Abstract.
Employing a phenomenological long-wavelength approach recently developed, both acoustic and optical phonons in nonpolar heterostructures are studied. Phonon modes in an arbitrary direction can be calculated without additional effort respect to high symmetry directions. A simple analytical expression for the dispersion relation in superlattices guides the physical discussion. We apply this to the calculation of phonon modes in unstrained short period isotopic Ge superlattices, in quantum wells and in strained short period Si/Ge superlattices. We find very good agreement with the results of other, more elaborated and costly calculations.
Similar content being viewed by others
References
B. Jusserand, M. Cardona, in Light Scattering in Solids V, edited by M. Cardona, G. Güntherodt (Springer-Verlag, Heidelberg, 1989)
R. Tsu, S.S. Jha, Appl. Phys. Lett. 20, 16 (1972); A.S. Barker, Jr. J.L. Merz, A.C. Gossard, Phys. Rev. B 17, 3181 (1978)
For a recent review see S. Baroni, S. de Gironcoli, A. Dal Corso, P. Giannozzi, Rev. Mod. Phys. 73, 515 (2001)
S.M. Rytov, Akust. Zh. 2, 71 (1956) [Sov. Phys. Acoust. 2, 68 (1956)]; C. Colvard, R. Merlin, M.V. Klein, A.C. Gossard, Phys. Rev. Lett. 43, 298 (1980); B. Jusserand, F. Alexandre, J. Dubard, D. Paquet, Phys. Rev. B 33, 2897 (1986); P. Santos, L. Ley, J. Mebert, O. Koblinger, Phys. Rev. B 36, 4858 (1987)
S. Tamura, J.P. Wolfe, Phys. Rev. B 35, 2528 (1987); S. Tamura, D.C. Hurley, J.P. Wolfe, Phys. Rev. B 38, 1427 (1988); and references therein
S. Mizuno, S. Tamura, Phys. Rev. B 45, 734 (1992); S. Mizuno, S. Tamura, Jpn J. Appl. Phys. 32, 2206 (1993)
E.B. Christoffel, Annu. Mater. Pura Appl. 8, 193 (1877); see also A.G. Every, Phys. Rev. Lett. 42, 1065 (1979); A.G. Every, Phys. Rev. B 22, 1746 (1980)
C. Trallero-Giner, F. García-Moliner, V.R. Velasco, M. Cardona, Phys. Rev. B 45, 11944 (1992); for a more detailed presentation see C. Trallero-Giner, R. P\’ erez-Alvarez, F. García-Moliner, Long wave polar modes in semiconductor heterostructures (Pergamon/Elsevier Science, London, 1998)
F. Comas, R. P\’ erez-Alvarez, C. Trallero-Giner, M. Cardona, Superlatt. Microstr. 14, 95 (1993); R. Pérez-Alvarez, V.R. Velasco, F. García-Moliner, Physica Scripta 51, 526 (1995)
F. de León-Pérez, R. P\’ erez-Alvarez, Phys. Rev. B 61, 4820 (2000)
F. de León Pérez, R. P\’ erez-Alvarez, Phys. Rev. B 62, 9915 (2000)
F. de León-Pérez, R. Pérez-Alvarez, Phys. Rev. B 63, 245304 (2001)
See F. García-Moliner, V.R. Velasco, Theory of Single and Multiple Interfaces (World Scientific, Singapore, 1992); V.R. Velasco, F. García-Moliner, Surf. Sci. Rep. 28, 123 (1997) and references therein
J. Spitzer, T. Ruf, M. Cardona, W. Dondl, R. Schorer, G. Abstreiter, E.E. Haller, Phys. Rev. Lett. 72, 1565 (1994); J. Spitzer, Ph.D. thesis, University of Stuttgart, 1994
S. de Gironcoli, E. Molinari, R. Shorer, G. Abstreiter, Phys. Rev. B 48, 8959 (1993); R. Shorer, G. Abstreiter, S. de Gironcoli, E. Molinari, H. Kibbel, H. Presting, Phys. Rev. B 49, 5406 (1994)
C. Trallero-Giner, F. Comas, Philosophical Magazine B 70, 583 (1994)
R. Pérez-Alvarez, F. de León-Pérez, Physica Scripta 58, 525 (1998)
R.A. Ghanbari, J.D. White, G. Fasol, C.J. Gibbings, C.G. Tupper, Phys. Rev. B 42, 7033 (1990); M.I. Alonso, M. Cardona, G. Kanellis, Solid State Commun. 69, 479 (1989)
Author information
Authors and Affiliations
Corresponding author
Additional information
Received: 21 July 2004, Published online: 5 November 2004
PACS:
63.20.Dj Phonon states and bands, normal modes, and phonon dispersion - 63.22. + m Phonons or vibrational states in low-dimensional structures and nanoscale materials - 68.65.Cd Superlattices
Rights and permissions
About this article
Cite this article
de León-Pérez, F., Pérez-Alvarez, R. Long-wavelength nonpolar phonons in semiconductor heterostructures. Eur. Phys. J. B 41, 451–456 (2004). https://doi.org/10.1140/epjb/e2004-00338-y
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2004-00338-y