Polar optical modes in heterostructures

Trallero‐Giner, C.; Pérez‐Álvarez, R.; Garcı́a-Moliner, F.

doi:10.1016/b978-008042694-5/50004-9

Cited by 13 publications

(33 citation statements)

References 51 publications

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“…We follow the approach to COP described in [23][24][25], where a system of coupled differential equations for the relative ion displacement u and the electric potential ϕ should be solved within each nanolayer of the considered nanostructure. The solutions obtained for each nanolayer must be matched at the corresponding interfaces, involving both mechanical and electric boundary conditions.…”

Section: Analytical Resultsmentioning

confidence: 99%

“…Within the long-wave limit, and also applying a continuum approach, a theoretically more reliable treatment was reported in Refs. [22][23][24][25]. The present work focuses on the application of this theory to the spherical QD/QW nanostructure, but we shall limit ourselves to the analysis of the so-called uncoupled modes representing polar optical oscillations of strict transversal character and mechanical nature.…”

Section: Introductionmentioning

confidence: 99%

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Transversal confined polar optical phonons in spherical quantum‐dot/quantum‐well nanostructures

Comas

Trallero‐Giner

Prado

et al. 2006

Physica Status Solidi (b)

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PACS 63. 22.+m, 73.21.La Confined polar optical phonons are studied in a spherical quantum-dot/quantum-well (QD/QW) nanostructure by using an approach that takes into account the coupling of electromechanical oscillations and is valid in the long-wave limit. This approach was developed a few years ago and provides results beyond the usually applied dielectric continuum approach (DCA), where just the electric aspect of the oscillations is considered. In the present paper we limit ourselves to the study of the so-called uncoupled modes, having a purely transversal character and not involving an electric potential. We display the dispersion curves for the frequencies considering three possible nanostructures, which show different bulk phonon curvatures near the Brillouin zone Γ-point and have been actually grown: ZnS/CdSe, CdSe/CdS and CdS/HgS. A detailed discussion of the results obtained is made, emphasizing the novelties provided by our treatment and the relevance of infrared spectroscopy in the characterization of the geometrical features of the QD/QW nanostructure.

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Section: Analytical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Transversal confined polar optical phonons in spherical quantum‐dot/quantum‐well nanostructures

Comas

Trallero‐Giner

Prado

et al. 2006

Physica Status Solidi (b)

Self Cite

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“…For both equations eigenvalues are ±k; k = ω c (n 0 + iξ 0 ) 2 − (n a sin θ) 2 for Equation (44) and…”

Section: The Anisotropic Layered Systemmentioning

confidence: 99%

“…(n e + iξ e ) 2 − (n a sin θ) 2 for Equation (45). Therefore in this case both components E 1 (z) and E 2 (z) can be calculated using a 2 × 2 associated transfer matrix as in the isotropic case.…”

Section: The Anisotropic Layered Systemmentioning

confidence: 99%

“…A wide range of physical and technological problems can be described by equations of motion that follow the Sturm-Liouville matrix equation pattern (see, for example [1,2] and [3], and citations therein). These problems includes many belonging to the elasticity theory (see for example [4]), electromagnetism [5] and other areas of classical physics.…”

Section: Introductionmentioning

confidence: 99%

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Sturm-Liouville Matrix Equation for the Study of Electromagnetic-Waves Propagation in Layered Anisotropic Media

Pernas-Salomón¹,

Pérez‐Álvarez²

2014

PIER M

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Abstract-We obtain a Sturm-Lioville matrix equation of motion (SLME) for the study of electromagnetic wave propagation in layered anisotropic structures. Conducting media were taken into account so that ohmic loss is considered. This equation can be treated using a 4 × 4 associated transfer matrix (T) in layered anisotropic structures, where the tensors: permittivity, permeability and the electric conductivity have a piecewise dependence on the coordinate perpendicular to the layered structure. We use the SLME eigenfunctions and eigenvalues to analyze qualitatively the numerical instability (Ωd problem) which potentially affects practical applications of the transfer matrix method. By means of the SLME coefficients we show analytically that T determinant value can be used to keep a check on the numerical accuracy of calculations. We derive equations to analyze wave propagation in linear layered isotropic structures. The SLME approach is applied on two typical layered structures to verify theoretical predictions and experimental results.

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SO phonons in spherical nanostructured quantum dots

Comas

Odriazola

2005

Physica Status Solidi (b)

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A theoretical model for a nanostructured spherical Quantum Dot (QD) is considered, where to a core sphere of semiconductor "1" it is added a concentric spherical layer of semiconductor "2", while this structure is assumed as imbedded in an infinite medium made of semiconductor "1". Using a long-wave continuum approach, the so-called dielectric continuum approach, we study the surface optical (SO) phonons associated with the two spherical interfaces of the nanostructure. The possible SO phonon frequencies are analyzed as a function of both the sizes of the structure and the angular momentum quantum number 1 2 … l = , , . We also calculate the electric potential provided by the SO phonons and derive an analytical expression for the electron -phonon interaction Hamiltonian. Different possible cases for semiconductors "1" and "2" are discussed, comparisons with previously published works on similar subjects are done and the experimental techniques allowing the possible determination of this kind of phonons are invoked.

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Polar optical modes in heterostructures

Cited by 13 publications

References 51 publications

Transversal confined polar optical phonons in spherical quantum‐dot/quantum‐well nanostructures

Transversal confined polar optical phonons in spherical quantum‐dot/quantum‐well nanostructures

Sturm-Liouville Matrix Equation for the Study of Electromagnetic-Waves Propagation in Layered Anisotropic Media

SO phonons in spherical nanostructured quantum dots

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