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.

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.

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.

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.

TRANSFER MATRIX METHOD FOR THE FRÖHLICH ELECTRON–INTERFACE OPTICAL PHONON INTERACTION IN MULTILAYER COAXIAL CYLINDRICAL QUANTUM-WELL WIRES

2004 ◽  
Vol 18 (03) ◽  
pp. 379-393 ◽  
Author(s):  
LI ZHANG ◽  
HONG-JING XIE
Keyword(s):  
Quantum Well ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Continuum Approximation ◽  
Phonon Modes ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Quantum Well Wire ◽  
Quantum Well Wires

Under dielectric continuum approximation, by adopting the transfer matrix method, interface optical (IO) phonon modes and the Fröhlich electron–IO-phonon interaction Hamiltonian in a multilayer coaxial cylindrical quantum-well wire (QWW) were deduced and investigated. Numerical calculations on a four-layer GaAs / Al x Ga 1-x As QWW have been performed. Results reveal that there are six branches of IO phonon modes. When the wave vector in z-direction kz and the azimuthal quantum number m are small, the dispersion frequencies of IO modes sensitively depend on kz and m. When kz and m are relatively large, with the increasing of kz and m, the frequency for each mode converges the limit frequency value of IO mode in single heterostructure, and the electrostatic potential distribution of each mode tends to be more and more localized at the interfaces, meanwhile, the coupling between the electron–IO-phonon becomes weaker and weaker. The calculation also shows that the phonon modes with higher frequencies have more significant contribution to the electron–phonon interaction. At last, it is found that kz and m have analogous effects on the frequencies and the electrostatic potentials of the IO phonons.

scholarly journals lntersubband Relaxation in Step Quantum Well Structures

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 289-293
Author(s):  
J. P. Sun ◽  
H. B. Teng ◽  
G. I. Haddad ◽  
M. A. Stroscio ◽  
G. J. Iafrate
Keyword(s):  
Quantum Well ◽  
Form Factors ◽  
Phonon Energy ◽  
Longitudinal Optical Phonon ◽  
Relaxation Rates ◽  
Phonon Modes ◽  
Quantum Well Structures ◽  
Bulk Phonon ◽  
Interface Phonons ◽  
Intersubband Relaxation

Intersubband relaxation due to electron interactions with the localized phonon modes plays an important role for population inversion in quantum well laser structures designed for intersubband lasers operating at mid-infrared to submillimeter wavelengths. In this work, intersubband relaxation rates between subbands in step quantum well structures are evaluated numerically using Fermi's golden rule, in which the localized phonon modes including the asymmetric interface modes, symmetric interface modes, and confined phonon modes and the electron – phonon interaction Hamiltonians are derived based on the macroscopic dielectric continuum model, whereas the electron wave functions are obtained by solving the Schrödinger equation for the heterostructures under investigation. The sum rule for the relationship between the form factors of the various localized phonon modes and the bulk phonon modes is examined and verified for these structures. The intersubband relaxation rates due to electron scattering by the asymmetric interface phonons, symmetric interface phonons, and confined phonons are calculated and compared with the relaxation rates calculated using the bulk phonon modes and the Fröhlich interaction Hamiltonian for step quantum well structures with subband separations of 36 meV and 50meV, corresponding to the bulk longitudinal optical phonon energy and interface phonon energy, respectively. Our results show that for preferential electron relaxation in intersubband laser structures, the effects of the localized phonon modes, especially the interface phonon modes, must be included for optimal design of these structures.

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.

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