Interface Optical Phonon Modes Research Articles

Cyclotron–interface phonon resonance line-width in asymmetric semiparabolic quantum wells

In this study, we investigated the cyclotron–interface phonon resonance line-width in GaAs/AlAs asymmetric semiparabolic quantum wells when electrons are scattered by symmetric (antisymmetric) interface optical phonons. The operator projection and profile methods were employed to calculate the expressions for the absorption power and the full width at half maximum (FWHM), respectively. We found that the electron–interface phonon interactions by the antisymmetric modes are weaker than those by the symmetric modes under all phonon emission and absorption cases. In addition, the FWHM is more dominant for interface phonon absorption compared with that for interface phonon emission. The interface optical phonon modes at the resonance peak with a lower-photon frequency are much more important for electron–interface optical phonon scattering than those at the resonance peak with a higher-photon frequency. Our results are consistent with previously reported experimental data.

Effect of optical phonons scattering on electron mobility in asymmetric AlGaN/GaN quantum wells

Abstract Based on the dielectric continuum model, uniaxial model and force balance equation, the electron mobility in asymmetric wurtzite AlxGa1-xN/GaN/AlyGa1-yN quantum wells (QWs) is investigated theoretically in consideration of optical phonon scattering and varieties of Al compositions x and y. The dispersion relations and potentials of interface, confssined, half space and propagation optical phonon modes are given by the transfer matrix method including the effect of two-mode transverse optical phonons. Contrary to symmetric QWs, one branch of interface optical phonons vanishes and transforms into half space or confined optical one in certain intervals of Al component, whereas the confined optical phonons exist in a wider Al component range. The electron mobility in asymmetric AlGaN/GaN QWs can be modulated to be higher than that in symmetric ones. It is found that the total electron mobility decreases at first, then induces steps and finally decreases as x increases for certain y. The electron mobility also shows strong temperature-dependence. A significant modification on electron mobility appears for a narrower GaN well layer. Our results indicate that the asymmetric AlGaN/GaN QWs can be modulated to exhibit better transport properties than symmetric ones.

Contribution of remote interface polar phonons in the hole mobility of diamond

The role of remote interface polar phonon modes on the electronic transport properties of dimensionally confined diamond structures have been investigated in detail. By employing a dielectric continuum model, scattering rates, hole mobility and relaxation times in mesoscopic diamond-based devices are calculated. The performance has been analyzed by inserting polar over layers on diamond with wide-band gap materials such as AlN or w − BN. We have shown that a Fröhlich potential due to the interface optical phonon modes in the upper layer is created, that decays into diamond resulting in the existence of a remote polar phonon potential in the material. Hole scattering from remote polar phonons dominate on the order of two or more in magnitude resulting in substantial decrease in hole mobility in diamond. Thus, the present research will provide a milestone for understanding interface phonons that penetrate to the two-dimensional hole gas (2DHG) in confined diamond structures as compared to their bulk counterpart and can also be applied to other polar materials used for doping.

AlGaAs/GaAs Triple Quantum Well Photodetector at $5~\mu \text{m}$ Wavelength—A Simulation Study

A novel AlGaAs/GaAs triple quantum well (QW) photodetector at 5- $\mu \text{m}$ wavelength has been proposed. The photodetector is designed with a double-resonance condition to achieve short tunneling time and large electron escape probability. The interface optical phonon modes and the phonon-assisted electron transition rates have been calculated. The electron escape probability is as high as 0.8 in the proposed photodetector, which is over two times higher than traditional phonon-assisted tunneling devices. Compared with QW infrared photodetectors, the noise current of the photodetector can be reduced dramatically ( $> 10^{13}$ times at 77 K and >4000 times at 300 K). In addition, the effects of delta doping on the absorption coefficients and scattering times of the triple QW photodetector are also investigated in detail. Delta doping at the middle of the well is much more desirable than uniform doping, in order to achieve large escape probability and high absorption coefficient.

Effects of the built-in electric field on polaron effects in a wurtzite ZnO/MgxZn1−xO quantum well

The effects of the built-in electric field on the polarons in wurtzite ZnO/MgxZn1−xO quantum wells are studied numerically via the improved Lee-Low-Pines intermediate coupling variational method. The contributions of the different branches of the optical phonons to the polaron energies of the ZnO/MgxZn1−xO quantum wells are calculated as functions of well width d and composition x. The anisotropy effects of the electronic effective masses, the dielectric constants, and the frequencies of the different branches of the phonon modes (including both the longitudinal-like and transverse-like confined optical phonon modes, the interface optical phonon modes and the half-space phonon modes) on the polaron energies are considered in the calculations. Comparisons between the cases with and without the built-in electric field (F ≠ 0 and F = 0) are made for the optical phonon contributions to the polaron energies for the different branches of the phonon modes. The results show that the built-in electric field has marked effects on the contributions of the phonons with the different modes; in detail, it makes positive contributions to the interface and the half-space phonons, but negative contributions to the confined phonons, and thus its effect on the total phonon contribution is not obvious. Detailed comparisons of the contributions of the symmetric and antisymmetric phonon modes to the polaron energies as functions of d and x are also presented and a heuristic argument is provided to explain the numerical results.

Influence of spin–orbit interactions on the polaron properties in wurtzite semiconductor quantum well

We have study the simultaneous effect of Rashba and Dresselhaus spin–orbit interactions on the polaron properties in wurtzite semiconductor quantum wells. The linear and cubic contributions of the bulk Dresselhaus spin–orbit coupling and the effects of phonon confinement on electron–optical-phonon interaction Hamiltonians are taken into account. We have found analytical solutions for the polaron energies as well as polaron effective mass within the range of validity of perturbation theory. It is shown that the polaron energy and effective mass correction are both significantly enhanced by the spin–orbit coupling. Wave number dependent phonon contribution on the electron energy has minima and varies differently of the spin-up and spin-down states. Polaron self-energy due to interface optical phonon modes has larger values than of the confined optical phonon modes ones. The polaron effective mass exhibits anisotropy and the contribution of the Dresselhaus spin–orbit coupling term on the polaron effective mass is dominated by Rashba one.

Effects of electron–optical phonon interactions on the polaron energy in a wurtzite ZnO/MgxZn1−xO quantum well**Project supported by the National Natural Science Foundation of China (Grant Nos. 11264027 and 11364030), the Project of Prairie Excellent Specialist of Inner Mongolia, China, and the “Thousand, Hundred and Ten” Talent Training Project Foundation of Inner Mongolia Normal University, China (Grant No. RCPY-2-2012-K-039).

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.

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.

Phonon confinement effect on the polaron states in a double quantum ring structure in the presence of electric and magnetic fields

In the framework of effective mass approximation the polaron problem in double quantum ring structures in the presence of perpendicular electric and magnetic fields with taken into account the effect of phonon confinement is considered. We derived general expressions for the normalized eigenfunctions of the confined optical and interface optical phonon modes and the dispersion relation for interface optical phonons as well as electron–confined optical phonon and electron–interface optical phonon Fröhlich interaction Hamiltonians in the double quantum ring system. Results reveal that the electron–optical phonon coupling leads to the decrease of the electron ground state energy. We have shown that the polaron energy exhibits a pronounced local maximum (minimuum) in dependence on an electric (magnetic) field which corresponds to the sharp decrease (increase) of the polaronic contributions due to confined optical and interface optical phonon modes.

One-phonon resonant electron Raman scattering in a cylindrical GaAs/AlAs quantum dot

We have presented a theoretical calculation of the differential cross section for the electron Raman scattering process associated with the interface optical phonon modes in cylindrical GaAs quantum dots (QDs) with a AlAs matrix. We consider the Fröhlich electron–phonon interaction in the framework of the dielectric continuum approach. The selection rules for the processes are studied. Singularities are found to be sensitively size-dependent, and, by varying the size of the QDs, it is possible to control the frequency shift in the Raman spectra. A discussion of the phonon behavior for QDs with different size is presented. Copyright © 2013 John Wiley & Sons, Ltd.

Effect of electron-optical phonon interaction on resonant tunneling in coupled quantum wells

The spatial distribution of the wave functions for electrons in a coupled-quantum-well system of GaAs/AlxGa1−xAs with triple barriers is discussed. Within the framework of the dielectric continuum model, the dispersion relations of interface optical phonon modes are given. Furthermore, the interaction between an electron and optical phonons and the ternary mixed crystal effect in these structures are investigated in detail. The optical phonon-assisted tunneling (PAT) is studied using the Fermi golden rule to obtain numerically the PAT currents. The results reveal that the interface optical phonons are more important than the confined longitudinal optical phonons. Only one PAT peak does appear when the middle barrier is wide enough or its Al component is high enough, and the peak moves to the higher applied voltage direction, whereas two PAT peaks do appear when the middle barrier is narrow enough or its Al component is low enough.

Polar optical phonon states and dispersive spectra of wurtzite ZnO nanocrystals embedded in zinc-blende MgO matrix

Based on the macroscopic dielectric continuum model and Loudon’s uniaxial crystal model, the polar optical phonon modes of a quasi-0-dimensional (Q0D) wurtzite spherical nanocrystal embedded in zinc-blende dielectric matrix are derived and studied. It is found that there are two types of polar phonon modes, i.e. interface optical (IO) phonon modes and the quasi-confined (QC) phonon modes coexisting in Q0D wurtzite ZnO nanocrystal embedded in zinc-blende MgO matrix. Via solving Laplace equations under spheroidal and spherical coordinates, the unified and analytical phonon states and dispersive equations of IO and QC modes are derived. Numerical calculations on a wurtzite/zinc-blende ZnO/MgO nanocrystal are performed. The frequency ranges of the IO and QC phonon modes of the ZnO/MgO nanocrystals are analyzed and discussed. It is found that the IO modes only exist in one frequency range, while QC modes may appear in three frequency ranges. The dispersive frequencies of IO and QC modes are the discrete functions of orbital quantum numbers l and azimuthal quantum numbers m. Moreover, a pair of given l and m corresponds to one IO mode, but to more than one branches of QC. The analytical phonon states and dispersive equations obtained here are quite useful for further investigating Raman spectra of phonons and other relative properties of wurtzite/zinc-blende Q0D nanocrystal structures.

Electron–phonon interaction in hemispherical quantum dot

Within the framework of the dielectric continuum (DC) model, the optical phonon modes and electron–optical-phonon interaction in hemispherical quantum dot are investigated. The proper eigenfunctions for longitudinal optical (LO) and interface optical (IO) phonon modes are constructed. After having quantized the eigenmodes, we derive the Hamiltonian operators describing the LO and IO phonon modes as well as the corresponding Fröhlich electron–phonon interaction. The dispersion relation of IO phonon modes is size independent. The potential applications of these results are also discussed.

Electron–interface-optical-phonon interaction in rectangular quantum wire and quantum dot

Under the dielectric continuum model and separation of variables, the interface optical (IO) phonon modes and electron–optical-phonon interaction in rectangular quantum wire and quantum dot embedded in a nonpolar matrix are studied. We found that there exist various types of IO phonon modes in rectangular nanostructures. The IO phonon modes in rectangular quantum wire include IO–propagating (IO–PR) and IO–IO hybrid phonon modes, while the IO phonon modes in rectangular quantum dot contain IO–IO–PR and IO–PR–PR hybrid phonon modes. The results of numerical calculation show that these hybrid phonon modes contain corner optical (CO) phonon modes and edge optical (EO) phonon modes. The potential applications of these results are also discussed.

Phonon States and Dispersive Spectra of Polar Optical Phonons in Quasi-One-Dimensional Nanowires of Wurtzite ZnO and Zinc-Blend MgO Semiconductors

Within the framework of the macroscopic dielectric continuum model and Loudon's uniaxial crystal model, the phonon modes of a wurtzite/zinc-blende one-dimensional (1D) cylindrical nanowire (NW) are derived and studied. The analytical phonon states of phonon modes are given. It is found that there exist two types of polar phonon modes, i.e. interface optical (IO) phonon modes and the quasi-confined (QC) phonon modes existing in 1D wurtzite/zinc-blende NWs. Via the standard procedure of field quantization, the Fröhlich electron-phonon interaction Hamiltonians are obtained. Numerical calculations of dispersive behavior of these phonon modes on a wurtzite/zinc-blende ZnO/MgO NW are performed. The frequency ranges of the IO and QC phonon modes of the ZnO/MgO NWs are analyzed and discussed. It is found that the IO modes only exist in one frequency range, while QC modes may appear in three frequency ranges. The dispersive properties of the IO and QC modes on the free wave-number kz and the azimuthal quantum number m are discussed. The analytical Hamiltonians of electron-phonon interaction obtained here are quite useful for further investigating phonon influence on optoelectronics properties of wurtzite/zinc-blende 1D NW structures.

Polar optical phonon states and their dispersive spectra of a wurtzite nitride superlattice with complex bases: transfer-matrix method

Based on the dielectric continuum model and transfer-matrix method, the completing polar optical phonon states in a wurtzite GaN-based superlattice (SLs) with arbitrary-layer complex bases are investigated. It is proved that $2^n$ types of phonon modes probably exist in a wurtzite nitride SL with $n$-layer complex bases. The analytical phonon states of these modes and their dispersive equations in the wurtzite GaN/Al$_{x}$Ga$_{1-x}$N SL structures are obtained. Numerical calculations on a three-layer GaN/Al$_{0.15}$Ga$_{0.85}$N/AlN complex bases SL are performed. Results reveal that there are interface optical (IO) phonon modes of one type only and four types of quasi-confined (QC) phonon modes in three-layer GaN/Al$_{0.15}$Ga$_{0.85}$N/AlN complex bases SLs. The dispersive spectra of phonon modes in complex bases SLs extend to be a series of frequency bands. The behaviors of QC modes reducing to IO modes are observed. The present theoretical scheme and numerical results are quite useful for analyzing the dispersive spectra of completing phonon modes and their polaronic effect in wurtzite GaN-based SLs with complex bases.

Electron–phonon interaction in fan-shaped quantum dot and quantum wire

The optical phonon modes and electron–optical-phonon interaction in fan-shaped quantum dot and quantum wire are studied with the dielectric continuum (DC) model and separation of variables. The explicit expressions for the longitudinal optical (LO) and interface optical (IO) phonon eigenmodes are deduced. It is found that there exist two types of IO phonon modes: top interface optical (TIO) phonon mode and arc interface optical (AIO) phonon mode, in a fan-shaped quantum dot. After having quantized the eigenmodes, we derive the Hamiltonian operators describing the LO and IO phonon modes as well as the corresponding Fröhlich electron–phonon interaction. The potential applications of these results are also discussed.

Pressure influence on bound polarons in a strained wurtzite GaN/AlxGa1−xN heterojunction under an electric field

The binding energies of bound polarons near the interface of a strained wurtzite GaN/AlxGa1−xN heterojunction are studied by using a modified LLP variational method and a simplified coherent potential approximation under hydrostatic pressure and an external electric field. Considering the biaxial strain due to lattice mismatch or epitaxial growth, the uniaxial strain effects and the influences of the electron–phonon interaction as well as impurity–phonon interaction including the effects of interface-optical phonon modes and half-space phonon modes, the binding energies as functions of pressure, the impurity position, areal electron density and the phonon effect on the Stark energy shift are investigated. The numerical result shows that the contributions from the interface optical phonon mode with higher frequency and the LO-like half space mode to the binding energy and the Stark energy shift are important and obviously increase with increasing hydrostatic pressure, whereas the interface optical phonon mode with lower frequency and the TO-like half space mode are extremely small and are insensitive to the impurity position and hydrostatic pressure. It is also shown that the conductive band bending should not be neglected.

The Influence of Cap and Defect Layer on Interface Optical-Phonon Modes in Finite Superlattices

Employing the transfer matrix method, we investigate the property of the interface optical-phonon modes (IOPMs) in a finite superlattice with a cap layer and a structural defect layer in the dielectric continuum approximation. In the present structure, there exist two types of defect IOPMs: localized modes and surface modes. The evolution of extended, localized and surface IOPMs can be clearly tracked with the thickness of the defect or cap layer. In some cases, degeneracy between surface IOPMs may occur, but the conservation of the total number of the IOPMs is always kept for every value of the transversal wave number. These results show that the spectra of these localized or surface IOPMs can be engineered by adjusting structural parameters.

极化子效应对核壳量子点中光学克尔效应的影响

The effect of the electron-phonon interaction on the Optical Kerr effect is investigated theoretically for electrons confined in a core-shell quantum dot.The interactions of electrons with different phonon modes in the core-shell system,including the confined longitudinal optical (LO) and the interface optical (IO) phonon modes,are investigated.It carried a detailed calculation of Optical Kerr effect on a ZnS/CdSe core-shell quantum dot as a function of pump photon energy with different incident photon energy and under different sizes.The results reveal that the polaron effects are quite important especially around the peak value of the third-order susceptibility.