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

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

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

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

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

[6]

[7] G Wulff. Xxv. zur frage der geschwindigkeit des wachsthums und der auflösung der krystallflächen. Zeitschrift für Kristallographie - Crystalline Materials, 34, 449(1901).

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

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

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

[11] R J Jaccodine. Surface energy of germanium and silicon. J Electrochem Soc, 110, 524(1963).

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

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

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

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

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

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

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

[19] J Y Lee, M Punkkinen, S Schönecker et al. The surface energy and stress of metals. Surf Sci, 674, 51(2018).

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

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

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

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

[24] L Vitos, A Ruban, H Skriver et al. The surface energy of metals. Surf Sci, 411, 186(1998).

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

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

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

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

[29] P Hohenberg, W Kohn. Inhomogeneous electron gas. Phys Rev, 136, B864(1964).

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

[31] W A Harrison. Theory of polar semiconductor surfaces. J Vac Sci Technol, 16, 1492(1979).

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

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

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

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

[36] S Nakamura, S Pearton, G Fasol. The blue laser diode: The complete story. Springer(2000).

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

[38] Ü Özgür, Y I Alivov, C Liu et al. A comprehensive review of ZnO materials and devices. J Appl Phys, 99, 041301(2005).

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

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

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

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

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

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

[45] J Y Rempel, B L Trout, M G Bawendi 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, 109, 19320(2005).

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

[47] Y Zhang, J Zhang, K Tse et al. Pseudo-hydrogen passivation: A novel way to calculate absolute surface energy of zinc blende (111)/(-1-1-1) surface. Sci Rep, 6, 20055(2016).

[48] Y Zhang, J Zhang, J Zhu. Stability of wurtzite semipolar surfaces: Algorithms and practices. Phys Rev Mater, 2, 073401(2018).

[49] Y Seta, T Akiyama, A M Pradipto et al. Absolute surface energies of semipolar planes of aln during metalorganicvapor phase epitaxy growth. J Cryst Growth, 510, 7(2019).

[50] R Mukherjee, S Bhowmick. Edge stabilities of hexagonal boron nitride nanoribbons: A first-principles study. J Chem Theory Comput, 7, 720(2011).

[51] D Cao, T Shen, P Liang et al. Role of chemical potential in flake shape and edge properties of monolayer MoS₂. J Phys Chem C, 119, 4294(2015).

[52] K Rapcewicz, B Chen, B Yakobson et al. Consistent methodology for calculating surface and interface energies. Phys Rev B, 57, 7281(1998).

[53] K Shiraishi. A new slab model approach for electronic structure calculation of polar semiconductor surface. J Phys Soc Jpn, 59, 3455(1990).

[54] N Chetty, R M Martin. First-principles energy density and its applications to selected polar surfaces. Phys Rev B, 45, 6074(1992).

[55] J A Appelbaum, G A Baraff, D R Hamann. GaAs(100): Its spectrum, effective charge, and reconstruction patterns. Phys Rev B, 14, 1623(1976).

[56] N Chetty, R M Martin. GaAs (111) and (1’-.2m”.3m’ ’.2m”-.3m’ 1’-.2m”.3m’ ’.2m”-.3m’ 1’-.2m”.3m’ ’.2m”-.3m’) surfaces and the GaAs/AlAs (111) heterojunction studied using a local energy density. Phys Rev B, 45, 6089(1992).

[57] N Moll, A Kley, E Pehlke et al. GaAs equilibrium crystal shape from first principles. Phys Rev B, 54, 8844(1996).

[58] L Manna, R Wang et al. First-principles modeling of unpassivated and surfactant-passivated bulk facets of wurtzite CdSe: A model system for studying the anisotropic growth of CdSe nanocrystals. J Phys Chem B, 109, 6183(2005).

[59] C E Dreyer, A Janotti, C G Van de Walle. Absolute surface energies of polar and nonpolar planes of GaN. Phys Rev B, 89, 081305(2014).

[60] J Zhang, Y Zhang, K Tse et al. New approaches for calculating absolute surface energies of wurtzite (0001)/(000-1): A study of ZnO and GaN. J Appl Phys, 119, 205302(2016).

[61] J Zhang, Y Zhang, K Tse et al. Hydrogen-surfactant-assisted coherent growth of GaN on ZnO substrate. Phys Rev Mater, 2, 013403(2018).

[62] T Akiyama, H Nakane, K Nakamura et al. Effective approach for accurately calculating individual energy of polar heterojunction interfaces. Phys Rev B, 94, 115302(2016).

[63] J V Pezold, P D Bristowe. Atomic structure and electronic properties of the GaN/ZnO (0001) interface. J Mater Sci, 40, 3051(2005).

[64] A B Yankovich, B Puchala, F Wang et al. Stable p-type conduction from Sb-decorated head-to-head basal plane inversion domain boundaries in ZnO nanowires. Nano Lett, 12, 1311(2012).

[65] M Wong, K Tse, J Zhu. New types of CZTS3112 grain boundaries: Algorithms to passivation. J Phys Chem C, 122, 7759(2018).

[66] X Dai, Y Deng, X Peng et al. Quantum-dot light-emitting diodes for large-area displays: Towards the dawn of commercialization. Adv Mater, 29, 1607022(2017).

[67] E Jang, S Jun, H Jang et al. White-light-emitting diodes with quantum dot color converters for display backlights. Adv Mater, 22, 3076(2010).

[68] H Masui, S Nakamura, S P DenBaars et al. Nonpolar and semipolar III-nitride light-emitting diodes: Achievements and challenges. IEEE Trans Electron Devices, 57, 88(2010).

[69] I Ho, G B Stringfellow. Solid phase immiscibility in GaInN. Appl Phys Lett, 69, 2701(1996).

[70] T Matsuoka. Unstable mixing region in wurtzite In_1–x–yGa_xAl_yN. J Cryst Growth, 189–190, 19(1998).

[71] A Koukitu, Y Kumagai. Thermodynamic analysis of group III nitrides grown by metal-organic vapour-phase epitaxy (MOVPE), hydride (or halide) vapour-phase epitaxy (HVPE) and molecular beam epitaxy (MBE). J Phys Condens Matter, 13, 32(2001).

[72] M Funato, M Ueda, Y Kawakami et al. Blue, green, and amber InGaN/GaN light-emitting diodes on semipolar {11-22} GaN bulk substrates. Jpn J Appl Phys, 45, 24(2006).

[73] T Wunderer, P Brückner, B Neubert et al. Bright semipolar GaInN/GaN blue light emitting diode on side facets of selectively grown GaN stripes. Appl Phys Lett, 89, 041121(2006).

[74] H Sato, R B Chung, H Hirasawa et al. Optical properties of yellow light-emitting diodes grown on semipolar (11-22) bulk GaN substrates. Appl Phys Lett, 92, 221110(2008).

[75] J E Northrup. GaN and InGaN (11-22) surfaces: Group-III adlayers and indium incorporation. Appl Phys Lett, 95, 133107(2009).

[76] Y Zhao, Q Yan, C Y Huang et al. Indium incorporation and emission properties of nonpolar and semipolar InGaN quantum wells. Appl Phys Lett, 100, 201108(2012).

[77] M Monavarian, S Metzner, N Izyumskaya et al. Indium-incorporation efficiency in semipolar (11-22) oriented InGaN-based light emitting diodes. SPIE OPTO, 9363, 2P(2015).

[78] R Bhat, G M Guryanov. Experimental study of the orientation dependence of indium incorporation in GaInN. J Cryst Growth, 433, 7(2016).

[79] T Wang. Topical review: Development of overgrown semi-polar GaN for high efficiency green/yellow emission. Semicond Sci Technol, 31, 093003(2016).

[80] T Takeuchi, H Amano, I Akasaki. Theoretical study of orientation dependence of piezoelectric effects in wurtzite strained GaInN/GaN heterostructures and quantum wells. Jpn J Appl Phys, 39, 413(2000).

[81] D A B Miller, D S Chemla, T C Damen et al. Band-edge electroabsorption in quantum well structures: The quantum-confined stark effect. Phys Rev Lett, 53, 2173(1984).

[82] T Takeuchi, S Sota, M Katsuragawa et al. Quantum-confined stark effect due to piezoelectric fields in GaInN strained quantum wells. Jpn J Appl Phys, 36, L382(1997).

[83] T J Baker, B A Haskell, F Wu et al. Characterization of planar semipolar gallium nitride films on spinel substrates. Jpn J Appl Phys, 44, L920(2005).

[84] C Herring. Some theorems on the free energies of crystal surfaces. Phys Rev, 82, 87(1951).

[85] D Du, D J Srolovitz, M E Coltrin et al. Systematic prediction of kinetically limited crystal growth morphologies. Phys Rev Lett, 95, 155503(2005).

[86] Y Enya, Y Yoshizumi, T Kyono et al. 531 nm green lasing of ingan based laser diodes on semi-polar 20-21 free-standing GaN substrates. Appl Phys Express, 2, 082101(2009).

[87] C Liu, A Šatka, L J Krishnan et al. Light emission from InGaN quantum wells grown on the facets of closely spaced GaN nano-pyramids formed by nano-imprinting. Appl Phys Express, 2, 121002(2009).

[88] W Bergbauer, M Strassburg, C Kölper et al. Continuous-flux movpe growth of position-controlled N-face GaN nanorods and embedded ingan quantum wells. Nanotechnology, 21, 305201(2010).

[89] B Leung, Q Sun, C D Yerino et al. Using the kinetic wulff plot to design and control nonpolar and semipolar GaN heteroepitaxy. Semicond Sci Technol, 27, 024005(2012).

[90] Y H Ko, J Song, B Leung et al. Multi-color broadband visible light source via GaN hexagonal annular structure. Sci Rep, 4, 5514(2014).

[91] B Foltynski, N Garro, M Vallo et al. The controlled growth of GaN microrods on Si (111) substrates by MOCVD. J Cryst Growth, 414, 200(2015).

[92] V Jindal, F Shahedipour-Sandvik. Theoretical prediction of GaN nanostructure equilibrium and nonequilibrium shapes. J Appl Phys, 106, 083115(2009).

[93] M Mandl, X Wang, T Schimpke et al. Group III nitride core-shell nano- and microrods for optoelectronic applications. Phys Status Solidi RRL, 7, 800(2013).

[94] M D Pashley. Electron counting model and its application to island structures on molecular-beam epitaxy grown GaAs (001) and ZnSe (001). Phys Rev B, 40, 10481(1989).

[95] A Kusaba, Y Kangawa, P Kempisty et al. Thermodynamic analysis of (0001) and (000-1) GaN metalorganic vapor phase epitaxy. Jpn J Appl Phys, 56, 070304(2017).

[96] T Akiyama, Y Seta, K Nakamura et al. Modified approach for calculating individual energies of polar and semipolar surfaces of group-III nitrides. Phys Rev Mater, 3, 023401(2019).

[97] X Zhang, J Xin, F Ding. The edges of graphene. Nanoscale, 5, 2556(2019).

[98] V I Artyukhov, Y Liu, B I Yakobson. Equilibrium at the edge and atomistic mechanisms of graphene growth. Proc Natl Acad Sci USA, 109, 15136(2012).

[99] C K Gan, D J Srolovitz. First-principles study of graphene edge properties and flake shapes. Phys Rev B, 81, 125445(2010).

[100] V I Artyukhov, Y Hao, R S Ruoff et al. Breaking of symmetry in graphene growth on metal substrates. Phys Rev Lett, 114, 115502(2015).

[101] S Okada. Energetics of nanoscale graphene ribbons: Edge geometries and electronic structures. Phys Rev B, 77, 041408(2008).

[102] K S Novoselov, A Mishchenko, A Carvalho et al. 2D materials and van der waals heterostructures. Science, 353, aac9439(2016).

[103] Y Stehle, H M Meyer, R R Unocic et al. Synthesis of hexagonal boron nitride monolayer: Control of nucleation and crystal morphology. Chem Mater, 27, 8041(2015).

[104] S Y Yang, G W Shim, S B Seo et al. Effective shape-controlled growth of monolayer MoS₂ flakes by powderbased chemical vapor deposition. Nano Res, 10, 255(2017).

[105] Y Chen, P Cui, X Ren et al. Fabrication of MoSe₂ nanoribbons via an unusual morphological phase transition. Nat Commun, 8, 15135(2017).

[106] J Li, Z Hu, Y Yi et al. Hexagonal boron nitride growth on Cu–Si alloy: Morphologies and large domains. Small, 15, 1805188(2019).

[107] Y Liu, S Bhowmick, B I Yakobson. Bn white graphene with ”colorful” edges: The energies and morphology. Nano Lett, 11, 3113(2011).

[108] E Machlin. Aspects of thermodynamics and kinetics relevant to materials science. Elsevier Science(2007).

[109] K Tse, M Wong, Y Zhang et al. Defect properties of Na and K in Cu₂ZnSnS₄ from hybrid functional calculation. J Appl Phys, 124, 165701(2018).

[110] J Gao, J Yip, J Zhao et al. Graphene nucleation on transition metal surface: Structure transformation and role of the metal step edge. J Am Chem Soc, 133, 5009(2011).

[111] J Coraux, A T N’Diaye, M Engler et al. Growth of graphene on Ir (111). New J Phys, 11, 039801(2009).

[112] X Song. Chemical vapor deposition growth of large-scale hexagonal boron nitride with controllable orientation. Nano Res, 8, 3164(2015).

[113] B Huang, H Lee, B L Gu et al. Edge stability of boron nitride nanoribbons and its application in designing hybrid bnc structures. Nano Res, 5, 62(2012).

[114] A Du, Y Chen, Z Zhu et al. Dots versus antidots: Computational exploration of structure, magnetism, and half metallicity in boron-nitride nanostructures. J Am Chem Soc, 131, 17354(2009).

[115] der Zande A M Van, P Y Huang, D A Chenet et al. Grains and grain boundaries in highly crystalline monolayer molybdenum disulphide. Nat Mater, 12, 554(2013).

[116] J V Lauritsena, M V Bollinger, E Lægsgaarda et al. Atomic-scale insight into structure and morphology changes of MoS₂ nanoclusters in hydrotreating catalysts. J Catal, 221, 510(2004).

[117] I Barin. Thermochemical data of pure substances. Wiley-VCH Verlag GmbH(2008).