The crystal-field and Zeeman splittings of the energy levels of Nd3+(4f3) 2S+1LJ in hexagonal phase AlN have been investigated. The multiplet manifolds of Nd3+(4f3) analyzed include the ground state, 4I9/2, and excited states 4I11/2, 4I13/2, 4F3/2, 4F5/2, 2H(2)9/2, 4F7/2, 4S3/2, 4G5/2, and 2G7/2. Experimental energy levels were obtained from analyses of the 12 K cathodoluminescence spectra from Nd3+-implanted films of AlN, and from the 15 K photoluminescence excitation spectra and the site-selective combined excitation-emission spectra (CEES) recently reported for in situ Nd-doped hexagonal AlN grown by plasma-assisted molecular beam epitaxy (PA-MBE). CEES results identify a main site and two minority sites for Nd3+ in both samples. Transition line strengths attributed to the ion in minority sites are relatively stronger in Nd:AlN than in Nd:GaN. The 15 K experimental Zeeman splitting of Nd3+ are analyzed in the PA-MBE grown AlN samples and compared with the Zeeman splitting observed in Nd:GaN. The crystal-field and Zeeman splittings were modeled using a parametrized Hamiltonian consisting of atomic and crystal-field terms. We considered possible site distortion due to the size of the implanted Nd ion that would reduce the site symmetry from C3v to C3 or C1h. However, no significant improvement was obtained using these lower symmetry models, leading us to conclude that C3v symmetry is a reasonable approximation for the main site Nd3+ ions in AlN.
©2012 Optical Society of America
The spectroscopic properties of the trivalent rare earth (RE3+) ions, together with the physical and electrical properties of the semi-conducting aluminum nitride (AlN) host, have attracted the attention of many investigators interested in developing these materials as optoelectronic components for an expanding market of photonic devices [1–4]. The host material (AlN) is a wide band gap semiconductor (6.2 eV) with a separation between valence and conduction bands that allows for optical absorption and emission over a wide frequency range, making possible numerous RE3+ sharp-line transitions observable due to the shielding of the electrons in the 4fn subshell by the filled 5s2 and 5p6 shells of the rare earth ion core [5–7]. The physical properties of AlN are desirable for devices, due to the mechanical toughness of the material, which is essentially free from moisture absorption and the effects of corrosion from different chemical substances [8,9]. It is generally stoichiometric in composition (although vacancies do appear) when prepared either as films or single-crystals [10–12]. The relatively high thermal conductivity (2.85 W/cm/C) is an important physical property when operating high power/high temperature control devices, where expelling heat quickly and efficiently is a performance requirement .
In the present study, we investigate the crystal-field splitting and the Zeeman splitting of the energy levels of Nd3+ in the hexagonal (huntite) phase of AlN. The energy (Stark) levels of the multiplet manifolds of Nd3+(4f3), written in LS notation as 2S+1LJ, include the ground state, 4I9/2, and the excited states 4I11/2, 4I13/2, 4F3/2, 4F5/2, 2H(2)9/2, 4F7/2, 4S3/2, 4G5/2, and 2G7/2. Some of the data that are modeled here have been reported recently by Metcalfe et al.  based on an analysis of the 15 K luminescence spectra of in situ Nd-doped AlN films grown by plasma-assisted molecular beam epitaxy (PA-MBE). Additionally, we have included experimental energy levels obtained from an analyses of unpublished cathodoluminescence (CL) spectra measured at 12 K by one of the authors (UV) for Nd-implanted AlN films grown on substrates of 6H-SiC (0001) by metal-organic chemical vapor deposition (MOCVD). Analyses of the CL spectra of Sm3+, Pm3+, Gd3+, and Tm3+ that involve similar film preparations of RE3+ ions in the hexagonal phase of AlN have been reported previously [13–15].
2. Analysis of the spectra
In the present study, films of hexagonal AlN, grown on substrates of 6H-SiC (0001) by metal-organic chemical vapor deposition (MOCVD), were obtained from commercial sources. During implantation (fluence: 1 x 1013 ions/cm2), samples were tilted to avoid channeling by incident ions. Post-implantation annealing was carried out in a vacuum tube furnace at pressures near 106 mbar and 1100 K for 30 minutes. Implanted samples were mounted on the head of a closed-cycle helium refrigerator located inside the vacuum chamber. Excitation was provided by an Auger electron gun that provided electrons with energies between 100 eV and 5 keV and beam currents between 0.01 and 150 μA. Luminescence from the sample was passed through a quartz window and focused onto the entrance slit of a Czerny-Turner spectrograph. The spectral output was observed by using various nitrogen-cooled detectors. Analysis of the Nd-implanted CL spectra provide confirmation for many of the energy (Stark) levels of Nd3+ analyzed from the spectra of in situ Nd-doped hexagonal AlN samples grown by PA-MBE .
Representative of the CL emission spectra is the 12 K spectrum shown in Fig. 1 for Stark level transitions between 4F3/2 and 4I9/2. Analysis of the strongest peaks observed in Fig. 1 leads to an energy level scheme that differs from the Stark levels previously reported for the main site of the 4I9/2 manifold . Subsequent CEES measurements by one of the present authors (VD) involving emission between the same manifolds confirms the experimental splitting of the 4I9/2 and 4F3/2 in Table 1(a) and the splitting of 4I9/2 in Fig. 1 for the main site. Weaker transitions observed in Fig. 1 can be traced to transitions that predict the levels listed for the minority site “b” . Analysis of the present CL emission spectra, representing transitions from 4F3/2 to the 4I11/2 and 4I13/2 multiplet manifolds, results in the terminal Stark levels reported in Table 1(a) (levels 6 through 18) that generally agree with the levels reported for the same manifolds given for the main or “a” site in . We lack site-selective data to assign enough levels to the “b” site to perform a similar modeling analysis. Instead, we concentrate on the crystal-field modeling of the main or “a” site of Nd3+ in AlN, where the number of experimental Stark levels (41) is sufficient to determine a possible site distortion. This includes all energy levels up to 17,000 cm−1 for the “a” site of Nd3+ in AlN except for the 4I15/2, 2H11/2 and 4F9/2 multiplet manifolds, where the CL and PLE spectra are too weak to provide an accurate analysis of the splitting.
The Nd site locations have been determined by Vetter et al. , using experimental emission channeling methods with ion-implanted 147Pm3+ in AlN as a short-lived weak beta decay lattice site probe. The results indicated that 56(6)% 147Nd3+ occupied Al sites by substitution with the remainder located in other sites, including nitrogen vacancies or interstitial sites in the lattice. Annealing the samples to temperatures of 873 K and 1373 K yield fractions of 58(5)% and 56(7)% of the 147Nd ions in Al sites by substitution. The lattice location of 147Pm was also determined by monitoring the K electrons of Pm in the same decay and found to be 58(8)% (873 K) and 44(6)% (1373 K). These results suggest that Nd competes effectively for different vacancy sites in the lattice, but that the majority of Nd ions appear to occupy the vacant Al site. It also appears that some Nd ions complex with nitrogen vacancies in the basal plane nearest the substituted Nd. In doing so the Nd ion shifts along an axis away from the higher C3v symmetry site to a site such as C1h, thus producing for these ions a lower symmetry that accounts for the observed multi-site spectra observed in both Nd:AlN  and Nd:GaN . The minority site spectra are relatively stronger in the AlN host. We conclude that the main site or “a” site refers to Nd3+ in Al3+ sites in the lattice. Given the relative size of Nd to Al and the vacancies in the lattice, distortion of the ligand configuration with respect to the undoped site is expected. Thus, we modeled the crystal field splitting considering symmetry reduction from C3v to either C3 or C1h symmetry in order to ascertain the sensitivity of the data to the symmetry.
To investigate the site symmetry, we performed descent in symmetry calculations from C3v to C3 (assuming the mirror plane symmetry is broken) and from C3v to C1h (assuming the mirror plane symmetry remains, but the three-fold rotation axis symmetry is broken). Even though the number of independent crystal-field parameters increases from 6 (in C3v symmetry) to 8 (in C3 symmetry) and 14 (in C1h symmetry), no significant improvement in the standard deviation of the energy-level fitting is achieved with the inclusion of these additional parameters. In C1h symmetry, the crystal field splitting of the 4F3/2 manifold is improved, but there is no significant improvement in the splitting of the other manifolds, including 4I9/2, relative to the modeling results obtained assuming C3v symmetry. Additionally, the calculations using C3v symmetry predict magnetic field splittings that are in better agreement with experiment than calculations assuming C1h symmetry. For that reason, the final modeling results reported below assume that the Nd3+ ions occupy the main site of C3v symmetry. Experimental and calculated energy levels for all Stark levels up to 17,000 cm−1 are listed in Tables 1(a) and 1(b) . Atomic and crystal-field parameters determined from the energy level fitting (Table 2 ) are used to determine the wave functions for Zeeman splitting and g-factor calculations.
3. Analysis of the Zeeman splitting
The Zeeman spectra were obtained at 15 K from the PA-MBE samples in magnetic fields up to 6 T. We made use of combined excitation emission spectroscopy (CEES) to differentiate between the magnetic field splitting of Stark levels of Nd3+ in the main (“a”) site (Tables 1(a) and 1(b) of this work) and the minority (“b”) site as labeled in . As an example, we considered the emission spectrum obtained by exciting the multiplet manifolds 4G5/2 (620 nm) and 2G7/2 (604 nm), and detecting the emission spectra from 4F3/2 to the ground-state manifold 4I9/2 (930 nm). The excitation, non-radiative relaxation, and subsequent emission follow separate site-distinctive channels for Nd3+ in the majority and minority sites. The Stark levels of the manifolds involved in this sequence, namely: 4G5/2, 2G7/2, 4F3/2, and 4I9/2, and the energies associated with each site, along with the magnetic field splitting of individual Stark levels, are listed in Table 3 . Unfortunately, the magnetic field splitting is large enough to measure with reasonable accuracy for only a limited number of states. These splittings correspond to g-factors greater than one and correspond to transitions in which only one of the involved levels has a significant splitting. In a majority of cases, the magnetic field splittings are smaller than previously observed for the same transitions in Nd:GaN. Moreover, the splittings are more difficult to resolve, due to the pronounced inhomogeneous broadening of the lines, as observed in the zero magnetic field spectra. These unresolved splittings correspond to g-factors smaller than about 0.5. Magnetic fields were applied parallel and perpendicular to the crystal-growth axis and compared to the spectrum in zero magnetic field.
Figure 2 shows an excerpt of our CEES data obtained for a sample at T = 15 K in a magnetic field of 6 T. The format of the figure, as well as the labels representing the transitions, correspond to the figure presented earlier in an analysis of the Zeeman spectra of hexagonal Nd3+ in GaN . The upper third of the present figure shows the data in zero magnetic field with excitation photon energy between 2.016 eV and 2.028 eV. Transitions from left to right are identified as E, an excitation transition, and A, B, C, and D, emission transitions with “a” and “b” sites identified with the appropriate transition. In the middle part of the figure, representing the sample parallel to the c-axis in a magnetic field of 6 T, we see the splitting of these transitions. The observed splittings of transitions associated with the “a” or main site resemble the Zeeman spectra taken in the same orientation for Nd3+ in GaN . For Nd3+ occupying the “a” site, we find that transition A does not split in this geometry, but transitions C and D do. Following the arguments made earlier  we conclude that the splitting of C and D is dominated by the ground state. In contrast to the splitting of C and D, and E for parallel fields, the most pronounced splittings are observed for A and B in perpendicular fields, as shown in the lower part of Fig. 2.
Assuming Nd3+ sites are approximated by C3v symmetry, the Stark levels listed in Tables 1(a) and 1(b) and Table 3 are labeled either Γ1/2 or Γ3/2. In this symmetry, all levels will split along the c-axis in a magnetic field. However, in a perpendicular field, only the Stark levels labeled Γ1/2 will split. In principle, symmetry assignments can be made to Stark levels based on observed magnetic field splittings in the latter orientation . The irreducible representations (irreps) Γ1/2 and Γ3/2 describing the symmetry of the wavefunction can be used interchangeably with the quantum number labels μ = ± 1/2 or μ = ± 3/2, respectively. The Stark levels assigned in Tables 1(a) and 1(b), column 3, and Table 3, column 3, are based on the crystal-field splitting calculation with the smallest rms deviation that has calculated Zeeman splittings consistent with the observed values. The ordering of the quantum labels in Table 3 are the same as those reported for Nd:GaN, with the exception of levels (4,5) and (54,55), which are reversed .
In Fig. 3 , the observed splitting of the ground state of Nd3+ is compared in the AlN and GaN host. The Zeeman spectra were obtained at 6 T and 15 K for the sample parallel to the magnetic field. Three sites are involved: the AlN site “a” or main site has a splitting of 1.3 meV (10.5 cm−1), site “b” has a splitting of 1.6 meV (12.9 cm−1), and the splitting in the “a” site in GaN is 1.4 meV (11.3 cm−1) . The splittings for both sites in AlN can also be observed in Fig. 2. We note that the splitting in the “a” site is somewhat smaller in AlN than in GaN, but the splitting in the AlN “b” site is larger and the transitions involved are inhomogeneously broadened more than the transitions in the “a” sites.
4. Crystal-field modeling studies
The 41 experimental Stark levels of Nd3+ in the main “a” site modeled in the present study are reported in Tables 1(a) and 1(b) for multiplet manifolds 4I9/2, 4I11/2,4I13/2, 4F3/2, 4F5/2, 2H(2)9/2, 4F7/2, 4S3/2, 4G5/2, and 2G7/2. We have an insufficient number of Stark levels identified with Nd3+ in the minority “b” site to carry out a crystal-field site study analysis for these levels. A parameterized Hamiltonian defined to operate within the entire 4f3 electronic configuration assuming that Nd3+ ions occupy sites of C3v symmetry in the “a” site was used to calculate the energy (Stark) levels. The model Hamiltonian is usually written in a form [7,17,18] that includes spherically symmetric “atomic” contributions, given by,
In C3v symmetry there are six independent crystal-field parameters: , , , , , and . The experimental Stark levels were modeled through use of a Monte Carlo method in which the six parameters were given random starting values and optimized using standard least-squares fitting between calculated and experimental levels. The best overall agreement gave a fitting standard deviation of 10.1 cm−1. This value can be compared to the standard deviation of 9.7 cm−1 obtained with the 14-parameter C1h crystal-field. We then tested the validity of these fits by comparing the Zeeman splitting calculated for a 6 T magnetic field with the experimental splittings. The energy level calculations determined from the C3v symmetry fit yielded results in closer agreement to experiment then those of the C1h symmetry fit. This indicates that the modest fitting improvement in the energy level calculations given by the C1h symmetry calculations may be an artifact of the increase in the number of fitted parameters, rather than having physical significance. For this reason, we report energy levels (Tables 1(a) and 1(b)) and Zeeman splittings (Table 3) calculated assuming C3v symmetry, along with the experimental values.
Tables 1(a) and 1(b) present energy levels and group theoretical irreducible representations (irreps), Γ1/2 and Γ3/2, calculated for C3v symmetry, along with the experimental energy levels for the main “a” site. The Zeeman data presented in Table 3 confirm that the calculated irreps are correctly ordered for the first four energy levels of the ground configuration, 4I9/2. Final atomic and crystal-field parameters are listed in Table 2. The overall fit has a standard deviation of 10.1 cm−1 (rms error = 8.0 cm−1). Nine of the 20 atomic parameters were allowed to vary in the fitting process, along with all six crystal-field parameters. Parameter uncertainties for these 15 parameters are given in parentheses after the parameter values. The other 11 atomic parameters were held fixed at previously determined values.
Table 3 presents experimental and calculated Zeeman splitting for the Stark levels of the 4I9/2, 4F3/2, 4G5/2 and 4G7/2 multiplet manifolds. In addition to the experimental and calculated Zeeman splittings for a 6 T magnetic field directed parallel and perpendicular to the crystallographic c-axis, 6 T Zeeman splittings for Nd:GaN  are given for comparison. We find the g-factor of the ground state somewhat smaller for Nd3+ in the main “a” site in AlN relative to GaN. The g-factor for the minority “b” site for Nd3+ in AlN is larger, however we lack sufficient optical data on the “b” site to further refine the details of the Zeeman splitting of this site. The inhomogeneous broadening of the transitions in the Zeeman spectra further reduces our ability to determine small g-factors associated with the Zeeman data of both the “a” and “b’ sites. However, a sufficient number of Stark levels are reported in Tables 1(a) and 1(b) for modeling of the crystal field and Zeeman splittings, which yield reasonable agreement between the calculated and experimental g-factors, as shown in Table 3.
5. Summary and conclusions
The crystal-field splitting of the energy levels of Nd3+ in AlN has been modeled assuming that the Nd3+ ions occupy vacant Al3+ sites in the “a” or main site in the lattice having an approximate C3v symmetry. Symmetries lower than C3v, such as C1h, were also examined to determine if size distortion involved a lower site symmetry. With the exception of an improved fit for the splitting of the 4F3/2 manifold when assuming C1h symmetry, no significant improvement was obtained for the remaining nine multiplet manifolds investigated, including 4I9/2. However, the experimental Zeeman data agree better with the calculated Zeeman splitting assuming C3v symmetry than it does when compared to the calculated Zeeman splitting based on C1h symmetry. We conclude that the best description of the crystal-field splitting and the Zeeman splitting are approximated by C3v symmetry. Comparisons were also made with the Zeeman data reported for Nd3+ in GaN, which we reported earlier using a C3v model for the crystal-field and Zeeman splitting as well. The ordering of Stark levels are similar with the exception that levels (4,5) and (54,55) are reversed. The g-factor of Nd3+ in the ground state of the main site is smaller in AlN than in GaN, but for the minority “b” site the g-factor is larger in AlN. Both Nd3+-doped nitrides in the hexagonal phase we examined exhibited spectra associated with minority sites. For roughly the same concentration of Nd, the minority site spectrum in AlN is stronger than observed in GaN. Given the size difference between Nd:Al, when compared to Nd:Ga, this is not surprising, given that vacancies found in both systems give rise to complexes with the dopant.
The Zeeman spectroscopy work was supported by NSF (grant # ECCS- 1140038).
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