Optical and microstructural characterization of Er$^{3+}$ doped epitaxial cerium oxide on silicon

Rare-earth ion dopants in solid-state hosts are ideal candidates for quantum communication technologies such as quantum memory, due to the intrinsic spin-photon interface of the rare-earth ion combined with the integration methods available in the solid-state. Erbium-doped cerium oxide (Er:CeO$_2$) is a particularly promising platform for such a quantum memory, as it combines the telecom-wavelength (~1.5 $\mu$m) 4f-4f transition of erbium, a predicted long electron spin coherence time supported by CeO$_2$, and is also near lattice-matched to silicon for heteroepitaxial growth. In this work, we report on the epitaxial growth of Er:CeO$_2$ thin films on silicon using molecular beam epitaxy (MBE), with controlled erbium concentration down to 2 parts per million (ppm). We carry out a detailed microstructural study to verify the CeO$_2$ host structure, and characterize the spin and optical properties of the embedded Er$^{3+}$ ions. In the 2-3 ppm Er regime, we identify EPR linewidths of 245(1) MHz, optical inhomogeneous linewidths of 9.5(2) GHz, optical excited state lifetimes of 3.5(1) ms, and spectral diffusion-limited homogenoeus linewidths as narrow as 4.8(3) MHz in the as-grown material. We test annealing of the Er:CeO$_2$ films up to 900 deg C, which yields modest narrowing of the inhomogeneous linewidth by 20% and extension of the excited state lifetime by 40%. We have also studied the variation of the optical properties as a function of Er doping and find that the results are consistent with the trends expected from inter-dopant charge interactions.

Optimizing the electron spin coherence of Er 3+ for quantum memory applications necessitates selection of an environment free from decoherence mechanisms, and for high-quality wide-bandgap crystals at cryogenic temperatures the leading factor of decoherence is nearby nuclear spins within the host material [19].A recent computational study identified that cerium dioxide (CeO 2 ) is an optimal host for maximizing electron spin coherence [19], due to the near-zero natural abundance of nuclear spins in its constituent elements [20].CeO 2 is additionally attractive as a host due to its low lattice mismatch (−0.4%) with silicon (Si), with heteroepitaxy on silicon providing an avenue for scalability of photonic and electronic quantum devices, as discussed in more detail elsewhere [7,9].
In this work, we benchmark Er-doped CeO 2 (Er:CeO 2 ) thin films grown on Si(111) by molecular beam epitaxy (MBE) for use in developing a telecom-wavelength interfaced spin qubit platform.Previous work on CeO 2 /Si epitaxy has focused mostly on microstructural studies [21,22,23,24].Inaba et al. [25] have examined Er:CeO 2 /Si down to 10,000 parts per million (ppm) Er and reported preliminary Er 3+ optical characterization results at 4 K, including an optical excited state lifetime (T 1 ) of 1.5 ms at 1512 nm.We extend this line of investigation by exploring significantly lower Er concentration regimes (1-100 ppm) than have been studied previously for CeO 2 .
We conduct a detailed study of the MBE-grown Er:CeO 2 /Si(111) system, starting with microstructural study of the thin film where we confirm that CeO 2 grows epitaxially on the Si(111) substrate with appropriate Ce 4+ valency.Examining the spin properties of the Er doped into the CeO 2 system by electron paramagnetic resonance (EPR), we identify results consistent with Er 3+ substituting into the cubic Ce 4+ site, and at concentrations of 2-3 ppm we measure EPR linewidths as low as 245(1) MHz.
We additionally examine the optical properties of the trivalent Er 3+ dopants at 3.5 K, identifying an optical inhomogeneous linewidth of 9.5(2) GHz, a spectral diffusion linewidth as narrow as 4.8(3) MHz, and an optical lifetime as long as 3.5(1) ms at 2-3 ppm doping levels.Of particular note is that the spectral diffusion linewidths found here via transient spectral hole burning -though broader than in bulk or with nanostructures built upon bulk samples as measured by spectral hole burning [26] or photon echo [12,27,28] -are narrower by an order of magnitude than other reports of spectral diffusion in thin film or nanostructured Er-doped oxides on silicon [6,7,8].
To elaborate upon our study we identify the trends by which the EPR, optical inhomogeneous, and spectral diffusion linewidths narrow and the excited state lifetime increases as a function of decreasing Er concentration.Additionally, we examine the effect of annealing the Er:CeO 2 films up to 900 °C, which yields modest narrowing of the inhomogeneous linewidth by 20% and extension of the excited state lifetime by 40%.

Epitaxial growth of Er:CeO 2
Er:CeO 2 thin films are grown epitaxially on Si(111)±0.5°substratesusing a Riber C21 DZ Cluster molecular beam epitaxy (MBE) system.Growths are carried out between 665-675 °C and initiated on a 7 × 7 reconstructed Si(111) surface.Metallic Er, Ce and molecular O 2 beams are used with a beam equivalent O 2 :Ce flux ratio of 20.Growths are observed in situ with a reflection high-energy electron diffraction (RHEED) system operated at 15 kV.We grow with erbium doping levels between 2-132 ppm and thicknesses between 200-940 ppm.Following deposition, films are cooled in the presence of oxygen flux.Further details are described in the supplemental information (S.I.).Where anneals are noted, samples are annealed after growth in an MTI OTF-1200X tube furnace at one atmosphere of 20.02% O 2 balanced with Ar.

Structural, spin, and optical characterization of epitaxial films
Cross-sectional XTEM studies are carried using a Thermo Fisher Spectra 200 operated at 200 keV in scanning transmission electron microscopy (STEM) mode.The same tool at the same voltage is used for energy-dispersive x-ray (EDX) spectroscopy.Specimens for XTEM and EDX are prepared using focused ion beam (FIB) milling [29].A four-circle Rigaku Smartlab diffractometer is used for X-ray diffration (XRD) scans, along with X-ray absorption spectroscopy (XAS) performed on beamline 29 ID-D of the Advanced Photon Source at Argonne National Laboratory.All microstructural measurements were conducted at room temperature.
Continuous wave (CW) X-band (9.5 GHz) EPR experiments are carried out with a Bruker ELEXSYS II E500 EPR spectrometer (Bruker BioSpin), equipped with a TE 102 rectangular EPR resonator (Bruker ER 4102ST).Field modulation at 100 kHz in combination with lock-in detection leads to first derivative-type CW EPR spectra.Measurements are performed at cryogenic temperatures between 4.0 and 4.2 K, with temperature governed by a helium gas-flow cryostat (ICE Oxford) and an ITC (Oxford Instruments).Er:CeO 2 samples are mounted with the static magnetic field parallel to the Si< 110 > axis.Measurements use a field modulation of 1 mT, a microwave power attenuation of 35 dB (from 200 mW), and a field step size of 0.2 mT.
Optical characterization is performed in a custom confocal microscopy setup designed for telecom C-band spectroscopy, with samples mounted in a cryostat at 3.5 K (s50 Cryostation, Montana Instruments).Time-resolved photoluminescence excitation (PLE) spectroscopy is done with 1.5 ms excitation pulses shaped by acousto-optic modulators (AOMs) and 7 ms collection intervals.The PLE signal is detected by a Quantum Opus superconducting nanowire single photon detector (SNSPD).Transient spectral hole burning (TSHB) measurements are enabled by the addition of a phase electro-optic modulator to the excitation path, yielding sidebands with a specific detuning from the laser carrier.Photoluminescence (PL) measurements are performed in the same setup with an alternative collection path routed to a low-noise InGaAs camera (PyLoN IR, Princeton Instruments) and the excitation laser operated continuously.Additional details of this setup are described elsewhere [8].111) alignment between the epilayer and substrate.This is further confirmed by cross-sectional TEM studies.Figure 1(b) shows a representative high-resolution bright field XTEM image with diffraction patterns shown in the inset.A 4 nm thick amorphous layer is observed at the CeO 2 /Si interface.We identified a mixed CeO x -SiO y composition across this layer via EDX (Figure 1(c)).Similar interfacial oxide layers have been observed in CeO 2 /Si previously [25] and are a well-known phenomenon in ionic oxides grown on Si [9,30], resulting from oxygen diffusion followed by catalytic oxidation of the buried silicon interface.Low-magnification bright field XTEM (see S.I. Figure S1 for an example) shows an epilayer threading dislocation density of ∼ 10 9 cm −2 .Similar threading defects can be seen in the XTEM studies of CeO 2 /Si by Inaba et al. [25].Threading segments do not relieve lattice mismatch strain, and we ascribe the formation of these threading defects to the initial stages of epitaxial growth of CeO 2 , possibly due to the formation of localized patches of oxidized silicon due to catalytic effects of the deposited CeO 2 .This effect may be controlled by adjusting the growth conditions and will be the subject of a later paper.

Results and Discussion
An ω-2θ XRD scan of a 3 ppm Er, 940 nm thick CeO 2 sample, as shown in Figure 2(a), yields a CeO 2 (111) refection with a full-width at half maximum (FWHM) of 630 arcsec, qualitatively consistent with the threading dislocation density observed.The peak separation between the Si(111) and CeO 2 (111) peaks is ∼700 arcsec indicating that most of the misfit strain remains elastically stored in the film.
To corroborate the crystal structure identified by XRD, XAS of the Ce M-edge on a 35 ppm Er, 240 nm thick CeO 2 on Si sample shows two sets of peaks related to the M5 and M4 transitions of electrons from 3d core orbitals to unoccupied p-and f-like symmetry orbitals, as seen in Figure 2(b).The positions of the main peaks at 883 eV (M5) and 901 eV (M4) relate to the electric-dipole allowed transitions to 4f states [31,32,33] and are consistent with the Ce 4+ valence state and the formation of CeO 2 (as opposed to Ce 3+ and Ce 2 O 3 ).The satellite peaks at 889 eV (Y') and 906.5 (Y) result from transition to 4f states in the condition band and are additional indicators of predominately Ce 4+ valency [34,35].Overall, spectral shape and peak separation are consistent with the Ce 4+ oxidation state, and peaks corresponding to Ce 3+ are not identifiable within the spectrum.This data together with the XRD and XTEM studies suggests that we have a CeO 2 film where the Ce 3+ concentration is likely less than 1%, based on the detection limit of the experimental setup.

EPR study on erbium incorporation into CeO 2
The incorporation of Er 3+ into the CeO 2 films is confirmed by identifying erbium-specific spin properties under EPR.Low-temperature EPR probes the lowest-lying level of the 4 I 15/2 manifold, where an effective spin-1/2 system is valid for identifying the features of the resultant spectra: In the effective spin-1/2 Hamiltonian H, the first term covers the Zeeman splitting of the electron spin states S proportional to the Bohr magneton µ B , the applied magnetic field B, and the effective g-factor produced by local structure.The second term accounts for the hyperfine interaction between the electron spin S and the nuclear spin I for Er isotopes with a non-zero nuclear spin, governed by the hyperfine splitting tensor A. Figure 3(a) shows a representative example of an EPR spectrum obtained from the 3 ppm Er, 940 nm thick CeO 2 sample.We identify a primary resonance peak near 100 mT surrounded by a set of lower-intensity resonance peaks.The primary peak arises from the absorption of the Er 3+ electron spin transition for the 77% of naturally abundant nuclear spin I = 0 Er isotopes (primarily 166 Er, 168 Er, and 170 Er).The lower-intensity peaks arise from the hyperfine interaction between the electron spins and the remaining naturally abundant nuclear spin I = 7/2 isotope ( 167 Er), which yields eight hyperfine peaks.Seven hyperfine peaks are easily identifiable adjacent to the primary peak; the eighth hyperfine peak is obscured by the primary peak [36].
The measured EPR spectrum (Figure 3(a), blue dots) is fitted (Figure 3(a), magenta dashed line) to the energy structure defined by Equation 1 to extract effective g-values, hyperfine parameters A, and EPR linewidths.Resonance peaks are described with first derivatives of Lorentzians, and the hyperfine peak locations are identified accounting for second-order perturbation in nuclear spin [37].We extract an effective value g = 6.812(5) and a hyperfine splitting of A = 687(1) MHz for the displayed sample.This g-factor is consistent with theoretical study of Er 3+ residing in a cubic crystal field symmetry [38], and is additionally consistent with experimental study of Er:CeO 2 in bulk and nanocrystal form [38,39]. Based on the cubic symmetry sites available in CeO 2 and the comparable size of the Ce 4+ and Er 3+ ions (0.97 Å and 1.004 Å ionic radii respectively for coordination number 8 [40]), we note that the Er ion likely substitutes into the Ce site [41,42] under this growth method.
The broadening of resonance peaks in EPR may result from a variety of factors, including magnetic dipole-dipole interactions (e.g.Er-Er) and strain due to defects (e.g.threading dislocations, vacancies, unintentional dopants).Focusing on the nuclear spin zero peak, we find that the EPR linewidth increases linearly with Er 3+ doping, as shown in Figure 3

Effect of erbium concentration on optical characteristics
We study the optical inhomogeneous linewidth Γ inh of the Er:CeO 2 films to characterize the ability to address transitions; the optical spectral diffusion limited linewidth Γ SD as a metric on the optical transition coherence; and the optical excited state lifetime T 1 to identify one of the significant time scales of an optical memory interface.
The 11 electrons present in the 4f shell of Er 3+ lead to a ground state electronic configuration of 4 I 15/2 (referred to as Z) and a first excited state electronic configuration of 4 I 13/2 (referred to as Y).These states split into 5 Z levels and 5 Y levels due to the cubic point symmetry of the host CeO 2 structure [44], which we confirmed by EPR.A diagram of the crystal field-split level structure is shown in Figure 4(a).
Figure 4(a) shows the PL spectrum of the 3 ppm Er, 940 nm thick CeO 2 sample excited with 1473 nm light, to the top of the 4 I 13/2 states.After excitation, a fast non-radiative decay process moves the excited population to Y 1 [45].Radiative decay from Y 1 to the Z levels allows us to observe four Y 1 − Z i transitions, consistent with the maximum five Z levels allowed by cubic symmetry.The highest energy transition, in this case Y 1 − Z 1 , is found to be at 1530.74(5) nm.We note that a complete level assignment of all crystal field levels is beyond the scope of this work, but that complete analysis will be published in a forthcoming work.
For additional optical characterization, we focus on the Z 1 − Y 1 transition due to its technological relevance at low temperature, with the readily accessible spin interface in Z 1 as discussed in the EPR section and the absence of the non-radiative processes found in Y >1 .We probe the Z 1 − Y 1 transition with higher spectral resolution using PLE, and examine its inhomogeneous linewidth as a function of Er doping density (Figure 4(b), black dots), using samples with thicknesses of 740-940 nm (see S.I. for a table of sample details).The inhomogeneous spread of the absorption line, which ranges from 9.5(2) at 3 ppm Er to 41 (7) GHz at 132 ppm Er, may be influenced by the presence of fluctuating electric fields caused by charged defects or strain in the vicinity of the optically active Er 3+ sites.Such defects can include other Er 3+ ions themselves (since, for example, the aliovalent Er 3+ on a Ce 4+ site will result in a negatively charged point defect Er ′ Ce , per Kröger-Vink notation [46]), charge compensating defects (e.g.positively charged oxygen vacancies) that are created as a result of the Er 3+ defects to maintain charge neutrality [41], and "grown-in" imperfections during crystal growth.
Taking these things into account, the inhomogeneous linewidth (Γ inh ) depends on the nature of the interaction between surrounding defects and the optically active emitters [47].In one scenario, the interaction energy between the emitter (Er 3+ ) and a nearby charged defect varies as ∼ 1/R 2 , where R is the defect-to-emitter distance, and one expects Γ inh ∝ n 2/3 , where n is the defect density [47].Alternatively, the effects of strain, random electric field gradients, or dipole-dipole interactions -all with interaction energy ∼ 1/R 3 -result in a linear dependence Γ inh ∝ n.Based on these models, we can describe the generic behavior of the linewidth to be: In Figure 4(b), we assume for this equation that n ∼ n Er , where n Er is the concentration of Er ′ Ce defects.Fitting Equation 2 to the measured dependence of the inhomogeneous linewidth upon the Er doping concentration (red dashed curve), we find that the b parameter dominates while the linear c parameter goes to zero.To specifically test the linear dependence case as well, we force a linear fit by setting b = 0 (blue dotted curve).We find that both fits capture the generic trend, though n

2/3
Er yields a slightly better fit.Based on this result we conclude that the Er-defect interaction energy may be either ∼ 1/R 2 (charge-dipole) or ∼ 1/R 3 (strain or second order Stark effect) according to Stoneham's analysis [47], but no definite inference of the defect's nature can be made at this stage.We make note that the ∼ 1/R 2 dependence requires presence of a static dipole formed in the excited Er that is unexpected in the centrosymmetric CeO 2 lattice, and may exist only due to lattice distortions presented by microstructural imperfections.Finally, we find that there is ∼10 GHz residual inhomogeneous broadening even at low Er concentrations of 2-3 ppm.This is most likely a consequence of grown-in crystalline imperfections during the thin film growth.
Continuing our optical study, we find that the optical excited state lifetime T 1 decreases with increasing Er 3+ density as shown in Figure 4(c) (black dots), from 3.5(1) ms at 2-3 ppm to 2.74(1) ms at 132 ppm.This may result from the opening up of additional nonradiative pathways with increased density of emitters and defects.A basic understanding may be obtained by applying the Inokuti-Hiroyama theory [48], which establishes enhancement of the decay rate as a function of the density of the surrounding defects n that can quench the excitation via energy transfer processes.Again assuming n ∼ n Er , we find the measured behavior can be fit adequately with the Inokuti-Hiroyama theory assuming electric dipole-dipole interactions with the intrinsic lifetime and critical concentration as free parameters, the result of which is shown in Figure 4(c) (red dashed line).Additional details on this analysis are presented in the S.I.We note that these results are consistent with the quenching centers being compensating defects whose concentration is dependent on the Er 3+ doping, although exact nature of these quenching centers can not be inferred at this point.
Finally, Figure 4(d) shows the dependence of the spectral diffusion-limited homogeneous linewidth, henceforth referred to as the spectral diffusion linewidth Γ SD , as a function of Er doping (black dots).The varying mean distance of dipole-dipole interactions between excited Er 3+ ions [4] results in a concentration dependence in the spectral diffusion linewidth.We confirm that this is reflected in the spectral diffusion linewidth increasing with doping, from 4.8(3) MHz at 2 ppm to 1465(66) MHz at 132 ppm.For a large ensemble of Er 3+ ions, each optically active ion experiences random instantaneous spectral diffusion (ISD) [49] caused by the dipole-dipole interaction with nearby excited Er ions.This results in additional dephasing manifest in the spectral diffusion, which for ISD-caused broadening should be linear in the density of the excited ions [49] indicating Γ SD = a + bn Er (red dashed line in Figure 4(d)).We emphasize the significant correlation between the doping density and spectral diffusion linewidth, particularly since at the lowest doping levels of 2-3 ppm we see spectral diffusion linewidths of ∼5 MHz for a millisecond-timescale TSHB measurement conducted at 3.5 K.

Effect of annealing on Er:CeO 2 optical characteristics
Though we are careful not to assume the nature of the defects leading to broadening and quenching in the doping series results, we speculate that these defects may be partially mitigated by post-growth annealing.Oxygen vacancies, for example, are a common side-effect of MBE processes due to the high-temperature, low-pressure environment used for growth and may be removed by annealing.Annealing is also a common step when processing samples produced by other means, e.g. after ion implantation of Er into bulk [50], and so is a useful point of comparison.
To study the effect of annealing we studied a 200 nm thick, 3 ppm Er:CeO 2 film on Si for 12 hours in 1 atmosphere of 20% O 2 /Ar, at different temperatures up to 900 °C (film roughening occurred beyond this temperature).Figures 5(a-c) show the dependencies of the PLE-measured inhomogeneous linewidth, radiative lifetime, and spectral diffusion linewidth of the Z 1 − Y 1 transition as a function of the annealing temperature.Annealing leads to modest improvements in Γ inh and T 1 of 20% and 40% respectively from their as-grown values.We ascribe these improvements due to the annealing out of "grown-in" crystal defects in the thin films.However, the spectral diffusion linewidth worsens at moderate temperatures and returns to the as-grown linewidth at the maximum temperature studied, and the process driving this behavior is unclear.
The trends in inhomogeneous linewidth Γ inh and the excited state lifetime (T 1 ) as a function of annealing temperature (T ) can be captured by assuming (i) a first-order reaction rate-limited process of thermally activated annihilation of the grown-in defects that affect the optical properties, and (ii) the suitability of the previously described power law relation and the Inokuti-Hirayama approach respectively for the defect concentration dependence upon Γ inh and T 1 .Details of these models are given in the S.I.We find that an Arrhenius-like activation energy E A in the range of 0.65 − 0.75 eV for the temperature-dependent first-order reaction rate constant leads to good fits for both Γ inh (Figure 5(a), red dashed line) and T 1 (Figure 5(b), red dashed line).This points to a density of grown-in, optically relevant defects that are being annihilated via thermally activated processes.

Conclusion
The Er:CeO 2 /Si system presents an attractive combination of benefits, as it is an ideal host oxide for a spin defect with its very low nuclear noise environment, and has low lattice mismatch for epitaxial growth on silicon.In this work, we have carried out a detailed microstructural and optical study of MBE-grown epitaxial Er:CeO 2 /Si in the 2-132 ppm Er doping range, yielding results relevant for development in quantum coherent device applications.We establish a baseline for this material in the context of key metrics for rare-earth doped oxide systems: as-grown films at 2-3 ppm Er doping show EPR linewidths as narrow as 245(1) MHz, optical inhomogeneous linewidths down to 9.5(2) GHz, an optical excited state lifetime as long as 3.5(1) ms, and a spectral diffusion-limited homogeneous linewidth as narrow as 4.8(3) MHz.Annealing to 900 °C improves the optical inhomogeneous linewidth and excited state lifetime by a modest 20% and 40 % respectively, yielding an inhomogeneous linewidth as narrow as 6.7(2) GHz and an optical excited state lifetime as long as 4.5(4) ms.
In studying the doping dependence of the optical parameters as a function of Er doping, we show that the functional dependence is consistent with a charge dipole-based interaction model between the Er emitters.Overall the optical linewidths for the thin films are broader than corresponding linewidths in high-quality bulk samples doped with Er, likely due to the larger number of grown-in defects such as threading dislocations formed during thin film growth.As such, our future research will target reducing defect densities via growth process optimization.We also note that the narrow ∼ 5 MHz spectral diffusion linewidths at 2-3 ppm Er doping are sufficiently low to begin exploring measurement techniques such as photon echo, which will allow us to directly probe optical coherence of Er 3+ in CeO 2 .

Figure 1 :
Figure 1: Epitaxy of a 3 ppm Er, 940 nm thick CeO 2 thin film on Si.(a) RHEED pattern of the epitaxial CeO 2 surface with the electron beam along the Si< 110 > azimuthal direction.(b) High resolution cross-sectional TEM of the Er:CeO 2 /Si structure showing epitaxial registry of the CeO 2 with the Si substrate, as well as a 4 nm thick amorphous layer between the film and substrate.Diffraction patterns are shown in the insets.(c) EDX scan across the CeO 2 /Si interface, showing that the amorphous layer is composed of a mixed Ce and Si oxide.Each intensity trace is normalized to the maximum counts for that element.

3. 1 Figure 1
Figure1(a) shows the RHEED pattern of a 3 ppm Er, 940 nm thick CeO 2 film on Si(111) immediately following growth, with the electron beam incident along the Si< 110 > azimuth.No significant changes in RHEED patterns are noted during growth or for different Er doping concentrations.The streaky pattern indicates a smooth, single-crystalline surface and is consistent with an epitaxial CeO 2 (111)/Si(111) alignment between the epilayer and substrate.This is further confirmed by cross-sectional TEM studies.Figure1(b) shows a representative high-resolution bright field XTEM image with diffraction patterns shown in the inset.A 4 nm thick amorphous layer is observed at the CeO 2 /Si interface.We identified a mixed CeO x -SiO y composition across this layer via EDX (Figure1(c)).Similar interfacial oxide layers have been observed in CeO 2 /Si previously[25] and are a well-known phenomenon in ionic oxides grown on Si[9,30], resulting from oxygen diffusion followed by catalytic oxidation of the buried silicon interface.

Figure 2 :
Figure 2: Additional microstructural study of as-grown Er:CeO 2 samples.(a) ω-2θ XRD scan of a 3 ppm Er, 940 nm thick CeO 2 thin film on Si.The FWHM of the CeO 2 peak is 630 arcsec.(b) X-ray absorption spectroscopy of a 35 ppm Er, 240 nm thick CeO 2 thin film on Si.The cerium M-edge is shown, as detected by total electron yield (TEY) mode and normalized to the maximum measured intensity.Consistent with Ce 4+ , the M5 and M4 peaks are at 883 eV and 901 eV respectively.The satellite peaks Y' and Y are observed at 889 eV and 906.5 eV respectively.

Figure 3 :
Figure 3: EPR study of Er:CeO 2 thin films on Si.EPR measurements are performed at 4.0-4.2K. (a) CW EPR resonance spectrum of Er:CeO 2 , obtained from a 3 ppm Er, 940 nm thick sample.A primary peak at ∼ 100 mT is produced by nuclear spin zero Er isotopes, and secondary peaks due to the less abundant 167 Er are visible around the main peak.The peak locations are obtained via fit using Eq.1 (magenta dashed line), and we obtain a g-value of g = 6.812(5) and a hyperfine splitting parameter of A = 687(1) MHz.(b) The Er spin resonance linewidth as a function of Er concentration, extracted from the primary peak of the CW EPR spectrum at each Er concentration (black circles).Uncertainty in the extracted linewidths are smaller than the data marker size.A linear fit to the Er concentration (red dashed line) matches the trend of the data, and is discussed further in the main text.

Figure 4 :
Figure 4: Optical study of Er:CeO 2 thin films on Si, with measurements performed at 3.5 K.The Er doping dependence fits in (b)-(d) are discussed in detail in the main text.(a) PL spectrum of a 3 ppm Er, 940 nm thick sample excited by 1473 nm light.Four transitions are found: Y 1 to Z 1−4 .The magenta line is shown to guide the eye.(b) Inhomogeneous linewidth of the Z 1 − Y 1 transition varies with Er concentration (black dots), where each point is the FWHM extracted from the Z 1 − Y 1 PLE peak (inset, blue dots) via a Lorentzian fit (inset, magenta line).Power law (red dashed line) and linear (blue dotted line) fits capture the general trend.(c) Optical excited state lifetime at the Z 1 − Y 1 transition varies with Er concentration (black dots), where each point is the time constant taken from an optical decay signal (inset, blue dots) by an exponential fit (inset, magenta line).The dependence of the lifetime on Er doping is fitted to the Inokuti-Hiroyama model (red dashed line).(d) Spectral diffusion linewidth at the Z 1 − Y 1 transition varies with Er concentration (black circles), where each point is the HWHM extracted from a TSHB measurement (inset, blue dots) via a Lorentzian fit (inset, magenta curve).A linear fit (red line) captures doping dependence.

Figure 5 :
Figure 5: Annealing study of a 3 ppm Er, 200 nm thick CeO 2 thin film on Si via 12-hour anneals in O 2 /Ar at 1 atmosphere, measuring optical properties as a function of annealing temperature.Optical measurements are performed at 3.5 K. Black squares indicate annealed samples, blue circles indicate the un-annealed as-grown sample as the built-in reference.Kinetic model extensions to the inhomogeneous linewidth and optical lifetime models (red dashed curves) are described in the text.(a) Inhomogeneous linewidths before and after annealing.(b) Optical lifetime of the Z 1 − Y 1 transition before and after annealing.(c) Spectral diffusion linewidth of the Z 1 − Y 1 transition before and after annealing.
(b) for a series of Er:CeO 2 /Si samples (740-940 nm thick, see S.I. for a table of sample details).A linear increase in linewidth with doping concentration may be associated with broadening due to magnetic dipole-dipole [43]ractions between spins[43], but we find that broadening due solely to the concentration of Er3+ions, Γ d-d , would have the values Γ d-d (2 ppm Er) = 0.2 MHz and Γ d-d (132 ppm Er) = 15.2MHz.Both of these values are significantly less than the observed linewidths from EPR measurement of those doping levels of 251 MHz and 1438 MHz respectively.The reason for this discrepancy remains unclear, but suggests that there are other potential dopant-driven broadening mechanisms at play.