[6] [6] WIRTHS S, GEIGER R, VON DEN DRIESCH N, et al. Lasing in direct-bandgap GeSn alloy grown on Si［J］. Nature Photonics, 2015, 9(2): 88-92.

[8] [8] HUSSAIN A M, WEHBE N, HUSSAIN M M. SiSn diodes: theoretical analysis and experimental verification［J］. Applied Physics Letters, 2015, 107(8): 082111.

[9] [9] THAI Q M, CHRETIEN J, BERTRAND M, et al. GeSn optical gain and lasing characteristics modelling［J］. Physical Review B, 2020, 102(15): 155203.

[10] [10] TRAN T T, HUDSPETH Q, LIU Y N, et al. Ion beam synthesis and photoluminescence study of supersaturated fully-relaxed Ge-Sn alloys［J］. Materials Science and Engineering: B, 2020, 262: 114702.

[11] [11] KONDRATENKO S V, DERENKO S S, MAZUR Y I, et al. Impact of defects on photoexcited carrier relaxation dynamics in GeSn thin films［J］. Journal of Physics Condensed Matter, 2020, 33(6): 065702.

[12] [12] LIN C Y, HUANG C H, HUANG S H, et al. Photoluminescence and electroluminescence from Ge/strained GeSn/Ge quantum wells［J］. Applied Physics Letters, 2016, 109(9): 091103.

[13] [13] TONKIKH A A, EISENSCHMIDT C, TALALAEV V G, et al. Pseudomorphic GeSn/Ge(001) quantum wells: examining indirect band gap bowing［J］. Applied Physics Letters, 2013, 103(3): 032106.

[14] [14] LAN H S, LIU C W. Band alignments at strained Ge1-x Snx/relaxed Ge1-y Sny heterointerfaces［J］. Journal of Physics D: Applied Physics, 2017, 50(13): 13LT02.

[15] [15] HUANG W Q, CHENG B W, XUE C L, et al. Comparative studies of band structures for biaxial (100)-, (110)-, and (111)-strained GeSn: a first-principles calculation with GGA+U approach［J］. Journal of Applied Physics, 2015, 118(16): 165704.

[17] [17] HUANG W Q, CHENG B W, XUE C L, et al. The band structure and optical gain of a new Ⅳ-group alloy GePb: a first-principles calculation［J］. Journal of Alloys and Compounds, 2017, 701: 816-821.

[18] [18] HUANG W Q, YANG H, CHENG B W, et al. Theoretical study of the bandgap regulation of a two-dimensional GeSn alloy under biaxial strain and uniaxial strain along the armchair direction［J］. Physical Chemistry Chemical Physics, 2018, 20(36): 23344-23351.

[19] [19] PENG L Z, LI X L, ZHENG J, et al. Room-temperature direct-bandgap electroluminescence from type-I GeSn/SiGeSn multiple quantum wells for 2 μm LEDs［J］. Journal of Luminescence, 2020, 228: 117539.

[20] [20] PENG L Z, LI X L, LIU Z, et al. Horizontal GeSn/Ge multi-quantum-well ridge waveguide LEDs on silicon substrates［J］. Photonics Research, 2020, 8(6): 899-903.

[21] [21] VON DEN DRIESCH N, STANGE D, RAINKO D, et al. Epitaxy of Si-Ge-Sn-based heterostructures for CMOS-integratable light emitters［J］. Solid-State Electronics, 2019, 155: 139-143.

[22] [22] MOONTRAGOON P, SOREF R A, IKONIC Z. The direct and indirect bandgaps of unstrained SixGe1-x-ySny and their photonic device applications［J］. Journal of Applied Physics, 2012, 112(7): 073106.

[23] [23] MOONTRAGOON P, PENGPIT P, BURINPRAKHON T, et al. Electronic properties calculation of Ge1-x-ySixSny ternary alloy and nanostructure［J］. Journal of Non-Crystalline Solids, 2012, 358(17): 2096-2098.

[24] [24] ZHAO C Z, SUN S Y, ZHU M M, et al. First-principle calculation of the band structure of Ge1-xSnx alloy by screened-exchange local-density approximation theory［J］. Applied Physics A, 2020, 126(2): 1-6.

[25] [25] GHOSH G, VAN DE WALLE A, ASTA M. First-principles calculations of the structural and thermodynamic properties of bcc, fcc and hcp solid solutions in the Al-TM (TM=Ti, Zr and Hf) systems: a comparison of cluster expansion and supercell methods［J］. Acta Materialia, 2008, 56(13): 3202-3221.

[26] [26] BEZI JAVAN M. First principles study of the electronic and optical properties of GaAs nanoparticles under the influence of external uniform electric field［J］. Physics Letters A, 2012, 376(45): 3241-3247.

[27] [27] CHOI J H, NA K D, LEE S C, et al. First-principles study on the formation of a vacancy in Ge under biaxial compressive strain［J］. Thin Solid Films, 2010, 518(22): 6373-6377.

[28] [28] HOSHINA Y, IWASAKI K, YAMADA A, et al. First-principles analysis of indirect-to-direct band gap transition of Ge under tensile strain［J］. Japanese Journal of Applied Physics, 2009, 48(4): 04C125.

[30] [30] XU K, LIAO N B. The structural characteristics and electrical of MoS2 and MoS2/graphene: a first-principles study［J］. IOP Conference Series: Earth and Environmental Science, 2021, 675(1): 012198.

[31] [31] YAAKOB M K, ZULKAFLI N M A, KASIM M F, et al. Structural phase instability, mixed-phase, and energy band gap change in BiFeO3 under lattice strain effect from first-principles investigation［J］. Ceramics International, 2021, 47(9): 12592-12599.

[32] [32] RANJAN R, PAREEK P, PANDEY S K, et al. Investigation of GeSn/SiGeSn nanostructured layer for sensors in mid-infrared application［C］//SPIE Photonics Europe. Proc SPIE 11345, Nanophotonics Ⅷ, Online Only. 2020, 1134: 247-252.

[33] [33] DU W, THAI Q M, CHRTIEN J, et al. Study of Si-based GeSn optically pumped lasers with micro-disk and ridge waveguide structures［J］. Frontiers in Physics, 2019, 7: 147. DOI: 10.3389/fphy.2019.00147.

[34] [34] Van De WALLE A, TIWARY P, JONG M D, et al. Efficient stochastic generation of special quasirandom structures［J］. Calphad, 2013, 42: 13-18.

[35] [35] SANG P P, WANG Q W, WEI W, et al. Semiconducting silicene: a two-dimensional silicon allotrope with hybrid honeycomb-kagome lattice［J］. ACS Materials Letters, 2021, 3(8): 1181-1188.

[36] [36] HUANG W Q, CHENG B W, XUE C L, et al. Comparative studies of clustering effect, electronic and optical properties for GePb and GeSn alloys with low Pb and Sn concentration［J］. Physica B: Condensed Matter, 2014, 443: 43-48.

[37] [37] MADELUNG O. Semiconductors: data handbook［M］. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004.

[38] [38] ADACHI S. Properties of group-Ⅳ, Ⅲ-V and Ⅱ-Ⅵ semiconductors［M］. Chichester, UK: John Wiley & Sons, Ltd, 2005.