Electronic band structures of Ge1−xSnx semiconductors: A first-principles density functional theory study

Abstract

We conduct first-principles total-energy density functional calculations to study the band structures in Ge 1Àx Sn x infrared semiconductor alloys. The norm-conserving optimized pseudopotentials of Ge and Sn have been constructed for electronic structure calculations. The composition-bandgap relationships in Ge 1Àx Sn x lattices are evaluated by a detailed comparison of structural models and their electronic band structures. The critical Sn composition related to the transition from indirect-to direct-gap in Ge 1Àx Sn x alloys is estimated to be as low as x $ 0.016 determined from the parametric fit. Our results show that the crossover Sn concentration occurs at a lower critical Sn concentration than the values predicted from the absorption measurements. However, early results indicate that the reliability of the critical Sn concentration from such measurements is hard to establish, since the indirect gap absorption is much weaker than the direct gap absorption. We find that the direct band gap decreases exponentially with the Sn composition over the range 0 < x < 0:375 and the alloys become metallic for x > 0.375, in very good agreement with the theoretical observed behavior [D. W. Jenkins and J. D. Dow, Phys. Rev. B 36, 7994, 1987]. For homonuclear and heteronuclear complexes of Ge 1Àx Sn x alloys, the indirect band gap at L-pointis is found to decrease homonuclear Ge-Ge bonds or increase homonuclear Sn-Sn bonds as a result of the reduced L valley. All findings agree with previously reported experimental and theoretical results. The analysis suggests that the top of valence band exhibits the localization of bond charge and the bottom of the conduction band is composed of the Ge 4s4p and/or Sn 5s5p atomic orbits. V

Energy Gap Tuning and Carrier Dynamics in Colloidal Ge1–xSnx Quantum Dots

“…Germanium is widely used as an infrared (IR) optical material in photodetectors, thermal imaging cameras, phosphors, and light-emitting diodes. − However, the major limitation for efficient use of Ge in optical/optoelectronic applications is its indirect bandgap, which requires phonons for optical transitions. It has been shown that the band structure of Ge can be modified by alloying with Sn to reduce the energy difference of first direct and indirect transitions, and beyond a certain Sn concentration (6–20%, depending on the strain) an indirect-to-direct bandgap crossover is expected. − Ge 1– x Sn x alloy has therefore attracted significant interest for the next generation of Si-compatible electronic and photonic devices. However, incorporation of Sn (bandgap, E g = 0.08 eV) dramatically reduces the fundamental energy gap of Ge 1– x Sn x alloy deep into the mid infrared (0.35–0.80 eV for x = 0.15–0.00), limiting its potential in visible to near-infrared (NIR) optoelectronics.…”

Short-range order in GeSn alloy

“…An important question is how the identified SRO affects the properties of GeSn alloy, considering nearly all existing theoretical studies [18][19][20][21][22][23][24][25][26]28,29 were carried out either by simple arithmetic average of randomly generated simulation cells, or by SQS that matches the correlation function of a truly random alloy. To answer this question, we calculate the direct band gap of GeSn alloy, which is a key property for mid-infrared applications.…”

“…This assumption has been employed to interpret experiments, [12][13][14][15][16][17] but more crucially, constitutes the foundation for nearly all theoretical predictions of GeSn alloys. [18][19][20][21][22][23][24][25][26][27][28][29] Indeed, commonly employed modeling methods, including virtual crystal approximation (VCA), coherent-potential approximation (CPA), and special quasi-random structure (SQS), 30 are all based on this assumption.…”

Structural Characterization of Oleylamine- and Dodecanethiol-Capped Ge1–xSnx Alloy Nanocrystals

“…Band gap engineering of Ge nanocrystals (NCs) can be achieved through alloying. It has been predicted that incorporation of Sn in a cubic Ge 1– x Sn x alloy structure would result in an indirect-to-direct band gap crossover. − Incorporation of the zero-gap semiconductor Sn lowers the overall energy of the conduction band of Ge, and the energy of the Γ point ( k = 0) is predicted to decrease more rapidly than that of the L point ( k ≠ 0), making the direct band gap transition lower in energy for the alloy . Using Vegard’s law and assuming properties are linearly dependent on composition, indirect-to-direct crossover has been interpolated to occur at x = 0.22 for Ge 1– x Sn x . , Other theoretical predictions place the indirect-to-direct crossover for unstrained Ge 1– x Sn x at Sn compositions ranging from x = 0.016 to 0.17, ,,,,,− with the range of x = 0.06–0.11 being generally accepted. − Computational studies have been employed to better understand the band structure and emission properties of Ge 1– x Sn x NCs. ,,, Emission similar in energy to the absorption onset is attributed to a fundamental energy gap transition, and nonradiative decay can occur from surface trap states caused by Sn incorporation and alloy disorder. , …”