Surface elastic waves in superlattices: Sagittal localized and resonant modes

Boudouti, El Houssaine El; Djafari‐Rouhani, Bahram; Nougaoui, A.

doi:10.1103/physrevb.51.13801

Cited by 29 publications

(20 citation statements)

References 18 publications

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“…L i are ␦ peaks associated with surface localized modes, whereas B i and T i refer to ␦ peaks of weight ͑Ϫ1/2͒ situated at the bottom and the top of the minibands [18][19][20][21][22] given by k 1 Dϭ0 and k 1 Dϭ . One can see that the positions of the surface modes are almost the same in the first two cases.…”

Section: Discussion Of the Resultsmentioning

confidence: 99%

“…1,2 Let us mention that surface and interface elastic waves of sagittal polarization in semi-infinite SLs were studied recently. 21,22 We obtain the local and total DOS associated with the SL substrate interface from knowledge of the corresponding Green's function, which is calculated here by using the theory of interface response in composite materials. 23 In this theory, the Green function g of a composite system can be written as 23…”

Section: Model and Methods Of Calculationmentioning

confidence: 99%

“…20 This is encountered also in the case of pure elastic waves polarized in the sagittal plane. 21,22 In this article, we will discuss shear horizontal waves associated with the free surface of a semi-infinite piezoeleca͒ Author to whom correspondence should be addressed; electronic mail: boudouti@sciences.univ-oujda.ac.ma tric SL or with its interface with a piezoelectric substrate. Let us mention that surface elastic waves in piezoelectric SLs were studied before, 2,3 however, to our knowledge, the variation of the density of states associated with the free surface of piezoelectric SLs has not yet been studied.…”

Section: Introductionmentioning

confidence: 99%

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Surface and interface shear horizontal acoustic waves in piezoelectric superlattices

Bousfia

Boudouti

Bria

et al. 2000

Journal of Applied Physics

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The propagation of acoustic waves of shear horizontal polarization in infinite and semi-infinite superlattices made of two piezoelectric media is studied within a Green's function method. Localized modes induced by a free surface of the superlattice or a superlattice/substrate interface are investigated theoretically. These modes appear as well-defined peaks of the total density of states inside the minigaps of the superlattice. The spatial localization of the different modes is studied by means of the local density of states. The surface of the superlattice and the superlattice/substrate interface are considered to be either metallized or nonmetallized. We show the possibility of the existence of interface modes, which are without analogue in the case of the interface between two homogeneous media ͑the so-called Maerfeld-Tournois modes͒. We also generalize to piezoelectric superlattices a rule about the existence and number of surface states, namely when one considers two semi-infinite superlattices together obtained by the cleavage of an infinite superlattice, one always has as many localized surface modes as minigaps, for any value of the wave vector k ʈ ͑parallel to the interfaces͒. Specific applications of these results are given for CdS-ZnO superlattices with a free surface or in contact with a BeO substrate.

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Section: Discussion Of the Resultsmentioning

confidence: 99%

Section: Model and Methods Of Calculationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Surface and interface shear horizontal acoustic waves in piezoelectric superlattices

Bousfia

Boudouti

Bria

et al. 2000

Journal of Applied Physics

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“…In particular, surface localized and resonant modes have been obtained and discussed in detail [17,18,23,24]. Experimentally, Brillouin scattering was performed on finite and semi-infinite SLs deposited on a substrate to observe some of the sagittal waves (Rayleigh, Sezawa) localized at the surface of the SL [26,29].…”

Section: Introductionmentioning

confidence: 99%

Sagittal Elastic Waves at the Interface between a Superlattice and a Substrate: Theoretical Analysis of the Density of States and Reflection Coefficientsrik

Bria

Boudouti

Nougaoui

et al. 2000

phys. stat. sol. (b)

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We investigate the existence and behavior of localized and resonant acoustic modes of sagittal polarization associated with the interface between a superlattice (SL) and a substrate. These modes appear as well‐defined peaks in the density of states, either inside the minigaps or inside the bulk bands of the SL and the substrate. It is shown that the interface modes strongly depend on the acoustic impedances of the substrate. Furthermore, a phonon incident on the superlattice from a substrate is partially reflected in the substrate, therefore the amplitudes and the phases of the reflection coefficients enable us to deduce the frequency ranges of the bulk bands and the minigaps of the superlattice as well as the frequency levels of the interface resonant modes. The densities of states and reflection coefficients, which are calculated as function of the frequency ω and the wave vector k∥(parallel to the interfaces), are obtained from an analytical determination of the Green's function for the superlattice/substrate interface. Specific application of our analytical results are given for a W/Al isotropic superlattice in contact with a substrate with different acoustic impedances.

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“…[5][6][7][8][9][10][11][12][13][14] It is expected that these localized modes also have different features according to the types of frequency gaps in which the localized modes exist. However, this has not been well recognized till date.…”

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Resonance and mode conversion of phonons scattered by superlattices with inhomogeneity

Mizuno

2003

Phys. Rev. B

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For phonons propagating through superlattices, ''intermode'' Bragg reflections due to the coupling of different polarization modes can occur besides ordinary ''intramode'' Bragg reflections, and corresponding frequency gaps are classified according to the types of Bragg reflection. We demonstrate the difference between localized modes generated in different types of frequency gaps in superlattices with inhomogeneity. In particular, we show for a superlattice with a free surface, a ''perfect'' resonant reflection associated with surfacelocalized modes is realized inside frequency gaps in which intermode Bragg reflections occur. This resonance can be interpreted as resonant tunneling through a symmetric double-barrier potential. DOI: 10.1103/PhysRevB.68.193305 PACS number͑s͒: 68.65.Ϫk, 62.65.ϩk, 63.20.Ϫe The noticeable behavior of phonons in periodic superlattices ͑SL's͒ is mainly related to the appearance of frequency gaps due to Bragg reflections of phonons. 1,2 Since Bragg reflections occur essentially as a result of the interference of waves, they are also seen in the propagation of photons and electrons through periodic media. 3 In the case of phonons, there exists an inherent type of Bragg reflection in addition to ordinary Bragg reflections. 4 When phonons are injected into interfaces of a SL at an angle, three modes of propagation-one longitudinal ͑L͒ and two transverse ͑T͒-are involved in the reflection and transmission processes. This leads to coupling between the modes and mode conversion at the interface. As a result of the multiple reflection by the interfaces of the periodic SL, ''intermode'' Bragg reflections can occur besides ordinary ''intramode'' Bragg reflections. For example, incident L phonons can be Bragg reflected as T phonons, i.e., the amplitudes of the reflected T phonons add up in phase but those of the reflected L phonons are canceled out. Therefore, the corresponding frequency gaps should be classified when mode-dependent characteristics of phonon propagation are investigated.On the other hand, a lot of studies have shown that an inhomogeneity embedded in a periodic SL causes localized vibrational modes inside the frequency gaps. [5][6][7][8][9][10][11][12][13][14] It is expected that these localized modes also have different features according to the types of frequency gaps in which the localized modes exist. However, this has not been well recognized till date. In the present paper, we study theoretically the localized modes generated in the different types of frequency gaps. We examine the resonant interaction of localized modes with acoustic phonons injected into SL's with inhomogeneity at an angle. We calculate the reflectance of phonons scattered by SL's with a free surface or defect layer. In particular, we show for the SL with a free surface that a ''perfect'' resonant reflection is realized inside the frequency gaps in which intermode Bragg reflections occur.First of all, we briefly summarize the features of phonons propagating through a periodic SL without inhomogeneity a...

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Surface elastic waves in superlattices: Sagittal localized and resonant modes

Cited by 29 publications

References 18 publications

Surface and interface shear horizontal acoustic waves in piezoelectric superlattices

Surface and interface shear horizontal acoustic waves in piezoelectric superlattices

Sagittal Elastic Waves at the Interface between a Superlattice and a Substrate: Theoretical Analysis of the Density of States and Reflection Coefficientsrik

Resonance and mode conversion of phonons scattered by superlattices with inhomogeneity

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