Sub-MHz homogeneous linewidth in epitaxial Y₂O₃: Eu³⁺ thin film on silicon

2.1 Epitaxial growth

Y₂O₃: Eu³⁺ (2 % Eu³⁺) was deposited by direct liquid injection chemical vapor deposition (DLI-CVD) on a commercial Si(111) wafer presenting a MBE-grown Gd₂O₃ film on top. Gd₂O₃ constitutes an excellent template due to a low lattice mismatch with Si (around 0.44 %), allowing for being epitaxially grown by MBE on this substrate [25]. The Gd₂O₃ film used in this investigation has a thickness of about 225 nm as confirmed by ellipsometry analysis (see Figure S1). Besides, XRD analysis confirmed that it is epitaxial on silicon with a mosaicity of about 0.24° around the [111] direction (see Figure S2). The multilayer structure is schematically represented in Figure 1(a). The home-built DLI-CVD reactor is described in detail in Ref. [20]. Beta-diketonate Y and Eu complexes (YTHD and EuTHD) with 3N purity were used as precursors. They were dissolved in mesitylene (99 % purity), flown into two independent injectors and vaporized at 200 °C. The vapors were carried to the reaction chamber by N₂, and O₂ was also flown to deposit the film. Deposition occurred at a pressure of 30 mbar with the substrate heated at 800 °C.

Figure 1:

Epitaxial Y₂O₃: Eu³⁺ thin film on Gd₂O₃/Si substrate. (a) Schematic view of the multilayer structure. (b) Y₂O₃: Eu³⁺ film surface morphology observed by scanning electron microscopy (SEM).

In the described deposition conditions, the epitaxial growth of Y₂O₃ directly on silicon is impaired by the unavoidable oxidation of the silicon wafer surface. This leads to the formation of an amorphous SiO₂ superficial layer on top of which Y₂O₃ tends to grow in a polycrystalline manner [20], [22]. To overcome this limitation, we took advantage here of the Gd₂O₃ buffer layer, grown by MBE under conditions that avoid the formation of an amorphous oxide interface. The MBE-grown Gd₂O₃ buffer layer provides in addition a low-lattice-mismatch (1.9 %) template for the subsequent epitaxial growth of Y₂O₃: Eu³⁺ in our CVD reactor.

The as-deposited Y₂O₃ film on Gd₂O₃/Si was observed under a scanning electron microscope (SEM) showing a rather uniform and smooth surface (Figures 1(b) and S4). A few square-shaped grains stand out, presenting sizes between 50 and 200 nm and a few cracks possibly related to thermal mismatch with the Si substrate. This surface morphology is in clear contrast with that of previously reported polycrystalline Y₂O₃ films [20], [22], of much rougher appearance, and with clearly distinguishable faceted grains and grain boundaries. The epitaxy of the Y₂O₃: Eu³⁺ film on the Gd₂O₃/Si template was confirmed by high-resolution X-ray diffraction analysis. θ/2θ scans were taken at different angles (Figures 2(a) and S3) evidencing single [111] out-of-plane orientation for the Y₂O₃: Eu³⁺ film, similar to that of the intermediate Gd₂O₃ layer and also of the Si(111) substrate (Figure 2(a)). A mosaicity of the order of 0.6° is also observed (Figure 2(b)), a reasonable value for an oxide film on silicon [26]. Definitive confirmation of the film epitaxy is given by the pole figures (Figure 2(c) and (d)), showing a single in-plane orientation of the Y₂O₃: Eu³⁺ thin film, therefore confirming single-domain epitaxy on Si.

Figure 2:

High-resolution X-ray diffraction (XRD) investigations. (a) θ/2θ scan showing [111] out-of-plane orientation for the Y₂O₃:Eu³⁺ film. (b) Omega scan around one of the (222) diffraction peaks yielding a mosaicity of 0.6°. (c, d) Pole figures showing in-plane orientation corresponding to that of the substrate, further confirming epitaxial growth. The arrows indicate the position of the diffraction spots in the reciprocal space.

2.2 Eu³⁺ emitters properties

The optical properties of Eu³⁺ ions embedded in the epitaxial film were investigated in view of their use as quantum emitters. Prior to the optical characterizations, the film was annealed in air for 2 h at 950 °C to cure defects in the aim of reducing the emitters homogeneous linewidth [22]. The efficient incorporation of Eu³⁺ dopants into the well-crystallized Y₂O₃ film was confirmed by analyzing the photoluminescence (PL) emitted by the sample under 532 nm excitation at room temperature. A strong emission peak at 611 nm was observed, corresponding to the Eu^{3+ 5}D₀ →⁷F₂ emission line in cubic Y₂O₃ (Figure 3(a)) [22]. This emission spectrum presents no difference with respect to that measured for the as-deposited film (see Figure S5), confirming the absence of parasitic phases that could originate from surface or interfacial diffusion during the annealing [22].

Figure 3:

Photoluminescence (PL) spectroscopy of Eu³⁺ ions in the Y₂O₃ thin film. (a) Room temperature PL spectrum showing several Eu³⁺ emission lines including the strong ⁵D₀ →⁷F₂ emission at 611 nm. (b) ⁵D₀ →⁷F₂ PL decay recorded at 50 mK and 611 nm under resonant ⁷F₀ →⁵D₀ excitation at 580.79 nm. The dashed orange line corresponds to a single exponential fit to the data yielding a population lifetime T ₁ = 0.95 ms for the ⁵D₀ excited state.

For probing the emission dynamics and optical homogeneous linewidth of Eu³⁺ ions, the thin film was mounted into a dilution refrigerator equipped with a home-built optical microscopy setup and excited using a tunable dye laser with a 300 kHz linewidth. Full experimental details are given in the Supplementary Materials (SM) document (Section 4). The lifetime (T ₁) of the ⁵D₀ excited state was then measured at 50 mK by resonantly exciting the ⁷F₀ →⁵D₀ transition at 580.79 nm (Figure 3(b)). A value of 0.95 ms was obtained by single-exponential adjustment, comparable to bulk Y₂O₃: Eu³⁺ radiative lifetime [27]. This result highlights the good crystalline quality and low defect content of the film, and establishes a lower limit to the optical homogeneous linewidth of 170 Hz (1/2πT ₁).

The optical inhomogeneous line of the ⁷F₀ ↔⁵D₀ transition is displayed in Figure 4(a). We observe a full width at half maximum (FWHM) of 132 GHz by monitoring the PL emission intensity at 611 nm as a function of the excitation wavelength. The measurement was carried out at three different excitation powers to rule out power broadening effects. The measured inhomogeneous linewidth is significantly broader than that expected for a nominal concentration of 2 %, which would be less than 40 GHz. This expectation is based on previous spectroscopic studies conducted on high-quality bulk Y₂O₃: Eu³⁺ samples with varying doping concentrations [28], assuming a linear trend with increasing concentration [29]. The measured linewidth of 132 GHz is comparable to that observed in annealed polycrystalline Y₂O₃: Eu³⁺ thin films with the same Eu³⁺ concentration (2 % at.) deposited via DLI-CVD. This broadening reveals the presence of a substantial number of static defects in the film, likely attributed to strain induce by the annealing treatment [22]. The 2 % Eu³⁺ concentration spectrally distributed over the 132 GHz lead to an average of ∼60 emitters per excitation bandwidth (300 kHz) in a diffraction-limited excitation volume. The intensity of the detected PL signals indicates however that we are collecting photons from at least 10³ ions which we attribute to a larger excitation volume and power broadening effects (see Section 5 discussion in SM).

Figure 4:

High resolution and coherent optical characterizations at mK temperature. (a) Inhomogeneous linewidth for the ⁵D₀ →⁷F₀ transition measured at three different excitation powers by scanning the excitation wavelength while monitoring the ⁵D₀ →⁷F₂ emission at 611 nm. A Gaussian curve fit to the data yields a full width at half maximum (FWHM) of 132 ± 5 GHz. The stars indicate spectral position within the linewidth of the ions probed in (c). (b) Spectral hole burned at 580.787 nm at a temperature of 800 mK (blue solid line). The dashed orange line correspond to a Lorentzian curve fit to the data yielding a hole width of 1.3 ± 0.4 MHz. (c) Homogeneous linewidth (left axis) and hole width (right axis) as a function of burn power measured at three different frequencies within the inhomogeneous line (see (a)). (d) Homogeneous linewidth as a function temperature (blue points). The dashed orange line corresponds to a fit to these data using eq. (1).

The optical homogeneous linewidth (Γ _h ) exhibited by the Eu³⁺ ions in the film was finally probed by persistent spectral hole burning. Spectral holes presenting a narrow width of the order of 1 MHz were recorded (Figure 4(b)), a value which is one order of magnitude lower than spectral holes measured at 3 K in polycrystalline CVD Y₂O₃: 2 % Eu³⁺ thin films [20], [22]. This result suggests that the epitaxial ordering achieved in the present CVD film goes along with a significantly lower decoherence probably due to a lesser amount of defects [30]. To gain a further insight into the dynamical mechanisms limiting Γ _h , spectral holes were measured at different spectral positions within the inhomogeneous line (labelled A, B and C and indicated by star symbols in Figure 4(a)) and also using different excitation powers. The obtained hole widths (Γ_hole) and resulting homogeneous linewidths (Γ _h ), estimated as Γ_hole/2-Γ_laser, with Γ_laser = 300 kHz, are displayed in Figure 4(c). A linear Γ _h broadening is observed when increasing power, but with a slope that decreases when the excitation wavelength is moved away from the center of the inhomogeneous line (C at 580.79 nm) towards the side (A at 580.82 nm). In other words, the observed power broadening effect is stronger when the excited ion ensemble increases, revealing an excitation-induced contribution to Γ _h in the Y₂O₃: Eu³⁺ film proportional to the number of excited ions [31]. Yet, a power-independent Γ _h between 200 and 300 kHz can be extrapolated for all probed excitation wavelengths at the zero power limit, showing no significative differences in the optical coherence properties of different ion ensembles within the inhomogeneous line. The evolution of Γ _h with temperature was also measured and is given in Figure 4(d). The obtained Γ _h (T) was fitted by

where Γ₀ represents the temperature-independent contribution to Γ _h , α is the coupling constant to the so-called two-level systems (TLS), or dynamical disorder modes characterized by a linear temperature dependence [32], and β the coupling constant to two-phonon Raman scattering processes [29]. Best-fit parameters to the data yield Γ₀ = 270 ± 87 kHz, α = 89 ± 14 kHz/K and β = 5 ± 1 × 10⁶ kHz/K⁷. The TLS contribution, indicative of the amount of dynamic disorder, is here 5 times lower than in previously reported polycrystalline CVD Y₂O₃: 2 % Eu³⁺ thin films [22] while comparable to that observed in optimized Y₂O₃: Eu³⁺ (0.3 % at.) nanoparticles of 100 nm size also probed by spectral hole burning (α = 132 kHz/K) [32].