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Surface properties of hexagonal Si and Ge: First-principles study of energetics, atomic relaxation, and electronic structure

Martin Keller1, Abderrezak Belabbes2,1, Jürgen Furthmüller1, Friedhelm Bechstedt1, and Silvana Botti3,1

  • 1Institut für Festkörpertheorie und -optik, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany
  • 2Department of Physics, Sultan Quaboos University, P.O. Box 36, PC 123, Muscat, Oman
  • 3Research Center Future Energy Materials and Systems, Interdisciplinary Centre for Advanced Materials Simulation, Faculty of Physics and Astronomy, Ruhr University Bochum, Universitätsstrasse 150, 44801 Bochum, Germany

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Phys. Rev. B 112, 195303 – Published 7 November, 2025

DOI: https://doi.org/10.1103/zq7r-s182

Abstract

Low-index surfaces of hexagonal (lonsdaleite) silicon and germanium polytypes, 2H-Si and 2H-Ge, are investigated using density functional theory calculations for structural optimization and approximate quasiparticle methods for electronic structure analysis. We examine the relaxed geometries of four surface orientations: (112¯0) a plane, (11¯00) m plane, (11¯02) r plane, and (0001) c plane, encompassing nine distinct terminations. Our calculations reveal a clear energetic hierarchy with surface excess energies increasing in the order: m plane < a plane < r plane < c plane. Surface atomic relaxations are driven by the tendency to eliminate dangling bonds through either pairing or complete filling/emptying with electrons, effectively rendering the surfaces insulating. This behavior is evidenced by the formation of energy gaps between surface-bound states within the fundamental band gap region when projected onto the bulk band structure. We apply approximate quasiparticle methods such as the hybrid functional HSE06 and the shell-LDA-1/2 approach for an accurate description of the band structures. We calculate surface-dependent ionization potentials and electron affinities, and compare our findings with previous results for diamond-structure Si and Ge crystals. These results provide fundamental insights into the surface physics of hexagonal group-IV semiconductors and their potential applications in nanoelectronics.

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Phys. Rev. B 112, 195303– Published 7 November, 2025
  • Received 20 June 2025
  • Revised 8 September 2025
  • Accepted 29 September 2025
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