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.

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.

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.

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.

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.

RECENT DEVELOPMENTS ON ELECTRON-PHONON INTERACTIONS IN STRUCTURES FOR ELECTRONIC AND OPTOELECTRONIC DEVICES

1998 ◽  
Vol 09 (01) ◽  
pp. 281-312 ◽  
Author(s):  
M. DUTTA ◽  
M. A. STROSCIO ◽  
K. W. KIM
Keyword(s):  
Quantum Wells ◽  
Quantum Wires ◽  
Quantum Cascade Lasers ◽  
Optoelectronic Devices ◽  
Longitudinal Optical ◽  
Optical Phonons ◽  
Phonon Modes ◽  
Cross Sectional ◽  
Device Applications ◽  
Dielectric Continuum

As device dimensions in electronic and optoelectronic devices are reduced, the characteristics and interactions of dimensionally-confined longitudinal-optical (LO) and acoustic phonons deviate substantially from those of bulk semiconductors. Furthermore, as würtzite materials are applied increasingly in electronic and optoelectronic devices it becomes more important to understand the phonon modes in such systems. This account emphasizes the properties of bulk optical phonons in würtzite structures, the properties of LO-phonon modes and acoustic-phonon modes arising in polar-semiconductor quantum wells, superlattices, quantum wires and quantum dots, with a variety of cross sectional geometries and, lastly, the properties of optical phonons in würtzite materials as predicted by the dielectric continuum model. Emphasis is placed on the dielectric continuum and elastic continuum models of bulk, confined and interface phonons. This article emphasizes device applications of confined phonons in GaAs-based systems and provides a brief discussion of carrier-LO-phonon interactions in bulk würtzite structures. This account also includes discussions on the use of metal-semiconductor heterointerfaces to reduce scattering and on the role of phonons in Fröhlich, deformation and piezoelectric interactions in electronic and optoelectronic structures; specific device applications high-lighted here include quantum cascade lasers, mesoscopic devices, thermoelectric devices and optically-pumped resonant intersubband lasers.

ONE-PHONON-ASSISTED ELECTRON RESONANT RAMAN SCATTERING IN FREE-STANDING QUANTUM WIRES

2007 ◽  
Vol 21 (17) ◽  
pp. 2989-3000
Author(s):  
XIANG-FU ZHAO ◽  
CUI-HONG LIU
Keyword(s):  
Raman Scattering ◽  
Quantum Wire ◽  
Quantum Wires ◽  
Longitudinal Optical ◽  
Phonon Modes ◽  
Free Standing ◽  
Surface Optical ◽  
Resonant Raman ◽  
Resonant Raman Scattering ◽  
Valence Bands

The scattering intensity (SI) for an electron resonant Raman scattering (ERRS) process in a free-standing semiconductor quantum wire of cylindrical geometry associated with bulk longitudinal optical (LO) phonon modes or the surface optical (SO) phonon modes is calculated for T=0 K . The Fröhlich interaction is considered to illustrate the theory for a GaAs system. Electron states are confined within a free-standing quantum wire (FSW). Single parabolic conduction and valence bands are assumed. The selection rules are studied. Numerical results and a discussion are also presented for various radii of the cylindrical quantum wires.

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.

TRANSFER MATRIX METHOD FOR ELECTRON-IO-PHONON INTERACTION IN ASYMMETRIC DOUBLE-BARRIER STRUCTURES

2001 ◽  
Vol 15 (27) ◽  
pp. 3539-3549 ◽  
Author(s):  
ZU WEI YAN ◽  
X. X. LIANG
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Phonon Modes ◽  
Phonon Interaction ◽  
Double Barrier ◽  
Long Wavelength ◽  
Dielectric Continuum ◽  
Modes Coupling ◽  
Dielectric Continuum Model

Within the framework of the dielectric continuum model, the interface-optical (IO) phonon modes and their interaction with electrons in an asymmetric double-barrier structure is studied by using a transfer matrix method. The dispersion equation of IO phonon modes and the electron-IO-phonon (e-IO-p) interaction Hamiltonian are derived. It is found that there are eight branches of IO-phonon modes coupling with electrons besides the confined LO-phonon modes. The numerical results are obtained for several GaAs/Al x Ga 1-x As systems. It is seen that the contributions of long-wavelength phonons to the e-IO-p coupling are important. The e-IO-p coupling related to the IO modes with the GaAs LO-frequency (phonon energy 36.25 meV) at the long-wavelength limit is strongest in the eight branches of IO-phonon 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.

DISPERSIONS AND FRÖHLICH ELECTRON–PHONON INTERACTION HAMILTONIAN OF PROPAGATING OPTICAL PHONON MODES IN QUASI-ONE-DIMENSIONAL WURTZITEGaN-BASED QUANTUM WELL WIRES

2007 ◽  
Vol 14 (05) ◽  
pp. 903-910 ◽  
Author(s):  
L. ZHANG ◽  
HONG-JING XIE
Keyword(s):  
Quantum Well ◽  
Quantum Wells ◽  
Optical Phonon ◽  
Detailed Comparison ◽  
Continuous Functions ◽  
Uniaxial Crystal ◽  
Phonon Modes ◽  
Phonon Interaction ◽  
One Dimensional ◽  
Quantum Well Wire

Based on the dielectric continuum model and Loudon's uniaxial crystal model, the propagating (PR) optical phonon modes and the Fröhlich-like electron–PR phonon interaction Hamiltonian in a quasi-one-dimensional (Q1D) wurtzite quantum well wire (QWW) structure are deduced and analyzed. Numerical calculations on AlGaN / GaN / AlGaN wurtzite QWW are performed. Results reveal that the dispersive frequencies of PR modes are the continuous functions of free wavenumber kzin z-direction and discrete functions of azimuthal quantum number m. The reduced behavior of the PR modes in wurtzite quantum systems is obviously observed. From the discussion of the electron–PR phonon coupling functions, it is found that the low-order PR modes in the case of small kzand m play a more important role in the electron–PR phonon interactions. Moreover, a detailed comparison of the PR modes in Q1D QWW structures with those in quasi-two-dimensional quantum wells are also carried out. The physical reasons resulting in the relationship and distinction in the two types of systems are also analyzed deeply.

Sign in / Sign up

Export Citation Format

Share Document