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.     

Polarons in a cylindrical quantum well wire with finite confining potential

The polaron self-energy and the correction to the electron effective mass in a cylindrical quantum well wire (QWW) are studied by the perturbation approach. The interactions of electrons with different phonon modes in the QWW system, including the confined longitudinal optical phonon modes, in the wire (LO1), in the barrier materials (LO2) and in the interface optical (IO) phonon modes, are considered. The result shows that the LO1 phonon’s contribution to the polaron self-energy increases gradually as the radius of the wire increases, and finally reaches that of the three-dimensional limit, while the LO2 phonon contributes only when the radius of the wire is very small. Also, the contribution of the IO phonon modes first increases quickly as the wire radius increases and soon reaches a maximum, then reduces to zero monotonically.     

极化子效应对ZnS/CdSe量子点三阶极化率的影响

在有效质量近似下,利用量子力学的密度矩阵理论,采用无限深势阱模型,从理论上计算了考虑极化子效应后在导带子带间跃迁时ZnS/CdSe柱型核壳结构量子点二次电光效应(QEOE)和电吸收过程(EA)的三阶极化率。通过数值计算,分析了电子-LO声子和电子-IO声子相互作用对ZnS/CdSe柱型核壳结构量子点二次电光效应和电吸收过程的三阶极化率的影响。结果表明,极化子效应对二次电光效应的三阶极化率χ⁽³⁾_QEDE和电吸收过程的三阶极化率χ⁽³⁾_EA都有很大影响,并且影响的大小与量子点的尺寸大小有关。     

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.     

极化子效应对核壳量子点中光学克尔效应的影响

在有效质量近似下利用量子力学的密度矩阵理论,采用无限深势阱模型解三维薛定谔方程得到电子的本征能量和波函数.从理论上计算了考虑极化子效应后,在导带子带间跃迁时ZnS/CdSe柱型核壳结构量子点光学克尔效应的三阶极化率.通过数值计算,分析了电子-LO声子和电子-IO声子相互作用对ZnS/CdSe柱型核壳结构量子点光学克尔效应的三阶极化率的影响.结果表明：极化子效应对光学克尔效应的三阶极化率 有很大影响,并且影响的大小与量子点的尺寸大小有关.       

Electron mobility for a model Al<Subscript>x</Subscript> Ga<Subscript>1-x</Subscript> As/GaAs heterojunction under pressure

A variational method and a memory function approach are adopted to investigate the electron mobility parallel to the interface for a model Al_xGa_1-xAs/GaAs heterojunction and its pressure effect by considering optical phonon modes (including both of the bulk longitudinal optical (LO) in the channel side and interface optical (IO) phonons). The influence of a realistic interface heterojunction potential with a finite barrier and conduction band bending are taken into account. The properties of electron mobility versus Al concentration, electronic density and pressure are given and discussed, respectively. The results show that the electron mobility increases with Al concentration and electronic density, whereas decreases with pressure from 0 to 40 kbar obviously. The Al concentration dependent and the electron density dependent contributions to the electron mobility from the scattering of IO phonons under pressure becomes more obvious. The variation of electron mobility with the Al concentration and electron density are dominated by the properties of IO and LO phonons, respectively. The effect of IO phonon modes can not be neglected especially for higher pressure and electronic density.     

One-phonon-assisted resonant electron Raman scattering of GaAs quantum dots in an AlAs matrix

We have presented a theoretical calculation of the differential cross section (DCS) for the electron Raman scattering (ERS) process associated with the bulk-like longitudinal optical (LO) and interface optical (IO) phonon modes in semiconductor quantum dots (QDs). Electron states are considered to be confined within the QDs. We consider the Fröhlich electron-phonon interaction in the framework of the dielectric continuum approach. We study selection rules for the processes. Some singularities in the Raman spectra are found and interpreted. A discussion of the phonon behavior for QDs with large and small size is presented. The numerical results are also compared with that of experiments.     

极化子效应对ZnS/CdSe核壳量子点光吸收系数的影响

在有效质量近似下,利用量子力学密度矩阵理论,从理论上研究了考虑极化子效应后核壳量子点中线性、三阶非线性以及总的光吸收系数在不同条件下随入射光能量变化的关系。通过数值计算,分析了电子-LO声子和电子-IO声子相互作用对ZnS/CdSe柱型核壳结构量子点光吸收系数的影响。结果表明,极化子效应对光吸收系数有很大影响,不同声子模式对光吸收系数影响大小不同。考虑电子-LO声子后,光吸收系数被大大提高。另外,入射光强和弛豫时间对系统的吸收系数也有很大影响。     

Resonant Raman scattering from CdTe/ZnTe self-assembled quantum dot structures

We report resonant Raman scattering results of CdTe/ZnTe self-assembled quantum dot (QD) structures. Photoluminescence spectra reveal that the band gap energies of the CdTe QDs decrease with the increase of CdTe thickness from 2.0 to 3.5 monolayers, which indicates that the size of the QDs increases. When the CdTe/ZnTe QD structures are excited by non-resonant excitation, a longitudinal optical (LO) phonon response from the ZnTe barrier material is observed at 206 cm⁻¹. In contrast, when the CdTe/ZnTe QD structures are resonantly excited near the band gap energy of the QDs, additional phonon modes emerge at 167 and 200 cm⁻¹, while the ZnTe LO phonon response completely disappears. The 167 cm⁻¹ mode corresponds to the LO phonon of the CdTe QDs. A spatially resolved Raman scattering from the cleaved edge of the QD sample reveals that the 200 cm⁻¹ mode is strongly localized at the interface between the CdTe QDs and ZnTe cap layer. This phonon mode is attributed to the interface optical (IO) phonon. The analytically calculated value of the IO phonon energy using a dielectric continuum approach, assuming a spherical dot boundary, agrees well with the experimental value.     

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 k_z and the azimuthal quantum number m arediscussed. 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.     

Fröhlich electron-interface and -propagating optical phonon interactions in a wurtzite multi-shell cylindrical heterostructure

Under the dielectric continuum model and Loudon's uniaxial crystal model, the polar optical phonon modes in a wurtzite multi-shell cylindrical heterostructure are analyzed and discussed. The analytical electrostatic potential functions are presented for all the five types of polar optical phonon modes including the interface optical (IO) modes, the propagating (PR) modes, the quasi-confined (QC) modes, the half-space-like (HSL) modes and the exactly confined (EC) modes. By adopting a transfer matrix method, the free IO and PR phonon fields and corresponding Fröhlich electron -IO and -PR interaction Hamiltonians are obtained via the method of electrostatic potential expansion. The analytical formulas are universal and can be applied to single, double and some complex cylindrical wurtzite quantum systems.     

Surface and interface optical phonon modes and electron-phonon interaction in a multi-shell spherical system

Within the framework of the dielectric continuum model, interface optical(IO) and surface optical(SO) phonon modes and the Fr?hlich electron-IO (SO) phonon interaction Hamiltonian in a multi-shell spherical system were derived and studied. Numerical calculation on CdS/HgS/H₂O and CdS/HgS/CdS/H₂O spherical systems have been performed. Results reveal that there are two IO modes and one SO mode for the CdS/HgS/H₂O system, one SO mode and four IO modes whose frequencies approach the IO phonon frequencies of the single CdS/HgS heterostructure with the increasing of the quantum number l for CdS/HgS/CdS/H₂O. It also showed that smaller l and SO phonon compared with IO phonon, have more significant contribution to the electron-IO (SO) phonon interaction. Received 16 October 2001 and Received in final form 23 January 2002 Published online 25 June 2002     

Polar Oscillation of Interface and Surface Optical Phonons in Free-Standing Cylindrical Quantum-Well Wires

Under dielectric continuum approximation, interface optical (IO) and surface optical (SO) phonon modes as well as the corresponding Fro^ehlich electron-phonon interaction Hamiltonian in a free-standing cylindrical quantum-well wire (QWW) are derived and studied. Numerical calculations on GaAs/AlzGa1-x 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 x in AlzGa1-x As material and the wavevector in z direction, kz. With the increasing of kz and quantum number m, the frequency of each IO mode approaches one of the two frequency values of the single GaAs/AlxGa1-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 and -SO phonons becomes weaker.     

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.     

Interface Optical Phonon Modes and Frohlich Electron-Phonon Interaction Hamiltonian in a Multi-shell Spherical Nanoheterosystem

Under dielectric continuum approximation, interface optical (IO) phonon modes and the Frohlich electron-IO phonon interaction Hamiltonian in a multi-shell spherical nanoheterosystem were derived and studied. Numericalcalculations on three-layer and four-layer CdS/HgS spherical nanoheterosystems have been performed. Results revealthat there are four IO phonon modes for the three-layer system and six IO phonon modes for the four-layer system.On each interface, there are two IO phonon modes, the frequency of one is between WTO,CdS and WLO,CdS, and that ofthe other is between WTO,HgS and WLO,HgS. With the increasing of quantum number l, the frequency of each IO modeapproaches one of the two frequency values of the single CdS/HgS heterostructure, and the potential for each IO modeis more and more localized at a certain interface, furthermore, the coupling between the electron-lO phonons becomes weaker.     

弱耦合多原子半无限晶体中的表面极化子的有效势

本文研究弱耦合多原子半无限晶体中表面极化子的性质。采用线性组合算符和幺正变换导出表面极化子的的有效势。     

Pressure effect on the electron mobility in AlAs/GaAs quantum wells

By taking the influence of optical phonon modes into account, this paper adopts the dielectric continuum phonon model and force balance equation to investigate the electronic mobility parallel to the interfaces for AlAs/GaAs semiconductor quantum wells (QWs) under hydrostatic pressure. The scattering from confined phonon modes, interface phonon modes and half-space phonon modes are analysed and the dominant scattering mechanisms in wide and narrow QWs are presented. The temperature dependence of the electronic mobility is also studied in the temperature range of optical phonon scattering being available. It is shown that the electronic mobility reduces obviously as pressure increases from 0 to 4GPa, the confined longitudinal optical (LO) phonon modes play an important role in wide QWs, whereas the interface optical phonon modes are dominant in narrow QWs, the half-space LO phonon modes hardly influence the electronic mobility expect for very narrow QWs.     

First-order Raman scattering in cylindrical wurtzite nanowire

We have presented a theoretical study on electron resonant Raman scattering (ERRS) process associated with the bulk longitudinal optical (LO), surface optical (SO) and quasi-confined (QC) phonon modes in a free-standing wurtzite nanowire (NW). We consider the Fröhlich electron–phonon interaction in the framework of the dielectric continuum model. Numerical calculations on the GaN material reveal that differential cross-section (DCS) is sensitive to the wire size. The bulk LO and high-frequency quasi-confined (QC₊) phonons make main contributions to the DCS and the impact of the SO phonon can be negligible in the ERRS process. Moreover, scattering intensity of the bulk LO phonon is strongly enhanced as the incident photon energy approaches the energy band-gap of the GaN.     

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.     

多原子半无限晶体中表面极化子的内部激发态

研究多原子半无限晶体中电子与表面光学(SO)声子耦合强,而与体纵光学(LO)声子耦合弱的极化子的激发态性质.采用线性组合算符和幺正变换方法导出与SO声子耦合强而与LO声子耦合弱情形下极化子的基态能量、第一内部激发态能量和激发能量.结果表明,多原子半无限晶体中与SO声子耦合强,而与LO声子耦合弱的极化子的基态能量、第一内部激发态能量不仅包含不同支LO声子和不同支SO声子与电子耦合的能量,而且也包含不同支SO声子之间相互作用贡献的附加能量.激发能量与体纵光学声子无关.