Elastic Moduli of GaAs at Moderate Pressures and the Evaluation of Compression to 250 kbar

McSkimin, H. J.; Jayaraman, A.; Andreatch, P.

doi:10.1063/1.1709884

Cited by 179 publications

(45 citation statements)

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“…For many applications, it is sufficient to consider only terms linear in the external hydrostatic pressure Results for pressure derivatives c ′ ij calculated on the basis of our estimates for second-and third-order elastic constants are shown in Tables IV and V. Table IV provides comparison with experimental results for Si 38 and GaAs. 39 The agreement is very good and shows that the results from the strain-energy relation reproduce the experimental values slightly better than findings based on strain-stress formula. Table V contains values of c ′ ij for zinc-blende nitrides and compares the present calculation with our previous work.…”

Section: Relation To Pressure Dependent Elastic Constantssupporting

confidence: 54%

Ab initiocalculations of third-order elastic constants and related properties for selected semiconductors

2007

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We present theoretical studies for the third-order elastic constants C ijk in zinc-blende nitrides AlN, GaN, and InN. Our predictions for these compounds are based on detailed ab initio calculations of strain-energy and strain-stress relations in the framework of the density functional theory. To judge the computational accuracy, we compare the ab initio calculated results for C ijk with experimental data available for Si and GaAs. We also underline the relation of the third-order elastic constants to other quantities characterizing anharmonic behaviour of materials, such as pressure derivatives of the second-order elastic constants c ′ ij and the mode Grüneisen constants for long-wavelength acoustic modes γ(q, j).Paper accepted to Phys. Rev. B.

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Section: Relation To Pressure Dependent Elastic Constantssupporting

confidence: 54%

Ab initiocalculations of third-order elastic constants and related properties for selected semiconductors

2007

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“…22 We take B 0 = 74.7 GPa and B ′ 0 = 4.67 as the GaAs bulk modulus and its derivative with respect to pressure, respectively. 23 We see from Fig. 1 that the pressure dependence of the binding energy of the various excitons is different: (i) ∆ CI (X 0 ) shows a small, nearly linear increase with pressure; changing about 7 % in the studied pressure range.…”

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confidence: 99%

Pressure effects on neutral and charged excitons in self-assembled (In,Ga)As∕GaAsquantum dots

2005

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By combining an atomistic pseudopotential method with the configuration interaction approach, we predict the pressure dependence of the binding energies of neutral and charged excitons: X 0 (neutral monoexciton), X − and X + (charged trions), and XX 0 (biexciton) in lens-shaped, selfassembled In0.6Ga0.4As/GaAs quantum dots. We predict that (i) with applied pressure the binding energy of X 0 and X + increases and that of X − decreases, whereas the binding energy of XX 0 is nearly pressure independent.(ii) Correlations have a small effect in the binding energy of X 0 , whereas they largely determine the binding energy of X − , X + and XX 0 . (iii) Correlations depend weakly on pressure; thus, the pressure dependence of the binding energies can be understood within the Hartree-Fock approximation and it is controlled by the pressure dependence of the direct Coulomb integrals J. Our results in (i) can thus be explained by noting that holes are more localized than electrons, so the Coulomb energies obeyThe energetics of excitons reflects a balance between single-particle energy levels E (e) and E (h) of electrons (e) and holes (h) in the system, and the many-particle carrier-carrier interactions, resulting from electron-hole Coulomb and exchange interactions.1,2,3 The variation of excitonic energies under pressure naturally reflects the corresponding variations in single-vs many-particle energies. Of particular interest are the pressure variations of excitons confined to nanosize dimensions such as in quantum dots. 4,5,6,7,8,9,10,11,12,13,14 Unlike the case of excitons in higher-dimensional systems, where binding and its pressure dependence reflects mostly manyparticle (correlation) effects, in zero-dimensional (0D) systems where the geometric dimensions are smaller than the excitonic radius, binding of neutral and charged excitons results from an interesting interplay between singleparticle and many-particle effects. Here, we use a realistic description of both single-particle and many-body effects in self-assembled In 0.6 Ga 0.4 As/GaAs quantum dots, showing how pressure affects the different components of exciton binding. We distinguish the neutral monoexciton X 0 (one e, one h), from the neutral biexciton XX 0(two e, two h), positive trion X + (one e, two h) and negative trion X − (two e, one h). While the effect of pressure on X 0 has been measured, 8,9,10,11,12,13 to the best of our knowledge, the optical spectroscopy of X − , X + and XX 0 under pressure has not yet been reported. For these reason, we provide definite predictions of the pressure effects. Each of the q-charged excitons has a spectrum of levels {ν}, of which the lowest is termed the "ground state of χ q " (χ = X, XX). This spectrum is usually expressed by expanding the many-body excitonic states |Ψ (ν) (χ q ) via a set of Slater determinants |Φ(χ q ) . The latter are constructed from single-particle electron and hole states and accommodate as many carriers as are present in χ q . The single-particle states are solutions to the effective Schrödinge...

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“…While McSkimin et al [6] give hydrostatic pressure data, the only uniaxial data in the literature appears to be that of Drabble and Brammer [7]. Drabble and Brammer do not give the raw data, nor the equations, but only the final c IJK .…”

Section: Xmentioning

confidence: 96%

“…We do this using both the uncorrected and the corrected Thurston and Brugger equations. Combining them with the hydrostatic data of McSkimin et al [6], we have an overdetermined system with error analysis. Using Eq.…”

Section: Xmentioning

confidence: 99%

“…Si [4] Si [5] Ge [4] GaAs [6,7] Pressure derivatives of second-order elastic constants The pressure derivatives of the second order elastic constants are very useful quantities. They are readily calculated from our effective second-order elastic constants [2,3] and are Table 1 differs by amounts significant compared with the errors and is to be preferred.…”

Section: Xmentioning

confidence: 99%

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Reliable non‐linear elastic constants

Dunstan

Bosher

2003

Physica Status Solidi (b)

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The values given in the literature for the third-order elastic constants c IJK of the standard semiconductors have long been suspect. We have applied modern statistical analysis to the raw data from which the databook c IJK were obtained, and we give revised values with reliable error estimates for Si, Ge and GaAs. The databook c IJK are appropriate for an expansion of the elastic energy of a body as a Taylor series in Lagrangian strain η IJ , but there are formidable mathematical difficulties in using Lagrangian strain in the analysis of physical problems. To facilitate such analysis, we introduce effective second-order elastic constants for materials under finite strain. From these, strain, stress and pressure derivatives are readily calculated. The pressure derivatives are given for Si, Ge and GaAs. Using the stress derivatives, the relationships between physical observables such as acoustic velocities and the databook c IJK can be obtained by simple algebra.Introduction Elastic constants have been measured for many materials and are required for any calculation of the effects of pressure, stress or strain. The second-order constants such as the Young's, bulk and shear moduli, and the tensor c IJ , are well-established and accurately known. The third-order constants c IJK are required for any accurate calculation of the effect of large stresses or deformations, but their literature values have long been regarded as suspect. In this paper, we show how they may be rehabilitated or refined using multi-variate linear regression analysis. We find that literature values for Ge and Si are in fact very good, while the data for GaAs requires significant reassessment. Just as important is the need to use an appropriate theory, without which good values of c IJK are vitiated.Third-order elastic constants have been regarded as suspect for at least three reasons. Firstly, there have been major discrepancies between the values of such quantities as the experimental determinations of the pressure coefficients of second-order elastic constants, c′ IJ , and the values calculated from experimental values of the third-order constants c IJK . Secondly, the experimental determinations with which we are concerned depend upon uniaxial stress experiments, and these are notoriously inaccurate. Thirdly, and perhaps most damaging, some of the authors of the experimental determinations have claimed completely unrealistic small errors. Our aim is therefore to establish reasonable values with justifiable error estimates.

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Elastic Moduli of GaAs at Moderate Pressures and the Evaluation of Compression to 250 kbar

Cited by 179 publications

References 13 publications

Ab initiocalculations of third-order elastic constants and related properties for selected semiconductors

Ab initiocalculations of third-order elastic constants and related properties for selected semiconductors

Pressure effects on neutral and charged excitons in self-assembled (In,Ga)As∕GaAsquantum dots

Reliable non‐linear elastic constants

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