2. 60th International Symposium on Molecular Spectroscopy Discovery: GaAs:Er system, 1983 The coincidence of the transition wavelength with the absorption minimum of semiconductor-based fibers The sharp spectrum lines  Disadvantages: The temperature quenching of the emission intensity H. Ennen, J. Schneider, G. Pomrenke, A. Axmann, Appl. Phys. Lett. 43, 943 (1983) Experiment The temperature insensitive wavelength Advantages:

3. 60th International Symposium on Molecular Spectroscopy Conclusion: Semiconductor hosts with larger band gaps exhibit less temperature quenching of Er 3+ luminescence. P. N. Favennec, H. L’Haridon, M. Salvi, D. Moutonnet, Y. L. Guillou, Electron. Lett. 25 (1989) Experiment Improvement: intensity vs. band gap, 1989

4. 60th International Symposium on Molecular Spectroscopy Experiment M. Thaik, U. Hömmerich, R. N. Schwartz, R. G. Wilson and J. M. Zavada, Appl. Phys. Lett. 71, 2641 (1997)

5. 60th International Symposium on Molecular Spectroscopy Theory The detailed energy splitting of Er 3+ center is unknown. Spin-orbit interaction needs to be considered. Ligand field effect under different local symmetries should be studied. Theoretical calculations are helpful to study transition mechanism. Possible transition frequencies under certain local symmetry could be estimated. Transition moment needs to be computed explicitly.

6. Theory ab initio spin-orbit configuration interaction singles (CIS) and singles and doubles (CISD) excitation calculations based on relativistic effective core potentials (RECP) are applied to calculate energies of the ground and excited states for a series of Er 3+ -centered clusters. Transition dipole moment calculations are performed based on the CI calculation results. All of the calculations are carried out by COLUMBUS package. Calculations Outline 60th International Symposium on Molecular Spectroscopy

7. Er substitutes the Ga site GaN crystals have two crystal structures: zinc blende and wurtzite Theory GaN Structure 60th International Symposium on Molecular Spectroscopy Theoretical estimate of  E zinc blende-wurzite = 0.952kJ/mol T d Symmetry (zinc blende) C 3v Symmetry (wurtzite) Second Shell 12 Ga 3+ added

8. ErN 4 9- (T d ) ErN 4 Ga 12 27+ (T d ) ErN 4 Ga 12 N 12 9- (T d ) ErN 4 Ga 12 N 12 Ga 6 9+ (T d ) ErN 4 Ga 12 27+ (C 3v ) Theory 60th International Symposium on Molecular Spectroscopy

9. Theory Brief Review for Er 3+ The atomic number of Erbium is 68. The electron configuration for Er 3+ is 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 4d 10 4f 11 5s 2 5p 6 The ground state term symbol for Er 3+ is 4 I 15/2. The 1.54 µm PL corresponds to 4 I 13/2  4 I 15/2 transition. Schematic diagram of the energy levels of a free Er 3+ ion and splitting of the 4f subshell levels in the field of T d symmetry. 60th International Symposium on Molecular Spectroscopy 4 I 13/2 4 I 15/2

10. 60th International Symposium on Molecular Spectroscopy Theory RECP and Basis Set Erbium 36-electron core developed by Ermler (unpublished) 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 Core Corresponding contracted Gaussian cc-pVDZ basis set (Our group) (5sd3p6f1g)/[3sd2p2f1g] Nitrogen 2-electron core developed by Christiansen (1985) 1s 2 Core Corresponding contracted Gaussian cc-pVDZ basis set (Pitzer) (4s4p1d)/[3s2p1d] Gallium 28-electron core developed by Ermler (1986) 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 Core

11. 60th International Symposium on Molecular Spectroscopy Theory

12. For virtual p orbital: Augmented primitive is used. For virtual f orbital: Freeing diffuse primitive method is applied. For g polarization orbital: CISD method is employed to optimize the exponent. P. A. Christiansen, J. Chem. Phys. 112, 10070 (2000) 60th International Symposium on Molecular Spectroscopy Theory

13. 60th International Symposium on Molecular Spectroscopy Theory Reference Space CIS 4f orbitals of Er 3+ (small reference, 57,239 CSFs) 5s, 5p, 4f orbitals of Er 3+ and 2s, 2p orbitals of N 3- (large reference, 888,979 CSFs) CISD 4f orbitals of Er 3+ (small reference, 6,504,680 CSFs) 5s, 5p, 4f orbitals of Er 3+ and 2s, 2p orbitals of N 3- (large reference, over one billion CSFs)

14. 60th International Symposium on Molecular Spectroscopy 29 atoms 35 atoms 4 I 13/2 E 1/2 6137.556159.12 G 3/2 6117.126135.64 E 5/2 6090.936104.59 E 5/2 6009.366016.82 G 3/2 5990.285994.71 4 I 15/2 G 3/2 215.00238.31 G 3/2 196.71212.71 E 5/2 33.4949.11 G 3/2 18.6322.13 E 1/2 0.00 Theory State Energy (cm -1 )

15. Electric Transitions E 1/2 —E 5/2 Electric dipole moment operator belongs to F 2 irreducible representation under T d symmetry. E 1/2 —G 3/2 E 5/2 —G 3/2 G 3/2 —G 3/2 22 possible transitions wavelengths correspond to 4 I 13/2  4 I 15/2. Theory 60th International Symposium on Molecular Spectroscopy Need to know the initial populations of the upper sublevels to compare to the spectrum.

16. ErN 4 Ga 12 N 12 Ga 6 9+ Cluster Theory 60th International Symposium on Molecular Spectroscopy 2 nd G 3/2 ->2 nd G 3/2 G 3/2 : from 4 I 13/2 G 3/2 : from 4 I 15/2 Transition Moments Squares

17. Conclusions and Future Work 60th International Symposium on Molecular Spectroscopy  T d clusters show a converged splitting pattern with the E 1/2 state as the ground state.  1.54 µm PL is tentatively assigned to the transition between 2 nd G 3/2 of 4 I 13/2 and 2 nd G 3/2 of 4 I 15/2.  Large clusters for both zinc blende and wurzite should be studied.