Elastic constants and related properties of tetrahedrally bonded BN, AlN, GaN, and InN

Kim, Kwiseon; Lambrecht, Walter R. L.; Segall, B.

doi:10.1103/physrevb.53.16310

Cited by 700 publications

(323 citation statements)

References 59 publications

Supporting

Mentioning

258

Contrasting

Unclassified

Order By: Relevance

“…18 Previous theoretical studies have also produced widely differing values, resulting in a large uncertainty range. [19][20][21] The error bars can, in part, be attributed to the band-gap problem of density functional theory (DFT) in the local-density or generalized gradient approximations (LDA and GGA). Moreover, not all previous studies include a relaxation of the internal displacement parameter u, which sensitively affects the crystal-field split- ting.…”

mentioning

confidence: 99%

Strain effects in group-III nitrides: Deformation potentials for AlN, GaN, and InN

Yan

Rinke

Scheffler

et al. 2009

Applied Physics Letters

164

120

View full text Add to dashboard Cite

A systematic density functional theory (DFT) study of strain effects on the electronic band structure of the group-III nitrides (AlN, GaN and InN) is presented. To overcome the deficiencies of the local-density and generalized gradient approximations (LDA and GGA) the Heyd-Scuseria-Ernzerhof hybrid functional (HSE) is used. Cross-checks for GaN demonstrate good agreement between HSE and exact-exchange based G0W0 calculations. We observe a pronounced nonlinear dependence of band-energy differences on strain. For realistic strain conditions in the linear regime around the experimental equilibrium volume a consistent and complete set of deformation potentials is derived.PACS numbers: 71.20. Nr, 71.70.Fk, 85.60.Bt The group-III nitride compounds and their alloys have recently received considerable attention as a versatile materials class. AlN, GaN and InN all crystallize in the wurtzite structure, but have vastly different band gaps ranging from 6.0 eV for AlN down to 0.7 eV for InN. For light emitting diodes (LEDs) 1 and laser diodes (LDs) 2,3 the group-III-nitrides are currently the only commercially available materials class for the green to the deep ultraviolet part of the spectrum, and future applications as chemical sensors, 4 in quantum cryptography 5 or in photocatalysis 6 are being explored. Applications in solid state lighting, however, are currently limited by loss mechanisms 7,8 and a deeper understanding of the fundamental materials properties is required. One crucial factor is the effect of strain.Due to the large differences in lattice parameters and thermal expansion coefficients between the substrate and the nitride overlayers, and between nitride layers with different alloy compositions, strain is always present in group-III-nitride based devices. Strain influences the optical properties, 9-11 in particular the energy of optical transitions, and for nonpolar or semipolar devices the polarization of the emitted light. 12 The effects of strain are characterized by the change of a transition energy (energy difference) upon application of strain, and the linear coefficient is defined as deformation potential. Together with the Luttinger (band) parameters, the deformation potentials constitute essential input for device modeling. 13 The experimental determination of deformation potentials is quite difficult, and aggravated by the fact that not all strain components can be determined accurately or without further approximations and that the deformation potentials cannot be isolated from each other, because uniaxial and biaxial strain cannot be applied separately. As a result the experimental data for GaN are scattered over a very large range. 10,11,14-17 For AlN and InN no experimental data are available, except for the hydrostatic deformation potential of the band gap in InN. 18 Previous theoretical studies have also produced widely differing values, resulting in a large uncertainty range. [19][20][21] The error bars can, in part, be attributed to the band-gap problem of density functional theory (DF...

show abstract

mentioning

confidence: 99%

Strain effects in group-III nitrides: Deformation potentials for AlN, GaN, and InN

Yan

Rinke

Scheffler

et al. 2009

Applied Physics Letters

164

120

View full text Add to dashboard Cite

show abstract

“…Table III summarizes Voigt-notation elastic stiffness coefficients, Young's moduli, and Poisson's ratio of InN predicted theoretically and evaluated experimentally. After the pioneering work of Kim et al, 8 several theoretical predictions of the elastic stiffness matrix and the Young's modulus were conducted using various frameworks of ab inito calculation, local density functional theory, generalized gradient approximation, and so on. 9,[11][12][13][14][15][16] The theoretical predictions seem to be rather scattered although the values for E c are in the range of 171-250 GPa, whereas those for E a are in the range of 146-236 GPa.…”

Section: B Elastic Parameters Of Innmentioning

confidence: 99%

“…Even now, however, such results are rather scattered for the utilized methods. [7][8][9][10][11][12][13][14][15][16] Indentation is widely used to determine the hardness of materials and is rather free from the limitations of other mechanical testing methods. Hardness is a material parameter indicating resistance against elastic/plastic deformation and is convenient as a measure similar to the yield stress or mechanical strength controlled by macroscopic motion of dislocations.…”

Section: Introductionmentioning

confidence: 99%

“…37 However, these values are somewhat lower than those predicted theoretically by several groups. [8][9][10][11][12][13]15,16 The InN films employed contained a high density of grown-in dislocations of ∼10 10 cm −2 , which may have caused some reduction of the Poisson's ratio. If anything, there is a possibility that wurtzite-structure nitrides are rather resistant to changes in the bond length when strained, as indicated by Wright 9 and Wagner and Bechstedt.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Elastic properties of indium nitrides grown on sapphire substrates determined by nano-indentation: In comparison with other nitrides

et al. 2015

View full text Add to dashboard Cite

The hardness of wurtzite indium nitride (α-InN) films of 0.5 to 4 μm in thickness was measured by the nano-indentation method at room temperature. After investigation of crystalline quality by x-ray diffraction, the hardness and Young’s modulus were determined to be 8.8 ± 0.4 and 184 ± 5 GPa, respectively, for the In (0001)- and N (0001̄)-growth faces of InN films. The bulk and shear moduli were then derived to be 99 ± 3 and 77 ± 2 GPa, respectively. The Poisson’s ratio was evaluated to be 0.17 ± 0.03. The results were examined comprehensively in comparison with previously reported data of InN as well as those of other nitrides of aluminum nitride and gallium nitride. The underlying physical process determining the moduli and hardness was examined in terms of atomic bonding and dislocation energy of the nitrides and wurtzite zinc oxide.

show abstract

“…In device applications, InN is often subjected to stress since it is found as a component of ternary or quaternary nitride alloys or as a very thin layer in heterostructures. In order to model the behaviour of films under hydrostatic or biaxial stress it is important to know the elastic constants C ij whose values are strongly affected by the force constants α and β for bond stretching and bond bending, respectively [2].…”

mentioning

confidence: 99%

Temperature dependent EXAFS of InN

Katsikini

Pinakidou

Paloura

et al. 2008

Physica Status Solidi (a)

View full text Add to dashboard Cite

The effect of temperature on the bonding environment of indium in an InN epilayer is studied using X‐ray absorption fine structure (EXAFS) spectroscopy. Shell‐by‐shell fitting of the EXAFS spectra reveals that, in the temperature range 80‐245 K, the change in the nearest neighbour distances is smaller than the uncertainty of the measurement. The Debye–Waller factor of the second neighbouring shell (In–In pair) shows strong temperature dependence. Fitting using the Einstein model yields an Einstein temperature equal to 193 K ± 5%. An alternative way of extracting information on the vibrational properties of the lattice is the simulation using the equation of motion method for the determination of the Debye–Waller factors. The used values of 120 N/m and 50 N/m of the force constants for In–N and In–In bond stretching, respectively, simulate satisfactory the spectra measured at five different temperatures in the range 80– 245 K. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

show abstract

Elastic constants and related properties of tetrahedrally bonded BN, AlN, GaN, and InN

Cited by 700 publications

References 59 publications

Strain effects in group-III nitrides: Deformation potentials for AlN, GaN, and InN

Strain effects in group-III nitrides: Deformation potentials for AlN, GaN, and InN

Elastic properties of indium nitrides grown on sapphire substrates determined by nano-indentation: In comparison with other nitrides

Temperature dependent EXAFS of InN

Contact Info

Product

Resources

About