Evaluation of the bond polarizabilities of zincblende‐type semiconductors: Application to the Raman spectra of disordered GaSb/AlSb (001) superlattices

Berdekas, D.; Ves, S.

doi:10.1002/pssb.201248164

Cited by 4 publications

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References 27 publications

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“…The corresponding D s 2 ( k ) dynamical matrix that contains the interactions between the atoms of the bulk AlAs crystal described by the new primitive cell, can be constructed in the same way. Then, we can construct the dynamical matrix D s ( k ) of the mixed crystal from the D s 1 ( k ) and D s 2 ( k ) dynamical matrices . It should be noted that the short‐range interactions Ga–Al of the mixed crystal, are calculated by averaging the corresponding Ga–Ga and Al–Al elements of both D s 1 ( k ) and D s 2 ( k ) dynamical matrices before multiplying them by the corresponding ion masses.…”

Section: Theoretical Modelmentioning

confidence: 99%

“…The calculation of P αβ (0 j ) within the BPM is carried out using the BP parameters α || , α ⊥ , and their derivatives

α_{| |}^{'}, α_{⊥}^{'}

with respect to the bond‐length change, for either bond Ga–As and Al–As. The expressions giving the above four parameters are

α_{| |} = \frac{V_{normalc}}{16 π} true[(ϵ_{normal∞} - 1) - ϵ_{normal∞}^{2} true(p_{11} - p_{12} true) true],

α_{⊥} = \frac{V_{normalc}}{16 π} true[(ϵ_{normal∞} - 1) + \frac{ϵ_{normal∞}^{2}}{2} true(p_{11} - p_{12} true) true],

{normalα}_{| |}^{'} = \frac{7}{{3 r}_{normalo}} α_{| |} + \frac{2}{{3 r}_{normalo}} α_{⊥} - \frac{ϵ_{normal∞}^{2} V_{normalc}}{16 π r_{normalo}} true(p_{11} + 2 p_{12} true) + \frac{\sqrt{3}}{4} P,

{normalα}_{⊥}^{'} = \frac{1}{{3 r}_{normalo}} α_{| |} + \frac{8}{{3 r}_{normalo}} α_{⊥} - \frac{ϵ_{\infty}^{2} V_{c}}{16 π ...}

…”

Section: Theoretical Modelmentioning

confidence: 99%

“…Parameter P is the first‐order polarizability change produced by the transverse vibrations defined as

P = a^{2} \frac{ϵ_{\infty}^{2}}{8 π} \frac{p_{11} - p_{12} - 2 p_{44}}{1 + true(4 B / μ ω_{T}^{2} true)},

α , µ , and ω Τ are, respectively, the lattice constant, the reduced mass of the zincblende primitive cell and the frequency of the doubly degenerate transverse optical mode of the bulk zincblende crystal. B is the first‐neighbor, short‐range, noncentral atomic force constant .…”

Section: Theoretical Modelmentioning

confidence: 99%

“…Next, we calculate the Raman spectra of the modes with longitudinal displacements, distant from resonance conditions, using the BPM formalism . For this purpose, we evaluate the values of the BP parameters for Ga–As and Al–As bonds using certain expressions that involve experimentally measurable quantities, like dielectric and elasto‐optic constants of the corresponding bulk crystals. Earlier, these BP values have been estimated either arbitrarily with no clear physical meaning or by using simplifying approximations .…”

Section: Introductionmentioning

confidence: 99%

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Investigation of the disorder of Ga_1–xAl_xAs mixed crystals. Part I: Small concentrations

Berdekas

2016

Physica Status Solidi (b)

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We present calculations of the Raman intensities scattered by the phonons of the mixed crystals Ga1–xAlxAs for five small concentrations up to x = 0.14, away from resonance conditions. Each mixed crystal is approached by a primitive cell, the volume of which is 64 times the volume of the bulk zincblende primitive cell. The phonons have been calculated using a version of a three‐dimensional Valence Overlap Shell Model (VOSM) and the Raman spectra with the bond‐polarizability model (BPM). The values of the bond‐polarizability (BP) parameters of Ga–As and Al–As bonds necessary for the calculation of the Raman intensities are, for the first time, not estimated arbitrarily, but we have evaluated them using certain relations involving directly measurable quantities. We also show that the frequencies of the AlAs LO(Γ)‐like modes and their Raman profiles and intensities as well, depend, for a given Al concentration, strongly on the way the cations are distributed over the mixed‐crystal cation planes. Concerning the GaAs LO(Γ)‐like modes, differences in the cation distribution affect only a little their frequencies and their intensities, but may result in pronounced left asymmetries of the profiles of the corresponding strong Raman peaks. The comparison between the calculated and the experimental Raman spectrum for the Ga0.86Al0.14As is very encouraging, especially when the mixed crystal is described by a disorder configuration where the Al ions are gathered to neighboring cation planes.

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Section: Theoretical Modelmentioning

confidence: 99%

“…The calculation of P αβ (0 j ) within the BPM is carried out using the BP parameters α || , α ⊥ , and their derivatives

α_{| |}^{'}, α_{⊥}^{'}

with respect to the bond‐length change, for either bond Ga–As and Al–As. The expressions giving the above four parameters are

α_{| |} = \frac{V_{normalc}}{16 π} true[(ϵ_{normal∞} - 1) - ϵ_{normal∞}^{2} true(p_{11} - p_{12} true) true],

α_{⊥} = \frac{V_{normalc}}{16 π} true[(ϵ_{normal∞} - 1) + \frac{ϵ_{normal∞}^{2}}{2} true(p_{11} - p_{12} true) true],

{normalα}_{| |}^{'} = \frac{7}{{3 r}_{normalo}} α_{| |} + \frac{2}{{3 r}_{normalo}} α_{⊥} - \frac{ϵ_{normal∞}^{2} V_{normalc}}{16 π r_{normalo}} true(p_{11} + 2 p_{12} true) + \frac{\sqrt{3}}{4} P,

{normalα}_{⊥}^{'} = \frac{1}{{3 r}_{normalo}} α_{| |} + \frac{8}{{3 r}_{normalo}} α_{⊥} - \frac{ϵ_{\infty}^{2} V_{c}}{16 π ...}

…”

Section: Theoretical Modelmentioning

confidence: 99%

“…Parameter P is the first‐order polarizability change produced by the transverse vibrations defined as

P = a^{2} \frac{ϵ_{\infty}^{2}}{8 π} \frac{p_{11} - p_{12} - 2 p_{44}}{1 + true(4 B / μ ω_{T}^{2} true)},

Section: Theoretical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Investigation of the disorder of Ga_1–xAl_xAs mixed crystals. Part I: Small concentrations

Berdekas

2016

Physica Status Solidi (b)

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Erratum: Evaluation of the bond polarizabilities of zincblende‐type semiconductors: Application to the Raman spectra of disordered GaSb/AlSb (001) superlattices [Phys. Status Solidi B 249, No. 8, 1521–1530 (2012)]

Berdekas¹,

Ves²

2012

Physica Status Solidi (b)

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Equations with reference to the zinc blende primitive cell volume are slightly changed. (ii) On page 1522, the paragraph after Eq. (10) should be changed. The current version which reads: ''where p ij are the components of the elasto-optic tensor of the bulk crystal and e 1 , a, r 0 , V c the high frequency dielectric constant, the lattice constant, the first neighbor distance and the bond volume of the bulk crystal, respectively. (The bond volume, V c , is defined as the volume of the cube occupied by the tetrahedrally coordinated bond. This volume is equal to the zinc blend primitive cell volume.)'' should be replaced by this new paragraph: ''where p ij are the components of the elasto-optic tensor of the bulk crystal and e 1 , a, r 0 , V c the high frequency dielectric constant, the lattice constant, the first neighbor distance, and the volume of the zinc blende primitive cell, respectively.'' These corrections do not influence the results obtained in the article, since the calculations were done with the proper volume V c , which is the volume of the primitive zincblende cell.

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Raman scattering by phonons of Ga1−xAlxSb mixed crystals

Berdekas

2013

Journal of Physics and Chemistry of Solids

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Evaluation of the bond polarizabilities of zincblende‐type semiconductors: Application to the Raman spectra of disordered GaSb/AlSb (001) superlattices

Abstract: Equations with reference to the zinc blende primitive cell volume are slightly changed.

Cited by 4 publications

References 27 publications

Investigation of the disorder of Ga_1–xAl_xAs mixed crystals. Part I: Small concentrations

Investigation of the disorder of Ga_1–xAl_xAs mixed crystals. Part I: Small concentrations

Erratum: Evaluation of the bond polarizabilities of zincblende‐type semiconductors: Application to the Raman spectra of disordered GaSb/AlSb (001) superlattices [Phys. Status Solidi B 249, No. 8, 1521–1530 (2012)]

Raman scattering by phonons of Ga1−xAlxSb mixed crystals

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Evaluation of the bond polarizabilities of zincblende‐type semiconductors: Application to the Raman spectra of disordered GaSb/AlSb (001) superlattices

Abstract: Equations with reference to the zinc blende primitive cell volume are slightly changed.

Cited by 4 publications

References 27 publications

Investigation of the disorder of Ga1–xAlxAs mixed crystals. Part I: Small concentrations

Investigation of the disorder of Ga1–xAlxAs mixed crystals. Part I: Small concentrations

Erratum: Evaluation of the bond polarizabilities of zincblende‐type semiconductors: Application to the Raman spectra of disordered GaSb/AlSb (001) superlattices [Phys. Status Solidi B 249, No. 8, 1521–1530 (2012)]

Raman scattering by phonons of Ga1−xAlxSb mixed crystals

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Investigation of the disorder of Ga_1–xAl_xAs mixed crystals. Part I: Small concentrations

Investigation of the disorder of Ga_1–xAl_xAs mixed crystals. Part I: Small concentrations