J. Phys. Chem. A 2010, 114, 7117–7120
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Er3+ Electronic Energy Levels in GaN Y. Yang and R. M. Pitzer* Department of Chemistry, The Ohio State UniVersity, 100 West 18th AVenue, Columbus, Ohio 43210 ReceiVed: January 21, 2010; ReVised Manuscript ReceiVed: May 7, 2010
The 4f11 4I13/2 f 4I15/2 emission of Er3+ at 1.54 µm, particularly in a GaN host crystal, has been of interest in optical communications for some time because of its transmission efficiency and temperature stability. Theoretical treatments of this transition are complicated by the large number of open-shell electrons, moderate relativistic effects, and splittings due to the crystalline field. We have modeled the system as a cluster of ions centered on an Er3+ ion and have used spin-orbit configuration interaction to study the electronic states involved. It is an unusual quantum theory problem in that single-excitation terms in the wave functions are of central importance. Introduction Rare earth ions doped into semiconductor hosts have been studied for applications in optoelectronics.1-3 Among the optical properties desired are photoluminescence almost independent of host and temperature. The emission of Er3+ ions at 1.54 µm is particularly of interest because it is in the region of minimal loss in optical fibers. These characteristics enable optical amplifiers to be built based on Er3+, which can be more efficient than signal conversion from optical to electrical, electrical amplification, and back-conversion to optical signals.4-6 Si has been considered as a host for Er3+, but the photoluminescence then showed a strong temperature dependence with significant quenching at room temperature,7,8 and Favennec et al. showed that a host such as GaN with a wider band gap would give much less thermal quenching.9 It has been observed10-14 that the photoluminescence of Er3+ in GaN decreases by only 10% in the temperature range of 15 to 550 K. Neutral erbium outer core and valence shells are 4s24p64d105s25p64f126s2, losing two electrons from 6s and one electron from 4f to form 4f11 Er3+, the form of erbium found in most compounds. Note that the 5s and 5p shells, while lower in energy than the 4f shell, have a greater radial extent. Therefore, the open 4f shell in Er3+ is spatially protected from strong interactions with neighboring atoms or ions. The ground state is 4f11 4I15/2. Relativistic effects for Er are moderately large and must be taken into account but are still significantly smaller than they are for actinides.15 The 1.54 µm luminescence comes from the 4I13/2 f 4I15/2 transition, effectively a spin-orbit transition in which only the J quantum number changes.16 This transition is forbidden by the parity selection rule and thus requires a noncentrosymmetric ligand field to acquire electricdipole intensity. Such a ligand field will also split both states into several states each, and the reduced symmetry will make some of the resulting transitions electric-dipole allowed. Rough estimates of the overall energy effects in Er3+ are 10 eV for electron-repulsion splitting, 1.0 eV for spin-orbit splitting, and 0.10 eV for ligand-field splitting,17 hence LS coupling and weakfield coupling. Previous related theoretical work has been limited because of the difficulty of the calculations. In 1992, Saito and Kimura used the XR method to study Er3+ in InP, GaP, and GaAs.17 * Corresponding author. E-mail:
[email protected].
They used a crude spin-orbit treatment based on ligand-field theory.18 In 2002, Beck studied the 4S3/2 f 4I15/2 laser transition using relativistic configuration interaction,19 treating relativistic effects and correlation energy, but not a ligand field. Computational Methods We computed the electronic energy levels of Er3+ doped into a GaN crystal (replacing a Ga3+ ion10,20) by carrying out calculations on a number of clusters centered on the Er3+ ion, 27+ 9, ErN4Ga12N12 , ErN4Ga12N12Ga69+, thereby ErN49-, ErN4Ga12 approximating the crystal field at the Er3+ ion to increasing accuracy.21,22 We then computed the intensities of all transitions between the split 4I13/2 and 4I15/2 energy levels. Our calculations used relativistic effective core potentials (RECPs), and their corresponding valence spin-orbit operators to replace the core electron shells of the inner ions of the clusters. The RECPs and spin-orbit operators were obtained using the methods developed by Christiansen and coworkers.23,24 For the Er3+ ion, the 1s through the 4p shells (36 electrons) are replaced.25 For the surrounding layer of N3- ions, the 1s shell is replaced,26 and for the next layer, all 28 electrons of the Ga3+ are replaced,27 so that the electrons in the orbitals of the inner layers will feel a hard core. The ions in additional layers were replaced by point charges. We used contracted Gaussian atomic orbitals to form the molecular orbitals (MOs). For Er, we optimized a (5sd3p6f1g)/ [3sd2p2f1g] set,28 where sd refers to sets of 3s and 3d orbitals with the same orbital exponents. For N, we used a (4s4p1d)/ [3s2p1d] set.29 The contraction method used for these RECP basis sets is that due to Christiansen.30 Therefore, the overall quality of the basis set is cc-pVDZ. The calculations were carried out by the multireference spin-orbit configuration-interaction singles and doubles (MRSOCISD) method,31 as implemented in the Columbus programs.32 The MOs were computed in a restricted HartreeFock calculation on the average energy of all high-spin (quartet) 4f11 wave functions. Then MRSOCISD calculations were carried out including all single-excitation (CIS) or all single- and doubleexcitation (CISD) configuration state functions (CSFs, spin-adapted configurations) from all of the above open-shell wave functions. All virtual orbitals were included. Transition dipole moments were computed for all transitions between the 4I13/2 set of states and the 4 I15/2 set of states. In calculating the single gas-phase corresponding
10.1021/jp100607y 2010 American Chemical Society Published on Web 06/10/2010
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J. Phys. Chem. A, Vol. 114, No. 26, 2010
Yang and Pitzer
TABLE 1: Splittings (inverse centimeters) for 4I States from Different Levels of CI for ErN49- Clusters level
4
4
I15/2
I13/2
state
CIS(7)
CIS(27)
4
CISD(7)
G3/2 E1/2 G3/2 E5/2 G3/2
0 16.78 161.39 175.88 204.66
0 12.17 189.92 193.86 242.73
0 36.10 178.76 220.96 223.60
E5/2 G3/2 E5/2 G3/2 E1/2
5519.76 5521.06 5521.24 5633.84 5658.94
6006.53 6125.09 6009.07 6144.07 6174.88
5474.51 5485.16 5593.57 5597.90 5623.15
TABLE 2: Convergence of CIS(27) Energy Splittings (inverse centimeters) for Td Clusters level
state
29 ions
35 ions
4
I15/2
E1/2 G3/2 E5/2 G3/2 G3/2
0 19 33 197 215
0 22 49 213 238
I13/2
G3/2 E5/2 E5/2 G3/2 E1/2
5990 6009 6091 6117 6138
5995 6017 6105 6136 6159
4
TABLE 3: CIS(27) Energy Splittings (inverse centimeters) for the Td and C3W 17-Ion Clusters
transition, we obtained 8487 cm-1, for which there is no direct comparison in standard tables33 where the only value given is 6480 cm-1 from a LaCl3 crystal. Results and Discussion Crystalline GaN exists in two polymorphs, wurtzite and zinc blende. The information available about their relative energy is a theoretical calculation,34 giving wurtzite more stable by 0.95 kJ/mol. The structure of a crystal resulting from epitaxial growth depends on the substrate,35,36 whereas thin layers grown by chemical vapor deposition may not be crystalline, showing
4
I15/2 states C3V
Td E1/2 G3/2
0 14
E5/2 G3/2
140 197
G3/2
250
E1/2 E1/2 E3/2 E1/2 E1/2 E3/2 E1/2 E3/2
I13/2 states
Td 0 18 20 143 208 225 271 280
C3V
G3/2
6003
E5/2 E5/2 G3/2
6020 6118 6151
E1/2
6181
E1/2 E3/2 E1/2 E1/2 E1/2 E3/2 E1/2
6006 6008 6028 6130 6164 6173 6203
several types of Er sites.37 We considered both types of crystalline structures in our calculations. The smallest cluster is ErN49- (5 ions), has Td symmetry and is the same for both polymorphs. Adding successive shells of 9ions gives clusters ErN4Ga27+ 12 (17 ions), ErN4Ga12N12 (29 ions), 9+ and ErN4Ga12N12Ga6 (35 ions), which we studied. The GaN structural parameters were used except that the Er-N distance was put at the measured value20 of 2.17 Å rather than the Ga-N value of 1.95 Å. Despite this 11% increase in the nearest neighbor distance, the change in the distance to the next-nearest neighbors (Er-Ga) from the value in GaN was
