Theory of AlN, GaN, InN and their alloys

Schilfgaarde, Mark van; Sher, A.; Chen, A.-B.

doi:10.1016/s0022-0248(97)00073-0

Cited by 183 publications

(89 citation statements)

References 57 publications

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“…The results for the equilibrium values ͑lattice constants͒ and for the elastic constants are listed in Table I and compared with values of previous first principles calculations. [6][7][8] Generally, a good agreement is found. A comparison with experiment is difficult since the stable modification of GaN is the wurtzite phase and zincblende GaN can be synthesized by epitaxial growth only.…”

Section: First Principles Calculationsmentioning

confidence: 89%

“…Whereas the properties of the binary compounds AlN, GaN, and InN have been calculated with different highly accurate first-principles methods [5][6][7][8][9][10] the investigation of their alloy properties is mainly based on empirical valence force field ͑VFF͒ models for atomic structure relaxation. Ho and Stringfellow 11 derived a temperature/alloy composition phase diagram with this method indicating a rather large miscibility gap with a critical temperature of 1250°C.…”

Section: Introductionmentioning

confidence: 99%

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Limits and accuracy of valence force field models forInxGa1−xNalloys

Grosse

Neugebauer

2001

Phys. Rev. B

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Formation energies, equilibrium geometries, and elastic properties of ordered In x Ga 1Ϫx N structures have been calculated employing density funcional theory. Based on these results, limits and accuracy of several valence force field ͑VFF͒ models are compared. While these empirical models have been shown to work reasonably well to describe zincblende III/V semiconductors we find significant deviations for group III nitrides ͑GaN, InN͒ and their alloys. We therefore propose a new model that correctly takes into account the long-range electrostatic interactions. Although only the elastic constants of the binary zincblende compounds and the formation energy difference to wurtzite are used as input, the model correctly describes the formation energies and structure of wurtzite binary compounds and ternary alloys.

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Section: First Principles Calculationsmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Limits and accuracy of valence force field models forInxGa1−xNalloys

Grosse

Neugebauer

2001

Phys. Rev. B

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“…General reviews, with extensive references, have been published on the properties of compound semiconductors and their pseudobinary alloys [1,2]. This review focuses on fundamental properties of the compounds and their pseudobinary alloys that can be calculated from an ab initio theoretical, or computational standpoint [for details see Ref.…”

Section: Introductionmentioning

confidence: 99%

“…The discussions will be couched in terms of a self-consistent, all-electron theory that employs full potentials between the electrons and ions and a linear muffin-tin orbital (LMTO) [6] basis [2,7]. This procedure takes proper account of the d states, which is essential to obtaining accurate results in materials like GaInN alloys.…”

Section: Introductionmentioning

confidence: 99%

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Computational Materials Science, an Increasingly Reliable Engineering Tool: Anomalous Nitride Band Structures and Device Consequences

Sher

Schilfgaarde

Berding

et al. 1999

MRS Internet j. nitride semicond. res.

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Computational materials science has evolved in recent years into a reliable theory capable of predicting not only idealized materials and device performance properties, but also those that apply to practical engineering developments. The codes run on workstations and even now are fast enough to be useful design tools. A review will be presented of the current status of this rapidly advancing field. Examples of the accuracy of the codes are displayed by comparing the predicted atomic volumes, and cohesive and excess energies of several materials with experiment. As a further demonstration of the methods, the band structures of AlN, GaN, and InN in wurtzite and zinc blende structures will be presented. There are anomalies in the conduction and valence bands of these materials. Some consequences on light emitting and power devices made from these materials will be examined.

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Summary of Electronic Structure Methods

Schilfgaarde

2002

Characterization of Materials

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Most physical properties of interest in the solid state are governed by the electronic structure—that is, by the Coulombic interactions of the electrons with themselves and with the nuclei. Because the nuclei are much heavier, it is usually sufficient to treat them as fixed. Under this Born‐Oppenheimer approximation, the Schrödinger equation reduces to an equation of motion for the electrons in a fixed external potential, namely, the electrostatic potential of the nuclei (additional interactions, such as an external magnetic field, may be added). Once the Schrödinger equation has been solved for a given system, many kinds of materials properties can be calculated. Ground‐state properties include the cohesive energy, or heats of compound formation, elastic constants or phonon frequencies, atomic and crystalline structure, defect formation energies, diffusion and catalysis barriers and even nuclear tunneling rates, magnetic structure, work functions, and the dielectric response. Excited‐state properties are accessible as well; however, the reliability of the properties tends to degrade—or requires more sophisticated approaches—the larger the perturbing excitation. Because of the obvious advantage in being able to calculate a wide range of materials properties, there has been an intense effort to develop general techniques that solve the Schrödinger equation from “first principles” for much of the periodic table. An exact, or nearly exact, theory of the ground state in condensed matter is immensely complicated by the correlated behavior of the electrons. Unlike Newton's equation, the Schrödinger equation is a field equation; its solution is equivalent to solving Newton's equation along all paths, not just the classical path of minimum action. For materials with wide‐band or itinerant electronic motion, a one‐electron picture is adequate, meaning that to a good approximation the electrons (or quasiparticles) may be treated as independent particles moving in a fixed effective external field. The effective field consists of the electrostatic interaction of electrons plus nuclei, plus an additional effective (mean‐field) potential that originates in the fact that by correlating their motion, electrons can avoid each other and thereby lower their energy. The effective potential must be calculated self‐consistently, such that the effective one‐electron potential created from the electron density generates the same charge density through the eigenvectors of the corresponding one‐electron Hamiltonian. This article resources the states of models electronic structure theory. The other possibility is to adopt a model approach that assumes some model form for the Hamiltonian and has one or more adjustable parameters, which are typically determined by a fit to some experimental property such as the optical spectrum. Today such Hamiltonians are particularly useful in cases beyond the reach of first‐principles approaches, such as calculations of systems with large numbers of atoms, or for strongly correlated materials, for which the (approximate) first‐principles approaches do not adequately describe the electronic structure. In this article, the discussion is limited to the first‐principles approaches. Local‐density approximation is powerful, but has limitations. By comparing it with other approaches strengths and weaknes are ilucidated.

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Theory of AlN, GaN, InN and their alloys

Cited by 183 publications

References 57 publications

Limits and accuracy of valence force field models forInxGa1−xNalloys

Limits and accuracy of valence force field models forInxGa1−xNalloys

Computational Materials Science, an Increasingly Reliable Engineering Tool: Anomalous Nitride Band Structures and Device Consequences

Summary of Electronic Structure Methods

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