Mixed Phonon Modes Research Articles

Hexagonal GaN nanostructure via electrochemical etching

Gallium nitride GaN thin films were deposited on Si (111) substrates using electrochemical deposition technique at 20 °C. SEM images and EDX results indicated that the growth of GaN films varies with the current density. XRD and Raman analyses showed the presence of hexagonal wurtzite and cubic zinc blende GaN phases with the crystallite size around 18–19 nm. Photoluminescence spectrum showed that the energy gaps of h-GaN/Si (111) and c-GaN/Si (111) were near 3.39 eV and 3.2 eV respectively at 300 K. Raman spectrum indicated the presence of mixed phonon modes of hexagonal and cubic GaN.

Phonon states of polar mixing optical modes in wurtzite ZnO-based coupling quantum dots

Within the framework of the macroscopic dielectric continuum model and Loudon's uniaxial crystal model, the phonon modes of a wurtzite ZnO-based coupling quantum dots (CQDs) are deduced and studied. The analytical phonon states of phonon modes are given. It is found that there are four types of polar phonon modes, i.e. the z-IO/ρ-QC modes, z-PR/ρ-IO modes, z-QC/ρ-QC modes and z-HS/ρ-IO modes coexisting in the wurtzite ZnO-based cylindrical CQDs. The energy ranges of these polar mixing phonon modes are analyzed and discussed. It is found that the z-IO/ρ-QC and z-PR/ρ-IO modes only exist in one frequency range, while z-QC/ρ-QC and z-HS/ρ-IO modes may appear in three frequency ranges. Based on the orthonormality relationships and a standard procedure of field quantization, the Fröhlich electron–phonon interaction Hamiltonians are obtained. The analytical Hamiltonians of electron–phonon interaction obtained here are quite useful for further investigating phonon influence on optoelectronics properties of wurtzite ZnO-based CQD structures.

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. ρ-IO/z-PR mixing modes and the z-IO/ρ-PR mixing modes existing in QoD wurtzite QDs. And each IO-PR mixing modes also have symmetrical and antisymmetrical forms. Via a standard procedure of field quantization, the Fröhlich 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 Q1D QWR systems are analyzed deeply from both of the viewpoints of physics and mathematics.

Synthesis of hexagonal and cubic GaN thin film on Si (111) using a low-cost electrochemical deposition technique

Gallium nitride GaN thin films were deposited on Si (111) substrates using electrochemical deposition technique at 20 °C. SEM images and EDX results indicated that the growth of GaN films varies with the current density. XRD and Raman analyses showed the presence of hexagonal wurtzite and cubic zinc blende GaN phases with the crystallite size around 18–19 nm. Photoluminescence spectrum showed that the energy gaps of h-GaN/Si (111) and c-GaN/Si (111) were near 3.39 eV and 3.2 eV respectively at 300 K. Raman spectrum indicated the presence of mixed phonon modes of hexagonal and cubic GaN.

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

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 interface optical phonon states and their dispersive properties of a wurtzite GaN quantum dot: quantum size effect

ohlich Hamiltonians of electron-(IO-PR) mixing phonons interaction are obtained. The orthogonal relations of polarization eigenvectors for these IO-PR mixing modes are also displayed. Numerical calculations for a wurtzite GaN cylindrical QD are focused on the quantum size effect on the dispersive properties of IO-PR mixing modes. The results reveal that both the radial-direction size and the axial-direction size have great effect 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 ireducingi the behavior of wurtzite quantum conned structures have been explicitly observed in the systems. Moreover, the behaviors that the IO-PR mixing phonon modes in wurtzite Q0D QDs reduce to the IO modes and PR modes in wurtzite Q2D QW and Q1D QWR systems are profoundly analyzed both from the viewpoint of physics and mathematics. These results show 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 analytical electron-phonon interaction Hamiltonians obtained here are useful in further analyzing the phonon effect on optoelectronic properties of wurtzite Q0D QD structures.

Vibration spectra of polar mixing optical phonon states and Fröhlich electron-phonon coupling behaviors in a wurtzite ZnO quantum dot

Based on the dielectric continuum model and Loudon's uniaxial crystal model, the interface-optical-propagating (IO-PR) mixing phonon states of a quasi-zero-dimensional (Q0D) wurtzite cylindrical quantum dot (QD) are investigated. It is found that there are two types of IO-PR mixing phonon modes, i.e. \rho-IO/z-PR mixing modes and the z-IO/\rho-PR mixing modes coexisting in Q0D wurtzite QDs. Numerical calculation on a wurtzite ZnO QD shows that the dispersion frequencies of the mixing modes are discrete functions of the azimuthal quantum number and axial wave-number. The calculated results agree well with the recent experimental spectra in ZnO QDs. An abnormal electron-phonon coupling strength is observed with the increase of the azimuthal quantum number and the order of phonon modes, which is attributed to the modulation effect of anisotropic dielectric functions of wurtzite ZnO crystal. The analytical Frölich-like Hamiltonian of electron-phonon interaction obtained here is quite useful for further analyzing phonon influence on optoelectronics properties of wurtzite Q0D QD structures. The present results can be reduced naturally to those of wurtzite quantum wires or quantum wells as the height or radius of cylindrical QD approaches infinity. This supports the validity and unity of phonon modes theories in wurtzite low-dimensional quantum systems.

Quantum size and dielectric effects of polar optical phonon spectra in wurtzite nitride quantum dots

Based on the macroscopic dielectric continuum model, the interface-optical-propagating (IO-PR) mixing phonon modes of a quasi-zero-dimensional wurtzite cylindrical quantum dot (QD) structure are derived and studied. 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., the ρ-IO/z-PR mixing modes and the z-IO/ρ-PR mixing modes, existing in wurtzite QDs. Each IO-PR mixing mode also has symmetrical and antisymmetrical forms. Via a standard procedure of field quantization, the Frohlich Hamiltonians of the electron-(IO-PR) mixing phonon interaction are obtained. The orthogonal relations of polarization eigenvectors for these IO-PR mixing modes are also displayed. Numerical calculations for a wurtzite GaN cylindrical QD are focused on the quantum size effect and the dielectric effect on the dispersive properties of IO-PR mixing modes. 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 structures has been found in the systems. Moreover, the behaviors that the IO-PR mixing phonon modes in wurtzite QDs reduce to the IO modes and the PR modes in wurtzite quantum well and quantum wire systems are analyzed deeply from the viewpoints of both physics and mathematics. These results show that the present theories of polar mixing phonon modes in wurtzite cylindrical QDs are consistent with the phonon mode theories in wurtzite quantum wells and quantum wire systems.

Polar optical phonon states and Fröhlich electron–phonon interaction Hamiltonians in a wurtzite nitride quantum dot

Within the framework of the macroscopic dielectric continuum model, the surface-optical-propagating (SO-PR) mixing phonon modes of a quasi-zero-dimensional (Q0D) wurtzite cylindrical quantum dot (QD) structure are derived and studied. The analytical phonon states of SO-PR mixing modes are given. It is found that there are two types of SO-PR mixing phonon modes, i.e. ρ-SO/ z-PR mixing modes and the z-SO/ ρ-PR mixing modes existing in Q0D wurtzite QDs. And each SO-PR mixing modes also have symmetrical and antisymmetrical forms. Via the standard procedure of field quantization, the Fröhlich Hamiltonians of electron–(SO-PR) mixing phonons interaction are obtained. And the orthogonal relations of polarization eigenvectors for these SO-PR mixing modes are also displayed. Numerical calculations on a wurtzite GaN cylindrical QD are carried out. The results reveal that the dispersive frequencies of all the SO-PR mixing modes are the discrete functions of phonon wave-numbers and azimuthal quantum numbers. The behaviors that the SO-PR mixing phonon modes in wurtzite QDs reduce to the SO modes and PR modes in wurtzite quantum well (QW) and quantum well wire (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 analytical electron–phonon interaction Hamiltonians obtained here are useful for further analyzing phonon influence on optoelectronics properties of wurtzite Q0D QD structures.

Infrared absorption by polar optical phonons in a CdS nanocrystal array consisting of quantum dots and quantum wires

Based on the results of experimental studies, it is shown that, when the effect of size quantization on the vibratory properties of CdS nanocrystals is insignificant, the absorption spectra of nanocomposites containing CdS quantum wires and quantum dots exhibit not only the peak associated with the transverse optical phonons but also two other pronounced peaks associated with electrostatic vibration modes. When the size of nanocrystals is so small that the effect of size quantization cannot be neglected, the structure of the reflection and transmission spectra becomes much more complicated because of the contribution of the mixed longitudinal-transverse phonon modes.

Localized mixed acoustic modes in non-cubic-axial superlattice with a cap layer

We study theoretically the properties of the localized mixed acoustic phonon modes lying in the interior minigap in a superlattice (SL) grown away from cubic axial of bulk material with a cap layer by using a transfer-matrix method. We find the appearance and the characteristics of the mixed localized modes in the interior minigap strongly depend on the growth direction and the structure parameters of the superlattice. Compared with the case in infinite superlattice with a structural defect layer, the localized modes exhibit some novel features. The dependence of the interior minigap width on the growth direction of the superlattice is also demonstrated. This provides a theoretical basis for experimental observation of the mixed localized acoustic modes and the interior minigap in SLs.

Mixed optical phonon modes in semiconductor nanocrystals synthesized in porous Al 2 O 3 matrix

This work is devoted to experimental and theoretical studies of optical phonons confined in CdS nanocrystals grown inside a porous alumina matrix. The complete sets of phonon modes, confined in a spherical quantum dot and in a cylindrical quantum wire, are considered in the framework of a continuum model, which allows the mixing of all the expected types of vibrations. It is shown that the calculated phonon-related response in the far-infrared spectral region agrees qualitatively with the measured spectra of typical samples, providing an explanation for a rather unusual structure of the reflection and transmission spectra. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Mixed vibrational modes of PbTe nanocrystallites

Far-infrared reflectance (20–700 cm−1) and Raman spectra of porous PbTe were studied. The spectral dependences found significantly differ from those observed in the case of bulk single-crystal PbTe. Aside from the transverse (TO) and longitudinal (LO) optical phonon modes, additional vibrational modes were detected in the spectra, whose frequencies are close to those in a bulk material. Their number and spectral positions are in satisfactory agreement with the results of calculations carried out to determine the vibrational mode frequencies for nanocrystallites taking into account boundary conditions at their surface. The macroscopic continuum model allows calculation of the frequencies of the mixed phonon modes in quantum dots by the simultaneous consideration of atomic displacements and the accompanying change in the electrostatic potential. It was found experimentally that the detected modes are mixed (LO-TO), as was predicted by theory. The data of atomic-force microscopy allowed us to estimate the average radius of quantum dots, which form the nanorelief of the porous PbTe layer.

Monte Carlo study of minority electronic transport in InGaAs: Effects of phonon mode splitting and dynamically screened electron-hole interactions

We present an ensemble Monte Carlo simulation of electronic transport in p-type In0.53Ga0.47As. The effects of mixed phonon modes and of dynamically screened electron-hole scattering on the velocity-field characteristics are examined. Our results show that a two phonon model yields smaller velocities at low fields and higher values beyond the intervalley transfer threshold. The dynamic screening leads to a field dependent velocity enhancement at moderate carrier densities.

Consistent density determination by Raman and photoluminescence experiments in completely confined e-h plasma in GaAs

The electron-hole plasma under 3-D carrier confinement is studied in GaAs by means of Raman scattering and photoluminescence measurements. We have demonstrated for the first time that under these well defined experimental conditions an excellent agreement is achieved for the plasma density values determined independently from single particle excitations, collective mixed plasmon-LO phonon modes and photoluminescence.

Cooling of high density electron-hole plasma

We generalize for high density electron-hole plasma, the previous theories [12] of temperature cooling of non-equilibrium hot plasma. Especially we take into account the cooling by emission of mixed longitudinal optical phonon and plasmon modes, these quasiparticles described by a non-equilibrium distribution function. We show that a strong slowing of the plasma cooling occurs, at high electron-hole density. We calculate for CdSe the temperature kinetics of plasma created by Yag laser (pulse duration 30 ps).

Elastic and photoelastic constants of NaCl, KBr and LiF by Brillouin scattering

Elastic and photoelastic constants of NaCl, KBr and LiF were determined from Brillouin frequency shifts and intensities. Reported differences between the hypersonic and ultrasonic elastic constants for KBr and LiF were not confirmed. For each material the constants were in good agreement with the ultrasonic values. Scattering from longitudinal, transverse and mixed phonon modes was clearly observed for each material.

Simple Model for the Energy Accommodation Coefficient

Quantum mechanical expressions for the energy accommodation of a gas at a solid surface are developed using the general theory of inelastic surface scattering as developed by Manson and Celli. Calculations are presented for the accommodation of helium at a simplified model of a tungsten surface. The phonon spectrum at the surface is taken to be that of a semi-infinite isotropic continuum, and contributions to the accommodation are obtained from bulk, mixed, and Rayleigh phonon modes. For temperatures not too small the calculations agree qualitatively with experiment, and exhibit the property that the accommodation is nearly independent of surface temperature over a large range.