For a critical examination of the dielectric continuum model as applied to a superlattice, we have introduced a microscopic model, which takes proper account of the long-range Coulomb interaction and yet permits easy solution for the long-wavelength LO and TO modes. With this model, it is shown that such long-wavelength modes approach different limits depending on directions of propagation relative to the axis of the superlattice. This demonstrates that to treat the confined bulklike modes in superlattices as modes of isolated slabs is inadequate.

Long-wavelength optic vibrations in a superlattice

We report the electron resonant Raman scattering (ERRS) process related to the longitudinal optical (LO), interface optical (IO) and quasi-confined (QC) phonons in a cylindrical GaN–AlN quantum well wire (QWW). We present the differential cross-section (DCS) and study the selection rules. Results reveal that the emitted photon frequency decreases with increasing the radius because of the size-selective Raman scattering effect and the built-in electric field. The contribution to the DCS mainly stems from the GaN-type LO (LO1), QC and IO phonons when the wire is thin, but the LO1 and QC phonons are dominant for the thick wire.

One phonon-assisted electron Raman scattering in a wurtzite cylindrical quantum well wire

The polar optical phonon states of four types of phonon modes including the interface optical (IO) modes, the propagating (PR) modes, the quasi-confined (QC) phonon modes in well-layer material (QCw), and the QC phonon modes in barrier-layer material (QCB) in a wurtzite GaN/AlxGa1–xN superlattice (SLs) are investigated within the dielectric continuum model framework. The analytical phonon states of the four types of modes and their dispersive equations in the wurtzite GaN/AlxGa1–xN SL structures are obtained. Numerical calculations on the dispersive spectra of phonon modes and the quantum size effect are performed for a wurtzite GaN/Al0.15Ga0.85N SL. Results reveal that dispersive curves of phonon modes in SLs form a series of frequency bands. The behaviors of QCw modes reducing to PR and IO modes are observed clearly. With the increase of well-layer GaN width d1 of the SLs, the dispersion of the QCB modes become weaker and weaker, and their frequency bands become narrower and narrower. But the PR, IO, and the QCw phonon modes become more dispersive, and the frequency bands of these modes become wider and wider as d1 increases. The present theoretical scheme and numerical results are quite useful for analyzing the dispersive spectra of full phonon modes and their polaronic effect in wurtzite GaN/AlGaN SL structures.

Full optical phonon states and their dispersive spectra of a wurtzite GaN/AlGaN superlattice: Quantum size effect

Within the framework of the macroscopic dielectric continuum model, the interface-optical-propagating (IO-PR) mixing phonon modes of a quasi-zero-dimensional (Q0D) wurtzite cylindrical quantum dot (QD) structure are derived and studied. The approximative analytical-phonon-states of IO-PR mixing modes are given. It is found that there are two types of IO-PR mixing phonon modes, i.e. ρ-IO/z-PR mixing modes and the z-IO/ρ-PR mixing modes existing in Q0D wurtzite QDs. And each IO-PR mixing modes also have symmetrical and antisymmetrical forms. Via a standard procedure of field quantization, the Frohlich Hamiltonians of electron-(IO-PR) mixing phonons interaction are obtained. And the orthogonal relations of polarization eigenvectors for these IO-PR mixing modes are also deduced. Numerical calculations of dispersive relation and electron-phonon coupling properties on a wurtzite GaN cylindrical QD are carried out. The behaviors that the IO-PR mixing phonon modes in wurtzite QDs reduce to the IO modes and PR modes in wurtzite QW and QWR systems are analyzed deeply from both of the viewpoints of physics and mathematics. The result shows that the present theories of polar mixing phonon modes in wurtzite cylindrical QDs are consistent with the phonon modes theories in wurtzite QWs and QWR systems. The coupling properties of electron-(IO-PR) mixing modes interactions are studied and analyzed in detail. An abnormal increase of electron-phonon coupling strength are observed as the azimuthal quantum numbers and order of phonon modes increase, which is ascribed to the modulation effect of different dielectric functions of wurtzite crystals in radius- and axial-directions. The analytical electron-phonon interaction Hamiltonians obtained here are useful for further investigating phonon influence on optoelectronics properties of wurtzite Q0D QD structures.

Polar optical phonon states and their electron-phonon coupling properties in a wurtzite nitride quantum dot

By employing the two-parameter variational approach, the donor-impurity states with surface optical (SO) phonons, also called SO phonon bound polarons in a quasi-one-dimensional (Q1D) wurtzite nanowire (NW) are investigated. Numerical calculations on a GaN NW are performed. The results reveal that the SO phonon contribution to the binding energy of the SO phonon bound polaron in GaN NWs reaches 200 meV, which is one order of magnitude larger than that of GaAs NWs with the same radius. The large contribution of SO phonons to the total binding energy is mainly ascribed to the stronger electron-phonon coupling constant in GaN materials. The calculated results of impurity binding energy are consistent with the recent experimental measurement of the active energy in GaN NW systems. The numerical results also shows that the two-parameter variational approach is necessary and suitable for the description of donor-impurity states in Q1D wurtzite GaN NW structures, especial for the NWs with a relatively small radius (such as R < 10 nm).

Surface polaronic effect on donor-impurity states of a wurtzite nitride nanowire: Two-parameter variational approach

The ground-state self-trapped energy and effective mass of the polaron in a freestanding wurtzite GaN nanowire (NW) are studied by employing the perturbation approach. Based on the dielectric continuum model and the Loudon uniaxial crystal model, the full polar optical phonon modes, i.e. quasi-confined (QC) phonon modes and surface optical (SO) phonon modes, in the one-dimensional (1D) wurtzite systems have been analyzed. The vibrating spectra of the two types of phonon modes and their electron–phonon coupling properties have been discussed and analyzed. The numerical results on the ground-state polaron self-trapped energy and correction of effective mass in the 1D GaN NWs reveal that these are far larger than those in 1D GaAs NW systems. The reasons resulting in this obvious difference in the two 1D structures can be attributed to the different electron–phonon coupling constants and electron effective masses of bulk materials constituted of the two types of 1D confined systems. Moreover, our calculated results regarding the polaronic self-trapped energy are consistent with the recent experimental observation in GaN NW systems.

Polaronic self-trapped energy and effective mass of a cylindrical wurtzite GaN nanowire

Based on the dielectric continuum model and Loudon's uniaxial crystal model, the full polar optical phonon modes including the propagating (PR) modes, quasi-confined modes, half-space (HS) modes and interface optical modes in a quasi-one-dimensional (Q1D) wurtzite rectangular nanowire (NW) structure are deduced and analyzed. The analytical phonon states, their dispersion equations, polar polarization eigenvectors and Frohlich electron–phonon interaction Hamiltonians are derived. Numerical calculations of quantum size effect on the dispersive spectra for these modes are performed on a wurtzite GaN/Al0.15Ga0.85N rectangular wurtzite NW. The dispersive features of the four types of phonon modes are analyzed. The behavior of the PR modes reducing to the corresponding HS modes is observed clearly in the dispersive curves of these modes, which reveals that the present theories of phonon modes are self-consistency and correct for the description of phonon modes in wurtzite Q1D rectangular NW. Moreover, there are some yielding points in the dispersive curves of the PR modes. These observations and results reveal that the confined dimensionality and cross-sectional shape influence greatly the dispersive properties of phonon modes in wurtzite quantum confined systems.

Dispersive spectra and Fröhlich electron–phonon interaction Hamiltonians of full polar optical phonon states in a wurtzite nitride nanowire: quantum size effect

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Polaronic self-trapped energy and effective mass of a cylindrical wurtzite GaN nanowire

Dispersive spectra and Fröhlich electron–phonon interaction Hamiltonians of full polar optical phonon states in a wurtzite nitride nanowire: quantum size effect