We present a comprehensive, up-to-date compilation of band parameters for the technologically important III–V zinc blende and wurtzite compound semiconductors: GaAs, GaSb, GaP, GaN, AlAs, AlSb, AlP, AlN, InAs, InSb, InP, and InN, along with their ternary and quaternary alloys. Based on a review of the existing literature, complete and consistent parameter sets are given for all materials. Emphasizing the quantities required for band structure calculations, we tabulate the direct and indirect energy gaps, spin-orbit, and crystal-field splittings, alloy bowing parameters, effective masses for electrons, heavy, light, and split-off holes, Luttinger parameters, interband momentum matrix elements, and deformation potentials, including temperature and alloy-composition dependences where available. Heterostructure band offsets are also given, on an absolute scale that allows any material to be aligned relative to any other.

Band parameters for III–V compound semiconductors and their alloys

https://www.bc.edu/content/dam/files/schools/cas_sites/physics/pdf/Ren/p85.pdf

Advances in the science and technology of carbon nanotubes and their composites: a review

I. Introduction: Conceptual vs Fundamental andComputational Aspects of DFT1793II. Fundamental and Computational Aspects of DFT 1795A. The Basics of DFT: The Hohenberg−KohnTheorems1795B. DFT as a Tool for Calculating Atomic andMolecular Properties: The Kohn−ShamEquations1796C. Electronic Chemical Potential andElectronegativity: Bridging Computational andConceptual DFT1797III. DFT-Based Concepts and Principles 1798A. General Scheme: Nalewajski’s ChargeSensitivity Analysis1798B. Concepts and Their Calculation 18001. Electronegativity and the ElectronicChemical Potential18002. Global Hardness and Softness 18023. The Electronic Fukui Function, LocalSoftness, and Softness Kernel18074. Local Hardness and Hardness Kernel 18135. The Molecular Shape FunctionsSimilarity 18146. The Nuclear Fukui Function and ItsDerivatives18167. Spin-Polarized Generalizations 18198. Solvent Effects 18209. Time Evolution of Reactivity Indices 1821C. Principles 18221. Sanderson’s Electronegativity EqualizationPrinciple18222. Pearson’s Hard and Soft Acids andBases Principle18253. The Maximum Hardness Principle 1829IV. Applications 1833A. Atoms and Functional Groups 1833B. Molecular Properties 18381. Dipole Moment, Hardness, Softness, andRelated Properties18382. Conformation 18403. Aromaticity 1840C. Reactivity 18421. Introduction 18422. Comparison of Intramolecular ReactivitySequences18443. Comparison of Intermolecular ReactivitySequences18494. Excited States 1857D. Clusters and Catalysis 1858V. Conclusions 1860VI. Glossary of Most Important Symbols andAcronyms1860VII. Acknowledgments 1861VIII. Note Added in Proof 1862IX. References 1865

/pdf/conceptual-density-functional-theory-btz9wwrxv9.pdf

Conceptual density functional theory.

We present a new hybrid meta exchange-correlation functional, called M05-2X, for thermochemistry, thermochemical kinetics, and noncovalent interactions. We also provide a full discussion of the new M05 functional, previously presented in a short communication. The M05 functional was parametrized including both metals and nonmetals, whereas M05-2X is a high-nonlocality functional with double the amount of nonlocal exchange (2X) that is parametrized only for nonmetals. In particular, M05 was parametrized against 35 data values, and M05-2X is parametrized against 34 data values. Both functionals, along with 28 other functionals, have been comparatively assessed against 234 data values:  the MGAE109/3 main-group atomization energy database, the IP13/3 ionization potential database, the EA13/3 electron affinity database, the HTBH38/4 database of barrier height for hydrogen-transfer reactions, five noncovalent databases, two databases involving metal−metal and metal−ligand bond energies, a dipole moment databas...

/pdf/design-of-density-functionals-by-combining-the-method-of-3dsa6vb61i.pdf

Design of Density Functionals by Combining the Method of Constraint Satisfaction with Parametrization for Thermochemistry, Thermochemical Kinetics, and Noncovalent Interactions.

We present a comprehensive and up-to-date compilation of band parameters for all of the nitrogen-containing III–V semiconductors that have been investigated to date. The two main classes are: (1) “conventional” nitrides (wurtzite and zinc-blende GaN, InN, and AlN, along with their alloys) and (2) “dilute” nitrides (zinc-blende ternaries and quaternaries in which a relatively small fraction of N is added to a host III–V material, e.g., GaAsN and GaInAsN). As in our more general review of III–V semiconductor band parameters [I. Vurgaftman et al., J. Appl. Phys. 89, 5815 (2001)], complete and consistent parameter sets are recommended on the basis of a thorough and critical review of the existing literature. We tabulate the direct and indirect energy gaps, spin-orbit and crystal-field splittings, alloy bowing parameters, electron and hole effective masses, deformation potentials, elastic constants, piezoelectric and spontaneous polarization coefficients, as well as heterostructure band offsets. Temperature an...

Band parameters for nitrogen-containing semiconductors

Analytical expressions for the velocities of the longitudinal and the torsional sound waves in single-walled carbon nanotubes are derived using Born's perturbation technique within a lattice-dynamical model. These expressions are compared to the formulas for the velocities of the sound waves in an elastic hollow cylinder from the theory of elasticity to obtain analytical expressions for the Young's and shear moduli of nanotubes. The calculated elastic moduli for different chiral and achiral ~armchair and zigzag! nanotubes using force constants of the valence force field type are compared to the existing experimental and theoretical data. vibration amplitude of several isolated MWNT's was ana- lyzed in a transmission electron microscope to eventually obtain 1.8 TPa for the average Young's modulus. Later on, this technique was applied to measure Young's modulus of isolated SWNT's in the diameter range 1.0 21.5 nm and an average value ^Y&51.2520.35/10.45 TPa was derived. 7 In another experimental approach 8 the MWNT's were pinned to a substrate by conventional lithography and the force was measured at different distances from the pinned point by atomic force microscope ~ATM!. The average Young's modulus for different MWNT's with diameters from 26 to 76 nm was found to be 1.2860.59 TPa. Recently, Young's and shear moduli of ropes of SWNT's were measured by sus- pending the ropes over the pores of a membrane and using ATM to determine directly the resulting deflection of the rope. 9 The theoretical estimation of the elastic moduli was accomplished exclusively by numerical second derivatives of the energy of the strained nanotubes. In the calculation of the elastic moduli of various SWNT's within a simple force- constant model 10 it was found that the moduli were insensi- tive to tube size and helicity and had the average values of ^Y&50.97 TPa and ^G&50.45 TPa. In several works, molecular-dynamics ~MD! simulation algorithms using the Tersoff-Brenner potential for the carbon-carbon interactions were implemented to relax the strained nanotubes and calcu- late their energy. 11-13 For tubes of diameter of 1 nm values for Y of 5.5 TPa ~Ref. 12! and 0.8 TPa ~Ref. 13! were ob- tained. A non-orthogonal tight-binding ~TB! scheme was ap- plied to calculate Young's modulus of several chiral and achiral SWNT's yielding an average value of 1.24 TPa. 14 Recently, the second derivative of the strain energy with re- spect to the axial strain, calculated with a pseudopotential density-functional-theory ~DFT! model for a number of SWNT's, 15 was found to vary slightly with the tube type and to have the average value of 56 eV. In this paper, we choose a different approach to the cal- culation of the elastic properties of SWNT's. Namely, we derive analytical expressions for the elastic ~Young's and shear! moduli of SWNT's using a perturbation technique due to Born 16 within a lattice-dynamical model for nanotubes. 17 This scheme has the advantage that the elastic moduli are consistent with the lattice dynamics of the nanotubes and that each of these moduli is obtained in one calculational step only. The essential features of a model of the lattice dynamics of SWNT's based on the explicit accounting for the helical symmetry of the tubes 17 are summarized in Sec. II A. This model is applied to study of the long-wavelength vibrations in nanotubes using Born's perturbation technique 16 and to obtain analytical expressions for the velocities of the longi- tudinal and the torsional sound waves in SWNT's ~see Sec. II B!. The comparison of these expressions with the formulas from the theory of elasticity for the velocities of these waves in an elastic hollow cylinder allows one to determine the Young's and shear moduli of the nanotubes. The calculated phonon dispersion of a (10,10) nanotube and elastic moduli for various chiral and achiral ~armchair and zigzag! nano- tubes using force constants of the valence force field ~VFF! type 18 are presented in Sec. III and discussed in comparison with the existing experimental and theoretical data.

/pdf/elastic-properties-of-single-walled-carbon-nanotubes-4u466rpfw4.pdf

Elastic properties of single-walled carbon nanotubes

Elastic properties of crystals of single-walled carbon nanotubes

Electronic and ground-state properties of both wurtzite- and rocksalt-structure AlN are evaluated in the local-density-functional formalism using nonlocal norm-conserving pseudopotentials. For the wurtzite structure we obtain a=3.129 \AA{} and c=4.988 \AA{} and an internal parameter of 0.3825, which deviates considerably from the ideal value. In the case of the rocksalt structure we get a=4.032 \AA{}. Both modifications are large-band-gap semiconductors with a direct gap in the wurtzite structure and an indirect gap in the rocksalt structure. The transition pressure from hexagonal to cubic was calculated to be 12.9 GPa, in reasonable agreement with the experimental value.

High-pressure properties of wurtzite- and rocksalt-type aluminum nitride

Universite´Pierre et Marie Curie, 4 Place Jussieu, F-75252 Paris Cedex 05, France~Received 14 May 1998!In this paper, the theory of lattice dynamics of single-walled carbon nanotubes is presented The screwsymmetry of the system is used to reduce the rank of the dynamical matrix to six, independent of the numberof atoms in the unit cell Calculations of the lattice dynamics are carried out within a valence force ﬁeld modeland of the Raman intensity—within a bond-polarizability model It is found that the breathing mode frequencyis inversely proportional to the radius of the tube that can be used for the characterization of the samples on thebasis of Raman-scattering data The results for the Raman intensity are compared to available Raman spectra@S0163-1829~98!06434-0#

/pdf/lattice-dynamics-of-single-walled-carbon-nanotubes-q6rnly60tn.pdf

V. E. Van Doren

Papers

Elastic properties of single-walled carbon nanotubes

Elastic properties of crystals of single-walled carbon nanotubes

High-pressure properties of wurtzite- and rocksalt-type aluminum nitride

Lattice dynamics of single-walled carbon nanotubes

Density Functional Theory and its Applications to Materials