Confined LO Phonons Research Articles

Temperature and hydrostatic pressure effects on exciton–phonon coupled states in semiconductor quantum dot

We studied theoretically the exciton–phonon coupled states in a cylindrical quantum dot (QD) under hydrostatic pressure and temperature effects. We calculated the exciton binding energy by using a variational approach within the effective-mass approximation. The stress is applied along the QD growth axis and the interactions of charge carriers (electron and hole) with both the confined LO phonon modes and surface phonons (TSO and SSO) are incorporated in our calculation. The effect of these three phonon modes on the exciton binding energy is discussed in the presence of pressure and temperature effects. The numerical computation for GaAs/Ga1-xAlxAs QD has shown that the exciton binding energy is very significant with increasing pressure and decreasing temperature. Both the exciton binding energy and its polaronic correction increase linearly with increasing stress. We investigated also the effects of the temperature and pressure on the integrated photoluminescence (PL) intensity, and show that at relatively high temperature the phonons have a noticeable effect on it. This physical parameter also shows a great dependence on pressure.

Analysis of hot electron effects on intersubband Raman laser in modulation‐doped GaAs/AlGaAs coupled double quantum wells

AbstractWe present a simulation of hot electron effects on inter‐subband Raman laser (IRL) consisting of modulation‐doped n‐type GaAs/AlGaAs coupled double quantum wells (CDQWs) with high 2D electron density. A time evolution for occupation number and electron temperature in each subband as well as the number of lasing Stokes photons are calculated self‐consistently for the modelled IRL. It is shown that Raman gain exhibits a characteristic reduction synchronizing an increase of Stokes photon density as time is evolved in sub‐nanosecond range. Then a saturation feature of output power is expected. The energy relaxation due to the confined LO phonons and the interface modes gives rise to interesting change of electron temperature in subband 1 and subband 2 during the Raman lasing. The threshold optical pumping intensity is estimated to be 50 kW/cm2. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Confined LO phonon limited free carrier absorption in quantum well wires

Confined LO phonon limited free carrier absorption in quantum well wires

Ground State of a Polaron in a Symmetric Triangular QuantumWell

We study the effects of electron–phonon interaction on the electronground state in a symmetric triangular quantum well, and calculate theground state energy of an electron in theGaAs/Al0.96Ga0.04As triangular quantum well including theeffects of the interaction between electrons and confined LO phonons byusing a modified Lee–Low–Pines variational method. The electron wavefunction in the triangular well is chosen as the Airy function. Thenumerical results are given and discussed.

Confined LO-phonon assisted tunneling in a parabolic quantum well with double barriers

The spatial dependence of the wave functions for electrons in a parabolic quantum well with double barriers has been calculated by using a transfer-matrix approach and compared with that of a rectangular quantum well. The phonon assisted tunneling currents are studied theoretically based on a dielectric continuum model. Only confined LO phonons are considered due to the destroyed interface character. It is found that the results are helpful in observing the current peaks for phonon assisted tunneling as expected. It indicates that the confined LO-phonon peaks are higher than that for rectangular wells. The influence on the current peaks of tunneling from phonons in the emitter barrier is more obvious for a parabolic well with a wider width.

Theory of carrier dynamics and time resolved reflectivity inInxMn1−xAs∕GaSbheterostructures

We present detailed theoretical calculations of two color, time-resolved pump-probe differential reflectivity measurements. The experiments modeled were performed on InMnAs/GaSb heterostructures and showed pronounced oscillations in the differential reflectivity as well as a time-dependent background signal. Previously, we showed that the oscillations resulted from generation of coherent acoustic phonon wavepackets in the epilayer and were not associated with the ferromagnetism. Now we take into account not only the oscillations, but also the background signal which arises from photoexcited carrier effects. The two color pump-probe reflectivity experiments are modeled using a Boltzmann equation formalism. We include photogeneration of hot carriers in the InMnAs quantum well by a pump laser and their subsequent cooling and relaxation by emission of confined LO phonons. Recombination of electron-hole pairs via the Schockley-Read carrier trapping mechanism is included in a simple relaxation time approximation. The time resolved differential reflectivity in the heterostructure is obtained by solving Maxwell's equations and compared with experiment. Phase space filling, carrier capture and trapping, band-gap renormalization and induced absorption are all shown to influence the spectra.

Theory of Intersubband Raman Laser in Modulation-doped Asymmetric Coupled Double Quantum Wells

A microscopic theory is developed for the laser gain due to stimulated intersubband electronic Raman scattering pumped by CO 2 laser in modulation-doped GaAs/AlGaAs asymmetric coupled double quantum wells (ACDQWs). Based on the charge-density-excitation (CDE) mechanism, the formula for electronic Raman scattering cross-section is given, taking into account the coupling between intersubband plasmon and optical phonons including GaAs confined LO phonons and interface phonons. Stimulated Raman gain factor is then derived from the cross-section. The optimization of Raman gain, the gain saturation and threshold condition are also discussed. Numerical analysis for temporal variation of stimulated Stokes photon density, subband populations and output Raman laser power is carried out by using the self-consistent conventional rate equations. The theory can predict the presence or lack of coupled modes in lasing in agreement with the recent experimental results.

Inter- and intra-subband relaxation of hot electrons in GaAs/AlGaAs quantum wells

In this work, we have studied the inter- and intra-subband scattering of hot electrons in quantum wells using the hot electron–neutral acceptor luminescence technique. We have observed direct evidence of the emission of confined optical phonons by hot electrons excited slightly above the n=2 subband in GaAs/Al 0.37Ga 0.63As quantum wells. Scattering rates of photoexcited electrons via inter- and intra-subband LO phonon emission were calculated based on the dielectric continuum model. We found that, for wide wells with the Al composition of our experiments, both the calculated and experimental results suggest that the scattering of the electrons is dominated by the confined LO phonon mode. In the calculations, scatterings among higher subbands are also dominated by the same type of phonon at well width of 10 nm.

Localized phonon-assisted electron tunneling in DBRT structure in quantizing magnetic field

A theory of confined and interface optical phonon-assisted electron tunneling in GaAs/AlAs double barrier resonant tunneling structure in the presence of quantizing magnetic field is developed. The excess current is calculated employing transfer matrix method. Electron interaction with confined LO phonons described by Huang and Zhu, slab mode and guided mode models is considered. The effect of interface modes is also incorporated. Numerical results obtained, based on Huang and Zhu model, are in conformity with experimental observations.

Observation of coherent optical phonons in GaAs/AlxGa1−xAs single heterojunctions

Time-resolved second-harmonic generation was used to generate and detect coherent longitudinal optical phonons in GaAs/AlxGa1−xAs single heterojunctions. Three coherent LOGaAs, LOGaAs - like, and LOAlAs - like phonons were launched by transiently screening the depletion field in the GaAs/AlxGa1−xAs interfacial region. The first and the last two phonon modes were assigned to confined LO phonons in the GaAs well and the AlxGa1−xAs barrier, respectively. The initial phase and dephasing time were determined for each phonon mode. The driving mechanism and dephasing process were investigated in the experiments.

Optical phonon–assisted magnetotunneling peaks inGaAs/AlxGa1−xAsdouble-barrier structures

The effect of the interface optical (IO) phonons and the confined LO phonons in a ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ emitter barrier and GaAs quantum well on the phonon-assisted tunneling through a double-barrier structure has been studied in the presence of a magnetic field in the direction of the current. The tunneling current densities are calculated and the numerical results for the typical ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ structures are given graphically. An alternative recognition of the phonon-assisted tunneling current peaks is suggested. Only one theoretical peak from the IO phonons and the confined LO phonons is easy to be observed for wide well systems. The second peak appears at the position corresponding to the emission of the confined higher-frequency branch LO phonon in the ternary mixed-crystal emitter barrier and can also be observed in the narrower-well systems.

Resonance Raman scattering in semiconductor quantum dots: Adiabatic versus time-dependent perturbation theory

The adiabatic theory of resonance one-phonon Raman scattering in semiconductor nanocrystals is revised and extended with perturbative non-adiabatic corrections, given by the Albrecht's B term. This theory is confronted with the time-dependent perturbation approach, pointing at their differences and similarities. It is shown that both theories are equivalent in the limit of weak electron-phonon coupling and non-degenerate or uncoupled resonant states. Evaluations of the A and B terms for the confined LO phonon in CdSe and CdS nanocrystals are reported. These evaluations show that the B term can usually be neglected.

Coherent confined LO phonons in70Ge/74Geisotope superlattices generated by ultrafast laser pulses

Generation of high-order coherent confined LO phonon modes by 20-fs ultrashort laser pulse irradiation was observed in a new class of nonpolar semiconductors; ${}^{70}\mathrm{Ge}{/}^{74}\mathrm{Ge}$ isotope superlattices. The phonon oscillations were Fourier transformed and compared with a theoretical calculation based on a planar force-constant model and a bond polarizability approach. The comparison between the calculated and Fourier transformed spectra shows clearly that the amplitudes of coherent phonons are determined solely by the degree of the atomic displacement and that only the Raman active odd-number-order modes are observable. The spectra taken with variety of polarization of pump beam show clearly that the generation mechanism of coherent phonons in nonpolar semiconductor like Ge is stimulated Raman scattering.

Generation of coherent confined LO phonons under the drift of two-dimensional electrons

Generation of coherent confined LO phonons under the drift of two-dimensional electrons

Coherent optical phonon generation by the electric current in quantum wells

This letter addresses the effect of generation of confined LO phonons by drifting electrons in quantum wells. We have derived a general formula for the phonon increment as a function of phonon wave vector, electron drift velocity, and structure parameters. Numerical estimates of the phonon increment and the phonon lifetimes have shown that AlAs/GaAs/AlAs and GaSb/InSb/GaSb quantum well structures can demonstrate the effect of coherent LO phonon generation by the electric current.

Binding energy of hydrogenic impurities in polar cylindrical quantumdot

We have studied the polaron effect on the binding energy of shallow hydrogenicimpurities in a cylindrical quantum dot using a variational approach for thefinite confinement potential. The interactions of charge carriers (electron andion) with both the confined LO phonon and surface phonons (SSO and TSO) aretaken into account. The effect of these three phonon modes on the bindingenergy of a shallow donor is examined. The emphasis is placed on the dependenceof the polaronic corrections on the quantum dot size. It is found that thecorrection due to the LO phonons is more important than that due to thesurface optical phonon modes.

Well-width dependence of electron-phonon interaction energies in quantum wells due to confined LO phonon modes

In the present paper, four confined LO phonon models have been used to calculate the electron--confined-LO-phonon interaction energy as a function of the well width, and the results are compared with each other. The explicit expression of the interaction energy for each phonon model is obtained within the intermediate-coupling approach. It is shown that the lattice dynamics boundary condition in addition to the electromagnetic boundary condition has only a modest effect on the interaction energy as long as the phonon eigenfunctions are orthonormal and complete. Because the guided model does not satisfy the electromagnetic boundary condition and the Huang-Zhu model does not satisfy the orthonormal condition, the numerical results of these two models are not in agreement with the other two models.

Local Ordering in GaN-Rich Ternary GaNP Alloys

ABSTRACTUsing micro-Raman scattering we have studied atomic distribution and the ordering effects in GaN-rich GaNP layers on (0001) sapphire substrates grown by electron cyclotron resonance molecular beam epitaxy (ECR-MBE). Raman spectrum from layers grown at higher temperatures (≥700°C) shows coexistence of GaP-rich region with cubic symmetry and GaN-rich region with hexagonal symmetry. Sharp TO and LO phonon lines, indicative of {111} ordering in the GaP region are observed. Increasing phosphorous (P >1.5%) in GaNP alloy leads to phase separation that is reflected in the suppression of GaN-like Raman modes. The phase-separated region shows an additional Raman line at 384 cm−1 between the TO and LO phonon of GaP due to strongly confined LO phonon in ordered {111} (GaP)n(GaN)m nanometer size clusters. Decreasing growth temperature increases the phosphorous concentration in the GaNP layer and disorder activated acoustic modes appear in the Raman spectrum as a result of symmetry break down. When phosphorous concentration reaches 8.2 % in the layer grown at 570°C, Raman spectrum shows broad amorphous like bands indicative of short-range ordering

Combined polaron states in magnetooptical effects in a quantum well

Combined polaron states in a rectangular quantum well in a strong magnetic field perpendicular to the well plane are discussed. These states are due to interaction between two discrete electron levels with different Landau quantum numbers (n and n1) and different size-quantization quantum numbers (m and m1) on the one hand and a confined LO phonon on the other under conditions of low temperature when the energy difference between the electronic levelsis equal or close to the energy of the confined LO phonon. The expression for the resonant magnetic field Hres at which a combined polaron is formed contains the energy difference between size-quantized levels, so it is a function of quantum well parameters. The separation ΔEres between branches in the energy spectrum of a combined polaron and Hres has been calculated as a function of the quantum well width d. The resonant field Hres can be reduced dramatically in comparison with the case m=m1. The case of size-quantization with n=n1 has been analyzed. The energy difference ΔEres is in the range (1–5)· 10−3 eV. The damping of combined polaron states due to the effect of anharmonicity on the LO phonon has been studied. Interband absorption and features in the reflection spectrum due to interband transitions have been calculated for an arbitrary ratio between the radiative and “phonon” lifetime of a combined polaron have been investigated.

Reconstruction of GaAs/AlAs (311) and (100) Interfaces: Raman Study

Phonon spectra of GaAs/AlAs superlattices (SLs) grown on facet surfaces (311)A,B and (100) surface were studied using Raman spectroscopy. Thickness of GaAs layers in (311) direction was varied from 1 to 10 monolayers, thickness of AlAs barriers was 8 monolayers. Using selection rules for (311)A and B surfaces, different polarisation geometries of Raman scattering were applied to study LO and TO modes. The splitting of TO x (atoms displace perpendicular to the facets on (311)A surface) and TOy (atoms displace parallel to the facets) modes observed for (311)A surface. In the case of (311)B SLs no splitting was observed. The phonon anisotropy of (311)A SLs can be indirect evidence of anisotropic structure of formed on (311)A GaAs surface quantum objects. The strong difference in photoluminescence spectra of (311)A and (311)B SLs was also observed. In the Raman spectra of the SL containing GaAs submonolayers grown on (2x4) reconstructed (100) surface, the triplet Raman peak corresponding to scattering on GaAs-like confined LO phonons was observed. The triplet structure appears due to additional lateral confinement of LO phonons in formed quantum objects. The calculations of Raman spectra were carried out using the model of rigid ions and Wolkenstain bond polarisability model. According to the calculations, the lateral localisation takes place when the thickness of AlAs barriers in lateral directions is 2 monolayers or more. The theoretical Raman spectra of the islands grown (in the context of a known model) on the (001)-(2x4) reconstructed surface are in surprisingly good agreement with the experimental ones. The calculations show that 70% of the islands contains less than 18 Ga atoms, what is in very good agreement with the recent STM data.