J. Semicond. > Volume 41?>?Issue 6?> Article Number: 061101

A brief review of formation energies calculation of surfaces and edges in semiconductors

Chuen-Keung Sin , Jingzhao Zhang , Kinfai Tse and Junyi Zhu ,

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Abstract: To have a high quality experimental growth of crystals, understanding the equilibrium crystal shape (ECS) in different thermodynamic growth conditions is important. The factor governing the ECS is usually the absolute surface formation energies for surfaces (or edges in 2D) in different orientations. Therefore, it is necessary to obtain an accurate value of these energies in order to give a good explanation for the observation in growth experiment. Historically, there have been different approaches proposed to solve this problem. This paper is going to review these representative literatures and discuss the pitfalls and advantages of different methods.

Key words: surfacefirst principlemorphology

Abstract: To have a high quality experimental growth of crystals, understanding the equilibrium crystal shape (ECS) in different thermodynamic growth conditions is important. The factor governing the ECS is usually the absolute surface formation energies for surfaces (or edges in 2D) in different orientations. Therefore, it is necessary to obtain an accurate value of these energies in order to give a good explanation for the observation in growth experiment. Historically, there have been different approaches proposed to solve this problem. This paper is going to review these representative literatures and discuss the pitfalls and advantages of different methods.

Key words: surfacefirst principlemorphology



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Zhang J, Zhao W, Zhu J. Missing links towards understanding the equilibrium shapes of hexagonal boron nitride: algorithm, hydrogen passivation, and temperature effects. Nanoscale, 2018, 10, 17683

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Tang C, Spencer M J S, Barnard A S. Activity of ZnO polar surfaces: an insight from surface energies. Phys Chem Chem Phys, 2014, 16, 22139

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[1]

Bristowe N C, Littlewood P B, Artacho E. Surface defects and conduction in polar oxide heterostructures. J Phys B, 2011, 83, 205405

[2]

Kahwaji S, Gordon R A, Crozier E D, et al. Surfactant-mediated growth of ferromagnetic Mn-doped Si. Phys Rev B, 2013, 88, 174419

[3]

Zhang J, Zhao W, Zhu J. Missing links towards understanding the equilibrium shapes of hexagonal boron nitride: algorithm, hydrogen passivation, and temperature effects. Nanoscale, 2018, 10, 17683

[4]

Tang C, Spencer M J S, Barnard A S. Activity of ZnO polar surfaces: an insight from surface energies. Phys Chem Chem Phys, 2014, 16, 22139

[5]

Dingreville R, Qu J, Cherkaoui M. Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films. J Mech Phys Solids, 2005, 53, 1827

[6]

Gibbs J W, The collected works of J. Willard Gibbs. Longmans, Green, 1928

[7]

Wulff G. Xxv. zur frage der geschwindigkeit des wachsthums und der aufl?sung der krystallfl?chen. Zeitschrift für Kristallographie - Crystalline Materials, 1901, 34, 449

[8]

Curie M P. Sur la formation des cristaux et sur les constantes capillaires de leurs différentes faces. Bull Soc Fr Mineral, 1885, 8, 145

[9]

Li H, Geelhaar L, Riechert H, et al. Computing equilibrium shapes of wurtzite crystals: The example of GaN. Phys Rev Lett, 2015, 115, 085503

[10]

Lang N D, Kohn W. Theory of metal surfaces: Charge density and surface energy. Phys Rev B, 1970, 1, 4555

[11]

Jaccodine R J. Surface energy of germanium and silicon. J Electrochem Soc, 1963, 110, 524

[12]

Tyson W R, Miller W A. Surface free energies of solid metals: Estimation from liquid surface tension measurements. Surf Sci, 1977, 62, 267

[13]

de Boer F R, Boom R, Mattens W C M, et al. Cohesion in metals: Transition metal alloys. Elsevier Scientific Pub. Co., 1988

[14]

Bonzel H P, Emundts A. Absolute values of surface and step free energies from equilibrium crystal shapes. Phys Rev Lett, 2000, 84, 5804

[15]

Bonzel H P, Nowicki M. Absolute surface free energies of perfect low-index orientations of metals and semiconductors. Phys Rev B, 2004, 70, 245430

[16]

Niessen A K, Miedema A R, de Boer F R, et al. Enthalpies of formation of liquid and solid binary alloys based on 3d metals: IV. alloys of cobalt. Physica B+C, 1988, 151, 401

[17]

Mills K C, Su Y C. Review of surface tension data for metallic elements and alloys: Part 1-pure metals. Int Mater Rev, 2006, 51, 329

[18]

Keene B J. Review of data for the surface tension of pure metals. Int Mater Rev, 1993, 38, 157

[19]

Lee J Y, Punkkinen M, Sch?necker S, et al. The surface energy and stress of metals. Surf Sci, 2018, 674, 51

[20]

Perdew J P, Tran H Q, Smith E D. Stabilized jellium: Structureless pseudopotential model for the cohesive and surface properties of metals. Phys Rev B, 1990, 42, 11627

[21]

Skriver H L, Rosengaard N M. Surface energy and work function of elemental metals. Phys Rev B, 1992, 46, 7157

[22]

Erschbaumer H, Freeman A J, Fu C L, et al. Surface states, electronic structure and surface energy of the Ag (001) surface. Surf Sci, 1991, 243, 317

[23]

Needs R J, Mansfield M. Calculations of the surface stress tensor and surface energy of the (111) surfaces of iridium, platinum and gold. J Phys Condens Matter, 1989, 1, 41

[24]

Vitos L, Ruban A, Skriver H, et al. The surface energy of metals. Surf Sci, 1998, 411(1/2), 186

[25]

Galanakis I, Papanikolaou N, Dederichs P H. Applicability of the broken-bond rule to the surface energy of the fcc metals. Surf Sci, 2002, 511, 1

[26]

Methfessel M, Hennig D, Scheffler M. Trends of the surface relaxations, surface energies, and work functions of the 4d transition metals. Phys Rev B, 1992, 46, 4816

[27]

Rodríguez A M, Bozzolo G, Ferrante J. Multilayer relaxation and surface energies of fcc and bcc metals using equivalent crystal theory. Surf Sci, 1993, 289, 100

[28]

Tran R, Xu Z, Radhakrishnan B, et al. Surface energies of elemental crystals. Sci Data, 2016, 3, 160080

[29]

Hohenberg P, Kohn W. Inhomogeneous electron gas. Phys Rev, 1964, 136, B864

[30]

Kohn W, Sham L J. Self-consistent equations including exchange and correlation effects. Phys Rev, 1965, 140, A1133

[31]

Harrison W A. Theory of polar semiconductor surfaces. J Vac Sci Technol, 1979, 16, 1492

[32]

Tasker P W. The stability of ionic crystal surfaces. J Phys C, 1979, 12(22), 4977

[33]

Nakamura S, Mukai T, Senoh M. Candel-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes. Appl Phys Lett, 1994, 64, 1687

[34]

Nakamura S, Senoh M, Nagahama S I, et al. InGaN-based multi-quantum-well-structure laser diodes. Jpn J Appl Phys, 1996, 35, L74

[35]

Nakamura S. The roles of structural imperfections in InGaN-based blue light-emitting diodes and laser diodes. Science, 1998, 281, 956

[36]

Nakamura S, Pearton S, Fasol G. The blue laser diode: The complete story. Springer, 2000

[37]

Bagnall D M, Chen Y F, Zhu Z, et al. Optically pumped lasing of zno at room temperature. Appl Phys Lett, 1997, 70, 2230

[38]

?zgür ?, Alivov Y I, Liu C, et al. A comprehensive review of ZnO materials and devices. J Appl Phys, 2005, 99, 041301

[39]

Guo L, Ji Y L, Xu H B, et al. Regularly shaped, single-crystalline ZnO nanorods with wurtzite structure. J Am Chem Soc, 2002, 124, 14864

[40]

Liu B, Bando Y, Tang C, et al. Wurtzite-type faceted single-crystalline gan nanotubes. Appl Phys Lett, 2006, 88, 093120

[41]

Zhang Y, Zhu J. Surfactant antimony enhanced indium incorporation on ingan (000-1) surface: A dft study. J Cryst Growth, 2016, 438, 43

[42]

Feibelman P J. Static quantum-size effects in thin crystalline, simple-metal films. Phys Rev B, 1983, 27, 1991

[43]

Chetty N, Martin R M. Determination of integrals at surfaces using the bulk crystal symmetry. Phys Rev B, 1991, 44, 5568

[44]

Zhang S B, Wei S H. Surface energy and the common dangling bond rule for semiconductors. Phys Rev Lett, 2004, 92, 086102

[45]

Rempel J Y, Trout B L, Bawendi M G, et al. Properties of the CdSe (0001), (000-1), and (11-20) single crystal surfaces: Relaxation, reconstruction, and adatom and admolecule adsorption. J Phys Chem B, 2005, 109, 19320

[46]

Jenichen A, Engler C, Rauschenbach B. Comparison of wurtzite and zinc-blende GaAs surfaces as possible nanowire side walls: Dft stability calculations. Surf Sci, 2013, 613, 74

[47]

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C K Sin, J Z Zhang, K Tse, J Y Zhu, A brief review of formation energies calculation of surfaces and edges in semiconductors[J]. J. Semicond., 2020, 41(6): 061101. doi: 10.1088/1674-4926/41/6/061101.

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Manuscript received: 20 December 2019 Manuscript revised: 23 January 2020 Online: Accepted Manuscript: 27 March 2020 Uncorrected proof: 17 April 2020 Published: 01 June 2020

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