Dielectric Function of NiO and Si from 25 meV to 6 eV: What’s the difference? Ayana Ghosh Department of Physics, University of Michigan-Flint Cayla M. Nelson, Travis I. Willett-Gies, Stefan Zollner Department of Physics, New Mexico State University, Las Cruces, NM FTIR ellipsometry: 2 to 40 mm (Sandia) http://ellipsometry.nmsu.edu NIR/VIS/QUV ellipsometry: 190 to 2500 nm, 77 to 800 K NSF: DMR-11104934

Dielectric Function of NiO and Si from 25 meV to 6 eV: What’s the difference? (Outline) Spectroscopic ellipsometry measures the absorption coefficient of materials: Infrared light: Atomic (lattice) vibrations Visible/UV light: Electronic excitations (VB to CB) Infrared Results NIR/VIS/UV Results Comparison with band structure calculations for NiO New Mexico State University Stefan Zollner, 03/07/2014, APS March meeting 2

Ellipsometry: How does it work ? We measure the change in the polarization state of light, when it is reflected by a flat surface. P plane S plane Angle of incidence Bulk sample Monochromator or Interferometer polarizer analyzer detector Φ Result: Optical constants versus photon energy Stefan Zollner, 03/07/2014, APS March meeting 3

Infrared Lattice Absorption Silicon: Diamond lattice NiO or NaCl: Rocksalt lattice Si-Si bonds are non-polar. Bonds: no dipole moment. No infrared absorption. Ni2+-O2- bonds are polar. Ni-O vibration has dipole moment. NiO Typical Lorentz oscillator e2=0 FTIR ellipsometry New Mexico State University Stefan Zollner, 03/07/2014, APS March meeting 4

Antiferromagnetism: Zone-folded TO phonon Rocksalt Crystal Structure (FCC): Single optical phonon. Antiferromagnetic ordering along (111). Small rhombohedral distortion. Lattice waves are reflected by the anti-parallel ordered spins along (111). (Or: L-point phonon folded back to G due to doubling the crystal size.) NiO cell Rooksby, Nature, 1943 NiO Reststrahlen Band Theory: e0=13.1 (Louie) e0=11.3 e¥=5.0 Zone-folded phonon TO LO Stefan Zollner, 03/07/2014, APS March meeting 5

NiO Band Structure I Atomic electron configurations: Ni: [Ar] 3d8 4s2 O: [He] 2s2 2p4 Ni2+O2-: 4s electrons of Ni are transferred to O 2p: Ni2+: [Ar] 3d8 4s0 O2-: [He] 2s2 2p6 This should be a metal, because only 8 of 10 d-states are filled. However: Transmission measurements show that NiO is an insulator with a fundamental band gap of about 0.8 eV. Compare: Newman, Phys. Rev. 1959. New Mexico State University Stefan Zollner, 03/07/2014, APS March meeting 6

NiO Band Structure II Let’s double the unit cell: 2 Ni and 2 O atoms per crystal cell: Ni(1): [Ar] 3d8 4s0 Ni(2): [Ar] 3d9 4s0 O(1): [He] 2s2 2p6 O(2): [He] 2s1 2p6 Every other O atom (ligand) transfers one electron to a Ni atom. Ligand (O) hole adds an extra d-electron to Ni. Antiferromagnetic ordering. Charge-transfer gap commonly assumed to be 4.0-4.5 eV. Most evidence from photoemission. Optical spectroscopy (transmission, ellipsometry) is usually ignored. Charge-transfer gap at 3.97 eV Newman & Chrenko, Phys. Rev. 114, 1507 (1959). Kang, Lee, & Lee, J. Kor. Phys. Soc. 50, 632 (2007). ? New Mexico State University Stefan Zollner, 03/07/2014, APS March meeting 7

NiO looks just like Silicon NiO:Charge-transfer gap at 3.97 eV Silicon: E1 at 3.4 eV ? The charge-transfer gap (CTG) of NiO at 4 eV looks just like the E1 gap of Si. NiO CTG energy decreases with increasing temperature. NiO CTG broadening increases with temperature. Just like Si: Phonon-related ? Compare: Vina, PRB, 1984 (Ge); Lautenschlager, PRB, 1987 (Si). New Mexico State University Stefan Zollner, 03/07/2014, APS March meeting 8

Failures of the Charge-Transfer Model for NiO Optical absorption between 0.8 and 3.5 eV. Too strong to be defect-related. Absorption decreases above room temperature. Several weak critical points between 0.8 and 4.0 eV. Charge-gap model is flawed. We need a full-zone band structure for NiO to compare with optical experiments. NiO Derivative analysis Charge-transfer gap at 3.97 eV Li, Riganese, Louie, Phys. Rev. B 71, 193102 (2005). Several critical points Lowest gap at 1.5 eV New Mexico State University Stefan Zollner, 03/07/2014, APS March meeting 9

Electron Structure: Band Gaps Peaks indicate interband transitions Valence band (flat): Ni(3d) states with some O Conduction band: Flat: Ni(3d) states (unfilled) Curved: Unfilled O states Strong 4.0 eV peak goes from Ni(3d) VB to Ni(3d) CB. Also observed in photoemission Weak peaks are transitions from many Ni(3d) VB states to the O(4s) band, only at G. Explains all experimental evidence. Several critical points Lowest gap at 1.5 eV J.L. Li & S.G. Louie, PRB, 2005 New Mexico State University Stefan Zollner, 03/07/2014, APS March meeting 10

Summary: NiO looks like Si in the VIS/UV, but it’s not like Si at all. NiO is a fascinating material. The antiferromagnetic ordering of the electron spins doubles the size of the crystal cell (4 atoms per cell instead of 2). This cell doubling causes a side-band of the Ni-O vibration (L-point phonon folded back to G). The cell doubling also makes NiO a charge-transfer insulator. A full-zone band structure is needed to understand the weak optical transitions below the charge-transfer gap at 4.0 eV. New Mexico State University Stefan Zollner, 03/07/2014, APS March meeting 11

Graduate Students: Lina Abdallah, Travis Willett-Gies, Nalin Fernando, Tarek Tawalbeh (Theory) Undergraduate Students: Cesar Rodriguez, Nathan Nunley, Khadijih Mitchell, Cayla Nelson, Laura Pineda, Eric DeLong, Chris Zollner (Cornell), Amber Medina, Maria Spies, Ayana Ghosh (Michigan-Flint) Collaborators: Igal Brener (CINT), Neha Singh, Harland Tompkins (J.A. Woollam Co.), S.G. Choi (NREL) Samples: Demkov (UT Austin), Alpay (Uconn), Droopad (Motorola), MTI (LAO), SurfaceNet (NiO) Flat & uniform films, at least 5 by 5 mm2, low surface roughness, films on single-side polished substrate Email: zollner@nmsu.edu New Mexico State University http://ellipsometry.nmsu.edu