Dual Space Analyzing Based on Symmetry Properties for Phonons fo Si Quantum Dot

Phonon modes in spherical Si quantum dots (QDs) with up to 7.9 nm in diameter are calculated by using the projection operators of the group theory into valence force field model. The phonons of dot modes in each of five irreducible representations (symmetries) are classified by using a dual space analysis method. It is found that the bulk-like modes with localization radius much smaller than the dot's radius have clearly pronounced bulk specific-k point parentage, T_λ(n, k_BZ, K_cut), from specific part of the Brillouin zone (BZ) (Γ-derived, X-derived etc.) and from definite bulk band (one in six modes). In Si dots of all sizes, each specific bulk-like dot mode has specific symmetry. The bulk TO(Γ)-like and the bulk LO(Γ)-like dot modes always have T₂ and A₁ symmetries, respectively. Except the bulk-A(Γ)-like dot modes of which the frequencies blue-shift as the dot size reducing, the bulk-like Γ-derived LO and TO dot modes and bulk-like X-derived TA and LA dot modes red-shift in frequency with decreasing dot size. There is almost not LO/TO mixing for bulk-like modes. As for the surface-like modes localized at the periphery of the dot, their eigenmodes have not a dominant bulk specific-k point parentage or a dominant BZ parentage around some special point. They are a superposition of many bulk bands with k from all over the bulk BZ. They have much significant mode mixing than the bulk-like phonons. The classification of dot modes based on the symmetry of group theory will bring advantageous to the discussion of Ramam spectrum, electron-phonon interaction and other phonon-assisted effects in QDs.     

Interaction between an electron and optical phonons in polar semiconductor heterostructures

Interface phonons and bulk-like longitudinaloptical (LO) phonons and their interaction with an electron are studied for a finite four-layer heterostructure (FFLHS). An analysis of the field eigenvectors shows that, in the vicinity of the Brillouin-zone center, an interface transverse-optical (TO) mode oscillates at the bulk LO frequency, and an interface LO mode oscillates at the bulk TO frequency. Analytic expressions and numerical illustrations for dispersion relations of interface modes and for electron-phonon coupling functions and scattering rates are obtained for finite, semi-infinite and infinite quantum well (QW) structures which are important special cases of an FFLHS. It is shown that the scattering rates depend strongly on the well width of a QW structure, and that interface modes are much more important than bulk LO modes when the well width is small. The calculated results also show that the usual selection rules for intersubband and intrasubband transitions break down in asymmetric heterostructures. Moreover, we have found an interesting result. That is, in comparison with the negligibly small interaction between an electron and the lowest-frequency interface-mode in symmetric single QWs and commonly used step QWs, this interaction may be very large in asymmetric single QWs and general step QWs.     

小尺寸Si/Ge量子点内应变和组分的拉曼光谱表征

本文详细地研究了原始生长和退火处理后的Si/Ge量子点的拉曼光谱。我们观测到了Si/Ge量子点的一系列本征的拉曼振动模以及Ge-Ge模的LO和TO声子峰间4.2cm-1的频率劈裂。通过这些参数,我们自洽地确定了原始生长的平面直径为20nm和高为2nm的Si/Ge量子点内Ge的平均组分为80%,平均应变为-3.4%。分析清楚地表明了这种小尺寸的Si/Ge量子点内的应变仍遵从双轴应变,并且应变的释放主要由量子点和Si隔离层间Si-Ge原子互扩散决定。     

Raman study of InAs quantum dots on GaAs/InP grown by low pressure metal-organic chemical vapor deposition

Raman spectra of InAs quantum dots (QDs) on InP substrate were investigated. Both longitudinal-optic (LO) and transverse-optic (TO) frequency of InAs QDs showed a large blue-shift comparing to its bulk due to the compressive strain in InAs QDs. Raman scattering of InAs QDs with a thin GaAs interlayer was studied. We obtained that the peak position of LO and TO mode of InAs QDs became larger blue-shifted when we inserted the GaAs layer. At the same time, we found a red-shift of the frequency of GaAs LO mode because of tensile strain. Theoretical calculation was performed and its prediction coincided with our experiment results well. They both showed that strain played an important role in formation of InAs QDs.     

Raman scattering in multilayer structures with CdTe quantum dots in ZnTe

Raman spectra in superlattices composed of layers of self-assembled CdTe quantum dots separated by ZnTe barriers are investigated. As the barrier thickness increases, a high-frequency shift of all peaks is observed, which is explained by a decrease in the lattice constant averaged over the volume of the entire structure. Peaks are found at a CdTe TO mode frequency of 140 cm^?1 and also at 120 cm^?1. The first peak is assigned to the symmetric Coulomb (interface) mode of the quantum dot material, and the low-frequency peak is assigned to the symmetric mode of the phonons captured in the quantum dot. This combination of modes in structures with quantum dots has not been observed previously.     

Raman scattering of Ge dot superlattices

Self-organised Ge dot superlattices grown by molecular beam epitaxy of Ge and Si layers utilizing Stranski-Krastanov growth mode were investigated by Raman spectroscopy. An average size of Ge quantum dots was obtained from transmission electron microscopy measurements. The strain and interdiffusion of Ge and Si atoms in Ge quantum dots were estimated from the analysis of frequency positions of optical phonons observed in the Raman spectra. Raman scattering by folded longitudinal acoustic phonons in the Ge dot superlattices was observed and explained using of elastic continuum theory. Received 25 January 2000     

Correct Evaluation of the Effect of Transverse Effective Charges on Phonons in AlAs Quantum Dots

An improved valence force field model (VFFM) is suggested to calculate the phonon modes in both bulk specimens and quantum dots (QDs) of AlAs taking account of the effect of transverse effective charges (TOs) correctly.The resultant dispersions of AlAs bulk phonons are in accord better with the results carefully fitted to the experimental data by using 11-parameters rigid-ion model, than those got by ordinary VFFM, especially in the region of near Г point. For AlAs QDs, TCs are evaluated bond by bond for each phonon mode of QD and its effect on the change of the force on atoms is taken into account to modify further the phonon spectrum. The frequency spectra and densities ofphonon states of d/fferent irreducible representations calculated by using improved VFFM are compared with the results of ordinary VFFM. The correct evaluation of the TOs is not only important in calculating the phonon spectrum of both bulk and QD specimens accurately, but is also in the further discussion of the electron-phonon (e-ph) interaction, which can be directly related to TCs of ions in QD.     

Folded acoustic phonons in Si/Ge superlattices with Ge quantum dots

The spectra of Raman scattering by folded acoustic phonons in Si/Ge superlattices with pseudomorphic layers of Ge quantum dots (QDs) grown by low-temperature (T = 250°C) molecular beam epitaxy are studied. New features of the folded phonon lines related to the resonant enhancement and unusual intensity ratio of the doublet lines that cannot be explained by the existing theory have been observed. The observed modes are shown to be related to the vibrations localized to the QDs and induced by the folded phonons of the Si spacer layers. The calculations performed in the model of a one-dimensional chain of atoms have allowed the nature of the localization of acoustic phonons attributable to a modification of the phonon spectrum of a thin QD layer to be explained. The observed intensity ratio of the folded phonon doublet lines is caused by asymmetry of the relief of the QD layers.     

Correct Evaluation of the Effect of Transverse Effective Charges on Phonons in AlAs Quantum Dots

An improved valence force field model (VFFM) is suggested to calculate the phonon modes in both bulk specimens and quantum dots (QDs) of AlAs taking account of the effect of transverse effective charges (TCs) correctly.The resultant dispersions of AlAs bulk phonons are in accord better with the results carefully fitted to the experimental data by using 11-parameters rigid-ion model, than those got by ordinary VFFM, especially in the region of near F point. For AlAs QDs, TCs are evaluated bond by bond for each phonon mode of QD and its effect on the change of the force on atoms is taken into account to modify further the phonon spectrum. The frequency spectra and densities of phonon states of different irreducible representations calculated by using improved VFFM are compared with the results of ordinary VFFM. The correct evaluation of the TCs is not only important in calculating the phonon spectrum of both bulk and QD specimens accurately, but is also in the further discussion of the electron-phonon (e-ph) interaction, which can be directly related to TCs of ions in QD.     

Kinetics of self-assembled InN quantum dots grown on Si (111) by plasma-assisted MBE

One of the scientific challenges of growing InN quantum dots (QDs), using Molecular beam epitaxy (MBE), is to understand the fundamental processes that control the morphology and distribution of QDs. A systematic manipulation of the morphology, optical emission, and structural properties of InN/Si (111) QDs is demonstrated by changing the growth kinetics parameters such as flux rate and growth time. Due to the large lattice mismatch, between InN and Si (~8%), the dots formed from the Strannski–Krastanow (S–K) growth mode are dislocated. Despite the variations in strain (residual) and the shape, both the dot size and pair separation distribution show the scaling behavior. We observed that the distribution of dot sizes, for samples grown under varying conditions, follow the scaling function.     

Study of surface and bulk acoustic phonon excitations in superlattices using picosecond ultrasonics

We have performed picosecond ultrasonic studies on the surface and bulk acoustic phonons in amorphous Mo/Si superlattices. Localized surface modes within the first, second, and sixth frequency gaps of the zone-folded phonons are observed. A selection rule derived from symmetry considerations provides new understanding of why certain modes are seen and not the others. The excitation strengths and detailed spectral features of these lines are studied, and the results are well explained by an elastic-continuum theory. It is found that the line shapes are significantly modified by the presence of bulk modes near the zone center.     

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 modesexisting in Q0D 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. 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.     

Exciton-phonon interaction in cylindrical semiconductor quantum dots

The exciton-longitudinal optical phonon interaction is theoretically investigated for the case of polar semiconductor cylindrical quantum dots embedded in semiconductor matrix. The theory is developed within the dielectric continuum model considering the Fröhlich interaction between electrons and confined bulk longitudinal optical phonons for a configurational interaction model of quantum dot. Representative longitudinal optical phonon mode for the exciton-phonon interaction is predicted for cylindrical InAs/GaAs quantum dots.     

Investigation of cavity modes and direct observation of Purcell enhancement in 2D photonic crystal defect microcavities

We demonstrate our ability to control and manipulate the optical modes in 2D Photonic Crystal Defect cavities and investigate their coupling to InGaAs self-assembled quantum dots. Our results enable us to probe the nature of individual cavity modes and directly investigate cavity QED phenomena. For the lowest mode volume cavities investigated, consisting of a single missing air hole within a hexagonal lattice, we have measured a clear Purcell enhancement of the light-matter interaction in the weak coupling regime. For QDs on-resonance with localized cavity modes this translates to a shortening of the quantum dot spontaneous emission lifetime by a factor 2 when compared to off-resonance dots.     

Vibration Spectrums of Polar Interface Optical Phonons in GaAs/AlAs Cylindrical Quantum Dots

The dispersions of the top interface optical phonons and the side interface optical phonons in cylindrical quantum dots are solved by using the dielectric continuum model. Our calculation mainly focuses on the frequency dependence of the IO phonon modes on the wave-vector and quantum number in the cylindrical quantum dot system. Results reveal that the frequency of top interface optical phonon sensitively depends on the discrete wave-vector in z direction and the azimuthal quantum number, while that of the side interface optical phonon mode depends on the radial and azimuthal quantum numbers. These features are obviously different from those in quantum well, quantum well wire, and spherical quantum dot systems. The limited frequencies of interface optical modes for the large wave-vector or quantum number approach two certain constant values, and the math and physical reasons for this feature have been explained reasonably.     

Size quantization of acoustic phonons in CuCl nanocrystals

It is shown that the mixed character of spheroidal vibrational modes of semiconductor quantum dots of spherical shape may lead to the appearance of a line in the low-frequency Raman spectra of nanocrystals whose spec-tral position is independent of the average radius of nanocrystals in the sample over a wide range of sizes. This effect is associated with the rapid saturation of the dispersion dependence for transversal acoustic phonons in the bulk semiconductor. The maximum radius of quantum dots at which the line indicated above is observed in the spectrum has been estimated.     

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.     

Carrier gas effects on the SiGe quantum dots formation

SiGe quantum dots (QDs) grown by ultra-high vacuum chemical vapor deposition using H₂ and He carrier gases are investigated and compared. SiGe QDs using He carrier gas have smaller dot size with a better uniformity in terms of dot height and dot base as compared to the H₂ carrier gas. There is a higher Ge composition and less compressive strain in the SiGe QDs grown in He than in H₂ as measured by Raman spectroscopy. The Ge content is higher for He growth than H₂ growth due to hydrogen induced Si segregation and the lower interdiffusivity caused by the more strain relaxation in the He-grown SiGe dots. The photoluminescence also confirms more compressive strain for H₂ growth than He growth. Hydrogen passivation and Ge-H cluster formation play an important role in the QDs growth.     

IR-active vibrational modes of CdTe and CdSe colloidal quantum dots and CdTe/CdSe core/shell nanoparticles and coupling effects

The frequencies of the vibrational modes of CdTe and CdSe quantum dots and CdTe/CdSe core/shell nanoparticles prepared by the colloid chemistry method are determined using IR transmission and IR reflection spectroscopy. The experimental IR transmission spectrum of CdTe and CdSe nanocrystals exhibits a broad minimum located between the frequencies of the transverse optical (TO) and longitudinal optical (LO) phonons of bulk CdTe and CdSe crystals. The frequencies of the modes for ensembles of CdTe and CdSe quantum dots are considerably shifted toward lower frequencies as compared to those calculated for single quantum dots. This is explained by the dipole-dipole interaction between quantum dots. The frequencies of modes for the structures with core/shell nanoparticles differ little from the calculated frequencies. This suggests a weakening of the interaction in these structures due to the enhancement of dielectric screening.     

量子点中磁激子的极化子效应

采用推广的LLP方法研究了自组织量子点中磁激子的极化子效应。考虑带电粒子和声子的相互作用,得到了激子能量随磁场的变化关系。结果表明,激子-声子的相互作用降低了激子的能量,但影响很小;极化子效应在没有外磁场时较明显,随着外磁场的增加,这种效应变得越来越弱。