Keating model

Abstract: A calculation of the third-order elastic constants of silicon, germanium, and other diamond-like crystals is presented which is based on a previously published method of setting up a suitable form for the elastic strain energy of a crystal. The six third-order constants are calculated in terms of three anharmonic first-and second-neighbor force constants and the two previously determined harmonic force constants. The experimental values of the six coefficients are well fitted by the theoretical expressions involving these three anharmonic force constants. The valence-electron interactions are discussed in the light of the values deduced for these force constants.

Abstract: Anharmonicity of the interatomic potential is taken into account for the quantitative simulation of the conduction and valence band offsets for strained semiconductor heterostructures. The anharmonicity leads to a weaker compressive hydrostatic strain than that obtained with the commonly used quasiharmonic approximation of the Keating model. Compared to experiment, inclusion of the anharmonicity in the simulation of strained InAs∕GaAs nanostructures results in an improvement of the electron band offset computed on an atomistic level by up to 100meV.

Abstract: A unified framework is suggested for the discussion of anharmonic phonon coupling constants and anharmonic elastic constants in diamond-structure materials. A summary is given, within this framework, of those anharmonic constants which have previously been determined experimentally or theoretically for silicon. New local-density total-energy calculations for X-point phonons in Si are used to add to this database of known anharmonic constants. It is proposed that empirical models for interatomic potentials should be constrained to fit this database. A generalized Keating model which has been fitted in this way, with two- and three-body couplings of third and fourth order, is presented. It can be used to calculate arbitrary anharmonic phonon couplings through fourth order.

Abstract: The theoretical calculation of the electronic structure of any constituent materials is the first step toward the interpretation and understanding of experimental data and reliable device design. This is essentially true for nanoscale devices where both the atomistic granularity of the underlying materials and the quantum-mechanical nature of charge carriers play critical roles in determining the overall device performance. In this paper, within a fully atomistic and quantum-mechanical framework, we investigate the electronic structure of wurtzite InN quantum dots (QDs) self-assembled on GaN substrates. The main objectives are threefold: 1) to explore the nature and the role of crystal atomicity, strain field, and piezoelectric and pyroelectric potentials in determining the energy spectrum and the wave functions; 2) to address the redshift in the ground state, the symmetry lowering and the nondegeneracy in the first excited state, and the strong band mixing in the overall conduction-band electronic states, which is a group of interrelated phenomena that has been revealed in recent spectroscopic analyses; and 3) to study the size dependence of the internal fields and its impact on the electronic structure as a whole. We also demonstrate the importance of 3-D atomistic material representation and the need for using realistically extended substrate and cap layers (multimillion-atom modeling) in studying the built-in structural and electric fields in these reduced dimensional QDs. The models used in this study are as follows: 1) valence-force-field Keating model for atomistic strain relaxation; 2) 20-band nearest neighbor sp 3 d 5 s* tight-binding model for the calculation of single-particle energy states; and 3) microscopically determined polarization constants in conjunction with an atomistic 3-D Poisson solver for the calculation of piezo- and pyroelectric contributions.