1. Cardona Symposium 20101 A Tale of Two Vacancies Peter Y. Yu Department of Physics, University of California & Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 Acknowledgments: Collaborators are Lei Liu, Wei Cheng, Zixun Ma and Samuel S. Mao. This work was supported by the Us Department Of Energy NNSA/NA-22, under Contract No. De-Ac02-05ch11231

2. Cardona Symposium 20102 OUTLINE INTRODUCTION MOTIVATIONS VACANCIES IN GROUP III-NITRIDES –FERROMAGNETISM DUE TO Ga VACANCIES –DOPING BY Gd VACANCIES IN Cd-CHALCOGENIDES –CODOPING WITH OXYGEN –EVIDENCE OF O 2 MOLECULES CONCLUSIONS ACKNOWLEDGMENTS

3. Cardona Symposium 20103 INTRODUCTION Vacancies are often introduced during crystal growth at high temperature Vacancies are important in determining the quality and electrical properties of semiconductors: –Vacancies allow impurities to diffuse more easily throughout a crystal –Vacancies involve dangling bonds and are electrically active, vacancies can cause self- compensation

4. Cardona Symposium 20104 MOTIVATIONS Vacancies are detected mainly by two methods: High Resolution TEM and Positron Annihilation. Otherwise they are difficult to detect Recent advances in First-Principle Density Functional Theory (DFT) make it possible to calculate the properties of vacancies Present work attempts to study their role in –(1) room temperature Ferromagnetism in GaN:Gd –(2) incorporation of Oxygen into CdTe in the formation of O 2

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6. 6 STORY 1 How Vacancies Produce Room Temperature Ferromagnetism In GaN

7. Cardona Symposium 20107 Ferromagnetism in GaN:Gd Room temperature Ferromagnetism was reported by at least 2 groups in GaN doped with Gd : “Magnetic, optical and electrical properties of GaN and AlN doped with rare- earth element Gd” by S. W. Choi, Y. K. Zhou, S. Emura, X. J. Lee, N. Teraguchi, A. Suzuki, and H. Asahi (2002-2006):  [Gd]:2-6%  Tc~400K  sample n-type with [e]>5x10 19 cm -3. “Gd-doped GaN: A very dilute ferromagnetic semiconductor with a Curie temperature above 300 K” by S. Dhar, L. Pérez, O. Brandt, A. Trampert, and K. H. Ploog (2005-2007)  [Gd]:10 16 -10 19 cm -3  Tc>300K  magnetic moment /Gd~4000  B  magnetic moment/Gd increases with defect concentration since ion- implanted sample has large moment than sample after annealing

8. Cardona Symposium 20108 Results of Ploog’s Group suggested that intrinsic defects played an important role in the Ferromagnetism.The nature and role of the intrinsic defect are, however, unclear. Our First-Principle Calculation suggests that: GaN:Gd is paramagnetic GaN containing Gd Ga +V N is also paramagnetic GaN containing Gd Ga +V Ga is ferromagnetic Surprisingly GaN containing only V GA is also ferromagnetic! Ferromagnetism in GaN:Gd

9. Cardona Symposium 20109 Computation Method Use spin-polarized DFT within the Generalized Gradient Approximation (GGA). Electron correlation important for the d and f electrons of Gd ions are included (approximation known as GGA+U ) Use Full-potential Linearized Augmented Plane Wave (FLAPW) as basis functions for calculating the electron eigenvalues and functions. Lei Liu, Peter Y. Yu, Zhixun Ma, and Samuel S. Mao. Ferromagnetism in GaN:Gd: A Density Functional Theory Study. Phys. Rev. Lett. 100, 127203 (2008)

10. Cardona Symposium 201010 Supercell model:GdGa 7 N 8 Gd atoms are separated by 3 atom layers to simulate long range interaction between Gd atoms.

11. Cardona Symposium 201011 f electrons GaN:Gd is Paramagnetic Band Structure of GaN:Gd: f-electrons in Gd ions are magnetized but the coupling between the moments is paramagnetic

12. Cardona Symposium 201012 GdGa 6 N 8 Supercell containing Gd and V Ga

13. Cardona Symposium 201013 GaN containing Gd Ga +V Ga is ferromagnetic! Ferromagnetism in GaN:Gd Top valence bands are 100% Polarized!

14. Cardona Symposium 201014 What is the source of the strong coupling between the Gd ions? Answer: coupling with the spin of holes introduced by Ga vacancies Ferromagnetism in GaN:Gd Pratibha Dev, Yu Xue, and Peihong Zhang. Defect-induced intrinsic magnetism in wide-gap III-nitrides. Phys. Rev. Lett. 100, 117204 (2008). Spin-resolved DOS of Ga Vacancy in GaN

15. Cardona Symposium 201015 How come the Gd magnetic moment is so large? Ferromagnetism in GaN:Gd (1)Local strain of Gd ion induces vacancies in the vicinity (2)The magnetic moment of Gd is enhanced by the 3 spins of each Ga vacancy nearby GdGa 6 N 8 10 0.7

16. Cardona Symposium 201016 Summary : Gd introduces Ga vacancies by producing tensile local strain Ga vacancies produce holes When the hole wave functions are localized enough (as in case of nitrides) they become spin polarized according to Hund’s Rule Coupling between the Gd and hole spins produce a strong ferromagnetic state. When the hole or Ga vacancy concentration is much higher than the Gd concentration the magnetic moment of Gd appears to be enhanced Ferromagnetism in GaN:Gd

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18. Cardona Symposium 201018 STORY 2 How Cd Vacancies allow O 2 Molecules to be incorporated into CdTe

19. Cardona Symposium 201019 CdTe is an important semiconductor for thin film solar cells Oxygen is a common impurity in the manufacture of solar cells. O replacing Te (O Te ) is an isovalent impurity. Since electronegativity of O>>electronegativity of Te, O will attract an electron to form O - which is a shallow acceptor. Mass of O<<Mass of Te so vibration of O Te is highly localized around O. These are called local vibration mode (LVM). LVM are very sharp and, therefore, sensitive probes of light impurities BACKGROUND

20. Cardona Symposium 2010 (G. Chen, I. Miotkowski, S. Rodriguez, and A. K. Ramdas, Phys. Rev. B 75, 125204 (2007).) Infrared Absorption Spectra of CdTe:O Sample Growth strategies: Excess CdO to provide oxygen and Excess Cd to suppress V Cd A single sharp line is observed: 0 = 349.8 cm -1 FWHM = 0.24 cm -1 Selection rule:  1   5

21. Cardona Symposium 2010 21 Chen et al. observe 2 high frequency modes at : 1 = 1096.78 cm -1 ; 2 = 1108.35 cm -1. At high T 1 and 2 merged into one mode with frequency:1104cm -1. They attributed these 2 modes to vibration of a complex: O Te -V Cd High Frequency Mode when V Cd Is Present In CdTe:O without excess Cd

22. Cardona Symposium 2010 Model Proposed by Chen et al. 22 Te Cd V Cd O c 1 2 N = 0 N = 1 11 11 33 E || c E  c 1 2

23. Cardona Symposium 2010 Dynamic Switching of V Cd -O complex 23 0 * As T increases Oxygen switches between sites: 1, 2, 3 and 4

24. Cardona Symposium 2010 Activation Energy for Switching 24 1/T W=42 meV

25. Cardona Symposium 2010 25 L. Zhang, J. T-Thienprasert, M.-H. Du, D. J. Singh, and S. Limpijumnong, Phys. Rev. Lett. 102, 209601 (2009) calculated, from first principle, the frequency of the O Te -V Cd complex and obtained <500 cm -1. Similar high frequency modes (>1000 cm -1 )have also been observed by Chen et al. in CdSe (G. Chen, J. S. Bhosale, I. Miotkowski, and A. K. Ramdas, Phys. Rev. Lett. 101, 195502 (2008)) so this complex is rather common in Cd chalcogenides. What is the identity of this complex of O in CdTe and CdSe? How to explain the dynamic switching? MOTIVATION FOR PRESENT WORK

26. Cardona Symposium 2010 Computational Method 26 First-Principle density-functional theory based on the GGA-PBE potential (J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996) ) Two commercial softwares: VASP (Vienna ab initio simulation package ) and MedeA (by Material Design )

27. Cardona Symposium 2010 Tests Of Softwares 27 Our resultExperiment CdTe Lattice Constant (nm) 0.6410.646 O-O bond length (nm) & stretching mode frequency (cm -1 ) 0.1236 ; 1548.20 0.1208 ; 1580 Local mode frequency of O Te (cm -1 ) 331.86349.8

28. Cardona Symposium 2010 New Model of Oxygen-V Cd Complex in CdTe 28 Ball-and-Stick model of the cell: Cd 31 Te 32 O 2 containing a V Cd (blue ball) and a O 2 molecule (red balls). The golden and green balls represent Te and Cd atoms, respectively. O-O is oriented along the [111] axis and is displaced from the Cd site. Symmetry of complex is C 3v

29. Cardona Symposium 2010 Defect Formation Energies in CdTe 29 DefectFormation Energy (our result) eV Formation Energy (Wei, Zhang and Zunger*) eV V o Cd 2.12.30 V - Cd 2.42 V -2 Cd 2.69 V Cd -O 2 1.2 * S. H. Wei, S. B. Zhang, and A. Zunger J. Appl. Phys. 87, 1304 (2000).

30. Cardona Symposium 2010 Normal Modes of O 2 Molecule in CdTe Vacancy 30 A 1 Modes E Modes O-O stretch:1112.5 cm -1 Rocking of the O 2 molecule:192.1 cm -1 Libration Mode at 315.7 cm -1 Rocking of the O 2 molecule:176.6 cm -1

31. Cardona Symposium 2010 IR activity of O-O Stretching Mode in CdTe 31 O-O Stretching Mode of O 2 in gas form is not infrared-active since it has even parity O 2 in V Cd of CdTe has no inversion symmetry and therefore can be infrared-active. The calculated charge difference between the two O atoms in CdTe is ~0.05e and the bond length is ~0.13 nm (0.1208 nm in gaseous O 2 ) giving an electric dipole moment of ~3 Debye.

32. Cardona Symposium 201032 Existence of Two IR modes in V Cd -O 2 1 peak (singlet) 2 peak (doublet)> 1 The energy to rotate the O 2 molecule by 90 o ~ energy of the libration mode=39 meV

33. Cardona Symposium 201033 Summary : Oxygen replacing Te has a LVM at ~350 cm -1. In the presence of V Cd Oxygen prefers to form molecule inside the V Cd The O 2 molecule is oriented along the [111] direction but displaced from the center of the vacancy. The two O atoms occupy in- equivalent sites so the O-O stretching mode is IR-active Charge transfer to the neighboring Te atoms weakens the O-O bond and lowers the O-O stretching mode frequency. The calculated O-O stretching mode frequency is in good agreement with experiment The existence of two modes at low T and their convergence at high T are also explained by theory LVM of Oxygen in CdTe

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35. Cardona Symposium 201035 Using first-principle density-functional theory we have studied the electronic and vibrational properties of vacancies in CdTe and GaN. In GaN vacancies can be induced by replacing the cations with large rare-earth ions like Gd. The Ga vacancies produce holes which are spin polarized. They strongly coupled to each other and to the Gd spins. These results explains recently reported observation of ferromagnetism in GaN:Gd above room temperature and the enhancement of the magnetic moment per Gd by intrinsic defects. In CdTe the cation vacancies are large thus allowing small molecules like oxygen to be located inside them and forming a new kind of molecular complex. The vibrational modes of these molecular-vacancy complexes in CdTe explain the sharp high frequency local vibration modes reported in CdTe. CONCLUSIONS

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37. Cardona Symposium 201037 ANNOUNCEMENT: FOURTH EDITION OF YU & CARDONA IS NOW AVAILABLE!