Bound polaron in a cylindrical quantum wire of a polar crystal

Xie, Hailiang; Chen, Chuan-Yu; Ma, Ben-Kun

doi:10.1103/physrevb.61.4827

Cited by 126 publications

(122 citation statements)

References 16 publications

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“…As pointed out by Xie et al [45], the Fröhlich electron-phonon interaction Hamiltonian based on the electrostatic potential continuum is quite close to that given by Huang-Zhu model [44], and it is suitable to study electron-optical phonon interaction relative to the electro-potential. Moreover, the calculated results of polaron binding energies in GaAs/ N-based quantum systems concluding the IO modes and confine/quasi-confined phonon modes supported and confirmed the reliability and reasonableness of electrostatic potential continuous BC [38,46]. Hence, the current theories and results still have important meanings.…”

Section: Qcsupporting

confidence: 74%

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Full optical phonon states and their dispersive spectra of a wurtzite GaN/AlGaN superlattice: Quantum size effect

Zhang

2011

Physica Status Solidi (b)

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The polar optical phonon states of four types of phonon modes including the interface optical (IO) modes, the propagating (PR) modes, the quasi-confined (QC) phonon modes in well-layer material (QC w ), and the QC phonon modes in barrier-layer material (QC B ) in a wurtzite GaN/Al x Ga 1-x N superlattice (SLs) are investigated within the dielectric continuum model framework. The analytical phonon states of the four types of modes and their dispersive equations in the wurtzite GaN/Al x Ga 1-x N SL structures are obtained. Numerical calculations on the dispersive spectra of phonon modes and the quantum size effect are performed for a wurtzite GaN/Al 0.15 Ga 0.85 N SL. Results reveal that dispersive curves of phonon modes in SLs form a series of frequency bands. The behaviors of QC w modes reducing to PR and IO modes are observed clearly. With the increase of well-layer GaN width d 1 of the SLs, the dispersion of the QC B modes become weaker and weaker, and their frequency bands become narrower and narrower. But the PR, IO, and the QC w phonon modes become more dispersive, and the frequency bands of these modes become wider and wider as d 1 increases. The present theoretical scheme and numerical results are quite useful for analyzing the dispersive spectra of full phonon modes and their polaronic effect in wurtzite GaN/AlGaN SL structures.

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Section: Qcsupporting

confidence: 74%

“…This will further influence the polaronic effect of various phonon modes on the carrier transport and other properties [37,38]. Considering the important facts discussed above, we will investigate the full polar optical phonon modes in wurtzite GaN-based SL systems.…”

mentioning

confidence: 99%

Full optical phonon states and their dispersive spectra of a wurtzite GaN/AlGaN superlattice: Quantum size effect

Zhang

2011

Physica Status Solidi (b)

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“…The NW surface roughness is taken into account as an additional elastic scattering mechanism. NW phonon confinement effects are considered and we calculate the coupling of electrons to longitudinal optical (LO) and surface optical (SO) phonons 23 , as well as confined acoustic phonons 18 .…”

Section: Nanowire Terahertz Quantum Cascade Lasersmentioning

confidence: 99%

Nanowire terahertz quantum cascade lasers

Grange

2014

Applied Physics Letters

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Quantum cascade lasers made of nanowire axial heterostructures are proposed. The dissipative quantum dynamics of their carriers is theoretically investigated using non-equilibrium Green functions. Their transport and gain properties are calculated for varying nanowire thickness, from the classical-wire regime to the quantum-wire regime. Our calculation shows that the lateral quantum confinement provided by the nanowires allows an increase of the maximum operation temperature and a strong reduction of the current density threshold compared to conventional terahertz quantum cascade lasers.Quantum cascade lasers (QCLs) 1 are semiconductor unipolar devices emitting coherent infrared radiation. Their active regions consist of stacked planar quantum wells (QWs) forming a superlattice along the growth direction. At first sight, a large part of the physical properties of QCLs can be qualitatively understood in a onedimensional picture, in particular for quantum confinement, tunneling processes and radiative transitions. Nevertheless, the free in-plane motion of the carriers provides a continuous energy reservoir (i.e. subbands) which plays a major role in the energy and phase relaxation processes. For QCLs operating in the terahertz (THz) range 2,3 , due to the relatively small energy separation between the subbands associated with the lasing levels, the non-radiative scattering processes are very efficient and are responsible for intrinsic limitations in terms of quantum efficiency and maximum operation temperature.Reducing the dimensionality of electronic systems is generally a way to increase the carrier lifetimes 4-7 . A strong magnetic field applied along the growth axis of a QCL quantizes the lateral motion in terms of Landau levels. Their energy tuning with magnetic field has been shown to be responsible for modulation of the level lifetimes 8,9 , allowing to demonstrate lasing up to higher temperature (225 K in ref. 10 ) than in usual THz QCLs (199 K in ref. 11 ). However, Landau levels remain highly degenerate so that their ideal discrete density of states is strongly broadened by disorder effects 12 . On the other hand, QCLs based on 0D nanostructures such as self-assembled or lithographically defined quantum dots (QDs) have been proposed [13][14][15][16] in order to achieve low threshold current and high operation temperature. However, a direct comparison of the device performances with respect to conventional THz QCLs is lacking, and the intermediate regime between the limiting cases coupled 0D QDs and coupled 2D QWs remains to be investigated.In this letter we propose QCLs based on nanowire (NW) superlattice heterostructures. Using the formalism of non-equilibrium Green functions (NEGF), we calculate charge transport and THz gain in laterally-quantized quantum cascade (QC) structures. We investigate the dynamics of charge carriers in QC structures having lateral dimensionality ranging from 2D to 0D, providing a direct comparison of NW QCLs and conventional QCLs. Quantum cascade lasers made of nanowire axia...

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“…ǫ t = ǫ z ), the dispersive equation (15) of anisotropic SL crystals will reduce to those of isotropic SLs [43]. In the situation, there are two types of phonon modes, i.e., the IO and the longitudinal-optical-like modes exist in the isotropic SL systems [21,22,43].…”

Section: -3mentioning

confidence: 99%

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

Zhang

2011

Physica E: Low-dimensional Systems and Nanostructures

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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/AlxGa 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.

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Bound polaron in a cylindrical quantum wire of a polar crystal

Cited by 126 publications

References 16 publications

Full optical phonon states and their dispersive spectra of a wurtzite GaN/AlGaN superlattice: Quantum size effect

Full optical phonon states and their dispersive spectra of a wurtzite GaN/AlGaN superlattice: Quantum size effect

Nanowire terahertz quantum cascade lasers

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

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