Valence-band structure and critical point energies of diamond along [100]

M. T. Edmonds, A. Tadich, M. Wanke, K. M. O'Donnell, Y. Smets, K. J. Rietwyk, J. D. Riley, C. I. Pakes, and L. Ley

Phys. Rev. B 87, 085123 – Published 19 February 2013

Abstract

Accurate valence-band dispersions $E (k_{⊥})$ have been determined for the technologically relevant Γ-Δ- $X$ symmetry direction of hydrogen-terminated diamond (100) using normal emission angle-resolved photoemission spectroscopy for photon energies between 30 and 206 eV. By analyzing the data using a free-electron final-state model, the emission features can be well understood by assuming primary cone transitions. Critical point energies in the valence band are in good agreement with self-consistent quasiparticle $G W$ calculations. Substantial modulations in the valence-band dispersion occurring in specific regions of the Brillouin zone have been traced to band crossings in the unoccupied free-electron final state. A one-band effective mass of (0.39 ± 0.30) $m_{0}$ is determined from the band dispersion close to the Γ point and compared with values in the literature.

Received 8 November 2012

DOI:https://doi.org/10.1103/PhysRevB.87.085123

Authors & Affiliations

M. T. Edmonds^1,*, A. Tadich^1,2, M. Wanke^1,3, K. M. O'Donnell², Y. Smets¹, K. J. Rietwyk¹, J. D. Riley¹, C. I. Pakes¹, and L. Ley^1,4

¹Department of Physics, La Trobe University, Bundoora, Victoria 3086, Australia
²Australian Synchrotron, 800 Blackburn Road, Clayton, Victoria 3168, Australia
³Institut für Physik, Technische Universität Chemnitz, Reichenhainer Str. 70, 01926 Chemnitz, Germany
⁴Institut für Technische Physik, Universität Erlangen, Erwin-Rommel Str. 1, 91058 Erlangen, Germany

^*mtedmonds@students.latrobe.edu.au

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Vol. 87, Iss. 8 — 15 February 2013

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Images

Figure 1
Normal emission angle-resolved energy distribution curves from the C(100):H surface as a function of photon energy $h v$ with the initial state energy referenced to the Fermi level. Spectra were taken (a) between $h ν = 30 - 80$ eV with a step size of 1 eV between 30–64 eV and 2 eV between 64–80 eV (b) between $h ν = 82 - 136$ eV with a step size of 2 eV between 82–112 eV and 10 eV between 116–136 eV, and (c) between $h ν = 146 - 206$ eV with a step size of 10 eV.Reuse & Permissions
Figure 2
Valence-band dispersions $E (\vec{k})$ of hydrogen-terminated diamond along the Γ-Δ- $X$ direction from normal emission spectra. Red squares represent the band dispersion and circles represent the dispersionless band features, both experimentally obtained. Solid lines represent the $G W$ calculated band structure and the dashed lines represent an MGGA band structure calculated by the authors.Reuse & Permissions
Figure 3
Constant initial state spectra (CIS) for photoelectrons emitted normal to the hydrogen-terminated diamond (100) surface for an initial state energy fixed at: (a) $Γ_{25}^{+ v}$ and (b) $X_{4 v}$ , with the photon energy stepped by 0.25 eV to map transitions into unoccupied final-state bands. (c) Calculated band structure of the conduction band where the solid lines represent the $G W$ band structure, dashed lines represent the MGGA band structure, and the red squares represent the extracted CIS critical point energies.Reuse & Permissions
Figure 4
(a) Red circles represent the measured photoelectron kinetic energy of the peaks identified in Fig. 1 as a function of $k_{⊥}$ determined from Eq. (1) using $V_{0}$ $=$ −22.06 eV, and free-electron bands along Γ- $X$ calculated for a diamond lattice (blue lines) relative to the vacuum level. (b) Measured initial state energy $E_{i}$ as a function of $k_{⊥}$ (data from Fig. 2). Red squares represent the valence-band dispersions and the blue circles represent surface related features. The maroon arrow indicates the primary cone band crossing with the $G_{11}$ secondary band in the zone folded FEFS model lined against the “kinks” in the measured occupied band structure.Reuse & Permissions
Figure 5
(a) Corrected valence-band dispersion of hydrogen-terminated diamond same as Fig. 2 except the initial state energies have been placed at $k_{⊥}$ points where they follow the expected band dispersion to account for the failure of the FEFS model at the final-state band crossing point. (b) Measured photoelectron kinetic energy as a function of corrected $k_{⊥}$ . Blue lines represent the calculated free-electron bands, corrected final-state dispersion of band 2 (red squares) and band 1 (green circles).Reuse & Permissions
Figure 6
Initial state energy $E_{i}$ relative to VBM vs $k^{2}$ close to the Γ point. Dashed line is a linear fit of the data, yielding an effective mass of $(0.39 \pm 0.30) m_{0}$ .Reuse & Permissions

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