Temperature-Dependent Anisotropic Refractive Index in β-Ga2O3: Application in Interferometric Thermometers

Abstract

An accurate knowledge of the optical properties of β-Ga₂O₃ is key to developing the full potential of this oxide for photonics applications. In particular, the dependence of these properties on temperature is still being studied. Optical micro- and nanocavities are promising for a wide range of applications. They can be created within microwires and nanowires via distributed Bragg reflectors (DBR), i.e., periodic patterns of the refractive index in dielectric materials, acting as tunable mirrors. In this work, the effect of temperature on the anisotropic refractive index of β-Ga₂O₃n(λ,T) was analyzed with ellipsometry in a bulk crystal, and temperature-dependent dispersion relations were obtained, with them being fitted to Sellmeier formalism in the visible range. Micro-photoluminescence (μ-PL) spectroscopy of microcavities that developed within Cr-doped β-Ga₂O₃ nanowires shows the characteristic thermal shift of red-infrared Fabry-Perot optical resonances when excited with different laser powers. The origin of this shift is mainly related to the variation in the temperature of the refractive index. A comparison of these two experimental results was performed by finite-difference time-domain (FDTD) simulations, considering the exact morphology of the wires and the temperature-dependent, anisotropic refractive index. The shifts caused by temperature variations observed by μ-PL are similar, though slightly larger than those obtained with FDTD when implementing the n(λ,T) obtained with ellipsometry. The thermo-optic coefficient was calculated.

Keywords: FDTD; ellipsometry; gallium oxide; nanowire; optical microcavity; photoluminescence; refractive index; thermometer.

Figure 1

Sketch of the orientations of the crystal and the reference system, for both (a) nanowires and (b) bulk Ga₂O₃ crystals.

Figure 2

Refractive index values for the three axes at 25 °C (298 K) and 325 °C (598 K) obtained from ellipsometry data from Ga₂O₃ bulk crystal.

Figure 3

Anisotropic permittivity as a function of the temperature in the RT—400 K range.

Figure 4

(a) SEM image of the microcavity patterned in a Cr-doped Ga₂O₃ nanowire, with the two DBRs indicated. (b) Comparison between RT μ-PL spectra from an as-grown nanowire and the microcavity shown in (a). Spectra were normalized and vertically shifted for the sake of clarity. (c) Blow up from (b) of the four main F-P resonance peaks observed in the microcavity, overlapping the broad phonon-assisted band in the near-IR range. Their positions are 714.2 nm, 723.0 nm, 732.1 nm and 741.3 nm and were labeled #1, #2, #3 and #4, respectively. (d) Detail of the evolution of the #3 resonant peak when changing the excitation power.

Figure 5

(a) Simulation procedure, with the schematic of the OptiFDTD Designer module. The red plane is the pulse source, while the green plane is the Poynting vector detection plane. The defined axes are shown in the lower, right corner. (b) Comparison of normalized experimental μ-PL spectra of peak #2 at three different temperatures (solid lines) with simulations at such temperatures, using both the anisotropic, temperature-dependent refractive index calculated from ellipsometry in this work (dashed lines) and that calculated from the data by Sturm et al. [11]. Dotted line shows the resonance at 360 K by using n_j(λ,T) obtained when multiplying by a 3.1 factor the dn/dT value calculated by ellipsometry in this work.