First-Principles Study of Non-Substitutional Point Defects in Germanium-Lead Alloys

doi:10.16553/j.cnki.issn1000-985x.2025.0142

Abstract

Abstract: Germanium-lead （Ge-Pb） alloys are recognized as one of the most promising silicon-compatible， high-efficiency luminescent materials. However， the attainment of high-quality alloys with elevated lead composition is significantly impeded by the pronounced tendency for lead surface segregation during crystal growth. To elucidate the underlying microscopic mechanisms of this segregation， first-principles calculations based on density functional theory （DFT） were employed. The properties of substitutional lead and non-substitutional point defects （VPbV） in Ge-Pb alloys were systematically investigated across varying lead compositions and under different doping conditions. It was found that an increase in lead composition elevates the formation energy of substitutional lead while concurrently reducing the formation energy of VPbV defects. This energetic trend indicates an enhanced propensity for lead surface segregation at higher lead concentrations. Furthermore， when the alloys are doped with hydrogen （H）， the formation energy of substitutional lead reduces relative to the undoped case， whereas the formation energy of VPbV defects increases. This modification in defect energetics demonstrates that hydrogen doping effectively suppresses lead surface segregation. These theoretical results provide a consistent explanation for the experimentally observed patterns of lead surface segregation. Consequently， this study not only offers crucial theoretical guidance for the material growth of high-quality Ge-Pb alloys but also demonstrates that the fundamental concepts and methodologies developed herein can be extended to the investigation of other group-IV alloys.

Key words: germanium-lead alloy; non-substitutional point defect; formation energy; bond energy; binding energy; density functional theory; first-principles calculation

CLC Number:

O731

JIA Mengjiang, HUANG Wenqi, WANG Hai, ZHENG Jun. First-Principles Study of Non-Substitutional Point Defects in Germanium-Lead Alloys[J]. Journal of Synthetic Crystals, 2025, 54(12): 2164-2172.

Figures/Tables 10

Fig.1 SQS-generated supercell model of Ge0.984Pb0.016. （a） Ge0.984Pb0.016 configuration schematic （gray： vacancy； red： Pb）；（b） H-doped Ge0.984Pb0.016 configuration schematic （gray： vacancy； red： Pb； pink： H）

Fig.2 Formation energy of VPbV in Ge0.984Pb0.016. （a） Comparison of VPbV formation energies across three charge states in Ge0.984Pb0.016；（b） enlarged view of the intersection region

Fig.3 Formation energies of VPbV （a） and substitutional Pb （b） in different SQS-generated models of Ge0.984Pb0.016

Fig.4 Formation energies of substitutional Pb （a） and VPbV （b） in Ge1-x Pb x

Fig.5 Bond energy of Ge—Pb （a） and binding energy of VPbV （b） in Ge1-x Pb x

Fig.6 Electron density distributions of Ge—Pb bond in Ge0.984Pb0.016 （a） and Ge0.969Pb0.031 （b）， electron density distributions of VPbV in Ge0.984Pb0.016 （c） and Ge0.969Pb0.031 （d）

Fig.7 Formation energies of monatomic H and dual H atoms in different atomic configurations of Ge0.969Pb0.031

Fig.8 Formation energies of substitutional Pb and VPbV in H-doping Ge0.969Pb0.031

Fig.9 Electron density distributions of VPbV in Ge0.969Pb0.031 without （a） and with H-doping （b）

Fig.10 Formation energy of VPbV as a function of H concentration in configuration I of Ge0.969Pb0.031

References 34

[1]	王子昊，王　霆，张建军. 硅基光电异质集成的发展与思考［J］. 中国科学院院刊， 2022， 37（3）： 360-367.
	WANG Z H， WANG T， ZHANG J J. Development and thinking of silicon photonics heterogenous integration［J］. Bulletin of Chinese Academy of Sciences， 2022， 37（3）： 360-367 （in Chinese）.
[2]	周治平，陈卫标，冯俊波，等. 硅基光电子及其前沿进展（特邀）［J］. 光学学报， 2024（1）： 0602002.
	ZHOU Z P， CHEN W B， FENG J B， et al. Silicon based optoelectronics and its frontier advances （invited）［J］.Acta Optica Sinica， 2024（1）： 0602002 （in Chinese）.
[3]	储　涛. 硅基光电子集成器件［J］. 光学与光电技术， 2019， 17（4）： 5-9.
	CHU T. Silicon-based optoelectronic integrated devices［J］. Optics & Optoelectronic Technology， 2019， 17（4）： 5-9 （in Chinese）.
[4]	孙生柳，黄文奇，张立鑫，等. 硅基Ⅳ族SiGeSn三元合金晶格结构、电子结构和光学性质的第一性原理［J］. 人工晶体学报， 2021， 50（12）： 2232-2239+2254.
	SUN S L， HUANG W Q， ZHANG L X， et al. First-principles study on lattice structure， electronic structure and optical properties of group-Ⅳ SiGeSn ternary alloy［J］. Journal of Synthetic Crystals， 2021， 50（12）： 2232-2239+2254 （in Chinese）.
[5]	朱元昊，温书育，何　力，等. 后摩尔时代硅基片上光源研究进展［J］. 微纳电子与智能制造， 2021， 3（1）： 136-149.
	ZHU Y H， WEN S Y， HE L， et al. Research progress of silicon light sources in the Post-Moore Era［J］. Micro/Nano Electronics and Intelligent Manufacturing， 2021， 3（1）： 136-149 （in Chinese）.
[6]	张　璐，柯少颖，汪建元，等. 硅基Ⅳ族材料外延生长及其发光和探测器件研究进展［J］. 中国科学：物理学力学天文学， 2021， 51（3）： 45-57.
	ZHANG L， KE S Y， WANG J Y， et al. Research progress in the epitaxial growth of silicon-based group Ⅳ materials， and their light emitters and photodetectors［J］. Scientia Sinica （Physica， Mechanica & Astronomica）， 2021， 51（3）： 45-57 （in Chinese）.
[7]	POLAK M P， SCHAROCH P， KUDRAWIEC R. The effect of isovalent doping on the electronic band structure of group IV semiconductors［J］. Journal of Physics D： Applied Physics， 2021， 54（8）： 085102.
[8]	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.
[9]	LIU X Q， ZHENG J， HUANG Q X， et al. Investigation of temperature and H₂ on GePb/Ge multiple quantum well growth［J］. Journal of Physics D： Applied Physics， 2024， 57（24）： 245108.
[10]	LIU X Q， ZHENG J， ZHOU L， et al. Growth of single crystalline GePb film on Ge substrate by magnetron sputtering epitaxy［J］. Journal of Alloys and Compounds， 2019， 785： 228-231.
[11]	SCHLIPF J， FRIEIRO J L， FISCHER I A， et al. Growth of patterned GeSn and GePb alloys by pulsed laser induced epitaxy［C］//2017 40th International Convention on Information and Communication Technology， Electronics and Microelectronics （MIPRO）. May 22-26， 2017， Opatija， Croatia. IEEE， 2017： 37-42.
[12]	MCCARTHY T T， MCMINN A M， LIU X Y， et al. Molecular beam epitaxy growth and characterization of GePb alloys［J］. Journal of Vacuum Science & Technology B， 2024， 42（3）： 032210.
[13]	YANG J Y， HU H Y， MIAO Y H. High quality morphology and high Hall mobility of GePb alloys formed by using implantation and annealing process［C］//Sixth Symposium on Novel Optoelectronic Detection Technology and Applications. December 3-5， 2019. Beijing， China. SPIE， 2020： 334.
[14]	LIU X Q， ZHENG J， ZHAO Y， et al. Germanium lead alloy on insulator grown by rapid melting growth［J］. Journal of Alloys and Compounds， 2021， 864： 158798.
[15]	LIU X Q， ZHENG J， HUANG Q X， et al. Growth and characterization of GePb/Ge multiple quantum wells［J］. Journal of Alloys and Compounds， 2023， 934： 167954.
[16]	YU J L， LIN G Y， XIA S L， et al. p-i-n photodetector with active GePb layer grown by sputtering epitaxy［J］. Applied Physics Express， 2024， 17（4）： 045501.
[17]	LIANG Y F， CHEN S D， JIN X C， et al. Group IV topological quantum alloy and the role of short-range order： the case of Ge-rich Ge_1- _x Pb _x ［J］. NPJ Computational Materials， 2024， 10： 82.
[18]	VENTURA C I， FUHR J D， BARRIO R A. Nonsubstitutional single-atom defects in the Ge_1- _x Sn _x alloy［J］. Physical Review B， 2009， 79（15）： 155202.
[19]	LONDOS C A， SGOUROU E N， CHRONEOS A. Defect engineering of the oxygen-vacancy clusters formation in electron irradiated silicon by isovalent doping： an infrared perspective［J］. Journal of Applied Physics， 2012， 112（12）： 123517.
[20]	HÖHLER H， ATODIRESEI N， SCHROEDER K， et al. Vacancy complexes with oversized impurities in Si and Ge［J］. Physical Review B， 2005， 71（3）： 035212.
[21]	FUHR J D， VENTURA C I， BARRIO R A. Formation of non-substitutional β-Sn defects in Ge_1- _x Sn _x alloys［J］. Journal of Applied Physics， 2013， 114（19）： 193508.
[22]	BARRIO R A， QUERALES FLORES J D， FUHR J D， et al. Non-substitutional Sn defects in Ge_1- _x Sn _x alloys for opto- and nanoelectronics［J］. Journal of Superconductivity and Novel Magnetism， 2013， 26（6）： 2213-2217.
[23]	DECOSTER S， COTTENIER S， WAHL U， et al. Lattice location study of ion implanted Sn and Sn-related defects in Ge［J］. Physical Review B， 2010， 81（15）： 155204.
[24]	CHRONEOS A， BRACHT H. Diffusion of n-type dopants in germanium［J］. Applied Physics Reviews， 2014， 1（1）： 011301.
[25]	ZUNGER A， WEI S H， FERREIRA L G， et al. Special quasirandom structures［J］. Physical Review Letters， 1990， 65（3）： 353-356.
[26]	WEI S， FERREIRA L G， BERNARD J E， et al. Electronic properties of random alloys： special quasirandom structures［J］. Phys Rev B Condens Matter， 1990， 42（15）： 9622-9649.
[27]	KRESSE G， FURTHMÜLLER J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set［J］. Physical Review B， 1996， 54（16）： 11169-11186.
[28]	BLÖCHL P E. Projector augmented-wave method［J］. Physical Review B， 1994， 50（24）： 17953-17979.
[29]	MONKHORST H J， PACK J D. Special points for Brillouin-zone integrations［J］. Physical Review B， 1976， 13（12）： 5188-5192.
[30]	MORENO J， SOLER J M. Optimal meshes for integrals in real- and reciprocal-space unit cells［J］. Physical Review B， 1992， 45（24）： 13891-13898.
[31]	GEE A T， HAYDEN B E， MORMICHE C， et al. The role of steps in the dynamics of hydrogen dissociation on Pt（533）［J］. The Journal of Chemical Physics， 2000， 112： 7660-7668.
[32]	CHRISTMANN K. Interaction of hydrogen with solid surfaces［J］. Surface Science Reports， 1988， 9（1/2/3）： 1-163.
[33]	CHEN Z， YUAN P， CHEN C L， et al. Balancing Pd-H interactions： thiolate-protected palladium nanoclusters for robust and rapid hydrogen gas sensing［J］. Advanced Materials， 2024， 36（51）： 2404291.
[34]	BIAN Z K， ZHANG Q K， ZHANG H M， et al. Effect of doping with M （M=Al， Pd， Ti， Ge） on the electronic structure and hydrogen diffusion behavior of amorphous silicon［J］. Computational and Theoretical Chemistry， 2024， 1242： 114915.