The bound polaron in a cylindrical quantum well wire with a finite confining potential

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

doi:10.1088/0953-8984/12/40/307

Cited by 60 publications

(39 citation statements)

References 35 publications

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“…In fact, this is completely analogous to the situations of the HS and (quasi-) confined modes in cubic (wurtzite) quantum systems [22,24,25,38]. When the outermost radius L is large enough, the influence of polarization charges at the outermost interface of ρ = L on the vibrating properties of the inner core and the well-layer materials as well as the other features should be quite weak [36,37]. Thus the electrostatic potentials of polar oscillations could be taken to be zero in the area ρ > L. Therefore, the additional BC Eq.…”

Section: Theorymentioning

confidence: 73%

“…Because of the importance of the dispersive frequencies of the free wave-number k z and azimuthal quantum-number m for further investigating the polaronic effect on the physical properties of the QWW structures [36,[39][40][41], we have computed and analyzed the dispersion properties of the PR and HS phonon modes on k z and m for a Q1D wurtzite Al 0.15 Ga 0.85 N/GaN/Al 0.15 Ga 0.85 N QWW in this section. The geometrical sizes of the QWW are as follows: the inner radius R 1 = 2a B , and the outer radius R 2 = 4a B (a B is the effective Bohr radius of wurtzite GaN material, which equals about 2.4 nm).…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…The maximal radial width L of the outermost Al 0.15 Ga 0.85 N dielectric matrix is assumed to be 20R 2 as in Ref. [36]. All the material parameters of nitride used in the calculations are cited from Refs.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…First, both J m (x) and Y m (x) are oscillating and degressive functions of x, namely, the functions J m (x) and Y m (x) will approach zero if x is large enough [30]. Secondly, this postulate (6) has already been adopted to describe the confined optical phonon modes of the outmost polar material in cubic cylindrical heterostructures, and the calculated results of bound polaron binding energy also shows this description is reasonable [36]. In physical essence, this treatment means that an Al x Ga 1−x N/GaN/Al y Ga 1−y N QWW with quite large outermostradius (L) located in vacuum or nonpolar dielectric matrix is assumed [36,37].…”

Section: Theorymentioning

confidence: 92%

“…Secondly, this postulate (6) has already been adopted to describe the confined optical phonon modes of the outmost polar material in cubic cylindrical heterostructures, and the calculated results of bound polaron binding energy also shows this description is reasonable [36]. In physical essence, this treatment means that an Al x Ga 1−x N/GaN/Al y Ga 1−y N QWW with quite large outermostradius (L) located in vacuum or nonpolar dielectric matrix is assumed [36,37]. Only the vibrating properties within the range of ρ < L are taken into account, and those out of the range (ρ > L) are neglected.…”

Section: Theorymentioning

confidence: 92%

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Confinement of polar optical phonons in quasi-one-dimensional Wurtzite GaN-based quantum well wires: propagating and half-space phonon modes

Zhang¹,

Shi²

2007

Open Physics

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Abstract:With the aid of the macroscopic dielectric continuum and Loudon's uniaxial crystal models, the propagating (PR) and half-space (HS) optical phonon modes and corresponding Fröhlich-like electron-phonon interaction Hamiltonians in a quasi-one-dimensionality (Q1D) wurtzite quantum well wire (QWW) structure are derived and studied. Numerical calculations on a wurtzite GaN/Al 0.15 Ga 0.85 N QWW are performed, and discussion is focused mainly on the dependence of the frequency dispersions of PR and HS modes on the free wave-number k z in the z-direction and on the azimuthal quantum number m. The calculated results show that, for given k z and m, there usually exist infinite branches of PR and HS modes in the high-frequency range, and only finite branches of HS modes in the low-frequency range in wurtzite QWW systems. The reducing behaviors of the PR modes to HS modes, and of the HS mode to interface phonon mode have been observed clearly in Q1D wurtzite heterostructures. Moreover, the dispersive properties of the PR and HS modes in Q1D QWWs have been compared with those in Q2D quantum well structures. The underlying physical reasons for these features have also been analyzed in depth.

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Section: Theorymentioning

confidence: 73%

Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Theorymentioning

confidence: 92%

Section: Theorymentioning

confidence: 92%

See 3 more Smart Citations

Confinement of polar optical phonons in quasi-one-dimensional Wurtzite GaN-based quantum well wires: propagating and half-space phonon modes

Zhang¹,

Shi²

2007

Open Physics

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Oscillating spectra of polar IO and SO phonons and electron–IO and SO phonon couplings in a freestanding wurtzite quantum wire

Zhang¹,

Shi²

2006

Physica Status Solidi (b)

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By employing the transfer matrix method, the polar interface optical (IO) and surface optical (SO) phonon modes and the corresponding Fröhlich electron -phonon interaction Hamiltonians in a freestanding multishell wurtzite cylindrical quantum wire (QWR) are derived and studied under the dielectric continuum approximation and Loudon's uniaxial crystal model. The present theoretical scheme can be looked on as a generalization of the previous studies regarding the IO phonon modes in quasi-one-dimensional (Q1D) wurtzite QWRs with a certain layer-number. Numerical calculations on a freestanding wurtzite GaN/AlN QWR are performed. The degenerating behaviors of the IO and SO phonon modes in the freestanding wurtzite QWR seem prominent in contrast to the situation of Q1D wurtzite QWR with infinite polar matrix. The calculations of the electron -phonon coupling function show that the high-frequency IO phonon branch and SO mode play a more important role in the electron -phonon interaction.

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Binding energies of bound polaron in a wurtzite nitride nanowire: Contributions of IO and QC phonon modes

Zhang

2011

Physica Status Solidi (b)

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By employing the two-parameter variational approach, the binding energies of bound polarons in a quasi-one-dimensional wurtzite nanowire (NW) are investigated. Two types of polar optical phonon modes, i.e., the interface optical (IO) and quasiconfined (QC) phonon modes of wurtzite NWs are taken in account. The results reveal that the phonon contribution to binding energy of bound polaron in GaN NWs reaches $370 meV. The quite large contribution of phonon modes to the total binding energy is mainly ascribed to the very strong electron-phonon coupling constant in GaN materials. Moreover, the IO modes plays more important role to the binding energies of bound polaron as the NW radius is small, while the QC modes dominates as the NW radius is relatively large. The calculated results of impurity binding energy are quite consistent with the recent experimental measurement. The numerical results also show that the two-parameter variational approach is necessary and suitable for the description of impurity states in wurtzite GaN NW structures. 1 Introduction Since the pioneering experimental work of Fan's group [1] on the synthesis of the first wurtzite GaN nanorods, the quasi-1-dimensional (Q1D) GaN-based nanowires (NWs) have attracted a considerable amount of attentions both in theoretical and experimental investigations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. This is mainly due to the following three evident facts: the nitride materials (including GaN, AlN, InN, and their ternary compounds, AlGaN and InGaN) with strong atomic bonding and wide and adjustable directbandgap, which make them quite potential as a basis for the creation of reliable high-temperature and high-frequency nano-optoelectronic devices such as field-effect-transistors (FETs), high-brightness blue/green light-emitting diodes and laser diodes as well as photodetectors [2][3][4][5]; Q1D structure' confinement of NWs for carriers in two dimensions and freedom in the last dimension, promising more efficient lasers and optical gain as well as possible applications for optical waveguide and photovoltaic elements in comparisons with quantum wells (QWs) and quantum dots (QDs) [6][7][8][9][10]; the Q1D NW systems also playing an important role in testing and understanding fundamental concepts, such as the role of dimensionality and size in optical, electrical, and mechanical properties [11][12][13][14][15][16].

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The bound polaron in a cylindrical quantum well wire with a finite confining potential

Abstract: The phonon modes of a quantum well wire, formed by a cylindrical polar semiconductor 1 (well material) (ρ Show more

Cited by 60 publications

References 35 publications

Confinement of polar optical phonons in quasi-one-dimensional Wurtzite GaN-based quantum well wires: propagating and half-space phonon modes

Confinement of polar optical phonons in quasi-one-dimensional Wurtzite GaN-based quantum well wires: propagating and half-space phonon modes

Oscillating spectra of polar IO and SO phonons and electron–IO and SO phonon couplings in a freestanding wurtzite quantum wire

Binding energies of bound polaron in a wurtzite nitride nanowire: Contributions of IO and QC phonon modes

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