Accurate electronic and optical properties of hexagonal germanium for optoelectronic applications

Abstract

High-quality defect-free lonsdaleite Si and Ge can now be grown on hexagonal nanowire substrates. These hexagonal phases of group-IV semiconductors have been predicted to exhibit improved electronic and optical properties for optoelectronic applications. While lonsdaleite Si is a well-characterized indirect semiconductor, experimental data and reliable calculations on lonsdaleite Ge are scarce and not consistent regarding the nature of its gap. Using ab initio density-functional theory, we calculate accurate structural, electronic, and optical properties for hexagonal Ge. Given the well-known sensitivity of electronic-structure calculations for Ge to the underlying approximations, we systematically test the performance of several exchange-correlation functionals, including meta-GGA and hybrid functionals. We first validate our approach for cubic Ge, obtaining atomic geometries and band structures in excellent agreement with available experimental data. Then, the same approach is applied to predict electronic and optical properties of lonsdaleite Ge. We portray lonsdaleite Ge as a direct semiconductor with only weakly dipole-active lowest optical transitions, small band gap, huge crystalfield splitting, and strongly anisotropic effective masses. The unexpectedly small direct gap and the oscillator strengths of the lowest optical transitions are explained in terms of symmetry and back-folding of energy bands of the diamond structure.

Continuous-Wave Magneto-Optical Determination of the Carrier Lifetime in Coherent Ge1−xSnx/Ge Heterostructures

“…where E g (0) and E g (x) are the direct band gaps of Ge and Ge 1−x Sn x , respectively, f (x) is the Ge character of the Ge 1−x Sn x conduction-band edge, and τ R (0) is the radiative lifetime associated with the direct band gap in Ge. Using our theoretical model, we compute τ R (0) = 7.72 ns, which is in good agreement with the value calculated from first principles by Rödl et al [46]. Our estimate of τ R , shown in the inset in Fig.…”

“…2(b), decreases with increasing Sn content, reaching a minimum value of 19.1 ns for x = 0.05. While this estimate ignores the impact of shortrange substitutional alloy disorder on the band structure [32] and considers only zone-center transitions [46], these effects are expected to produce only minor quantitative changes to the computed τ R . This theoretical estimate does not consider phonon-assisted recombination.…”

Direct-bandgap emission from hexagonal Ge and SiGe alloys

“…As a consequence, for Hex-Ge the band folding effect results in a direct bandgap at the Γ-point with a magnitude close to 0.3 eV, as shown in the calculated band structure in Fig. 1d 14 .…”

Starke Lichtemission in hexagonalen Ge‐ und SiGe‐Halbleitern

“…Theoretische Berechnungen sagen voraus, dass Germanium in der hexagonalen Lonsdaleit‐Struktur, dem Pendant zur Wurtzit‐Struktur der für die Optoelektronik wichtigen III‐V‐ und II‐VI‐Halbleiter, ein direkter Halbleiter ist. Durch die geänderte Kristallsymmetrie geht dabei der indirekte optische Übergang im kubischen Germanium in einen direkten optischen Übergang über (Abbildung ) . Tatsächlich ist es der Gruppe von Erik Bakkers an der TU Eindhoven (Niederlande) kürzlich gelungen, nicht nur hexagonales Silizium , sondern auch hexagonales Germanium sowie hexagonale Silizium‐Germanium‐Mischkristalle (SiGe) auf Substraten von wurtzitischen Galliumphosphid‐ beziehungsweise Galliumarsenid‐Nanodrähten zu wachsen .…”

“…In Einklang mit den theoretischen Vorhersagen ist das neuartige Germanium ein direkter Halbleiter, wenn auch mit einem sehr schwachen optischen Übergang an der Bandlücke. Außerdem ist die fundamentale Bandlücke mit circa 0,3 eV im Vergleich zu kubischem Germanium, das eine Bandlücke von etwa 0,7 eV besitzt, deutlich kleiner (Abbildung ) .…”