Skip to main content

Thermodynamics of Epitaxial Layer-Growth

  • Chapter
Epitaxy of Semiconductors

Part of the book series: Graduate Texts in Physics ((GTP))

  • 4469 Accesses

Abstract

Growth requires some deviation from thermodynamic equilibrium. This chapter outlines the driving force for equilibrium-near growth of a crystal in terms of macroscopic quantities. We consider a thermodynamic description for the transition of a gaseous or liquid phase to the solid phase. The initial stage of layer growth requires a nucleation process. We discuss the energy of a surface and illustrate the nucleation of a layer and the occurrence of different growth modes.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 89.95
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. K.Th. Wilke, J. Bohm, Kristallzüchtung (Harry Deutsch, Thun/Frankfurt am Main, 1999) (in German)

    Google Scholar 

  2. M. Quillec, C. Daguet, J.L. Benchimol, H. Launois, In x Ga1−x As y P1−y alloy stabilization by the InP substrate inside an unstable region in liquid phase epitaxy. Appl. Phys. Lett. 40, 325 (1982)

    Article  ADS  Google Scholar 

  3. M.J. Jou, Y.T. Cherng, H.R. Jen, G.B. Stringfellow, Organometallic vapor phase epitaxial growth of a new semiconductor alloy: GaP1−x Sb x . Appl. Phys. Lett. 52, 549 (1988)

    Article  ADS  Google Scholar 

  4. W.A. Jesser, D. Kuhlmann-Wilsdorf, On the theory of interfacial energy and strain of epitaxial overgrowths in parallel alignment on single crystal substrates. Phys. Status Solidi 19, 95 (1967)

    Article  Google Scholar 

  5. D.M. Wood, A. Zunger, Epitaxial effects on coherent phase diagrams of alloys. Phys. Rev. B 40, 4062 (1989)

    Article  ADS  Google Scholar 

  6. S.Yu. Karpov, N.I. Podolskaya, I.A. Zhmakin, A.I. Zhmakin, Statistical model of ternary group-III nitrides. Phys. Rev. B 70, 235203 (2004)

    Article  ADS  Google Scholar 

  7. S.Yu. Karpov, Suppression of phase separation in InGaN due to elastic strain. MRS Internet J. Nitride Semicond. Res. 3, 16 (1998)

    Google Scholar 

  8. W. Kossel, Zur Theorie des Kristallwachstums. Nachr. Akad. Wiss. Gött. Math.-Wiss. Kl., 135–143 (1927) (in German)

    Google Scholar 

  9. I.N. Stranski, Zur Theorie des Kristallwachstums. Z. Phys. Chem. 136, 259 (1928) (in German)

    Google Scholar 

  10. R. Shuttleworth, The surface tension of solids. Proc. Phys. Soc. A 63, 444 (1950)

    Article  ADS  Google Scholar 

  11. I.V. Markov, Crystal Growth for Beginners (World Scientific, Singapore, 1995)

    Google Scholar 

  12. J.J. Métois, J.C. Heyraud, SEM studies of equilibrium forms: roughening transition and surface melting of indium and lead crystals. Ultramicroscopy 31, 73 (1989)

    Article  Google Scholar 

  13. A.A. Stekolnikov, J. Furthmüller, F. Bechstedt, Absolute surface energies of group-IV semiconductors: dependence on orientation and reconstruction. Phys. Rev. B 65, 115318 (2002)

    Article  ADS  Google Scholar 

  14. N. Moll, A. Kley, E. Pehlke, M. Scheffler, GaAs equilibrium crystal shape from first principles. Phys. Rev. B 54, 8844 (1996)

    Article  ADS  Google Scholar 

  15. N. Moll, M. Scheffler, E. Pehlke, Influence of stress on the equilibrium shape of strained quantum dots. Phys. Rev. B 58, 4566 (1998)

    Article  ADS  Google Scholar 

  16. Q.K.K. Liu, N. Moll, M. Scheffler, E. Pehlke, Equilibrium shapes and energies of coherent strained InP islands. Phys. Rev. B 60, 17008 (1999)

    Article  ADS  Google Scholar 

  17. B. Voigtländer, M. Kawamura, N. Paul, V. Cherepanov, Formation of Si/Ge nanostructures at surfaces by self-organization. J. Phys. Condens. Matter 16, S1535 (2004)

    Article  ADS  Google Scholar 

  18. M.A.K. Zilani, Y.Y. Sun, H. Xu, L. Liu, Y.P. Feng, X.-S. Wang, A.T.S. We, Reactive Co magic cluster formation on Si(111)-7×7. Phys. Rev. B 72, 193402 (2005)

    Article  ADS  Google Scholar 

  19. W.J. Ong, E.S. Tok, Configuration dependent critical nuclei in the self assembly of magic clusters. Phys. Chem. Chem. Phys. 9, 991 (2007)

    Article  Google Scholar 

  20. U. Köhler, L. Andersohn, B. Dahlheimer, Time-resolved observation of CVD-growth of silicon on Si(111) with STM. Appl. Phys. A 57, 491 (1993)

    Article  ADS  Google Scholar 

  21. W.K. Burton, N. Cabrera, F.C. Frank, The growth of crystals and the equilibrium structure of their surface. Philos. Trans. R. Soc. Lond. A 243, 299 (1951)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. A.R. Smith, V. Ramachandran, R.M. Feenstra, D.W. Grewe, M.-S. Shin, M. Skowronski, J. Neugebauer, J.E. Northrup, Wurtzite GaN surface structures studied by scanning tunneling microscopy and reflection high energy electron diffraction. J. Vac. Sci. Technol. A 16, 1641 (1998)

    Article  ADS  Google Scholar 

  23. U. Köhler, Kristallwachstum unter dem Rastertunnelmikroskop. Phys. Bl. 51, 843 (1995) (in German)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Pohl, U.W. (2013). Thermodynamics of Epitaxial Layer-Growth. In: Epitaxy of Semiconductors. Graduate Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32970-8_4

Download citation

Publish with us

Policies and ethics