1. Introduction

Interest in the detailed interpretation of the spectroscopic properties of wide band gap semiconductors such as the III-nitrides GaN and AlN doped with trivalent rare earth ions (RE³⁺) has grown rapidly in recent years as the optoelectronic properties of these materials have been successfully exploited in photonic devices [1–4]. Within the band gap of AlN (approximately 6.1 eV), numerous sharp-line absorption and emission spectra of the RE³⁺ ions are observed due to transitions within the 4fⁿ subshell that is well shielded from the lattice by the filled 5s² and 5p⁶ shells of the rare earth ion core [5–7]. The large optical window associated with hexagonal AlN is also transparent to the absorption and emission spectra arising from vacuum ultraviolet states of the RE³⁺ ions, transitions that are usually not observed in insulator hosts such as garnets, oxides and fluorides due to lattice absorption.

The physical properties of rare earth-doped AlN are attractive for purposes of application in that they have high fracture toughness, are relatively non-corrosive, and exhibit high thermal conductivity, although doping reduces the thermal conductivity somewhat [8,9]. Yet, the preparation and detailed optical characterization of the doped materials still provide challenges and opportunities that call for fundamental spectroscopic studies. The technologies of thin film, single crystal, and ceramic rare earth-doped AlN sample preparation and growth have improved greatly over recent years [10–12]. Experimental techniques that include specific wavelength laser excitation and up-conversion dynamics to probe observed multi-site RE³⁺ spectra can be carried out to investigate local RE³⁺ site symmetries together with methods of electron spin resonance (EPR), Zeeman spectroscopy, and site-selective combined excitation and emission spectroscopy [13–15]. Because of the importance of Er³⁺ as an infrared laser, its upconversion capabilities, and its use in fiber-optic amplifiers by the communications industry, we have carried out the following detailed crystal-field splitting analysis of the multi-site spectra of Er³⁺ in single crystal AlN.

We begin by reporting the multi-site cathodoluminescence (CL) spectra of Er³⁺ in single-crystal hexagonal phase AlN obtained at 12 K between 320 nm and 775 nm. The spectra represent emission transitions from the lower energy (Stark) level of Er³⁺(4f¹¹) ²P_3/2 to the Stark levels of the ground state, ⁴I_15/2, and excited multiplet manifolds ⁴I_13/2, ⁴I_11/2, ⁴I_9/2, ⁴F_9/2 and ⁴S_3/2. The CL spectra include transitions from both Stark levels of ⁴S_3/2 to ⁴I_15/2, which confirm the energy (Stark) level splitting of ⁴I_15/2. All observed strong, sharp spectra are accounted for by assuming transitions from two Er sites, which we designate as principle sites “a” and “b”, with a few generally weak lines attributed to additional sites.

We also report refinements of the spectrofluorometric experiments and interpretation of Merkle et al. [16]. These site selection data identify most of the ⁴I_15/2, ⁴I_13/2, ⁴I_11/2 and ⁴I_9/2 energy levels for Er³⁺ in the principal “a” site in a ceramic Er:AlN sample, and confirm levels derived from the CL data. Thus, the site selection data guide the identification of lines associated with one principle site in the CL spectra.

Recent emission channeling experiments and lattice location studies of RE³⁺ in 2H-AlN by Vetter et al. [17] indicate that the main sites for RE³⁺ ions doped into hexagonal AlN occupy vacant cation (Al) sites, although a number of substitutional minority sites are found as well. Yang et al. [14], after reviewing possible local sites for Er³⁺ in single crystal hexagonal AlN, concluded that C_3v symmetry for Er³⁺ in a sample with a concentration of about 10¹⁶ cm⁻³ agreed with their EPR analysis. Such low RE³⁺ doping, however, precludes observation of the details of the weak 4f¹¹ spectrum of Er³⁺. A much larger concentration of Er³⁺ is needed to observe, analyze, and model the optical spectroscopy.

However, for larger amounts of Er³⁺, the local site symmetry can be distorted during crystal growth since the radius of Er³⁺ is larger than the radius of the Al³⁺ it replaces. This causes stress on the surrounding environment. In fact, local-density functional modeling by Petit et al. [18] suggests that a neighboring oxygen ion or neighboring nitrogen vacancy next to Er³⁺ may substitute for a basal-plane N to form complexes such as Er³⁺-O_N or Er³⁺-V_N with C_1h symmetry. In effect, the Er³⁺ ions that occupy Al vacancies of C_3v symmetry may shift along the c-axis toward the basal plane into a site of C_1h symmetry in order to reduce the local stress associated with its size. Thus, the site symmetry of Er³⁺ in the present study could be C_3v or lower, possibly depending on the amount and distribution of Er³⁺ ions in the lattice.

To identify the appropriate symmetry, we performed descent in symmetry calculations from C_3v to C₃ (assuming the mirror plane symmetry is broken) and from C_3v to C_1h (assuming the mirror plane remains, but the three-fold rotation symmetry axis is broken). The crystal-field splitting of the energy levels of Er³⁺ in each site is modeled assuming each of these symmetries, as discussed in section 4.

2. Experimental details

Single crystals of hexagonal phase aluminum nitride (2H-AlN) doped with trivalent erbium were grown by a temperature gradient method under high temperature and high pressure [19] with the use of a belt-type high pressure, high temperature (HP-HT) apparatus designed to grow materials having similar physical crystalline properties [20,21]. Li₃AlN₂, together with Ba₃Al₂N₄, was used as the solvent. The solvent was mixed with ErF₃ and packed into a molybdenum sample chamber. Both steps were carried out under a dry nitrogen atmosphere. The assembled cell was then compressed to 6.5 GPa and heated to 1400 °C for 4.5 hours and quenched to room temperature by shutting off the heater power supply. The end product resulted in lightly colored crystals with diameters up to 0.4 mm and a maximum size of less than 0.5 mm on a side parallel to the c-axis.

The crystal structure was confirmed by x-ray diffraction (XRD) with a Bruker AXS D8 Advance, which is equipped with a Cu K-alpha x-ray source. Figure 1 shows a typical XRD pattern of the Er³⁺-doped AlN crystals mounted on a silicon substrate using silver paste. None of the XRD measurements indicated the formation of any other phase, including rare-earth rich phases within the AlN crystals. The hexagonal structure (wurzite phase) of AlN was confirmed [22,23]. The space group is _{$C_{6v}^4(P{6}_{3}mc)$}, with both Al and N occupying C_3v sites in the unit cell. Earlier emission channeling experiments [17] identify the location of the majority of RE³⁺ as substituting for Al³⁺ in cation vacancies, some of which may form complexes with nitrogen vacancies.

 

Fig. 1 The XRD pattern showing the hexagonal structure of AlN doped with Er³⁺; conductive silver paste is used in supporting the samples.

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The CL spectra were obtained from crystals mounted on the head of a closed-cycle helium refrigerator positioned within a vacuum chamber. An electronically controlled calibrated resistive heater was maintained at a selected sample temperature while the spectra were recorded. The CL spectra were obtained at several temperatures from approximately 12 K to room temperature in order to record any temperature dependence in the spectra. A SPECS Eq. (22) Auger electron gun was used as the excitation source that produced electrons having energies between 100 eV and 5 keV and beam currents between 0.01µA and 150 µA. The CL spectra were produced by electrons excited to 5 keV with a beam current of 2 µA/mm². The emission was passed through a quartz window and a pair of UV-coated lenses before reaching the entrance slit of a 1.0 m Czerny-Turner spectrograph (Jobin-Yvon 1000M). The spectrograph was equipped with holographic gratings blazed at 250 nm with 1200 lines/mm and at 1000 nm with 600 lines/mm, and calibrated using a Hg arc standard. Resolution of the spectra was better than 0.05 nm for the sharpest transitions. Detection was carried out with a nitrogen-cooled CCD camera that recorded the spectra between 300 nm and 1000 nm. Uncertainty in the wavelength measurements was approximately 0.02 nm. The methods used to record the CL spectra are similar to the methods we reported earlier [24–28].

Site selection spectroscopy was performed on ceramic Er:AlN material, as exemplified in Fig. 2 and described in [16], using techniques very similar to those reported therein. Upgrades to the optical cryostat facilitated measurements at temperatures both lower and higher than the 20 K at which most spectra in that work were taken. Fluorescence spectra were taken with spectral band pass as narrow as 0.3 nm, and excitation wavelengths could be selected to a typical specificity of 0.2 nm.

 

Fig. 2 Fluorescence of ceramic Er:AlN due to excitation of one of the principal site’s absorption lines. The arrows indicate the peaks at about 1544.5 and 1558.25 nm, discussed in the text.

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3. Data analysis

The multi-site CL spectral lines obtained at 12 K between 320 nm and 775 nm are listed in Table 1 (column 2) for Er³⁺(4f¹¹) energy levels, including the ground state, ⁴I_15/2, and excited states ⁴I_13/2, ⁴I_11/2, ⁴I_9/2, ⁴F_9/2, and ⁴S_3/2. Using empirical methods of energy differences between transition energies and temperature dependent peak characteristics, more than 97% of the spectra reported in column 2 can be accounted for in terms of two sites, with the remaining 3% of the spectra likely associated with other Er sites for which there is insufficient data for analysis. The transitions numbered in column 5 are identified as site “a” under cols. 6-8 and site “b” under cols. 9 and 10. Column 5 identifies the transition from the lower energy (Stark) level of ²P_3/2 to one of the J + 1/2 terminal Stark levels within each ^2S+1L_J multiplet manifold listed in column 1. The transition numbers also correspond to the emission peaks identified in Figs. 3 through 9.

Table 1. CL spectrum (12 K) of Er:AlN from the lowest Stark component of ²P_3/2 at 31076 cm⁻¹ (site “a”) and 31069 cm⁻¹ (site “b”)^a

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The experimental Stark levels inferred from CL of the single crystal material may be compared with those inferred from site selection spectroscopy of the ceramic. To facilitate this comparison, higher resolution temperature-dependent measurements for selected excitation wavelengths have been used to refine the level assignments for the principal site reported in Merkle et al. [16]. The great majority of the assignments are confirmed, and are within one or two wave numbers of the originally reported values, as may be seen by comparing column 7 of Table 1 with [16]. In the case of the ⁴I_9/2 manifold, our new data shift the energy levels lower by as much as 6 cm⁻¹, but the splittings are only subtly changed. However, there are a few exceptions to this overall agreement, which can affect the assignment of levels in the CL data and the fitting of crystal field theory to the data.

The first reassignment occurs in the ⁴I_15/2 manifold. Fluorescence spectra of Er³⁺ in the principal site for several different wavelengths in its excitation spectrum indicate that the 1558.25 nm fluorescence line’s intensity at the lowest temperatures is weak and inconsistent, though as the temperature is increased it grows rapidly, as exemplified in Fig. 2. This supports [16]’s prediction of hot bands at about that wavelength, but calls into question its assignment of an energy level at 98 cm⁻¹ based on this line. However, a moderately weak fluorescence line at 1544.5 nm is much more consistent for different principal site excitation wavelengths and its intensity varies only weakly with temperature, as can be seen in Fig. 2. This is much more consistent with expectations for a transition from the lowest ⁴I_13/2 level. On the basis of this transition, we conclude that the fourth energy level in ⁴I_15/2 is not at 98 cm⁻¹, but rather is at 43 cm⁻¹.

The other reassignments resulting from our refined site selection spectra involve ⁴I_11/2 states. A detailed excitation spectrum of the principal site fluorescence refines the energy of the transition reported as 10108 cm⁻¹ in [16] to 10105 cm⁻¹, and reveals three additional excitation transitions at 10150, 10170 and 10187 cm⁻¹. The final two of these agree satisfactorily with energy levels assigned from the CL data, but the transition energies 10105 and 10150 cm⁻¹ cannot plausibly be associated with any CL feature. In addition, the crystal field modeling to be reported in a later section cannot account for these features if they represent ground state absorption.

The existence of ⁴I_15/2 states at 43 and 135 cm⁻¹ suggests explanations for these excitation lines in terms of hot band absorption. The 10105 cm⁻¹ line is satisfactorily consistent with a transition from the level at 135 cm⁻¹ to that observed in CL at 10237 cm⁻¹, and 10150 cm⁻¹ is consistent with a transition between the levels at 43 and 10193 cm⁻¹. We conclude that the ⁴I_11/2 levels observed by site selection spectroscopy are the five given in column 7 of Table 1.

Figure 3 includes peaks 1 through 14 from the 12 K CL spectrum that represent transitions from the lower Stark level of ²P_3/2 to the ground state manifold ⁴I_15/2. Peak 1 is a shoulder that represents the transition from the initiating Stark level in ²P_3/2 at 31076 cm⁻¹ to the ground state Stark level of Er³⁺ in the “a” site (Table 1). Peak 2 consists of two unresolved transitions, one transition from the initiating Stark level in ²P_3/2 at 31069 cm⁻¹ to the ground state Stark level of Er³⁺ in the “b” site and a second transition from the initiating Stark level of Er³⁺ in the “a” site to the first excited Stark level at approximately 7 cm⁻¹. This analysis of the splitting is confirmed by the site selection data in Table 1 (column 7) for Er³⁺ in the “a” site. The overlap of these peaks requires deconvolution of the spectra for peaks 1 and 2. The uncertainty in separation between peaks is less than a wave number, so that in Table 1 we list the energy for both transitions as 31069 cm⁻¹. To further support this assignment we have observed emission spectra from ⁴S_3/2 to ⁴I_15/2 for Er³⁺ in the “a” site that unambiguously identifies the 7 cm⁻¹ splitting between the ground state and the first excited Stark level. Emission peaks at 321.9 nm and 322.14 nm in Table 1 are very weak. They establish Stark levels at 30 cm⁻¹ and 43 cm⁻¹, respectively, that are confirmed by site selection spectroscopy. The emitting level of the “b” site can also be established from energy differences from that site to lower energy Stark levels established from emission by ⁴S_3/2.

 

Fig. 3 The 12 K CL spectrum of Er³⁺ in AlN between 320 nm and 327 nm representing transitions from ²P_3/2 to ⁴I_15/2.

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The CL emission spectra shown in Fig. 4 for peaks 42 through 55 were analyzed as transitions from both Stark levels of ⁴S_3/2 to the Stark levels of the ⁴I_15/2 manifold for Er³⁺ in both sites. The figure includes detector noise due to the narrow slits required to resolve the transitions observed from the two emitting Stark levels of the ⁴S_3/2 manifold in both sites to eight expected terminal Stark levels of ⁴I_15/2. Analysis of the CL spectrum confirms all eight Stark levels of the ⁴I_15/2 manifold reported in both sites in Table 1. The splitting of the ⁴S_3/2 manifold is 20 cm⁻¹ (site “a”) and 18 cm⁻¹ (site “b”). This splitting is shown in Fig. 5 and Table 1. We list only emission from ²P_3/2 in Table 1 since the emission from ⁴S_3/2 simply confirms the splitting of the ground state manifold.

 

Fig. 4 The 12 K CL spectrum of Er³⁺ in AlN between 551 nm and 566 nm representing transitions from ⁴S_3/2 to ⁴I_15/2.

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Fig. 5 The 12 K CL spectrum of Er³⁺ in AlN between 768 nm and 773 nm representing transitions from ²P_3/2 to ⁴S_3/2.

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Perhaps the simplest spectra analyzed that demonstrate the dominance of two Er³⁺ sites in this crystal are the spectra shown in Fig. 5, representing the sharp, well defined transitions from the lower Stark level of ²P_3/2 to the two Stark components of ⁴S_3/2. The four peaks (65 through 68) identify the splitting of the ⁴S_3/2 in the “a” and “b” sites and provide the energies for the emitting Stark levels used to analyze the crystal-field splitting of the ⁴I_15/2 manifold described in the preceding paragraph. The difference in energy between the multiplet barycenters of ⁴S_3/2 of Er³⁺ in the “a” and “b” sites is comparable to the energy shift found between the ground-state Stark level of Er³⁺ in both sites as well, suggesting the impurity traps represented by these two sites have nearly the same depth.

The spectra representing transitions from ²P_3/2 to ⁴I_11/2 are shown in Fig. 6 . At first glance, it appears that exactly J + 1/2 expected peaks (27 through 32) are observed for a single site. However, a closer look indicates that each peak appears to have a discernible shoulder, suggesting that the peaks may be deconvoluted into two peaks with nearly the same energy. The results from deconvolution suggest the experimental Stark levels for this manifold for the “a” and “b” sites reported in Table 1. Stark levels 10192 cm⁻¹ and 10211 cm⁻¹ in the “a” site are similar to levels assigned by analysis of the site selection spectra. The experimental Stark levels for ⁴I_11/2 of Er³⁺ in both sites are also in reasonable agreement with calculated energy values listed in columns 8 and 10 of Table 1 that are based on the modeling studies described in the following section.

 

Fig. 6 The 12 K CL spectrum of Er³⁺ in AlN between 476 nm and 482 nm representing transitions from ²P_3/2 to ⁴I_11/2.

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Figures 7 and 8 show the 12 K CL emission spectra representing transitions from ²P_3/2 to ⁴I_9/2, and ²P_3/2 to ⁴F_9/2, respectively. The transitions are represented by peaks 33 through 41 and peaks 56 through 64. Peak 33 is very weak and broad, and probably represents two separate transitions observed in the spectrum between 530 and 531 nm. In Fig. 7, five strong peaks can be assigned to transitions that identify five Stark levels within the ⁴I_9/2 “a” site manifold based on comparison with levels determined by site selection spectra listed in column 7 of Table 1. The remaining peaks and terminal Stark levels are identified with the “b” site, with the exception of peak 38 which is presently unassigned. In Fig. 8, nine peaks and a shoulder (on peak 54) are observed and ten terminal Stark levels are expected from the ²P_3/2 to ⁴F_9/2 in those sites.

 

Fig. 7 The 12 K CL spectrum of Er³⁺ in AlN between 530 nm and 538 nm representing transitions from ²P_3/2 to ⁴I_9/2.

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Fig. 8 The 12 K CL spectrum of Er³⁺ in AlN between 620.5 nm and 627.5 nm representing transitions from ²P_3/2 to ⁴F_9/2.

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Five of these transitions were assigned to the “a” site and the remaining five to the “b” site using methods of energy differences. Peaks in both figures are sharp and relatively intense, and limited by spectral resolution of the spectrograph, suggesting they may have relatively large emission cross sections. The difference in manifold splitting of ⁴I_9/2 and ⁴F_9/2 provides an important distinction between sites in the subsequent modeling studies of the crystal-field splitting of these states.

The CL emission spectra, representing transitions from ²P_3/2 to ⁴I_13/2 (levels 15 through 26 in Fig. 9 ), are perhaps the most difficult to analyze in the entire set of data given the number of similar energy differences between Stark levels and the inhomogeneous broadening of the peaks. Ambiguity is greatly reduced by comparing the peaks and transitions that give the experimental energy level scheme of Stark levels selected for the “a” site in Table 1 (column 6) with the experimental Stark levels for the ⁴I_13/2 manifold analyzed from the site selection spectroscopy. The remaining peaks and subsequent terminal Stark levels then can be assigned by process of elimination to Stark levels of Er³⁺ in the “b” site, in column 9 of Table 1. The experimental Stark levels expected for ⁴I_13/2 for Er³⁺ in both “a” and “b” sites in Table 1 agree well with the assignments made from the site selection spectroscopy and with the results of the crystal-field modeling studies reported in the next section.

 

Fig. 9 The 12 K CL spectrum of Er³⁺ in AlN between 405.5 nm and 411.5 nm representing transitions from ²P_3/2 to ⁴I_13/2.

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4. Modeling the crystal field splitting

The 34 identified experimental Stark levels for each of the two principle (“a” and “b”) sites, representing every Stark component of the seven lowest-energy multiplet manifolds of Er³⁺ along with the lowest Stark component of the emitting ²P_3/2 multiplet in single-crystal hexagonal phase AlN, are reported in Tables 2 and 3 for the main “a” and “b” sites, respectively. These energy levels are modeled using a parameterized Hamiltonian written in standard practice [29,30] that consists of spherically symmetric “atomic” contributions given by,

Table 2. Crystal-field splitting for energy levels of site “a” of Er³⁺:AlN using wavefunctions of C_3v and C_1h symmetry

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Table 3. Crystal-field splitting for energy levels of site “b” of Er³⁺:AlN using wavefunctions of C_3v and C_1h symmetry

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_{$B_0^2$}, _{$B_2^2+i{S}_2^2$}, _{$B_0^4$}, _{$B_2^4+i{S}_2^4$}, _{$B_4^4+i{S}_4^4$}, _{$B_0^6$}, _{$B_2^6+i{S}_2^6$}, _{$B_4^6+i{S}_4^6$}, and_{$B_6^6+i{S}_6^6$}. As with C₃ symmetry, one of the 15 crystal-field parameters can be set to zero via appropriate rotation about the parametrization z-axis, with standard convention setting _{$S_2^2=0$}. This results in 14 independent crystal-field parameters in C_1h symmetry. The experimental Stark levels are modeled through use of a Monte Carlo method [31,32] in which each of the independent crystal-field parameters is given random starting values between −1000 and + 1000 cm⁻¹ and optimized using standard least-squares fitting between calculated and experimental levels.

Based on 34 Stark levels for each site and assuming C_3v site symmetry for the Er³⁺ ion, the final overall standard deviation between calculated-to-experimental Stark levels for site “a” is 8.7 cm⁻¹ (rms error = 7.0 cm⁻¹) and for the same number of Stark levels for site “b”, the overall standard deviation is 8.3 cm⁻¹ (rms error = 6.7 cm⁻¹). Table 2, columns 4-7 compare the modeling results for site “a” with experimental energy values given in column 2. Calculated irreducible representations (irreps) (Γ_1/2 and Γ_3/2) and the largest M_J components are given for each doublet level as determined by the best fit of the data to C_3v symmetry. The results for site “b” are given in Table 3 using the same format as for Table 2. The atomic and crystal-field parameters that are used to obtain these results are given in Table 4 . Six of the 20 atomic parameters were allowed to vary in the fitting process, along with all six crystal-field parameters. Parameter uncertainties for these twelve parameters are given in parentheses after the parameter values. The other 14 atomic parameters were held fixed at previously determined values. Stark levels calculated using these parameters are also given in Table 1, columns 8 and 10.

Table 4. Calculated atomic and crystal-field parameters in C_3v symmetry for Er³⁺:AlN

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When we carried out the modeling calculations assuming C₃ site symmetry for the Er³⁺ ion, there was no significant improvement in the calculated-to-experimental fitting, with higher standard deviations for both the site “a” and “b” fittings.

Modeling calculations using C_1h site symmetry showed a modest improvement in the fittings, with the standard deviation for the site “b” fitting decreasing from 8.3 to 7.6 cm⁻¹ (rms error decreasing from 6.7 to 4.9 cm⁻¹). For the site “a” fitting, the standard deviation was almost unchanged (going from 8.7 to 8.8 cm⁻¹), though the rms error decreased from 7.0 to 5.7 cm⁻¹. The right-hand columns of Tables 2 and 3 present the energy level calculations using C_1h symmetry. As can be seen from these two tables, the additional crystal-field parameters allowed in C_1h symmetry improve the energy level calculations for specific levels of ⁴I_15/2 and ⁴I_13/2 multiplets.

Table 5 presents the C_1h crystal-field parameters determined for both sites “a” and “b”. For comparison, the C_3v parameters, transformed to the coordinate system used by the C_1h parametrization by Euler rotations α = 90°, β = 90°, are given to the left of the C_1h parameters for each site. The fitting improvement using C_1h parameters is statistically significant, indicating that the true site symmetry for both the “a” and “b” sites is most likely C_1h. However, as can be seen from Table 5, the uncertainties in the values of the C_1h crystal-field parameters are large, and in most cases are larger than the difference between the C_3v and the C_1h parameter values. The large parameter value uncertainties means that the wavefunctions generated by the C_1h Hamiltonian will be less reliable for the purposes of deducing other properties of the systems, such as calculated Zeeman splittings. The relatively small differences between the C_3v and the C_1h parameter values indicate that it is reasonable to use an approximate C_3v symmetry to model these systems.

Table 5. Calculated crystal-field parameters, comparing C_3v symmetry calculations with C_1h symmetry for Er³⁺:AlN

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Using wavefunctions generated from the C_3v modeling studies for both sites, we calculated the Zeeman splitting and g-factors for the Stark levels of the ground ⁴I_15/2 manifold. The Zeeman splitting calculated for an external magnetic field of 0.15 T, along with resulting calculated g-values (g_|| and g_⊥), are listed in Table 6 for site “a” and in Table 7 for site “b”. We have compared these calculated results with experimental values for g_|| and g_⊥ obtained from an investigation of the EPR spectrum on single-crystal Er³⁺ in AlN [14]. Only one Er³⁺ site was observed in the EPR study, with experimental g-values for the ground state Stark level reported as g_|| = 4.337 and g_⊥ = 7.647. The experimental g-values agree with the calculated values g_|| = 5.5 and g_⊥ = 6.1 given in Table 6 for site “a”, and do not agree with the calculated values g_|| = 14.7 and g_⊥ = 1.0 given in Table 7 for site “b”. We therefore conclude that the Er³⁺ ions occupy site “a” in the dilute sample used for the EPR study.

Table 6. Splitting of “a” site crystal-field energy levels of Er³⁺:AlN in a 0.15 T magnetic field (in cm⁻¹), and resultant g-values for the ground multiplet ⁴I_15/2

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Table 7. Splitting of “b” site crystal-field energy levels of Er³⁺:AlN in a 0.15 T magnetic field (in cm⁻¹), and resultant g-values for the ground multiplet ⁴I_15/2

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5. Summary and conclusions

With support from analyses of site-selective spectroscopy, the cathodoluminescence (CL) spectra of Er³⁺(4f¹¹) in single-crystal hexagonal phase of AlN have been assigned to two principal sites in the lattice. The 12 K CL spectrum obtained between 320 nm and 775 nm was analyzed for the J + 1/2 Stark levels of the ground-state ⁴I_15/2 and excited state ⁴I_13/2, ⁴I_11/2, ⁴I_9/2, ⁴F_9/2, and ⁴S_3/2 multiplet manifolds. The emission to the Stark levels of these manifolds came from the lower-energy Stark level of the ²P_3/2 multiplet, with additional data coming from the ⁴S_3/2 → ⁴I_15/2 emission. More than 97% of the observed CL spectra were accounted for in terms of the two principal sites. More than 65 peaks and shoulders were evaluated and a number of deconvolution studies were carried out on problematic features.

A crystal-field splitting calculation was carried out for each site using a parameterized Hamiltonian that included atomic and crystal-field terms for states of Er³⁺(4f¹¹)^2S+1L_J. The identification of two Er³⁺ sites in AlN suggested a descent in symmetry calculation from C_3v to C_1h for each site, since Er³⁺ has a larger ionic radius than Al³⁺, and is expected to cause stress on the surrounding environment, especially when doped into AlN in sufficient quantities to observe the optical spectrum of the 4f → 4f transitions. Likewise, Er³⁺ may substitute for a basal-plane N to form complexes such as Er³⁺-O_N or Er³⁺-V_N with C_1h symmetry. Er³⁺ ions in Al³⁺ sites may shift along the c-axis toward the basal plane into a site of C_1h symmetry to lower the energy of Er³⁺ as a trap impurity in AlN. The modeling of the Er³⁺ site symmetry gave interesting results, as shown in Table 5. For site “a” the C_1h crystal-field fitting gave a slightly higher standard deviation than obtained for C_3v symmetry, while for site “b” the C_1h fitting gave a statistically-significant lower standard deviation than for C_3v symmetry. However, for most of the crystal-field parameters given in Table 5, the difference between the C_3v and C_1h symmetry parameter values is less than the statistical uncertainty in the C_1h symmetry crystal-field parameters. Therefore, we conclude that C_3v remains a reasonable approximate symmetry for Er³⁺ ions in both sites of AlN, and that wavefunctions generated using the assumption of C_3v symmetry may be used reasonably for calculation of other optical properties, such as Zeeman splittings of the states.