Nanowire-Based Optical Microcavities

A field of great interest for photonic applications is semiconductor micro and nanowires, since thanks to the modification of the composition of the material or the creation of artificial optical structures it is possible to control its optical properties.<br/>A key photonic structure is the set of optical micro- and nanocavities based on distributed Bragg reflectors (DBR), obtained by periodic modulations of the refractive index in dielectric media. The creation of this type of structures in semiconductor micro- and nanowires broadens their potential applications as micro and nanoscale light sources.<br/>Among the materials of great interest for this type of applications is gallium oxide in its monoclinic phase (β-Ga₂O₃), a transparent conductive oxide (TCO) that presents a high thermal and chemical stability and high resistance to radiation, key properties for use under extreme conditions. Its bandgap of 4.8 eV results in a transparency range from infrared to deep UV. Among the optically active dopants that efficiently emit light along this transparency range, Cr³⁺ results in an intense photoluminescence (PL) yield in the red-near-infrared (NIR) range due to its intra-ionic transitions. DBR-based optical microcavities made of Ga₂O₃:Cr micro- and nanowires show very interesting applications [1].<br/>An analysis of the thermal dependence of the spectral resonances in such optical cavities was recently reported and applied to develop a new wide-range thermometer [1]. Spatial confinement of light within the cavity results in Fabry-Perot-type NIR-red spectral resonances, whose positions depend on temperature. This effect is mainly due to a change in the refractive index and, to a lesser extent, to a change in the length of the optical cavity. The monoclinic crystal structure results in an anisotropic refractive index, thus being necessary a detailed analysis to fully understand the optical behaviour. However, only a few previous works have been devoted to this topic in β-Ga₂O₃, therefore being still only partially understood [2,3].<br/>In this work, the temperature-dependent refractive indices along the main axes have been obtained experimentally by ellipsometry in bulk monocrystalline β-Ga₂O₃. These results have been implemented in analytical and finite-difference time-domain simulation models of the resonances in the nanowires to further evaluate their spectral behaviour with temperature.<br/><br/>[1] M. Alonso-Orts, D. Carrasco, J. M. San Juan, M. L. Nó, A. de Andrés, E. Nogales, and B. Méndez, “Wide dynamic range thermometer based on luminescent optical cavities in Ga₂O₃: Cr nanowires,” Small 18, 2105355 (2022).<br/>[2] I. Bhaumik, R. Bhatt, S. Ganesamoorthy, A. Saxena, A. K. Karnal, P. K. Gupta, A. K. Sinha, and S. K. Deb, "Temperature-dependent index of refraction of monoclinic<br/>Ga₂O₃ single crystal," Appl. Opt. 50, 6006-6010 (2011).<br/>[3] C. Sturm, J. Furthmüller, F. Bechstedt, R. Schmidt-Grund, and M. Grundmann, "Dielectric tensor of monoclinic Ga₂O₃ single crystals in the spectral range 0.5–8.5 eV", APL Materials 3, 106106 (2015).