Polar Quasi-Confined Optical Phonon Modes in Wurtzite Quasi-One-Dimensional GaN/Al_xGa_(1-x)N Quantum Well Wires

Based on the dielectric continuum model and Loudon＇s uniaxial crystal model,quasi-confined （QC） optical phonon modes and electron-QC phonon coupling functions in quasi-one-dimensional （QID） wurtzite quantum well wires （QWWs） are deduced and analyzed. Numerical calculations on an AIN/GaN/AIN wurtzite QWW are performed. The results reveal that the dispersions of the QC modes are quite obvious only when the free wavenumber kz in the z-direction and the azimuthal quantum number m are small. The reduced behavior of the QC modes in wurtzite quantum systems is clearly observed. Through the discussion of the electron-QC mode coupling functions,it is found that the lower-frequency QC modes in the high-frequency region play a more important role in the electron-QC phonon interactions. Moreover,our computations also prove that kz and m have a similar influence on the electron-QC phonon coupling properties.

Effects of electron–optical phonon interactions on the polaron energy in a wurtzite ZnO/Mg_xZn_(1-x)O quantum well

We investigated the properties of polarons in a wurtzite ZnO/MgxZn1-xO quantum well by adopting a modified Lee–Low–Pines variational method, giving the ground state energy, transition energy, and phonon contributions from various optical-phonon modes to the ground state energy as functions of the well width and Mg composition. In our calculations, we considered the effects of confined optical phonon modes, interface-optical phonon modes, and half-space phonon modes, as well as the anisotropy of the electron effective band mass, phonon frequency, and dielectric constant. Our numerical results indicate that the electron–optical phonon interactions importantly affect the polaronic energies in the ZnO/MgxZn1-xO quantum well. The electron–optical phonon interactions decrease the polaron energies. For quantum wells with narrower wells, the interface optical phonon and half-space phonon modes contribute more to the polaronic energies than the confined phonon modes. However, for wider quantum wells, the total contribution to the polaronic energy mainly comes from the confined modes. The contributions of the various phonon modes to the transition energy change differently with increasing well width. The contribution of the half-space phonons decreases slowly as the QW width increases, whereas the contributions of the confined and interface phonons reach a maximum at d ≈ 5.0 nm and then decrease slowly. However,the total contribution of phonon modes to the transition energy is negative and increases gradually with the QW width of d.As the composition x increases, the total contribution of phonons to the ground state energies increases slowly, but the total contributions of phonons to the transition energies decrease gradually. We analyze the physical reasons for these behaviors in detail.

Built-in electric field effect on cyclotron mass of magnetopolarons in a wurtzite In_xGa_(1-x)N/GaN quantum well

The cyclotron mass of magnetopolarons in wurtzite InxGa1-xN/GaN quantum well is studied in the presence of an external magnetic field by using the Larsen perturbation method. The effects of the built-in electric field and different phonon modes including interface, confined and half-space phonon modes are considered in our calculation. The results for a zinc-blende quantum well are also given for comparison. It is found that the main contribution to the transition energy comes from half-space and interface phonon modes when the well width is very small while the confined modes play a more important role in a wider well due to the location of the electron wave function. As the well width increases, the cyclotron mass of magnetopolarons first increases to a maximum and then decreases either with or without the built-in electric field in the wurtzite structure and the built-in electric field slightly reduces the cyclotron mass. The variation of cyclotron mass in a zinc-blende structure is similar to that in a wurtzite structure. With the increase of external magnetic field, the cyclotron mass of polarons almost linearly increases. The cyclotron frequency of magnetopolarons is also discussed.

Phonon-assisted intersubband transitions in wurtzite GaN/In_x Ga_(1-x) N quantum wells

A detailed numerical calculation on the phonon-assisted intersubband transition rates of electrons in wurtzite CaN/InxGal-xN quantum wells is presented. The quantum-confined Stark effect, induced by the built-in electric field, and the ternary mixed crystal effect are considered. The electron states are obtained by iteratively solving the coupled SchrSdinger and Poisson equations. The dispersion properties of each type of phonon modes are considered in the derivation of Fermi＇s golden rule to evaluate the transition rates. It is indicated that the interface and half- space phonon scattering play an important role in the process of 1 2 radiative transition. The transition rate is also greatly reduced by the built-in electric field. This work can be helpful for the structural design and simulation of new semiconductor lasers.

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 Froehlich 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.

Polar Mixing Optical Phonon Spectra in Wurtzite GaN Cylindrical Quantum Dots: Quantum Size and Dielectric Effects

The interface-optical-propagating （IO-PR） mixing phonon modes of a quasi-zero-dimensional （QOD） wurtzite cylindrical quantum dot （QD） structure are derived and studied by employing the macroscopic dielectric continuum model. The 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. p-IO//z-PR mixing modes and the z-IO//p-PR mixing modes existing in QOD wurtzite QDs. And each IO-PR mixing modes also have symmetrical and antisymmetrieal forms. Via a standard procedure of field quantization, the Frohlich Hamiltonians of electron-（IO-PR） mixing phonons interaction are obtained. Numerical calculations on a wurtzite GaN cylindrical QD are performed. The results reveal that both the radial-direction size and the axial-direction size as well as the dielectric matrix have great influence on the dispersive frequencies of the IO-PR mixing phonon modes. The limiting features of dispersive curves of these phonon modes are discussed in depth. The phonon modes ＂reducing＂ behavior of wurtzite quantum confined systems has been observed obviously in the structures. Moreover, the degenerating behaviors of the IO-PR mixing phonon modes in wurtzite QOD QDs to the IO modes and PR modes in wurtzite Q2D QW and QID QWR systems are analyzed deeply from both of the viewpoints of physics and mathematics.