Fully analytic valence force fields for the relaxation of group-IV semiconductor alloys: elastic properties of group-IV materials calculated from first principles

Tanner, Daniel S. P.; Broderick, Christopher A.; Kirwan, Amy C.; Schulz, Stefan; O’Reilly, Eoin P.

doi:10.48550/arxiv.2110.11888

Cited by 1 publication

(12 citation statements)

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“…We have recently calculated the equilibrium lattice parameter a 0 , relaxed second-order elastic constants C 11 , C 12 and C 44 , and secondorder inner elastic constant B xx for these materials in Ref. 46. Here, we extend these calculations to compute the third-order bulk modulus B and inner elastic constants B 1xx and B 1yy .…”

Section: A Density Functional Theory Calculationsmentioning

confidence: 89%

“…12 , and 46,52 For brevity, we do not recapitulate the relationship between the relaxed third-order elastic constants C i jk and their unrelaxed counterparts C (0) i jk . Details of these relationships can be found in Ref.…”

Section: A Density Functional Theory Calculationsmentioning

confidence: 99%

“…-are as described for the LDA calculations of the harmonic elastic properties in Ref. 46. The results of our DFT calculations are summarised in Table I.…”

Section: A Density Functional Theory Calculationsmentioning

confidence: 99%

“…The anharmonic VFF potential is based closely on the harmonic VFF potential we have recently developed to enable efficient and accurate lattice relaxation of group-IV alloys and nanostructures. 46 The harmonic VFF potential of Ref. 46 was parametrised analytically by expressing the force constants of the potential in terms of the relaxed second-order elastic constants C i j and the internal strain (Kleinman) parameter ζ , so that these linear elastic properties are exactly reproduced by the potential without recourse to numerical fitting.…”

Section: Introductionmentioning

confidence: 99%

“…46 The harmonic VFF potential of Ref. 46 was parametrised analytically by expressing the force constants of the potential in terms of the relaxed second-order elastic constants C i j and the internal strain (Kleinman) parameter ζ , so that these linear elastic properties are exactly reproduced by the potential without recourse to numerical fitting. Here, to better capture the harmonic lattice dynamical properties, we effect an adjusted analytic parametrisation to use the second-order inner elastic constant B xx in place of ζ , so that the harmonic terms of the potential exactly reproduce C i j and the zone-centre transverse optical (TO) phonon frequency ω TO .…”

Section: Introductionmentioning

confidence: 99%

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Raman spectroscopy of group-IV Ge$_{1-x}$Sn$_{x}$ alloys: theory and experiment

Tanner¹,

Raha²,

Doherty³

et al. 2021

Preprint

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Ge 1−x Sn x alloys are a promising candidate material to realise direct-gap group-IV semiconductors for applications in Si-compatible electronic and photonic devices. Here, we present a combined theoretical and experimental analysis of Raman spectroscopy in Ge 1−x Sn x alloys. We describe liquid-vapour-solid growth and structural characterisation of Ge 1−x Sn x (x ≤ 8%) nanowires displaying high crystalline quality, and investigate the structural and vibrational properties of the nanowires using Raman spectroscopy. Our theoretical analysis is based on a fully analytic anharmonic valence force field (VFF) potential, which describes exactly -i.e. without recourse to numerical fitting -the secondorder elastic constants, third-order bulk modulus, selected second-and third-order inner elastic constants and, as a consequence, the zone-centre transverse optical phonon mode frequency and its hydrostatic and axial strain dependence. We compute bulk elastic properties via density functional theory to parametrise the VFF potential for Ge 1−x Sn x alloys, and apply the VFF potential to explicitly compute the Raman spectra of realistic, disordered Ge 1−x Sn x alloy supercells. Our atomistic theoretical calculations quantitatively capture: (i) the evolution of the measured Raman spectra with Sn composition x, (ii) demonstrate explicitly that the presence of short-range alloy disorder can significantly impact the shift coefficients a and b that respectively describe the dependence of the Raman shift on Sn composition and pseudomorphic strain, (iii) elucidate the origin of the so-called "disorder activated" mode identified in previous experimental investigations, and (iv) allow for detailed atomic-scale interpretation of measured Raman spectra. Overall, our analysis provides insight relevant to the characterisation of this emerging material system.

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Section: A Density Functional Theory Calculationsmentioning

confidence: 89%

Section: A Density Functional Theory Calculationsmentioning

confidence: 99%

“…-are as described for the LDA calculations of the harmonic elastic properties in Ref. 46. The results of our DFT calculations are summarised in Table I.…”

Section: A Density Functional Theory Calculationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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