Epitaxial Er-doped Y2O3 on Silicon for Quantum Coherent Devices

Rare-earth ions (REIs) have incomplete 4f shells and possess narrow optical intra-4f transitions due to shielding from electrons in the 5s and 5p orbitals, making them good candidates for solid-state optical quantum memory. The emission of Er3+ in the telecom C-band (1530 nm–1565 nm) makes it especially attractive for this application. In order to build practical, scalable devices, the REI needs to be embedded in a non-interacting host material, preferably one that can be integrated with silicon. In this paper, we show that Er3+ can be isovalently incorporated into epitaxial Y2O3 thin films on Si (111). We report on the synthesis of epitaxial, single-crystalline Er:Y2O3 on Si with a narrow inhomogeneous linewidth in the photoluminescence (PL) spectra, 5.1 GHz (<100 mK), and an optical excited state lifetime of 8.1 ms. The choice of Y2O3 was driven by its low nuclear spin and small lattice mismatch with Si. Using PL and electron paramagnetic resonance, we show that Er3+ substitutes for Y in the crystal lattice. The role of interfacial SiOx, diffusion of silicon into the film, and the effect of buffer layers on the inhomogeneous PL linewidth are examined. We also find that the linewidth decreased monotonically with film thickness but surprisingly exhibits no correlation with the film crystalline quality, as measured by the x-ray rocking curve scans, suggesting other factors at play that limit the inhomogeneous broadening in Y2O3 films.


I. Introduction
The need for quantum memory devices has been increasingly apparent in networked coherent quantum systems that use an optical quantum communication link within a distributed network of processors, or a secure communication network that uses quantum repeaters [1][2][3] . The role of a quantum memory is to store quantum information during entanglement events, and multiple mechanisms and systems for storage have been identified by researchers 4,5 . A promising and convenient approach among them is to use the spin-optical interfaces of rare-earth ions (REIs) [6][7][8][9][10] . Rare-earth ions have full 5s and 5p orbitals that shield the inner 4f levels from the local environment resulting in narrow 4f−4f electronic transitions. This shielding results in a low spectral diffusion not achievable in other systems such as the nitrogen-vacancy center defects 9 .
Additionally, they are well suited for development of coherent microwave to optical transduction 11 . These properties make REIs ideal for solid-state optical quantum memory systems, provided they can be embedded in a sufficiently inert (low nuclear spin and no unpaired electrons) solid-state host material and are capable of being modulated electrically or optically in an efficient manner. Among REIs, Er 3+ is particularly attractive since it has an optical transition (~1535 nm for 4 I13/2 → 4 I15/2) that lies in the telecom C-band (λ = 1530 nm -1565 nm), enabling the use of existing in-ground fiber links and leveraging the extremely low transmission loss in this wavelength range (0.2 dB/km).
Properties of active REIs in Y2O3 nanoparticle and ceramic hosts have been extensively studied in the past [12][13][14][15][16][17][18][19] . This includes a reported optical homogeneous linewidth of 85.6 kHz in Eu:Y2O3 14 , and spin coherence time of 2.9 ms, also in Eu:Y2O3 19 . These studies have been covered in detail in recent reviews [20][21][22] . For crystalline host materials the focus has been on bulk single crystals such as yttrium orthosilicate (Y2SiO5 or YSO), yttrium vanadate (YVO4 or YVO), and yttrium aluminum garnet (Y3Al5O12 or YAG). These studies [23][24][25][26][27] have demonstrated long coherence times for the hyperfine transitions in these host materialscoherence time is a key metric for the duration that quantum information can be stored in a system. Recent work, using a combination of methods, has demonstrated a hyperfine coherence time of 1.3 seconds (T = 1.4 K, B = 7 T) in an Er 3+ :YSO host 26 and over 6 hours (T = 2 K) for Eu 3+ 27 . Recent studies have also demonstrated nanophotonic devices that can be used to isolate single atoms in these systems. For instance, Dibos et al. 6 explored fabricating an evanescently coupled structure out of silicon and stamping onto the bulk. A different approach used focused ion beam milling to create nanobeam structures from bulk single crystal 28 . These demonstrations show the promise of REIs, but they are limited by bulk platforms and fabrication methods that are not scalable. From a device perspective, deployment of REIs for quantum memory needs a convenient and scalable means of interrogating the REIi.e. storing quantum information and retrieving it from memory.
One way of accomplishing scalability and compact operability is via the use of Er 3+ ions embedded in a thin film solid-state host that can be grown and integrated directly onto a silicon platform, enabling potential integration with silicon photonic components and fabrication of low mode volume, high Q-factor compact resonators, and electronics that will enable us to address the hyperfine states. Evaluation of the optical and microstructural properties of Er doped epitaxial rare earth oxides thin films has not been done before. This is the objective of the current research, and in this paper we explore and evaluate the microstructural, chemical and optical properties of Er 3+ in epitaxial Y2O3 and (LaxY1-x)2O3 oxide heterostructures on Si wafers for their suitability in scalable quantum memories. The host material is preferred to be single-crystalline to minimize heterogeneous variations in the environment surrounding embedded REI ions that are expected to induce additional spin-lattice, spin-spin relaxation pathways and reduce the optical and spin coherence times. There are a few considerations that govern the selection of a good host material for optically active REIs -(i) A cubic host is preferable with low lattice mismatch between the host material and silicon for high−quality epitaxial growth and silicon integration, (ii) Low or zero nuclear and electron spin is preferred in the host material, (iii) Isovalent incorporation of the REI ion at a substitutional site, and (iv) Low optical loss or absorption in the telecom band When considering Er 3+ , several rare-earth sesquioxides satisfy criteria (i) and (iii) (small lattice mismatch and isovalence). Among these, the lowest nuclear spin is offered by Y2O3, Gd2O3, Tb2O3 with nuclear spins of 1/2, (0, 3/2) and (0, 3/2) respectively, along with lattice mismatches of -2.4%, -0.48%, and -1.22%. Among these Y possesses no unpaired electrons, which could be a source of magnetic noise. Further, the ionic radii of Y 3+ and Er 3+ are similar (Shannon radius of 102 pm and 103 pm respectively) and therefore, local strain effects are expected to be minimal. Additionally, as yttrium has only one stable isotope with ½ nuclear spin, it provides a uniform distribution of nuclear spins around Er 3+ ions. These properties make Y2O3 an attractive host material for erbium.
While the growth of epitaxial Y2O3/Si structures has been studied before using both Molecular Beam Epitaxy (MBE) 29,30 and pulsed laser deposition (PLD) techniques 31,32 , Er-doped Y2O3 (Er:Y2O3) and the evaluation of such heterostructures for quantum memory and related devices remains unexplored. In this paper, we demonstrate the successful epitaxial growth of Er:Y2O3 on Si (111) substrates and carry out a detailed microstructural and optical characterization study of these films. Through careful optimization of the growth conditions, we show that narrow photoluminescence (PL) inhomogeneous linewidths (7.9 GHz at 4K) for the first optical transition of Er 3+ can be obtained, indicating that Y2O3 epitaxial films can act as an inert, high quality host for Er 3+ . The hyperfine levels from the 7/2 nuclear spin isotope 167 Er can be seen clearly in the Electron Paramagnetic Resonance (EPR) spectrum. We show that the catalytic interfacial oxidation of the Si/Y2O3 interface, the diffusion of silicon into the oxide layer and possible diffusion/contamination effects from surfaces are key material phenomena that need to be controlled and demonstrate how a buffer layer approach can mitigate these effects. No significant correlation between the Er 3+ PL linewidths and the crystal quality as determined by X-ray rocking curves was observed, indicating that structural distortions due to mosaicity and dislocations in the film may not play a significant role for quantum device development in such heterostructures. On the other hand, we observe a clear inverse correlation between PL linewidth and film thickness, lending further support to the potential role of the proximity of surfaces and interfaces. Finally, we show that alloying this system (Y2O3) with a high quantity of lanthanum, which leads to a closer lattice matching condition 29 , also results in broadening of the PL linewidth.

A. Growth of epitaxial thin films
Epitaxial growths of Y2O3 thin films were performed on Si (111) substrates in a Riber oxide MBE system with a background pressure of ~10 -10 torr. Substrates were prepared using a piranha clean followed by a dilute hydrofluoric acid (HF) dip. Epitaxial growth was initiated on 7×7 reconstructed Si (111) surfaces. A range of substrate temperatures between 600 °C to 920 °C was explored for growth. High purity (4N in total metal basis, 5N in rare earth metal basis) 33 erbium, lanthanum and yttrium were evaporated using high-temperature effusion cells and an RF plasma source was used for oxygen (325 W, 2.8 sccm) corresponding to a pressure of ~2×10 -5 torr in the growth chamber. Er concentrations between 10 ppm -200 ppm were used for different samples by varying the Er cell temperature between 700 °C and 900 °C respectively. Higher concentration was needed to get a good PL intensity during measurements.
We compared the inhomogeneous linewidth for concentrations in this range (10, 50, 200ppm) and did not find any significant differences. Er concentration was estimated using an Er2O3 film grown with Er cell temperature of 1200 °C and extrapolating the vapor pressure 34 to lower cell temperatures. The epitaxial growth was monitored in situ with reflection high-energy electron diffraction (RHEED).

B. Film characterization
Y2O3 (a = 10.60 Å, space group Ia3 ̅ , Z=16) has a bixbyite structure with 32 cation (Y 3+ ) sites out of which 24 are non-centrosymmetric C2 sites and 8 are centrosymmetric C3i sites 35 . Out of these, there are 6 magnetically inequivalent for C2 and 4 for C3i. Given the similar ionic radii, Er 3+ is expected to substitute for Y 3+ at both sites during growth.
Ex situ structural characterization was performed using a high-resolution X-ray diffractometer (Bruker D8 Discover). Optical characterization was realized in a confocal microscopy setup.
Off-resonant optical spectra were obtained following excitation with a 976 nm laser and the emission detected using a nitrogen-cooled InGaAs camera. Resonant optical spectra for the transition at ~ 1535 nm were realized using a tunable C-band laser (ID photonics CoBrite DX1) with the PL detected using a single nanowire single photon detector (SNSPD, Quantum Opus).
In this case, the excitation and the PL signal were temporally isolated from each other using a combination of optical switches and acousto-optic modulators. The samples were mounted on a copper cold-finger in a closed-cycle cryostat (Montana Instruments). All reported measurements in this setup were performed at 4K unless otherwise noted in the text.

8
A dilution fridge setup was used for the mK measurement and a schematic is provided in the supplementary information (SI). The sample was mounted on a three-axis nano-positioner via a copper plate. The laser pulses (Toptica CTL1500) were generated by two tandem acoustooptic modulators (AOMs) with ~100 dB on/off ratio. The pulse sequence with 15 ms pulse width and 10 Hz repetition rate was focused with an aspheric lens pair. The reflected light was collected and delivered to a superconducting nanowire detector (SNSPD) on the cold plate in the same fridge. An optical switch inserted in front of the SNSPD blocks the strong excitation pulse and transmits the emitted light.
X-band EPR was conducted using a Bruker Elexsys E500 system equipped with a variabletemperature cryostat (Oxford). The measurements were performed in a flow cryostat at 4.2 K.
The g-factors were calibrated for homogeneity and accuracy by comparison to the Mn 2+ standard in a SrO matrix (g = 2.0012 + 0.0002) 36 and by using coal samples with g = 2.00285 ±0.00005 37 , respectively.
High-resolution transmission electron microscopy (HRTEM) was carried out using the Argonne Chromatic Aberration-corrected TEM (ACAT, FEI Titan 80-300ST TEM/STEM) with a field-emission gun and an image corrector to correct both spherical and chromatic aberrations, enabling a resolution limit better than 0.8 Å at an accelerating voltage of 200 kV.
High-angle annular dark-field imaging and energy-dispersive X-ray spectroscopy mapping were carried out using a Talos F200X S/TEM (operating at accelerating voltage of 200 kV) equipped with an X-FEG gun and a Super X-EDS system.

B. Engineering the film-interfaces
The high-resolution TEM image of the film/substrate interface and the energy dispersive spectroscopy (figure 3), indicates two amorphous layers, one of which is caused by Si oxidation at the Si interface. This SiOx layer transitions to a phase consisting of Y, Si, and O that is proximal to the Y2O3 film. This transition is due to the catalytic behavior of rare−earth oxide overlayers that results in silicon oxidation 38 4(e)). This decrease in PL linewidth is attributed to an increased separation between the active Er 3+ ions from the film/substrate interface. Further decrease in the PL linewidth was observed when the Er 3+ ions are away from top interface, condition shown in 4(f). The inhomogeneous linewidth for this sample was found to be 19.6 GHz. This sandwiching of the optically active Er 3+ :Y2O3 layer between undoped Y2O3 helped reduce the inhomogeneous linewidth by about 50%, suggesting that proximity of the interfaces contributes to the broadening seen here. Why does this occur? We believe that the bottom interface and the top surface acts as gateways for impurity diffusion into the Y2O3 layer. We speculate that these could be trace amounts of Si (from the Si substrate) and/or OH groups and oxygen vacancies (from the top surface exposed to the ambient). Si diffusion is suggested from our EDS scans and oxygen and OH groups are known to be fast diffusing species 40,41 in ionic oxides. Such impurities could cause inhomogeneous linewidth broadening of the Er emission via localized charge defect formation from aliovalent substitutional, or interstitial accommodation of these impurities or defects in the vicinity of the Er ions.
Due to a large lattice mismatch with Si (2.4% tensile), relaxed Y2O3 will contain dislocations that relieve the elastic strain. It has been shown that alloying Y2O3 with La can reduce the lattice mismatch with silicon 29 . To explore the use of using a lattice-matched host material for

C. Spectroscopic Characterization
The presence of Er 3+ and its incorporation into the crystal structure was supported by EPR measurements and confirmed through the PL data. Figure 5(b) shows the EPR spectra for a 650 nm Er:Y2O3 film at 4.2 K (Er concentration ~ 10 ppm). Naturally occurring Er has multiple isotopes − 166 Er, 167 Er, 168 Er, 170 Er − which constitute 33.50%, 22.87%, 26.98%, 14.91% of naturally occurring erbium, respectively. 167 Er is the only isotope with non-zero nuclear spin (spin = 7/2). The contribution from 167 Er is seen as eight smaller peaks in figure 5(b) distributed around the main peak at 548.24 ± 0.2 G that comes from the zero nuclear spin isotopes. A schematic is shown in figure 5(a). The relative intensities of these peaks are indicative of the abundance of different isotopes. The g-factor calculated for the central peak from the data shown in figure 5(b) is 12.2and is attributed to be a composite of the contributions coming from the Er 3+ ion at the C2 sites 44 .
The crystal field effect breaks the spherical symmetry of the free ion and this results in the splitting of the ground state ( 4 I15/2) into 8 Stark levels and the first excited state ( 4 I13/2) into 7 Stark levelswhere the number of levels is dictated by the total angular momentum quantum number 13 . Stark levels for the C2 sites are represented as Zi (Z1 to Z8) for the split 4 I15/2 levels and Yi (Y1 to Y7) for the split 4 I13/2 levels as shown in figure 5(a), and similarly as Yi' and Zi' for the C3i sites. Figure 5(c) shows the PL data collected at 10 K in the wavelength range 1500 nm -1600 nm. Emission peaks in this range is due to transitions between the Stark level manifold of the first excited state ( 4 I13/2) and the ground state ( 4 I15/2). Using data reported in literature 45   impurity diffusion, as discussed earlier in this paper. Our best PL linewidth for C2 site emission was found to be 7.9 GHz at 4 K and 5.1 GHz at 7 mK (base plate temperature on which the sample is mounted) as shown in figure 6(b). We estimate the actual sample temperature from laser heating to be <100 mK (SI). The two measurements of the linewidths were carried out in two different measurement setups in order to gain more confidence in the data. The small difference in linewidths in our view, is most likely due to laser frequency calibration between the two setups and is not significant enough to suggest a temperature dependence of linewidth.
In comparison to our thin film results, an inhomogeneous linewidth of 0.42 GHz and 2 GHz have been reported 15,20 in bulk Er:Y2O3 polycrystalline (ceramic) and bulk single crystal systems. The optical excitation state decay measured for the PL in our samples was found to be 8.1 ms (shown in figure 6(c)) which is comparable to the reported value of 8.5 ms in bulk single crystal 20 and ~6X longer than the lifetime of 1.5 ms reported for Er:Y2O3 ALD grown thin films 10 . Why are the thin film linewidths broader that those reported in bulk films? In addition to the diffusion of impurities such as hydroxyl ions and silicon from neighboring interfaces, an important factor may be the effect of oxygen vacancies in subsurface regionsthese are known charge defects in many ionic oxides.

IV. Conclusion
The rare earth ion, Er +3 offers attractive properties suitable for use as a quantum memory: a spin-optical interface, narrow photoluminescence linewidth, low spectral diffusion, and an emission wavelength in the telecom band. This, paired with Y2O3's low absorption in that wavelength range and epitaxial compatibility with Si makes Er:Y2O3 thin films on Si a promising materials platform for quantum technologies. We have successfully demonstrated the growth of Er:Y2O3 epitaxial thin films on Si(111) and, using spectroscopic techniques, demonstrated that the erbium substitutes for yttrium in the bixbyite structure at both the C2 and C3i sites where the optical decay lifetime obtained for the C2 sites is comparable to that of bulk single crystals. We have further carried out a detailed microstructural and optical study of these epitaxial films. We have shown how bottom and top spacer (or buffer) layers can improve the Er photoluminescence linewidths in thin films. We show, importantly, that unlike band-edgerelated photoluminescence in semiconductors the photoluminescence of the Er 3+ emission (Γinh) is unaffected by crystal quality as determined by X-ray rocking curve linewidths.
However, we show that the photoluminescence linewidths are directly correlated to film thickness indicating surface and interface effects and potential impurity effects related to surfaces/interfaces. Lattice engineering using La leads to improvement in the mismatch with silicon but degrades the Γinh significantly. Finally, we show that by optimizing the epitaxial growth conditions, we can obtain ultra-narrow linewidths of 5.1 GHz in a dilution fridge setup (<100 mK) indicative of high quality Er 3+ incorporation in a largely non-interacting host. Our next step would be measurement of coherence times on this thin-film system and comparison to values observed in bulk.

Supplementary Material
See supplementary materials for details on dilution fridge setup, further characterization and lattice match calculations for the lanthanum alloyed films.