中文版 | English


Alternative Title
Name pinyin
CHAI Haozhi
School number
070205 凝聚态物理
Subject category of dissertation
07 理学
Mentor unit
Publication Years
Submission date
Place of Publication


Other Abstract

       Mature semiconductor processes allow the heterogeneous integration of germanium onto silicon wafers, so that the excellent optoelectronic properties of germanium can be fully utilized without increasing manufacturing costs. The special structure and growth kinetics shown in the lateral epitaxial growth of germanium on patterned silicon substrates provide new ideas for research and device fabrication in the field of optoelectronics, but the growth mechanism has not yet been well understood. Due to the complexity of the chemical vapor deposition process, it is difficult to directly observe and measure the evolutionary phenomena occurring during the growth process, so we study the growth process using the phase field method in this thesis.
       The phase field model is based on Ginzburg-Landau free energy and nonequilibrium thermodynamics, coupled with the evolution equations of the concentration field and the phase field, and solved using the finite element method. The concentration field is constructed by introducing a vertical downward germanium atomic flux in the simulation domain. We find that crystal morphology evolution is mainly controlled by the surface deposition of gas-phase atoms, and surface atom migration driven by energy minimization. The specific morphology and growth behavior are modulated by two mechanisms:
       The anisotropic-isotropic transition of growth mode is induced by the curvature of the mask, which determines the direction of atomic migration on the crystal surface. In the early stage of lateral growth, the crystal geometry is similar to that of the mask, and the atoms tend to migrate into the crystal surface sites corresponding to the mask with large curvature to reduce the surface area and surface energy. Under curvature induction, the lateral growth shows anisotropic growth mode until the growth fronts have a circular shape with the same curvature, and then the growth mode switches to isotropic way.
       The formation of the cavity is modulated by the atomic concentration on the crystal surface. In the early stage of lateral growth, there is a steady concentration gradient layer on the surface. When the growth fronts are close to each other, the atomic supply is not sufficient to maintain the uniform advancement of the growth fronts. Under the effect of geometric shielding, the lower sides of the growth fronts stop growing, while the upper sides continue growing until coalescence. This behavior of growing at different speeds leads to the formation of a cavity underneath the coalescence point. In addition, we introduce the anisotropic crystal surface energy of germanium to reproduce the inner structure of the cavity.

Other Keyword
Training classes
Enrollment Year
Year of Degree Awarded
References List

[1] RICKMAN A. The commercialization of silicon photonics[J]. Nature Photonics, 2014, 8(8): 579-582.
[2] ZHOU Z, CHEN R, LI X, et al. Development trends in silicon photonics for data centers[J]. Optical Fiber Technology, 2018, 44: 13-23.
[3] Nocerino E. The semiconductor multiplication system for photoelectrons in a vacuum silicon photomultiplier tube and related front end electronics[D]. Napoli: Università degli studi di Napoli Federico II, 2016.
[4] MICHEL J, LIU J, KIMERLING L C. High-performance Ge-on-Si photodetectors[J]. Nature Photonics, 2010, 4(8): 527-534.
[5] YUAN Y, HUANG Z, ZENG X, et al. High Responsivity Si-Ge Waveguide Avalanche Photodiodes Enhanced by Loop Reflector[J]. IEEE Journal of Selected Topics in Quantum Electronics, 2022, 28(2): 1-8.
[6] ARMAND PILON F T, NIQUET Y M, CHRETIEN J, et al. Investigation of lasing in highly strained germanium at the crossover to direct band gap[J]. Physical Review Research, 2022, 4(3): 033050.
[7] FADALY E M T, DIJKSTRA A, SUCKERT J R, et al. Direct-bandgap emission from hexagonal Ge and SiGe alloys[J]. Nature, 2020, 580(7802): 205-209.
[8] CHAISAKUL P, MARRIS-MORINI D, FRIGERIO J, et al. Integrated germanium optical interconnects on silicon substrates[J]. Nature Photonics, 2014, 8(6): 482-488.
[9] LIU J, BEALS M, POMERENE A, et al. Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators[J]. Nature Photonics, 2008, 2(7): 433-437.
[10] LIU J, SUN X, CAMACHO-AGUILERA R, et al. Ge-on-Si laser operating at room temperature[J]. Optics Letters, 2010, 35(5): 679-681.
[11] PILLARISETTY R. Academic and industry research progress in germanium nanodevices[J]. Nature, 2011, 479(7373): 324-328.
[12] XIANG J, LU W, HU Y, et al. Ge/Si nanowire heterostructures as high-performance field-effect transistors[J]. Nature, 2006, 441(7092): 489-493.
[13] DU Y, XU B, WANG G, et al. Growth of high-quality epitaxy of GaAs on Si with engineered Ge buffer using MOCVD[J]. Journal of Materials Science: Materials in Electronics, 2021, 32(5): 6425-6437.
[14] TANG T, YU T, YANG G, et al. Investigation into the InAs/GaAs quantum dot material epitaxially grown on silicon for O band lasers[J]. Journal of Semiconductors, 2022, 43(1): 012301.
[15] BOSI M, ATTOLINI G. Germanium: Epitaxy and its applications[J]. Progress in Crystal Growth and Characterization of Materials, 2010, 56(3-4): 146-174.
[16] TORIUMI A, NISHIMURA T. Germanium CMOS potential from material and process perspectives: Be more positive about germanium[J]. Japanese Journal of Applied Physics, 2018, 57(1):010101.
[17] WANG B, MU J. High-speed Si-Ge avalanche photodiodes[J]. PhotoniX, 2022, 3(1): 8.
[18] MO Y, SAVAGE D E, SWARTZENTRUBER B S, et al. Kinetic pathway in Stranski-Krastanov growth of Ge on Si(001)[J]. Physical Review Letters, 1990, 65(8): 1020-1023.
[19] SLACK G A, BARTRAM S F. Thermal expansion of some diamondlike crystals[J]. Journal of Applied Physics, 1975, 46(1): 89-98.
[20] CURRIE M T, SAMAVEDAM S B, LANGDO T A, et al. Controlling threading dislocation densities in Ge on Si using graded SiGe layers and chemical-mechanical polishing[J]. Applied Physics Letters, 1998, 72(14): 1718-1720.
[21] LUAN H-C, LIM D R, LEE K K, et al. High-quality Ge epilayers on Si with low threading-dislocation densities[J]. Applied Physics Letters, 1999, 75(19): 2909-2911.
[22] VANAMU G, DATYE A K, ZAIDI S H. Epitaxial growth of high-quality Ge films on nanostructured silicon substrates[J]. Applied Physics Letters, 2006, 88(20):204104.
[23] SEIDL J, GLUSCHKE J G, YUAN X, et al. Regaining a Spatial Dimension: Mechanically Transferrable Two-Dimensional InAs Nanofins Grown by Selective Area Epitaxy[J]. Nano Letters, 2019, 19(7): 4666-4677.
[24] KROGSTRUP P, ZIINO N L, CHANG W, et al. Epitaxy of semiconductor-superconductor nanowires[J]. Nature Materials, 2015, 14(4): 400-406.
[25] YAMAMOTO Y, ZAUMSEIL P, SCHUBERT M A, et al. Influence of annealing conditions on threading dislocation density in Ge deposited on Si by reduced pressure chemical vapor deposition[J]. Semiconductor Science and Technology, 2018, 33(12): 124007.
[26] NAYFEH A, CHUI C O, SARASWAT K C, et al. Effects of hydrogen annealing on heteroepitaxial-Ge layers on Si: Surface roughness and electrical quality[J]. Applied Physics Letters, 2004, 85(14): 2815-2817.
[27] LANGDO T A, LEITZ C W, CURRIE M T, et al. High quality Ge on Si by epitaxial necking[J]. Applied Physics Letters, 2000, 76(25): 3700-3702.
[28] PARK J S, CURTIN M, HYDRICK J M, et al. Low-Defect-Density Ge Epitaxy on Si(001) Using Aspect Ratio Trapping and Epitaxial Lateral Overgrowth[J]. Electrochemical and Solid-State Letters, 2009, 12(4): H142-H144.
[29] YAKO M, ISHIKAWA Y, WADA K. Coalescence induced dislocation reduction in selectively grown lattice-mismatched heteroepitaxy: Theoretical prediction and experimental verification[J]. Journal of Applied Physics, 2018, 123(18): 185304.
[30] FALUB C V, VON KANEL H, ISA F, et al. Scaling hetero-epitaxy from layers to three-dimensional crystals[J]. Science, 2012, 335(6074): 1330-1304.
[31] WEN R T, WANG B, MICHEL J. Unpredicted Internal Geometric Reconfiguration of an Enclosed Space Formed by Heteroepitaxy[J]. Nano Letters, 2020, 20(1): 540-545.
[32] BIN AMIN M F, MOTOMURA K, HIZAWA T, et al. Reduced threading dislocation density in a germanium epitaxial film coalesced on an arrayed silicon-on-insulator strip[J]. Japanese Journal of Applied Physics, 2022, 61(9): 095506.
[33] HE Y, WANG J, HU H, et al. Coalescence of GaAs on (001) Si nano-trenches based on three-stage epitaxial lateral overgrowth[J]. Applied Physics Letters, 2015, 106(20): 202105.
[34] YAKO M, ISHIKAWA Y, ABE E, et al. Defects and their reduction in Ge selective epitaxy and coalescence layer on Si with semicylindrical voids on SiO2 masks[J]. IEEE Journal of Selected Topics in Quantum Electronics, 2018, 24(6): 1-7.
[35] PARK J-S, BAI J, CURTIN M, et al. Facet formation and lateral overgrowth of selective Ge epitaxy on SiO2-patterned Si(001) substrates[J]. Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures, 2008, 26(1): 117-121.
[36] JULIAN N, MAGES P, ZHANG C, et al. Coalescence of InP Epitaxial Lateral Overgrowth by MOVPE with V/III Ratio Variation[J]. J Electronic Materials, 2012, 41(5): 845-852.
[37] MULLINS W W. Theory of Thermal Grooving[J]. Journal of Applied Physics, 1957, 28(3): 333-339.
[38] KHENNER M, BRAUN R J, MAUK M G. A model for isotropic crystal growth from vapor on a patterned substrate[J]. Journal of Crystal Growth, 2002, 235(1-4): 425-438.
[39] KHENNER M, BRAUN R J, MAUK M G. A model for anisotropic epitaxial lateral overgrowth[J]. Journal of Crystal Growth, 2002, 241(3): 330-346.
[40] YAKO M, KAWAI N, MIZUNO, et al. The kinetics of Ge lateral overgrowth on SiO2[J]. MRS Advances, 2015, 1(23): 1703-1708.
[41] BERGAMASCHINI R, ISA F, FALUB C V, et al. Self-aligned Ge and SiGe three-dimensional epitaxy on dense Si pillar arrays[J]. Surface Science Reports, 2013, 68(3-4): 390-417.
[42] 刘磊, 任晓敏, 周静, 等. 横向外延过生长磷化铟材料的生长速率模型[J]. 物理学报, 2007, 56(5): 3570-3576.
[43] 戴显英, 金国强, 董洁琼, 等. 锗硅硅异质结材料的化学气相淀积生长动力学模型[J]. 物理学报, 2011, 60(6): 065101.
[44] CHEN L-Q. Phase-Field Models for Microstructure Evolution[J]. Annual Review of Materials Research, 2002, 32(1): 113-140.
[45] BOETTINGER W J, WARREN J A, BECKERMANN C, et al. Phase-field simulation of solidification[J]. Annual Review of Materials Research, 2002, 32: 163-194.
[46] TONKS M R, AAGESEN L K. The Phase Field Method: Mesoscale Simulation Aiding Material Discovery[M]//CLARKE D R. Annual Review of Materials Research, Vol 49. 2019: 79-102.
[47] AMBATI M, GERASIMOV T, DE LORENZIS L. A review on phase-field models of brittle fracture and a new fast hybrid formulation[J]. Computational Mechanics, 2014, 55(2): 383-405.
[48] AMBATI M, GERASIMOV T, DE LORENZIS L. Phase-field modeling of ductile fracture[J]. Computational Mechanics, 2015, 55(5): 1017-1040.
[49] SHEN J, XU J, YANG J. The scalar auxiliary variable (SAV) approach for gradient flows[J]. Journal of Computational Physics, 2018, 353: 407-416.
[50] LOHSE D, ZHANG X. Physicochemical hydrodynamics of droplets out of equilibrium[J]. Nature Reviews Physics, 2020, 2(8): 426-443.
[51] CHENG Q, SHEN J. Multiple Scalar Auxiliary Variable (MSAV) Approach and its Application to the Phase-Field Vesicle Membrane Model[J]. SIAM Journal on Scientific Computing, 2018, 40(6): A3982-A4006.
[52] ZHANG T, WOLGEMUTH C W. A general computational framework for the dynamics of single- and multi-phase vesicles and membranes[J]. Journal of Computational Physics, 2022, 450: 110815.
[53] SALVALAGLIO M, BACKOFEN R, VOIGT A. Thin-film growth dynamics with shadowing effects by a phase-field approach[J]. Physical Review B, 2016, 94(23): 235432.
[54] SALVALAGLIO M, BACKOFEN R, BERGAMASCHINI R, et al. Faceting of Equilibrium and Metastable Nanostructures: A Phase-Field Model of Surface Diffusion Tackling Realistic Shapes[J]. Crystal Growth & Design, 2015, 15(6): 2787-2794.
[55] SALVALAGLIO M, BERGAMASCHINI R, BACKOFEN R, et al. Phase-field simulations of faceted Ge/Si-crystal arrays, merging into a suspended film[J]. Applied Surface Science, 2017, 391: 33-38.
[56] STEWART J A, SPEAROT D E. Phase-field models for simulating physical vapor deposition and grain evolution of isotropic single-phase polycrystalline thin films[J]. Computational Materials Science, 2016, 123: 111-120.
[57] STEWART J A, SPEAROT D E. Physical vapor deposition of multiphase materials with phase nucleation via a coupled phase-field approach[J]. Computational Materials Science, 2018, 143: 71-79.
[58] STEWART J A, SPEAROT D E. Phase-field simulations of microstructure evolution during physical vapor deposition of single-phase thin films[J]. Computational Materials Science, 2017, 131: 170-177.
[59] YANG S, ZHONG J, CHEN M, et al. A Parametric Three-Dimensional Phase-Field Study of the Physical Vapor Deposition Process of Metal Thin Films Aiming at Quantitative Simulations[J]. Coatings, 2019, 9(10): 607.
[60] DE DONNO M, ALBANI M, BERGAMASCHINI R, et al. Phase-field modeling of the morphological evolution of ringlike structures during growth: Thermodynamics, kinetics, and template effects[J]. Physical Review Materials, 2022, 6(2): 023401.
[61] ALBANI M, BERGAMASCHINI R, MONTALENTI F. Dynamics of pit filling in heteroepitaxy via phase-field simulations[J]. Physical Review B, 2016, 94(7): 075303.
[62] ALBANI M, GHISALBERTI L, BERGAMASCHINI R, et al. Growth kinetics and morphological analysis of homoepitaxial GaAs fins by theory and experiment[J]. Physical Review Materials, 2018, 2(9): 093404.
[63] MASULLO M, BERGAMASCHINI R, ALBANI M, et al. Growth and Coalescence of 3C-SiC on Si(111) Micro-Pillars by a Phase-Field Approach[J]. Materials, 2019, 12(19): 3223.
[64] AAGESEN L K, COLTRIN M E, HAN J, et al. Phase-field simulations of GaN growth by selective area epitaxy from complex mask geometries[J]. Journal of Applied Physics, 2015, 117(19): 194302.
[65] HAO Y, BHARATHI M S, WANG L, et al. The role of surface oxygen in the growth of large single-crystal graphene on copper[J]. Science, 2013, 342(6159): 720-723.
[66] XU X, ZHANG Z, QIU L, et al. Ultrafast growth of single-crystal graphene assisted by a continuous oxygen supply[J]. Nature Nanotechnology, 2016, 11(11): 930-935.
[67] KEBLINSKI P, MARITAN A, TOIGO F, et al. Continuum model for the growth of interfaces[J]. Physical Review E, 1996, 53(1): 759-778.
[68] SUO Z, ZHAO X, GREENE W. A nonlinear field theory of deformable dielectrics[J]. Journal of the Mechanics and Physics of Solids, 2008, 56(2): 467-486.
[69] HONG W, ZHAO X H, ZHOU J X, et al. A theory of coupled diffusion and large deformation in polymeric gels[J]. Journal of the Mechanics and Physics of Solids, 2008, 56(5): 1779-1793.
[70] LIU H, CHENG A, WANG H, et al. Time-fractional Allen–Cahn and Cahn–Hilliard phase-field models and their numerical investigation[J]. Computational & Mathematics with Applications, 2018, 76(8): 1876-1892.
[71] KIM J, JEONG D, YANG S-D, et al. A finite difference method for a conservative Allen–Cahn equation on non-flat surfaces[J]. Journal of Computational Physics, 2017, 334: 170-181.
[72] YOON S, JEONG D, LEE C, et al. Fourier-Spectral Method for the Phase-Field Equations[J]. Mathematics, 2020, 8(8): 1385.
[73] OLSHANSKII M, XU X, YUSHUTIN V. A finite element method for Allen–Cahn equation on deforming surface[J]. Computational & Mathematics with Applications, 2021, 90: 148-158.
[74] KEITA S, BELJADID A, BOURGAULT Y. Efficient second-order semi-implicit finite element method for fourth-order nonlinear diffusion equations[J]. Computer Physics Communications, 2021, 258: 107588.
[75] SIEM E J, CARTER W C. Orientation-dependent surface tension functions for surface energy minimizing calculations[J]. Journal of Materials Science, 2005, 40(12): 3107-3113.
[76] GAI Z, YANG W S, ZHAO R G, et al. Macroscopic and nanoscale faceting of germanium surfaces[J]. Physical Review B, 1999, 59(23): 15230-15239.
[77] WULFF G. XXV. Zur Frage der Geschwindigkeit des Wachsthums und der Auflösung der Krystallflächen[J]. Zeitschrift für Kristallographie - Crystalline Materials, 1901, 34(1-6): 449-530.
[78] MARKS L D, PENG L. Nanoparticle shape, thermodynamics and kinetics[J]. Journal of Physics-Condensed Matter, 2016, 28(5): 053001.
[79] STOFFEL M, RASTELLI A, TERSOFF J, et al. Local equilibrium and global relaxation of strained SiGe/Si(001) layers[J]. Physical Review B, 2006, 74(15):155326.
[80] ROBINSON J T, RASTELLI A, SCHMIDT O, et al. Global faceting behavior of strained Ge islands on Si[J]. Nanotechnology, 2009, 20(8): 085708.

Academic Degree Assessment Sub committee
Domestic book classification number
Data Source
Document TypeThesis
DepartmentDepartment of Materials Science and Engineering
Recommended Citation
GB/T 7714
柴浩智. 单晶锗横向外延生长的相场法模拟[D]. 深圳. 南方科技大学,2022.
Files in This Item:
File Name/Size DocType Version Access License
11930234-柴浩智-材料科学与工程(8163KB) Restricted Access--Fulltext Requests
Related Services
Recommend this item
Usage statistics
Export to Endnote
Export to Excel
Export to Csv
Altmetrics Score
Google Scholar
Similar articles in Google Scholar
[柴浩智]'s Articles
Baidu Scholar
Similar articles in Baidu Scholar
[柴浩智]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[柴浩智]'s Articles
Terms of Use
No data!
Social Bookmark/Share
No comment.

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.