Theory of surface and interface transverse elastic waves in {ital N}-layer superlattices

Journal Article · Fri Nov 01 04:00:00 EST 1996 · Physical Review, B: Condensed Matter

DOI:https://doi.org/10.1103/PhysRevB.54.14728· OSTI ID:402433

El Boudouti, E H ^[1]; Djafari-Rouhani, B; Akjouj, A; Dobrzynski, L ^[1]

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1. Laboratoire de Dynamique et Structure des Materiaux Moleculaires, Centre National de la Recherche Scientifique (URA 801), Universite des Sciences et Technologies de Lille, UFR de Physique, F-59655 Villeneuve d`Ascq Cedex (France)

{ital N}-layer superlattices are formed out of a periodic repetition of {ital N} different slabs. Such materials for {ital N}=3 and 4 are now easily grown by molecular-beam epitaxy. We present closed form expressions for localized and resonant transverse elastic waves associated with the surface of a semi-infinite {ital N}-layer superlattice, with or without a cap layer, and in contact either with vacuum or with a homogeneous substrate. We also calculate the corresponding Green{close_quote}s- function and densities of states. These general results are illustrated by a few applications to four-layer superlattices made of Nb-Fe-Nb-Cu and Nb-Cu-Nb-Cu. We show that increasing the number of the layers in each unit cell of the superlattice increases, in general, the number of the minigaps and surface modes. We generalize some of the results obtained previously in the case of two-layer superlattices, namely, (i) the creation from an infinite superlattice of a free surface gives rise to {delta} peaks of weight ({minus}1/4) in the density of states, at the edges of the superlattice bulk bands; (ii) by considering together the two complementary semi-infinite superlattices obtained by cleavage of an infinite superlattice along a plane parallel to the interfaces, one always has as many localized surface modes as minigaps, for any value of the wave vector {bold k}{sub {parallel}} (parallel to the interfaces). Finally, we investigate the localized and resonant modes associated with the presence of a cap layer on top of the superlattice. {copyright} {ital 1996 The American Physical Society.}

• OSTI ID: 402433
• Journal Information: Physical Review, B: Condensed Matter, Journal Name: Physical Review, B: Condensed Matter Journal Issue: 20 Vol. 54; ISSN PRBMDO; ISSN 0163-1829
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
COPPER
ELASTICITY
ENERGY GAP
ENERGY-LEVEL DENSITY
GREEN FUNCTION
IRON
LOCALIZED STATES
NIOBIUM
SUPERLATTICES
WAVE PROPAGATION