POLAR VIBRATION SPECTRA OF INTERFACE AND SURFACE OPTICAL PHONONS AND THEIR FRÖHLICH ELECTRON-PHONON INTERACTIONS IN FREESTANDING SYMMETRICAL AND ASYMMETRICAL WURTZITEGaN/Ga1-xAlxNMULTI-LAYER HETEROSTRUCTURES

2006 ◽  
Vol 20 (05) ◽  
pp. 559-578 ◽  
Author(s):  
LI ZHANG ◽  
JUN-JIE SHI
Keyword(s):  
Quantum Wells ◽  
Electrostatic Potential ◽  
Uniaxial Crystal ◽  
Wave Number ◽  
Phonon Modes ◽  
Electron Phonon Interaction ◽  
Surface Optical ◽  
Electron Phonon Coupling ◽  
Crystal Model ◽  
Dielectric Continuum

Under the dielectric continuum model and Loudon's uniaxial crystal model, by adopting the transfer matrix method, the dispersion properties of the interface optical (IO) and surface optical (SO) phonon modes and their couplings with electrons in multi-layer coupling wurtzite quantum wells (QWs) are deduced and analyzed via the method of electrostatic potential expanding. Numerical calculations on a freestanding symmetrical wurtzite QW and an asymmetrical wurtzite QW have been performed. Results reveal that, in general, there are four branches of IO and two branches of SO phonon modes in the systems. The dispersions of these IO and SO phonon modes are obvious only when the free two-dimensional phonon wave number ktparallel to the heterostructure interfaces is small. The degenerating behavior for these phonon modes has been clearly observed for small kt. When ktis relatively large, with the increase in kt, the frequencies of the IO and SO phonon modes converge to some definite limiting frequencies in corresponding wurtzite single planar heterostructure. This feature have been analyzed in depth from the mathematical and physical viewpoints. The calculations of electron-phonon coupling function show that, the electrostatic potential distribution of the IO and SO mode in freestanding symmetrical wurtzite QW is either symmetrical or is antisymmetrical; but that in freestanding asymmetrical wurtzite QW is neither symmetrical nor is antisymmetric. The calculation also shows that the SO modes and the short wavelength phonon modes play a more important role in the electron-phonon interaction.

POLAR INTERFACE-OPTICAL VIBRATIONAL SPECTRA IN A WURTZITE GaN/AlN RECTANGULAR QUANTUM WIRE

2006 ◽  
Vol 13 (01) ◽  
pp. 75-80 ◽  
Author(s):  
L. ZHANG
Keyword(s):  
Quantum Wells ◽  
Quantum Wire ◽  
Quantum Wires ◽  
Uniaxial Crystal ◽  
Wave Number ◽  
Phonon Modes ◽  
Crystal Model ◽  
Limited Frequency ◽  
Dielectric Continuum ◽  
Dielectric Continuum Model

Under the dielectric continuum model and Loudon's uniaxial crystal model, the interface optical (IO) phonon modes in a quasi-one-dimensional (Q1D) wurtzite rectangular quantum wire are deduced and analyzed. Numerical calculation on a wurtzite GaN/AlN rectangular wurtzite quantum wire was performed. Results reveal that the dispersion frequencies of IO modes sensitively depend on the geometric structures of the Q1D wurtzite rectangular quantum wires. The degenerating behavior of the IO phonon modes in the Q1D wurtzite rectangular quantum wire has been clearly observed for small free wave number kz in z-direction. The limited frequency behaviors of IO modes have been analyzed deeply, and detailed comparisons with those in wurtzite planar quantum wells and cylindrical quantum wires are also done. Moreover, once the anisotropy of the wurtzite material has been ignored, the present theories can be naturally reduced to the situation of Q1D cubic rectangular quantum wire systems.

DISPERSION OF INTERFACE OPTICAL PHONONS AND THEIR COUPLING WITH ELECTRONS IN ASYMMETRICAL WURTZITEGaN/Ga1-xAlxNQUANTUM WELLS

2005 ◽  
Vol 12 (03) ◽  
pp. 433-442
Author(s):  
LI ZHANG ◽  
SONG GAO ◽  
JUN-JIE SHI
Keyword(s):  
Frequency Dispersion ◽  
Uniaxial Crystal ◽  
Phonon Modes ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Electron Phonon Coupling ◽  
Crystal Model ◽  
Physical Reasons ◽  
Dielectric Continuum ◽  
Dielectric Continuum Model

Within the framework of the dielectric continuum model and Loudon's uniaxial crystal model, the properties of frequency dispersion of the interface optical (IO) phonon modes and the coupling functions of electron–IO-phonon interaction in an asymmetrical wurtzite quantum well (QW) are deduced and analyzed via the method of electrostatic potential expansion. Numerical results reveal that in general, there are four branches of IO phonon modes in the systems. The dispersions of the four branches of IO phonon modes are obvious only when the free wavenumber ktin xy plane is small. The degenerating behavior of all the four branches of IO phonon modes in the asymmetric wurtzite QWs has been clearly observed for small kt. When ktis relatively large, with the increase of kt, the frequencies of the IO phonon modes converge to the four definite limiting frequencies in the corresponding wurtzite single planar heterostructure. This feature is obviously different from that in symmetric wurtzite QW, and the mathematical and physical reasons have been analyzed in depth. The calculations of electron–phonon coupling function show that the electrostatic distribution of the IO modes is neither symmetrical nor antisymmetrical, and the high-frequency IO phonon branches and the short-wavelength IO phonon modes play a more important role in the electron–phonon interaction.

SIZE AND DIELECTRIC DEPENDENCE OF INTERFACE AND SURFACE OPTICAL PHONONS SPECTRA IN WURTZITE GaN/AlN QUANTUM WELL WIRES

2006 ◽  
Vol 20 (28) ◽  
pp. 1809-1824 ◽  
Author(s):  
LI ZHANG
Keyword(s):  
Quantum Well ◽  
Electrostatic Potential ◽  
Low Frequency ◽  
Detailed Comparison ◽  
Uniaxial Crystal ◽  
Dielectric Constants ◽  
Phonon Modes ◽  
Electron Phonon Interaction ◽  
Surface Optical ◽  
Quantum Well Wire

By employing the method of electrostatic potential expansion, the interface optical (IO) and surface optical (SO) phonon modes and the corresponding Fröhlich-like electron-phonon interaction Hamiltonian in a Q1D wurtzite cylindrical quantum well wire (QWW) embedded in nonpolar dielectric matrix are derived and studied based on the dielectric continuum model and Loudon's uniaxial crystal model. Numerical calculations for a wurtzite GaN/AlN QWW are mainly focused on the size- and dielectric-dependent IO and SO phonon spectra and electron-IO (SO) phonons coupling functions. Results reveal that, in general, there are two branches of IO phonon modes and one branch of SO mode in the system. The dispersions of the IO and SO modes are obvious only when the radii ratio β and the dielectric constant of nonpolar matrix ∊d is small. The limiting frequencies of IO and SO modes for very large β have been analyzed in depth from both physical and mathematical viewpoints. The reducing behaviors of some modes have been clearly observed. Via the discussion of electrostatic potential spacial distributions of the IO and SO modes, we find that the QWW structures and dielectric constants of nonpolar matrix have little influence on the low-frequency IO mode, but they can greatly affect the potential distributions of high-frequency IO and SO modes. Detailed comparison of the dispersion behaviors of the modes and electron-phonon coupling properties in the Q1D wurtzite QWWs with those in wurtzite QWs and cubic quantum dots has also been made. Furthermore, part of the theoretical results derived in the present paper is consistent with the relatively experimental conclusion.

DISPERSION OF THE QUASI-CONFINED OPTICAL PHONONS IN WURTZITE GaN/AlN MULTIPLE QUANTUM WELLS

2007 ◽  
Vol 21 (25) ◽  
pp. 4407-4418
Author(s):  
WEN DENG HUANG ◽  
SHU YI WEI ◽  
YA JIE REN ◽  
YA HUI WANG
Keyword(s):  
Quantum Wells ◽  
Uniaxial Crystal ◽  
Strain Effect ◽  
Multiple Quantum ◽  
Optical Phonons ◽  
Phonon Modes ◽  
Crystal Model ◽  
Dielectric Continuum ◽  
Dielectric Continuum Model ◽  
Confined Phonons

Within the framework of the dielectric-continuum model and Loudon's uniaxial crystal model, the dispersions of the quasi-confined optical phonons in arbitrary wurtzite multiplelayer heterostructures are solved by using the transfer-matrix method. The dispersion relations of the quasi-confined phonons are investigated for GaN/AlN single QW and coupled QWs. The confinement of the quasi-confined phonons leads to a quantization of qz, j characterized by an integer m that defines the order of corresponding quasi-confined modes. The quasi-confined modes are more dispersive for decreasing m (i.e., for decreasing qz, j, the bands formed by the dispersion curves are narrower for higher order quasi-confined modes. The strain effect of QW structures has a clear influence on the dispersion behavior of the quasi-confined phonon modes and improves the frequency of the quasi-confined phonons.

Effects of ternary mixed crystals on interface/surface optical phonon in spherical core-shell quantum dots

2019 ◽  
Vol 33 (06) ◽  
pp. 1950068
Author(s):  
Y. Liu ◽  
L. P. Liu ◽  
Y. Xing ◽  
X. X. Liang
Keyword(s):  
Mixed Crystals ◽  
Core Shell ◽  
Phonon Modes ◽  
Electron Phonon Interaction ◽  
Interface Surface ◽  
Photoelectric Properties ◽  
Surface Optical ◽  
Spherical Core ◽  
The One ◽  
Dielectric Continuum

Within the framework of the dielectric continuum approach and modified random-element-isodisplacement model, the optical vibration mode in a spherical core-shell quantum dot (CSQD) consisting of ternary mixed crystals (TMCs) are investigated. The dispersion relation and electron–phonon interaction Hamiltonian are derived. As a typical case, the numerical results for [Formula: see text] and [Formula: see text] CSQDs are obtained and discussed. Taking the one- and two-mode behaviors of TMCs into account, the effects of TMCs on interface/surface optical (IO/SO) phonon show that there are 3 and 5 branches of IO/SO phonon modes in [Formula: see text] and [Formula: see text] CSQDs for a given component of TMC, respectively. It is also found that the IO/SO phonon frequencies and electron–phonon interactions are strongly dependent on the component of TMCs and the size of CSQDs. We hope this work would be useful for the study of the phonon-related photoelectric properties in CSQDs consisting of TMCs.

THE QUASI-CONFINED OPTICAL PHONONS IN WURTZITE SYMMETRY MULTIPLE QUANTUM WELLS

2006 ◽  
Vol 20 (22) ◽  
pp. 1367-1381 ◽  
Author(s):  
WEN-DENG HUANG ◽  
SHU-YI WEI ◽  
YA-JIE REN
Keyword(s):  
Quantum Wells ◽  
Equation Of Motion ◽  
Uniaxial Crystal ◽  
Multiple Quantum Wells ◽  
Multiple Quantum ◽  
Single Quantum Well ◽  
Crystal Model ◽  
Dielectric Continuum ◽  
Dielectric Continuum Model ◽  
Confined Phonons

Within the framework of the dielectric-continuum model and Loudon's uniaxial crystal model, the equation of motion for p-polarization field in wurtzite multiplayer symmetry heterostructures are solved for the quasi-confined phonon (QC) modes. The polarization eigenvector, the dispersion relation, and the electron-QC interaction Fröhlich-like Hamiltonian are derived by using the transfer-matrix method. The analytical theory and formulas can be directly applied to the single quantum well (QW) and multiple quantum wells (QWs), and superlattices (SLs). The dispersion relations and the electron-QC coupling strength are investigated for a wurtzite GaN/Al 0.15 Ga 0.85 N single QW. The results show that there are infinite branches of the dispersion curve with definite symmetry with respect to the center of the QW structure. The confinement of the quasi-confined phonons in the QW leads to a quantization of qz,j characterized by an integer m that defines the order of corresponding quasi-confined modes. The QC modes are more dispersive for decreasing m. The QC modes display an interface behavior in the barrier and a confined behavior in the well. When q⊥ is small, the symmetric modes have more contribution to electron-QC interaction than the antisymmetric modes.

Confinement of polar optical phonons in quasi-one-dimensional Wurtzite GaN-based quantum well wires: propagating and half-space phonon modes

Open Physics ◽  
2007 ◽  
Vol 5 (3) ◽  
Author(s):  
Li Zhang ◽  
Jun-Jie Shi
Keyword(s):  
Quantum Well ◽  
Half Space ◽  
Low Frequency ◽  
Uniaxial Crystal ◽  
Wave Number ◽  
Frequency Range ◽  
Phonon Modes ◽  
Quantum Well Structures ◽  
Electron Phonon Interaction ◽  
Quantum Well Wire

AbstractWith the aid of the macroscopic dielectric continuum and Loudon’s uniaxial crystal models, the propagating (PR) and half-space (HS) optical phonon modes and corresponding Fröhlich-like electron-phonon interaction Hamiltonians in a quasi-one-dimensionality (Q1D) wurtzite quantum well wire (QWW) structure are derived and studied. Numerical calculations on a wurtzite GaN/Al0.15Ga0.85N QWW are performed, and discussion is focused mainly on the dependence of the frequency dispersions of PR and HS modes on the free wave-number k z in the z-direction and on the azimuthal quantum number m. The calculated results show that, for given k z and m, there usually exist infinite branches of PR and HS modes in the high-frequency range, and only finite branches of HS modes in the low-frequency range in wurtzite QWW systems. The reducing behaviors of the PR modes to HS modes, and of the HS mode to interface phonon mode have been observed clearly in Q1D wurtzite heterostructures. Moreover, the dispersive properties of the PR and HS modes in Q1D QWWs have been compared with those in Q2D quantum well structures. The underlying physical reasons for these features have also been analyzed in depth.

scholarly journals Многократное изменение электрон-фононного взаимодействия в квантовых ямах с диэлектрически различными барьерами

2022 ◽  
Vol 56 (1) ◽  
pp. 101
Author(s):  
А.Ю. Маслов ◽  
О.В. Прошина
Keyword(s):  
Quantum Wells ◽  
Charged Particles ◽  
Strong Interactions ◽  
Asymmetric Structure ◽  
Optical Phonons ◽  
Phonon Modes ◽  
Phonon Interaction ◽  
Barrier Materials ◽  
Electron Phonon Interaction ◽  
Order Of Magnitude

Abstract The specific features of the interaction of charged particles with polar optical phonons have been studied theoretically for quantum wells with the barriers that are asymmetric in their dielectric properties. It is shown that the interaction with interface phonon modes makes the greatest contribution in narrow quantum wells. The parameters of the electron-phonon interaction were found for the cases of different values of the phonon frequencies in the barrier materials. It turned out that a significant (by almost an order of magnitude) change in the parameters of the electron-phonon interaction can occur in such structures. This makes it possible, in principle, to trace the transition from weak to strong interactions in quantum wells of the same type but with different compositions of barrier materials. The conditions are found under which an enhancement of the electron-phonon interaction is possible in an asymmetric structure in comparison with a symmetric one with the barriers of the same composition.

Scattering Rates in a Semiconductor Heterostructure: The Electron–Phonon Coupling

1998 ◽  
Vol 12 (16n17) ◽  
pp. 1719-1728 ◽  
Author(s):  
F. Comas ◽  
F. Castro ◽  
J. L. Gondar
Keyword(s):  
Quantum Wells ◽  
Quantum Wires ◽  
Phenomenological Theory ◽  
Applied Theory ◽  
Airy Functions ◽  
Electron Phonon Interaction ◽  
Semiconductor Heterostructure ◽  
Electron Phonon Coupling ◽  
The Subject ◽  
Scattering Rates

We investigate Scattering-Rates due to the electron–phonon interaction in a Semiconductor Heterostructure (SH) on the basis of a phenomenological theory for Polar Optical Phonons (POP) in semiconductor nanostructures which was proposed in the latter times. The applied theory has led to a plausible description of POP in Quantum-Wells, Quantum-Wires and Quantum-Dots. Using this theory we find an explicit expression for the electron–phonon Hamiltonian with direct application to a SH. Scattering Rates are calculated by applying this Hamiltonian and also a realistic wave-function for the electron states (using Airy functions) is considered. The obtained results are discussed in detail and compared with previous works on the subject.

Effects of Density and Diameter on Surface Optical Phonon Modes in GaAs Nanowire Bundles

2020 ◽  
Vol 20 (7) ◽  
pp. 4444-4449
Author(s):  
Jeung Hun Park ◽  
Richard S. Kim ◽  
Se-Jeong Park ◽  
Choong-Heui Chung
Keyword(s):  
Optical Phonon ◽  
Fill Factor ◽  
Average Diameter ◽  
Red Shift ◽  
Phonon Modes ◽  
Optical Phonon Mode ◽  
Surface Optical ◽  
Gaas Nanowire ◽  
Dielectric Continuum ◽  
Dielectric Continuum Model

We report the systematic investigation of the surface optical phonon modes in Au-catalyzed GaAs nanowires grown on an Au pre-patterned GaAs(111)B substrate using μ-Raman spectroscopy. We employed electron-beam dose rate as a control parameter during the substrate patterning step for adjusting the nanowire base diameter and coverage, which are independent from the nanowire growth conditions. We have experimentally studied the effect of the fill factor and average diameter on the surface optical phonon modes and explained the red-shift and broadening of the surface optical phonon frequencies by employing the dielectric continuum model. The surface optical phonon mode shift is exhibited to be sensitive to fill factor, rather than base diameter. The decrease in the average diameter from 280 nm to 180 nm results in the asymmetric broadening and red-shift of the surface optical phonon frequency (~1.83 cm−1) but the theoretical calculation from the isolated single nanowire-based dielectric continuum model cannot solely explain the behaviors of the surface optical phonon mode. In contrast, the change in the fill factor from 0.01 to 0.83 results in a shift of the surface optical phonon frequency (~6.5 cm−1) from the GaAs bulk value. The red-shift and asymmetric broadening of the surface optical phonons, in an agreement with the Maxwell-Garnett approximation, are consequences of dipolar interaction of randomly aligned neighboring nanowires and the polar nature of GaAs nanowire bundles. This work suggests the pre-patterning parameter dependent surface optical phonon characteristics of GaAs nanowire bundles which are of great importance in the nondestructive characterization of low-dimensional opto-electronic materials and devices.

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