1. Introduction

Rare earth sesquioxides, R₂O₃ (R is rare earth), have been attracting considerable attention for several decades as platforms for many potential applications in various fields such as lasers and optical amplifiers [1–3], phosphors in biomedical imaging [4], and high-k dielectrics [5,6]. It is known that rare earth sesquioxides can form a cubic bixbyite structure in several stable phases, and, interestingly, the lattice constants of all of them are generally twice that of the Si (111) plane (a = 5.43 Å). Consequently, they can grow epitaxially on a Si (111) surface, and we can obtain structural flexibility and functionality, such as heterostructures formed by different rare-earth compositions of R₂O₃ and steric structures like optical waveguides or cavities fabricated by nano-processing or selective area growth.

Among the sesquioxides, Er₂O₃ will be particularly important for photonics applications, such as light sources, optical amplifiers, and optical quantum memories, because the weakly perturbed intra-4f transition in erbium ions can interact with telecom-band (1.5 μm) photons. Recently, a few groups have reported the successful growth of epitaxial Er₂O₃ thin layers on Si (111) substrates by using the molecular beam epitaxy (MBE) method [7,8]. The layers show good optical quality with sharp emission at the wavelength of around 1.5 μm from the discrete Stark energy levels of Er³⁺ 4f orbitals. However, the control of Er³⁺ ion density in the epitaxial layers is required for the optical-device applications, because the Er³⁺ atomic density in the Er₂O₃ is huge (2.7 x 10²² cm⁻³) and various types of energy transfers are induced by the interactions among the dense Er³⁺ ions [9]. For achieving of high-performance optical devices, it is essential to reveal the Er³⁺ concentration-dependence of the population dynamics, including the energy transfer process, in such sesquioxide layers.

In this paper, we describe the MBE growth and optical characteristics of epitaxial sesquioxide alloy (Er_xSc_1-x)₂O₃. Using MBE, we grew epitaxial (Er_xSc_1-x)₂O₃ layers on Si (111) substrates with various Er compositions, i.e., various distances between the Er³⁺ in the crystal. In order to reveal the population dynamics in Er³⁺ in the grown (Er_xSc_1-x)₂O₃ layers, we systematically investigate the photoluminescence (PL) spectra and their decay lifetimes at the lowest and up-converted optical transition energies at the liquid helium temperature as a function of the Er composition. Direct correlation between concentration quenching and energy transfer up-conversion (ETUC) in high-quality (Er_xSc_1-x)₂O₃ epitaxial layers is discussed from the viewpoint of the population dynamics based on these experimental results.

2. Experiments

The lattice constants of Er₂O₃ and Sc₂O₃ are a = 10.54 and 9.85 Å, respectively. A unit cell of cubic R₂O₃ contains 32 rare-earth ions, which are located at 24 sites with C₂ (non-inversion) symmetry and eight sites with C_3i (inversion) symmetry. The nearest neighbor distances of Er³⁺ ions between the C₂−C₂, C₂−C_3i, and C_3i−C_3i sites in Er₂O₃ are 1.945, 2.656, and 5.268 Å, respectively. Sc₂O₃ is completely transparent for photons in the visible-to-telecom-band range [10]. Some of the Er³⁺ ions are replaced with Sc³⁺ ions to control the distance between the Er³⁺ ions as shown Fig. 1(a). (Er_xSc_1-x)₂O₃ crystals with x = 1.000-0.012 and the thickness of about 50 nm were grown on Si (111) surfaces with 7 × 7 reconstruction by MBE at a growth temperature of 715°C. The streak pattern of the reflection high-energy electron diffraction was maintained during the growth (not shown). The composition of the grown films was determined by Rutherford backscattering. An ω−2θ scan of the X-ray diffraction (XRD) measurements after growth showed that single crystal (ErSc)₂O₃ layers were grown, and crystal quality was approximately equivalent in all Er compositions (Fig. 1(b)). Moreover, we found that the Er concentration-dependency of the lattice constant of (Er_xSc_1-x)₂O₃ satisfied Vegard's law. Thus, we can assume macroscopic uniformity of Er³⁺ distribution in the grown samples. The cross-sectional image obtained with a transmission electron microscope (TEM) also proved that the (ErSc)₂O₃ was epitaxially grown on the Si (111) surface (Fig. 1(c)).

 

Fig. 1 (a) Unit cell of bixbyite (ErSc)₂O₃ crystal. In this schematic, Er³⁺ at the C₂ site are replaced by Sc³⁺. (b) XRD ω-2θ scan. Red and black curves show x = 1.000 and 0.027, respectively. (c) Cross-sectional TEM image of grown (ErSc)₂O₃. (d) Energy diagram of Er³⁺ ions in Y₂O₃ (Ref. 11).

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The as-grown samples were mounted in a continuous flow liquid helium cryostat and the temperature was kept at 4 K. PL and PL excitation (PLE) spectra were obtained by using an excitation source consisting of a continuous-wave tunable laser (1520-1560 nm, spectral width of 400 kHz) with an Er-doped fiber amplifier (EDFA). This wavelength range corresponds to the energy of the first excited state (⁴I_13/2 manifold) as shown in Fig. 1(d) [11]. The excitation laser was focused on a spot with a diameter of about 15 μm and an incident angle of 45 degrees through an objective lens. The PL from the sample was collected perpendicularly with a different objective lens that had a numerical aperture of 0.40. The PL spectra in the 1.5-μm and visible wavelength regions were observed with an InGaAs photodiode array and a Si-CCD camera through spectrometers, respectively, and the sensitivities of both detectors were calibrated for a comparison of the spectrum intensity. The spectral resolution was about 60 μeV, which corresponds to 0.48 cm⁻¹. The time-resolved PL was measured by using a pulsed laser equipped with an acousto-optic modulator and a streak camera (Hamamatsu C11293S). We used rectangular pulse with 2.5-ms width, which is longer than the decay lifetime of the (ErSc)₂O₃. The spectral and temporal resolutions of this system were 500 μeV (4.03 cm⁻¹) and 20 ps (for a 1 ns scan range), respectively.

3. Results and discussion

Figure 2(a) shows the PL spectra of various Er compositions (x = 1.000-0.012) under the resonant excitation of the third level from the bottom of the first excited Stark manifold in the C_3i site (Y’₃ level in ⁴I_13/2) with an excitation power of 5 mW. Table 1 summarizes the number of Er³⁺ ions per unit cell, the Er³⁺-ion density, and average distance for the grown samples. Note that the PL spectrum mapping shows no changes of intensity, peak position and linewidth in 5 mm x 5 mm scanned area for all samples (not shown). In addition to XRD results, this is also the evidence of uniformity of the Er³⁺ distribution in the layer. The strongest PL peak at a wavelength of 1548 nm with x = 1.000 corresponds to the transition between bottom Stark energy levels in the first excited and ground states in the C_3i site (from Y’₁ in ⁴I_13/2 to Z’₁ in ⁴I_15/2) [12]. The transition energy of this peak shifts to 1551 nm because the crystal field surrounding Er³⁺ is changed by decreasing the Er composition [1,13]. Thepeak intensity per one Er³⁺ ion normalized by the Er³⁺ density and layer thickness and the PL fullwidth at halfmaximum (FWHM) of the main Y’₁−Z’₁ transition are summarized as a function of Er composition in Fig. 2(b). The efficiency of optical transition in a Er³⁺ decreases with increasing Er³⁺ density up to x = 0.270. This is known as concentration quenching, which is caused by the enhancement of the energy migration among the Er ions and its capture by the non-radiative centers [14–16]. In general, the emission lifetime under this migration quenching should be reduced rapidly because the fast non-radiative relaxation becomes dominant. However, the measured lifetimes of the main Y’₁−Z’₁ transition measured under the same excitation condition as shown in Figs. 2(a) and 2(b) are almost a constant value of 2 ms below x = 0.270 as shown in Figs. 2(c) and 2(d). Here, all the emission decay curves are fitted by using single exponential function I_PL∝exp(τ/τ_r). This behavior suggests that the concentration quenching in epitaxial (ErSc)₂O₃ is not mainly caused by an increase in the population capturing probability at the non-radiative centers with the higher Er composition. In contrast, the transition efficiency around x = 1.000 seems to slightly recover, and the lifetime reduces rapidly to 140 μs toward x = 1.000.

 

Fig. 2 (a) PL spectra of various Er compositions under the resonant excitation of the assigned Y’₃ level in the C_3i site. (b) PL peak intensity and FWHM of the Y’₁-Z’₁ transition as a function of Er composition. The dotted curves are guides for the eye. (c) Time-resolved PL of (Er_xSc_1−x)₂O₃ with x = 1.000 and 0.054, detected at the Y’₁-Z’₁ transition. Red curves show the calculated results by using Eq. (1) with the parameters in Table 2. (d) Er composition dependence of PL decay time.

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Table 1. Summary of the number of Er³⁺ ions per unit cell, the Er³⁺ density, and the average distance for grown (Er_xSc_1-x)₂O₃ samples.

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To analyze these population dynamics in (ErSc)₂O₃, we focus on the effect of the ETUC in Er³⁺. The ETUC means that the cooperative up-conversion (Auger like process) between Er³⁺ occurs and, as the result, photons with a wavelength shorter than the excitation one are emitted [9]. Figures 3(a) and 3(b) show PLE color plots of an Er₂O₃ sample under ⁴I_13/2 manifold excitation (1520-1550 nm) and the PLE spectra detected at the energy levels of ⁴S_3/2 (around 550 nm) and ⁴I_13/2 manifolds. Strong PL caused by the ETUC from the higher statesin the Er³⁺ 4f orbital is observed only when the excitation wavelength corresponds to the Stark energy level of the ⁴I_13/2 manifold. The UC PL was observed in all (ErSc)₂O₃ grown samples, but its intensity was greatly reduced by decreasing the Er composition as shown in Fig. 3(c). The PL peaks from the various UC states (UCSs: ²H_9/2, ⁴S_3/2, ⁴F_9/2, ⁴I_9/2, ⁴I_11/2) correspond to the predicted transitions between the Stark levels and the ground state (⁴I_15/2) in the C₂ site, while optical transitions above the ⁴I_13/2 state in the C_3i site are not observed [11].

 

Fig. 3 PLE color plots of Er₂O₃ detected at (a) ⁴S_3/2 and (b) ⁴I_13/2 manifolds under ⁴I_13/2 manifold excitation. The noise of the center part in the PLE color plots at the ⁴I_13/2 manifold is caused by scattering from the excitation laser. UC spectra of (Er_xSc_1-x)₂O₃ with (c) x = 1.000, (d) 0.054 and (e) 0.012, respectively. The spectrum intensity of (c) and (d) is multiplied by 6 and 35, respectively.

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To estimate the ETUC rates from the first excited state, we investigate the excitation power dependence on the PL intensity under the resonant excitation of the Y₁ state for samples where x = 1.000, 0.054 and 0.012. Figures 4(a)-4(c) show the integrated PL intensity of the transition from the ⁴I_13/2 manifold and UCSs to the ground energy level of the ⁴I_15/2 manifold. Here each PL intensity is not normalized by the Er³⁺ density, and the PL spectra from various UCSs are integrated in the 500 (⁴S_3/2) to 1020 nm (⁴I_11/2) wavelength region to treat them as originating from a single UCS. To reproduce this excitation power dependence, we consider the energy transfer model (Fig. 4(d)) [17,18] and solve the steady-state rate equations based on this model as follows:

 

Fig. 4 (a)-(c) Integrated PL intensity of the transition from the ⁴I_13/2 manifold and UCSs to the ground energy level of ⁴I_15/2 manifold. Red, black and blue filled circles indicate the transition from the ⁴I_13/2 manifold in the C₂ and C_3i sites and UCSs to the ⁴I_15/2 manifold, respectively. (d) Calculation model for the rate equation analysis.

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Table 2. Summary of the measured values (A_i) and obtained transfer rates (B_ij) in ms⁻¹ units.

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Here we consider the population dynamics in (ErSc)₂O₃ on the basis of the above experimental results. We observed concentration quenching in (ErSc)₂O₃ with a constant emission lifetime with single exponential decay as shown in Figs. 2(b) and 2(d). Moreover, we measured the UC luminescence for all Er compositions (Fig. 3) and found that the ETUC rate is greatly enhanced with increasing Er composition (Fig. 4 and Table 2). These results indicate that the concentration quenching in epitaxial (ErSc)₂O₃ mainly originates from the population that escapes from the excited states to the UCS by ETUC (UC quenching in intra-ion) and that the contribution of the population transfer among Er³⁺ sites to the non-radiative centers (migration quenching in inter-ion) is very small. In the steady-state rate equation analysis, all of the energy transfer rates B_ij is 1/10 or less than the linear decay rates A_i at x < 0.054. Therefore, the weight of these B_ij to the lifetime (dn_{1 or 3}/dt) will be insignificant. In fact, the calculation results, which is obtained by the time evolution analysis using the same rate equation (Eq. (1)) with the parameters in Table 2, also reproduce well the measured PL lifetime as shown red curves in Fig. 2(c). Therefore, we conclude that the mechanism of the concentration quenching in epitaxial (Er_xSc_1-x)₂O₃ mainly originates from the UC quenching by the enhancement of the UC rate B₃₄ below the Er composition x = 0.270. In contrast, the average distance between Er³⁺ in (ErSc)₂O₃ with x > 0.3 becomes less than 5 Å, and this will induce wavefunction overlapping [20,21] and an increase in the coherence volume of the Er³⁺ ions. At present, we expect the revival of the PL intensity and fast decay at x = 1.000 is caused by this coherent effect, although we need further study of the contribution of the UC and migration quenching at the high Er-composition region.

4. Conclusion

In conclusion, we grew epitaxial (Er_xSc_1-x)₂O₃ layers with various Er compositions on Si (111) substrates by MBE and optically investigated the peculiar characteristics of concentration quenching at the wavelength of around 1.5 μm. Concentration quenching with increasing Er composition was observed in grown (Er_xSc_1-x)₂O₃, although the emission lifetime of 2 ms was maintained from x = 0.012 to 0.270. An analysis of the excitation power dependence of the PL intensity, including the UC emission, revealed that this concentration quenching in high-quality epitaxial (Er_xSc_1-x)₂O₃ layers mainly originates from the UC quenching with the enhancement of the UC rate. Our results provide a guide for the exploration of other rare-earth sesquioxides and those alloys, and they will contribute to the development of novel optical devices that use rare earth materials on Si substrates.