Crystal field and Zeeman splittings for energy levels of Nd<sup>3+</sup> in hexagonal AlN

doi:10.1364/OME.2.001176

Crystal field and Zeeman splittings for energy levels of Nd³⁺ in hexagonal AlN

John B. Gruber, Gary W. Burdick, Ulrich Vetter, Brandon Mitchell, Volkmar Dierolf, and Hans Hofsäss »View Author Affiliations

Optical Materials Express, Vol. 2, Issue 9, pp. 1176-1185 (2012)
http://dx.doi.org/10.1364/OME.2.001176

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▸ Article Outline
– Abstract
1. Introduction
2. Analysis of the spectra
3. Analysis of the Zeeman splitting
4. Crystal-field modeling studies
5. Summary and conclusions
– References and links

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Abstract

The crystal-field and Zeeman splittings of the energy levels of Nd³⁺(4f³) ²^S⁺¹L_J in hexagonal phase AlN have been investigated. The multiplet manifolds of Nd³⁺(4f³) analyzed include the ground state, ⁴I_9/2, and excited states ⁴I_11/2, ⁴I_13/2, ⁴F_3/2, ⁴F_5/2, ²H(2)_9/2, ⁴F_7/2, ⁴S_3/2, ⁴G_5/2, and ²G_7/2. 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 C_3v to C₃ or C_1h. However, no significant improvement was obtained using these lower symmetry models, leading us to conclude that C_3v symmetry is a reasonable approximation for the main site Nd³⁺ ions in AlN.

1. Introduction

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

J. Steckl and J. M. Zavada, “Optoelectronic properties and applications of rare-earth-doped GaN,” MRS Bull. 24, 33–38 (1999).

–4

N. Hirosaki, R.-J. Xie, K. Inoue, T. Sekiguchi, B. Dierre, and K. Tamura, “Blue-emitting AlN:Eu²⁺ nitride phosphor for field emission displays,” Appl. Phys. Lett. 91(6), 061101 (2007). [CrossRef]

]. 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

R. Judd, Operator Techniques in Atomic Spectroscopy (McGraw-Hill, 1963).

–7

G. Blasse and B. Granmaier, Luminescent Materials (Springer-Verlag, 1994).

]. 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

S. M. Sze, Semiconducting Devices, Physics and Technology (Wiley, 1985)

W. J. Tropf, M. E. Thomas, and T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics (McGraw-Hill, 1995), Vol. 2.

]. It is generally stoichiometric in composition (although vacancies do appear) when prepared either as films or single-crystals [10

D. Readinger, G. D. Metcalfe, H. Shen, and M. Wraback, “GaN doped with neodymium by plasma-assisted molecular beam epitaxy,” Appl. Phys. Lett. 92(6), 061108 (2008). [CrossRef]

–12

G. A. Slack, R. A. Tanzilli, R. O. Pohl, and J. W. Vandersande, “The intrinsic thermal conductivity of AIN,” J. Phys. Chem. Solids 48(7), 641–647 (1987). [CrossRef]

]. 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 [12

G. A. Slack, R. A. Tanzilli, R. O. Pohl, and J. W. Vandersande, “The intrinsic thermal conductivity of AIN,” J. Phys. Chem. Solids 48(7), 641–647 (1987). [CrossRef]

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 ²^S⁺¹L_J, include the ground state, ⁴I_9/2, and the excited states ⁴I_11/2, ⁴I_13/2, ⁴F_3/2, ⁴F_5/2, ²H(2)_9/2, ⁴F_7/2, 4S_3/2, ⁴G_5/2, and ²G_7/2. Some of the data that are modeled here have been reported recently by Metcalfe et al. [11

G. D. Metcalfe, E. D. Readinger, R. Enck, H. Shen, M. Wraback, N. T. Woodward, J. Poplawsky, and V. Dierolf, “Near-infrared photoluminescence properties of neodymium in in situ doped AlN grown using plasma-assisted molecular beam epitaxy,” Opt. Mater. Express 1(1), 78–84 (2011). [CrossRef]

] 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

J. B. Gruber, U. Vetter, H. Hofsäss, B. Zandi, and M. F. Reid, “Spectra and energy levels of Gd³⁺ (4f⁷) in AlN,” Phys. Rev. B 69(19), 195202 (2004). [CrossRef]

–15

J. B. Gruber, U. Vetter, H. Hofsäss, B. Zandi, and M. Reid, “Spectra and energy levels of Tm³⁺ (4f¹²),” Phys. Rev. B 70(24), 245108 (2004). [CrossRef]

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 [11

Representative of the CL emission spectra is the 12 K spectrum shown in Fig. 1 for Stark level transitions between ⁴F_3/2 and ⁴I_9/2. 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 ⁴I_9/2 manifold [11

]. Subsequent CEES measurements by one of the present authors (VD) involving emission between the same manifolds confirms the experimental splitting of the ⁴I_9/2 and ⁴F_3/2 in Table 1(a) and the splitting of ⁴I_9/2 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” [11

]. Analysis of the present CL emission spectra, representing transitions from ⁴F_3/2 to the ⁴I_11/2 and ⁴I_13/2 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 [11

]. 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 ⁴I_15/2, ²H_11/2 and ⁴F_9/2 multiplet manifolds, where the CL and PLE spectra are too weak to provide an accurate analysis of the splitting.

Fig. 1 The 12 K CL spectrum of transitions from ⁴F_3/2 to ⁴I_9/2. The strongest peaks are associated with Nd³⁺ ions in the main “a” site.

Table 1(a) Crystal-field splitting for energy levels of Nd³⁺:AlN (part 1)

²^S⁺¹L_J^a	Doublet Level	Irrep (Γ)	M_J ^a	E_exp (cm⁻¹)	E_calc (cm⁻¹)	ΔΕ (cm⁻¹)
⁴I_9/2	1	3/2	± 9/2	0	–6	6
	2	1/2	± 1/2	150	129	21
	3	1/2	± 5/2	226	228	–2
	4	3/2	± 3/2	298	294	4
	5	1/2	± 7/2	405	410	–5
						σ = 10.1^b
⁴I_11/2	6	1/2	± 11/2	1908	1916	–8
	7	1/2	± 1/2	1948	1961	–13
	8	3/2	± 3/2	1973	1988	–15
	9	1/2	± 5/2	2064	2073	–9
	10	1/2	± 7/2	2130	2130	0
	11	3/2	± 9/2	2140	2140	0
						σ = 9.5
⁴I_13/2	12	1/2	± 13/2	3868	3860	8
	13	1/2	± 1/2	3926	3928	–2
	14	3/2	± 3/2	3953	3943	10
	15	1/2	± 5/2	3965	3965	0
	16	1/2	± 7/2	4090	4094	–4
	17	3/2	± 9/2	4129	4121	8
	18	1/2	± 11/2	4146	4143	3
						σ = 6.0
⁴I_15/2	19	3/2	± 15/2		5859
	20	1/2	± 5/2		5949
	21	1/2	± 1/2		6020
	22	3/2	± 3/2		6023
	23	1/2	± 13/2		6112
	24	1/2	± 11/2		6301
	25	3/2	± 9/2		6305
	26	1/2	± 7/2		6341
⁴F_3/2	27	1/2	± 1/2	10935	10952	–17
	28	3/2	± 3/2	10976	10965	11
						σ = 14.6
⁴F_5/2	29	3/2	± 3/2	11917	11912	5
	30	1/2	± 5/2	11941	11942	–1
	31	1/2	± 1/2	12036	12043	–7
						σ = 5.1
²H(2)_9/2	32	1/2	± 7/2	12058	12049	9
	33	3/2	± 3/2	12070	12067	3
	34	1/2	± 1/2	12108	12101	7
	35	1/2	± 1/2	12128	12120	8
	36	3/2	± 9/2	12173	12185	–12
						σ = 8.3
⁴F_7/2	37	1/2	± 5/2	12865	12875	–9
	38	3/2	± 3/2	12936	12929	7
⁴S_3/2	39	1/2	± 1/2	12975	12975	0
⁴F_7/2	40	1/2	± 7/2	12990	12992	–2
⁴S_3/2	41	3/2	± 3/2	13000	13001	–1
⁴F_7/2	42	1/2	± 7/2	13031	13031	0
						σ = 4.8
⁴F_9/2	43	1/2	± 1/2		13945
	44	3/2	± 9/2		13957
	45	3/2	± 3/2		14045
	46	1/2	± 5/2		14084
	47	1/2	± 7/2		14131

^aThe largest M_J component to the Stark level wave function.

^bThe rms deviation for each multiplet in cm⁻¹. The overall standard deviation is 10.1 cm⁻¹.

The Nd site locations have been determined by Vetter et al. [14

U. Vetter, J. B. Gruber, A. S. Nijjar, B. Zandi, G. Ohl, U. Wahl, B. DeVries, H. Hofsäss, and M. DietrichU. VetterJ. B. GruberA. S. NijjarB. ZandiG. OhlU. WahlB. DeVriesH. HofsässM. Dietrichthe ISOLDE Collaboration, “Crystal field analysis of Pm³⁺ (4f⁴) and Sm³⁺ (4f⁵) and lattice location studies of ¹⁴⁷Nd and ¹⁴⁷Pm in w-AlN,” Phys. Rev. B 74(20), 205201 (2006). [CrossRef]

], 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 C_3v symmetry site to a site such as C_1h, thus producing for these ions a lower symmetry that accounts for the observed multi-site spectra observed in both Nd:AlN [11

] and Nd:GaN [16

J. B. Gruber, G. W. Burdick, N. T. Woodward, V. Dierolf, S. Chandra, and D. K. Sardar, “Crystal-field analysis and Zeeman splittings of energy levels of Nd³⁺ (4f³) in GaN,” J. Appl. Phys. 110(4), 043109 (2011). [CrossRef]

]. 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 C_3v to either C₃ or C_1h 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 C_3v to C₃ (assuming the mirror plane symmetry is broken) and from C_3v to C_1h (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 C_3v symmetry) to 8 (in C₃ symmetry) and 14 (in C_1h symmetry), no significant improvement in the standard deviation of the energy-level fitting is achieved with the inclusion of these additional parameters. In C_1h symmetry, the crystal field splitting of the ⁴F_3/2 manifold is improved, but there is no significant improvement in the splitting of the other manifolds, including ⁴I_9/2, relative to the modeling results obtained assuming C_3v symmetry. Additionally, the calculations using C_3v symmetry predict magnetic field splittings that are in better agreement with experiment than calculations assuming C_1h symmetry. For that reason, the final modeling results reported below assume that the Nd³⁺ ions occupy the main site of C_3v 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.

Table 1(b) Crystal-field splitting for energy levels of Nd³⁺:AlN (part 2)

²^S⁺¹L_J^a	Doublet Level	Irrep (Γ)	M_J ^a	E_exp (cm⁻¹)	E_calc (cm⁻¹)	ΔΕ (cm⁻¹)
²H(2)_11/2	48	1/2	± 7/2		15060
	49	1/2	± 9/2		15089
	50	1/2	± 5/2		15108
	51	1/2	± 3/2		15162
	52	1/2	± 1/2		15177
	53	1/2	± 11/2		15182
⁴G_5/2	54	3/2	± 3/2	16038	16039	–1
	55	1/2	± 5/2	16127	16130	–3
	56	1/2	± 1/2	16330	16327	3
						σ = 2.5
⁴G_7/2	57	1/2	± 7/2	16559	16568	–9
	58	3/2	± 3/2	16593	16600	–7
	59	1/2	± 5/2	16627	16621	6
	60	1/2	± 1/2	16648	16636	12
						σ = 8.9

^aThe largest M_J component to the Stark level wave function.

^bThe rms deviation for each multiplet in cm⁻¹. The overall standard deviation is 10.1 cm⁻¹.

Table 2 Calculated atomic and crystal-field parameters (in cm⁻¹) for Nd³⁺:AlN and Nd³⁺:GaN [16

]^a

Parameter	Nd³⁺:AlN (cm⁻¹)		Nd³⁺:GaN (cm⁻¹)
E_avg	20951	(170)	21766	(57)
F₂	49242	(1630)	56414	(503)
F₄	55222	(338)	52840	(216)
F₆	19666	(755)	25322	(399)
α	22.8		22.8
β	–896	(12)	–856	(15)
γ	1695		1695
ζ	669	(16)	753	(9)
T₂	2197	(244)	1578	(83)
T₃	23	(3)	24	(3)
T₄	37		37
T₆	–241		–241
T₇	399		399
T₈	301		301
M₀	0.95		0.95	(0.77)
M₂	0.56 M₀		0.56 M₀
M₄	0.38 M₀		0.38 M₀
P₂	3945	(327)	2299	(128)
P₄	0.75 P₂		0.75 P₂
P₆	0.50 P₂		0.50 P₂
_{$B_{0}^{2}$}	109	(51)	242	(40)
_{$B_{0}^{4}$}	1811	(61)	617	(53)
_{$B_{3}^{4}$}	± 1113	(65)	± 1516	(30)
_{$B_{0}^{6}$}	136	(61)	–434	(30)
_{$B_{3}^{6}$}	± 414	(42)	± 366	(25)
_{$B_{6}^{6}$}	–458	(44)	–69	(44)

^aValues in parenthesis indicate uncertainties (in cm⁻¹) in fitted parameters; other parameters were held fixed.

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 [11

]. As an example, we considered the emission spectrum obtained by exciting the multiplet manifolds ⁴G_5/2 (620 nm) and ²G_7/2 (604 nm), and detecting the emission spectra from ⁴F_3/2 to the ground-state manifold ⁴I_9/2 (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: ⁴G_5/2, ²G_7/2, ⁴F_3/2, and ⁴I_9/2, 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.

Table 3 Splitting of 4f³ (main site) crystal-field energy levels in a 6 T magnetic field (in cm⁻¹), and resultant g-values for energy levels of Nd³⁺:AlN

²^S⁺¹L_J	Energy Level (cm⁻¹)	Doublet Level	Irrep (Γ)	Magnetic field \|\| c-axis				Magnetic field ⊥ c-axis
²^S⁺¹L_J	Energy Level (cm⁻¹)	Doublet Level	Irrep (Γ)	ΔE_exp (GaN)^a	ΔE_exp	ΔE_calc	g_exp	ΔE_exp (GaN)^a	ΔE_exp	ΔE_calc	g_exp
⁴I_9/2	0	1	3/2	11.3	10.5	13.4	4.1 ± 0.4	0.3	0.3	0.0	0.11 ± 0.2
	150	2	1/2	0.4	0	2.8	<0.5	8.1	8.9	9.8	3.5 ± 0.3
	226	3	1/2	7.0	0	4.2	<0.5	0	>2	6.8	>1
	298	4	3/2	11.5^b	>2	10.0	>1	0^b	—	0.0	—
	405	5	1/2	0.2^b	—	7.4	—	—	—	6.8	—

⁴F_3/2	10935	27	1/2	1.3	—	2.2	—	0.7	—	1.7	—
	10976	28	3/2	2.0	—	3.3	—	0	—	0.0	—

⁴G_5/2	16038	54	3/2	2.3^b	—	2.5	—	0^b	—	0.0	—
	16127	55	1/2	—	—	4.2	—	—	—	0.6	—
	16330	56	1/2	2.7	—	4.1	—	2.3	—	0.1	—

⁴G_7/2	16559	57	1/2	—	—	14.6	—	—	—	1.0	—
	16593	58	3/2	—	—	8.1	—	—	—	0.2	—
	16627	59	1/2	0	—	9.4	—	2.9	—	2.0	—
	16648	60	1/2	—	—	4.0	—	1.1	—	5.4	—

^aExperimental splittings for GaN from [16

^bLevels (4,5) and (54,55) reversed for GaN, compared to AlN.

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 [16

]. 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 [16

]. 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 [16

] 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.

Fig. 2 The CEES data obtained at 15 K. Labels E, A, B, C, and D represent transitions between ⁴F_3/2 to ⁴I_9/2 in sites “a” (indicated with white dotted lines) and “b”(indicated with black dotted lines). The top spectrum is taken in zero magnetic field; the lower two spectra are obtained with the sample oriented with the c-axis parallel and perpendicular, respectively, to a magnetic field of 6 T.

Assuming Nd³⁺ sites are approximated by C_3v symmetry, the Stark levels listed in Tables 1(a) and 1(b) and Table 3 are labeled either Γ_1/2 or Γ_3/2. 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 Γ_1/2 will split. In principle, symmetry assignments can be made to Stark levels based on observed magnetic field splittings in the latter orientation [16

]. The irreducible representations (irreps) Γ_1/2 and Γ_3/2 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 [16

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) [16

]. 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.

Fig. 3 Splitting of the ground state of Nd³⁺ in the “a” and “b” sites of AlN compared with Nd:GaN; Zeeman spectra of all three sites were obtained at 6 T and 15 K with the sample parallel to the magnetic field.

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 ⁴I_9/2, ⁴I_11/2,⁴I_13/2, ⁴F_3/2, ⁴F_5/2, ²H(2)_9/2, ⁴F_7/2, ⁴S_3/2, ⁴G_5/2, and ²G_7/2. 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 C_3v symmetry in the “a” site was used to calculate the energy (Stark) levels. The model Hamiltonian is usually written in a form [7

G. Blasse and B. Granmaier, Luminescent Materials (Springer-Verlag, 1994).

,17

W. T. Carnall, G. L. Goodman, K. L. Rajnak, and R. S. Rana, “A systematic analysis of the spectra of the lanthanides doped into single crystal LaF₃,” J. Chem. Phys. 90(7), 3443–3457 (1989). [CrossRef]

,18

J. Newman and B. Ng, Crystal-Field Handbook (Cambridge University Press, 2000).

] that includes spherically symmetric “atomic” contributions, given by,

\begin{array}{l} Η_{A} = E_{a v g} + \sum_{k} F^{k} f_{k} + α L (L + 1) + β G (G_{2}) + γ G (R_{7}) + \sum_{i} T^{i} t_{i} \\ + ς_{s o} A_{s o} + \sum_{k} P^{k} p_{k} + \sum_{j} M^{j} m_{j} \end{array}

(1)

and non-spherically-symmetric contributions from the one electron crystal field,

H_{cf} = \sum_{k, q} B_{q}^{k} C_{q}^{(k)}

(2)

In C_3v symmetry there are six independent _{$B_{q}^{k}$} crystal-field parameters: _{$B_{0}^{2}$}, _{$B_{0}^{4}$}, _{$B_{3}^{4}$}, _{$B_{0}^{6}$}, _{$B_{3}^{6}$}, and _{$B_{6}^{6}$}. 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 C_1h 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 C_3v symmetry fit yielded results in closer agreement to experiment then those of the C_1h symmetry fit. This indicates that the modest fitting improvement in the energy level calculations given by the C_1h 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 C_3v symmetry, along with the experimental values.

Tables 1(a) and 1(b) present energy levels and group theoretical irreducible representations (irreps), Γ_1/2 and Γ_3/2, calculated for C_3v 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, ⁴I_9/2. 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 ⁴I_9/2, ⁴F_3/2, ⁴G_5/2 and ⁴G_7/2 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 [16

] 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 C_3v symmetry. Symmetries lower than C_3v, such as C_1h, 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 ⁴F_3/2 manifold when assuming C_1h symmetry, no significant improvement was obtained for the remaining nine multiplet manifolds investigated, including ⁴I_9/2. However, the experimental Zeeman data agree better with the calculated Zeeman splitting assuming C_3v symmetry than it does when compared to the calculated Zeeman splitting based on C_1h symmetry. We conclude that the best description of the crystal-field splitting and the Zeeman splitting are approximated by C_3v symmetry. Comparisons were also made with the Zeeman data reported for Nd³⁺ in GaN, which we reported earlier using a C_3v 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.

Acknowledgments

The Zeeman spectroscopy work was supported by NSF (grant # ECCS- 1140038).

References and links

1.	J. Steckl and J. M. Zavada, “Optoelectronic properties and applications of rare-earth-doped GaN,” MRS Bull. 24, 33–38 (1999).
2.	W. M. Jadwisienczak, H. J. Lozykowski, I. Berishev, A. Bensaoula, and I. G. Brown, “Visible emission from AlN doped with Eu and Tb ions,” J. Appl. Phys. 89(8), 4384–4390 (2001). [CrossRef]
3.	S. R. M. Levinshtein and M. Shur, Properties of Advanced Semiconductor Materials (Wiley, 2001).
4.	N. Hirosaki, R.-J. Xie, K. Inoue, T. Sekiguchi, B. Dierre, and K. Tamura, “Blue-emitting AlN:Eu²⁺ nitride phosphor for field emission displays,” Appl. Phys. Lett. 91(6), 061101 (2007). [CrossRef]
5.	R. Judd, Operator Techniques in Atomic Spectroscopy (McGraw-Hill, 1963).
6.	B. G. Wybourne, Spectroscopic Properties of Rare-Earths (Wiley, 1965).
7.	G. Blasse and B. Granmaier, Luminescent Materials (Springer-Verlag, 1994).
8.	S. M. Sze, Semiconducting Devices, Physics and Technology (Wiley, 1985)
9.	W. J. Tropf, M. E. Thomas, and T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics (McGraw-Hill, 1995), Vol. 2.
10.	D. Readinger, G. D. Metcalfe, H. Shen, and M. Wraback, “GaN doped with neodymium by plasma-assisted molecular beam epitaxy,” Appl. Phys. Lett. 92(6), 061108 (2008). [CrossRef]
11.	G. D. Metcalfe, E. D. Readinger, R. Enck, H. Shen, M. Wraback, N. T. Woodward, J. Poplawsky, and V. Dierolf, “Near-infrared photoluminescence properties of neodymium in in situ doped AlN grown using plasma-assisted molecular beam epitaxy,” Opt. Mater. Express 1(1), 78–84 (2011). [CrossRef]
12.	G. A. Slack, R. A. Tanzilli, R. O. Pohl, and J. W. Vandersande, “The intrinsic thermal conductivity of AIN,” J. Phys. Chem. Solids 48(7), 641–647 (1987). [CrossRef]
13.	J. B. Gruber, U. Vetter, H. Hofsäss, B. Zandi, and M. F. Reid, “Spectra and energy levels of Gd³⁺ (4f⁷) in AlN,” Phys. Rev. B 69(19), 195202 (2004). [CrossRef]
14.	U. Vetter, J. B. Gruber, A. S. Nijjar, B. Zandi, G. Ohl, U. Wahl, B. DeVries, H. Hofsäss, and M. DietrichU. VetterJ. B. GruberA. S. NijjarB. ZandiG. OhlU. WahlB. DeVriesH. HofsässM. Dietrichthe ISOLDE Collaboration, “Crystal field analysis of Pm³⁺ (4f⁴) and Sm³⁺ (4f⁵) and lattice location studies of ¹⁴⁷Nd and ¹⁴⁷Pm in w-AlN,” Phys. Rev. B 74(20), 205201 (2006). [CrossRef]
15.	J. B. Gruber, U. Vetter, H. Hofsäss, B. Zandi, and M. Reid, “Spectra and energy levels of Tm³⁺ (4f¹²),” Phys. Rev. B 70(24), 245108 (2004). [CrossRef]
16.	J. B. Gruber, G. W. Burdick, N. T. Woodward, V. Dierolf, S. Chandra, and D. K. Sardar, “Crystal-field analysis and Zeeman splittings of energy levels of Nd³⁺ (4f³) in GaN,” J. Appl. Phys. 110(4), 043109 (2011). [CrossRef]
17.	W. T. Carnall, G. L. Goodman, K. L. Rajnak, and R. S. Rana, “A systematic analysis of the spectra of the lanthanides doped into single crystal LaF₃,” J. Chem. Phys. 90(7), 3443–3457 (1989). [CrossRef]
18.	J. Newman and B. Ng, Crystal-Field Handbook (Cambridge University Press, 2000).

OCIS Codes
(020.7490) Atomic and molecular physics : Zeeman effect
(260.3800) Physical optics : Luminescence
(260.6580) Physical optics : Stark effect

ToC Category:
Fluorescent and Luminescent Materials

History
Original Manuscript: June 25, 2012
Revised Manuscript: July 24, 2012
Manuscript Accepted: July 25, 2012
Published: August 1, 2012

Citation
John B. Gruber, Gary W. Burdick, Ulrich Vetter, Brandon Mitchell, Volkmar Dierolf, and Hans Hofsäss, "Crystal field and Zeeman splittings for energy levels of Nd³⁺ in hexagonal AlN," Opt. Mater. Express 2, 1176-1185 (2012)
http://www.opticsinfobase.org/ome/abstract.cfm?URI=ome-2-9-1176

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References

J. Steckl and J. M. Zavada, “Optoelectronic properties and applications of rare-earth-doped GaN,” MRS Bull.24, 33–38 (1999).
W. M. Jadwisienczak, H. J. Lozykowski, I. Berishev, A. Bensaoula, and I. G. Brown, “Visible emission from AlN doped with Eu and Tb ions,” J. Appl. Phys.89(8), 4384–4390 (2001). [CrossRef]
S. R. M. Levinshtein and M. Shur, Properties of Advanced Semiconductor Materials (Wiley, 2001).
N. Hirosaki, R.-J. Xie, K. Inoue, T. Sekiguchi, B. Dierre, and K. Tamura, “Blue-emitting AlN:Eu2+ nitride phosphor for field emission displays,” Appl. Phys. Lett.91(6), 061101 (2007). [CrossRef]
R. Judd, Operator Techniques in Atomic Spectroscopy (McGraw-Hill, 1963).
B. G. Wybourne, Spectroscopic Properties of Rare-Earths (Wiley, 1965).
G. Blasse and B. Granmaier, Luminescent Materials (Springer-Verlag, 1994).
S. M. Sze, Semiconducting Devices, Physics and Technology (Wiley, 1985)
W. J. Tropf, M. E. Thomas, and T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics (McGraw-Hill, 1995), Vol. 2.
D. Readinger, G. D. Metcalfe, H. Shen, and M. Wraback, “GaN doped with neodymium by plasma-assisted molecular beam epitaxy,” Appl. Phys. Lett.92(6), 061108 (2008). [CrossRef]
G. D. Metcalfe, E. D. Readinger, R. Enck, H. Shen, M. Wraback, N. T. Woodward, J. Poplawsky, and V. Dierolf, “Near-infrared photoluminescence properties of neodymium in in situ doped AlN grown using plasma-assisted molecular beam epitaxy,” Opt. Mater. Express1(1), 78–84 (2011). [CrossRef]
G. A. Slack, R. A. Tanzilli, R. O. Pohl, and J. W. Vandersande, “The intrinsic thermal conductivity of AIN,” J. Phys. Chem. Solids48(7), 641–647 (1987). [CrossRef]
J. B. Gruber, U. Vetter, H. Hofsäss, B. Zandi, and M. F. Reid, “Spectra and energy levels of Gd3+ (4f7) in AlN,” Phys. Rev. B69(19), 195202 (2004). [CrossRef]
U. Vetter, J. B. Gruber, A. S. Nijjar, B. Zandi, G. Ohl, U. Wahl, B. DeVries, H. Hofsäss, M. Dietrich, and the ISOLDE Collaboration, “Crystal field analysis of Pm3+ (4f4) and Sm3+ (4f5) and lattice location studies of 147Nd and 147Pm in w-AlN,” Phys. Rev. B74(20), 205201 (2006). [CrossRef]
J. B. Gruber, U. Vetter, H. Hofsäss, B. Zandi, and M. Reid, “Spectra and energy levels of Tm3+ (4f12),” Phys. Rev. B70(24), 245108 (2004). [CrossRef]
J. B. Gruber, G. W. Burdick, N. T. Woodward, V. Dierolf, S. Chandra, and D. K. Sardar, “Crystal-field analysis and Zeeman splittings of energy levels of Nd3+ (4f3) in GaN,” J. Appl. Phys.110(4), 043109 (2011). [CrossRef]
W. T. Carnall, G. L. Goodman, K. L. Rajnak, and R. S. Rana, “A systematic analysis of the spectra of the lanthanides doped into single crystal LaF3,” J. Chem. Phys.90(7), 3443–3457 (1989). [CrossRef]
J. Newman and B. Ng, Crystal-Field Handbook (Cambridge University Press, 2000).

Appl. Phys. Lett.

N. Hirosaki, R.-J. Xie, K. Inoue, T. Sekiguchi, B. Dierre, and K. Tamura, “Blue-emitting AlN:Eu2+ nitride phosphor for field emission displays,” Appl. Phys. Lett.91(6), 061101 (2007). [CrossRef]
D. Readinger, G. D. Metcalfe, H. Shen, and M. Wraback, “GaN doped with neodymium by plasma-assisted molecular beam epitaxy,” Appl. Phys. Lett.92(6), 061108 (2008). [CrossRef]

J. Appl. Phys.

W. M. Jadwisienczak, H. J. Lozykowski, I. Berishev, A. Bensaoula, and I. G. Brown, “Visible emission from AlN doped with Eu and Tb ions,” J. Appl. Phys.89(8), 4384–4390 (2001). [CrossRef]
J. B. Gruber, G. W. Burdick, N. T. Woodward, V. Dierolf, S. Chandra, and D. K. Sardar, “Crystal-field analysis and Zeeman splittings of energy levels of Nd3+ (4f3) in GaN,” J. Appl. Phys.110(4), 043109 (2011). [CrossRef]

J. Chem. Phys.

W. T. Carnall, G. L. Goodman, K. L. Rajnak, and R. S. Rana, “A systematic analysis of the spectra of the lanthanides doped into single crystal LaF3,” J. Chem. Phys.90(7), 3443–3457 (1989). [CrossRef]

J. Phys. Chem. Solids

G. A. Slack, R. A. Tanzilli, R. O. Pohl, and J. W. Vandersande, “The intrinsic thermal conductivity of AIN,” J. Phys. Chem. Solids48(7), 641–647 (1987). [CrossRef]

MRS Bull.

J. Steckl and J. M. Zavada, “Optoelectronic properties and applications of rare-earth-doped GaN,” MRS Bull.24, 33–38 (1999).

Opt. Mater. Express

G. D. Metcalfe, E. D. Readinger, R. Enck, H. Shen, M. Wraback, N. T. Woodward, J. Poplawsky, and V. Dierolf, “Near-infrared photoluminescence properties of neodymium in in situ doped AlN grown using plasma-assisted molecular beam epitaxy,” Opt. Mater. Express1(1), 78–84 (2011). [CrossRef]

Phys. Rev. B

J. B. Gruber, U. Vetter, H. Hofsäss, B. Zandi, and M. F. Reid, “Spectra and energy levels of Gd3+ (4f7) in AlN,” Phys. Rev. B69(19), 195202 (2004). [CrossRef]
U. Vetter, J. B. Gruber, A. S. Nijjar, B. Zandi, G. Ohl, U. Wahl, B. DeVries, H. Hofsäss, M. Dietrich, and the ISOLDE Collaboration, “Crystal field analysis of Pm3+ (4f4) and Sm3+ (4f5) and lattice location studies of 147Nd and 147Pm in w-AlN,” Phys. Rev. B74(20), 205201 (2006). [CrossRef]
J. B. Gruber, U. Vetter, H. Hofsäss, B. Zandi, and M. Reid, “Spectra and energy levels of Tm3+ (4f12),” Phys. Rev. B70(24), 245108 (2004). [CrossRef]

Other

J. Newman and B. Ng, Crystal-Field Handbook (Cambridge University Press, 2000).
S. R. M. Levinshtein and M. Shur, Properties of Advanced Semiconductor Materials (Wiley, 2001).
R. Judd, Operator Techniques in Atomic Spectroscopy (McGraw-Hill, 1963).
B. G. Wybourne, Spectroscopic Properties of Rare-Earths (Wiley, 1965).
G. Blasse and B. Granmaier, Luminescent Materials (Springer-Verlag, 1994).
S. M. Sze, Semiconducting Devices, Physics and Technology (Wiley, 1985)
W. J. Tropf, M. E. Thomas, and T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics (McGraw-Hill, 1995), Vol. 2.

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Crystal field and Zeeman splittings for energy levels of Nd3+ in hexagonal AlN