Branches Of Interface Optical Phonon Modes Research Articles

Interface optical phonon-assisted scattering rates in wurtzite nitride step quantum wells with strong built-in electric field

The interface optical (IO) phonon-assisted electron scattering rates in wurtzite GaN-based asymmetrical step quantum wells (QWs) are theoretically investigated by adopting the usual Fermi golden rule. Based on the dielectric continuum model and Loudon’s uniaxial crystal model, the analytical IO phonon states and their dispersive equation as well as the Fröhlich electron–phonon interaction Hamiltonian are derived. Taking into consideration the effects of strong built-in electric field (BEF) and the band nonparabolicity, the exact electronic eigen-states in the step QW are obtained with the aid of the two Airy functions. Numerical calculations on a wurtzite AlN/GaN/AlxGa1−xN/AlN step QW are performed. It is found that there are four branches of IO phonon modes in the asymmetric nitride step QWs, which is obviously different from the situation of symmetrical GaN/AlN single and coupling QWs. This is mainly ascribed to the asymmetry of the step QW structures studied here. The calculated results show that the intrasubband and intersubband scattering rates in wurtzite step QWs are one order of magnitude larger than those in GaAs-based step QWs, which is attributed to the larger electron–phonon coupling constants of GaN-based materials. The intrasubband scattering rates in wurtzite step QWs depend on the structural parameters in a similar manner as in cubic GaAs-based step QWs, but the intersubband scattering rates here show obviously different dependent behavior on the structural parameters. This is ascribed to the effects of the strong BEF and the band nonparabolicity. Moreover, the high-frequency IO modes play more important role to the total scattering rates than the low-frequency ones. And the contributions of the low-frequency IO modes could be neglected when analyzing the electron–phonon scattering processes in wurtzite step QWs.

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

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 interface and surface optical vibration spectra in multi-layer wurtzite quantum wires: transfer matrix method

The polar interface optical (IO) and surface optical (SO) phonon modes and the corresponding Frohlich electron–phonon–interaction Hamiltonian in a freestanding multi-layer wurtzite cylindrical quantum wire (QWR) are derived and studied by employing the transfer matrix method in the dielectric continuum approximation and Loudon's uniaxial crystal model. A numerical calculation of a freestanding wurtzite GaN/AlN QWR is performed. The results reveal that for a relatively large azimuthal quantum number m or wave-number kz in the free z-direction, there exist two branches of IO phonon modes localized at the interface and only one branch of SO mode localized at the surface in the system. The degenerating behaviours of the IO and SO phonon modes in the wurtzite QWR have also been clearly observed for a small kz or m. The limiting frequency properties of the IO and SO modes for large kz and m have been explained reasonably from the mathematical and physical viewpoints. The calculations of electron–phonon coupling functions show that the high-frequency IO phonon branch and SO mode play a more important role in the electron–phonon interaction.

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

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.

Polar interface optical phonon modes and Fröhlich electron–phonon interaction Hamiltonians in wurtzite quantum well wires

Within the framework of the dielectric continuum approximation and Loudon's uniaxial crystal model, the interface optical (IO) phonon modes and the corresponding Fröhlich electron–phonon interaction Hamiltonian in a wurtzite AlN/GaN/AlN quantum well wire (QWW) are derived and studied. Numerical calculations are mainly focused on the frequency dispersion of the IO phonons and electron–phonon interaction coupling function. 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 axial direction wave number kz or the azimuthal quantum number m is small. The degenerating behaviour of the IO phonon modes in wurtzite QWW has also been observed for small kz or m. When kz or m are relatively large, with the increasing of them, the frequencies of these IO phonon modes converge to the two definite limiting frequencies in wurtzite single planar heterostructure, and this feature has been explained reasonably from the mathematical and physical viewpoints. The calculations of the electron–phonon coupling function show that, though some branches of IO phonon modes exchange their localized positions with each other at a large m, there always exist two branches of IO phonon modes localized on each interface. The high-frequency IO phonon modes compared with the low-frequency ones play a more important role in the electron–phonon interaction. Detailed comparison of the dispersion behaviours of the IO phonons and electron–IO phonon couplings properties in wurtzite QWWs with those in zinc-blende QWWs has also been made.

Interface and surface optical phonons in a free-standing [formula omitted] cylindrical quantum-well wire

Under dielectric continuum approximation, interface optical (IO) and surface optical (SO) phonon modes as well as the corresponding Fröhlich electron–phonon interaction Hamiltonian in a free-standing cylindrical quantum-well wire (QWW) were derived and studied. Numerical calculations on GaAs / Al x Ga 1 - x As cylindrical QWWs have been performed. Results reveal that, in the case of taking the “two-mode” behavior of the Al x Ga 1 - x As material into account, there have four branches of IO phonon modes and two branches of SO phonon mode, and the dispersion frequencies of IO or SO phonon modes sensitively depend on the Al mole fraction x in Al x Ga 1 - x As material and the wave-vector in z direction k z . With the increasing of k z and quantum number m, the frequency of each IO mode approaches one of the two frequency values of the single GaAs / Al x Ga 1 - x As heterostructure, and the electrostatic potential distribution of the phonon mode tends to be more and more localized at a certain interface or surface, meanwhile, the coupling between the electron-IO or -SO phonon becomes weaker.

Polar Oscillation of Interface and Surface Optical Phonons in Free-Standing Cylindrical Quantum-Well Wires**The project supported partly by Natural Science Foundation of Guangdong Province of China

Under dielectric continuum approximation, interface optical (IO) and surface optical (SO) phonon modes as well as the corresponding Fröhlich electron-phonon interaction Hamiltonian in a free-standing cylindrical quantum-well wire (QWW) are derived and studied. Numerical calculations on As cylindrical QWW are performed. Results reveal that there are two branches of IO phonon modes and one branch of SO phonon mode, and the dispersion frequencies of IO or SO phonon modes sensitively depend on the Al mole fraction in As material and the wave-vector in direction, . With the increasing of and quantum number , the frequency of each IO mode approaches one of the two frequency values of the single As heterostructure, and the electrostatic potential distribution of the phonon mode tends to be more and more localized at a certain interface or surface, meanwhile, the coupling between the electron-IO and -SO phonons becomes weaker.

TRANSFER MATRIX METHOD FOR THE FRÖHLICH ELECTRON–INTERFACE OPTICAL PHONON INTERACTION IN MULTILAYER COAXIAL CYLINDRICAL 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.