Computational Materials Science, an Increasingly Reliable Engineering Tool: Anomalous Nitride Band Structures and Device
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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. 2]. Its purpose is twofold: first to summarize much of what electronic structure theory has contributed recently to the understanding of some aspects of the III-nitride alloys; and, second, to provide some foundation for modem techniques, to provide the nonspecialist with a basis to assess the validity and limitations of the techniques employed in the literature. Section 2 introduces the virtues and limitations of the local-density approximation (LDA) [3] and two higher order corrections, gradient corrections [4] and screened exchange [5]. 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 GalnN alloys. Section 3 summarizes some recent results on fundamental properties of nitride alloys [2,8]. Section 4 is devoted to concluding remarks. 2. GENERAL THEORY An exact, or nearly exact, theory of the ground state in condensed matter is immensely complicated by the correlated behavior of the electrons. 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 an effective G 5.1
Mat. Res. Soc. Symp. Proc. Vol. 537 Q Materials Research Society
external field. The effective field consists of the coulombic interaction of electrons+nuclei, plus an additional effective potential that originates in the correlated electronic motion. This potential must be calculated self-consistently, such that the effective one-electron potential created from the electron density generates through the eigenvectors of the corresponding one-electron Hamiltonian, the same charge density. 2.1
The Local-Density Approximation
The LDA approximates the formally exact (but unknown) energy functional as one that consists of the coulomb energy, plus a functional of the density, dubbed the "exchangecorrelation" energy density. This ansatz leads, as in the Hartree-Fock [9] case, to an equation of motion for electrons moving independently in an effective field, except that in LDA the potential is strictly local. The local form of this potential vastly simplifies the computational effort. Unlike in Hartree-Fock theory, there is no formal justification for associating the eigenvalues of the LDA Hamiltonian with energy bands. However, in one sense, the LDA is an approximation to Hartree-Fock theory where there is a formal justification for this interpretation. Thus, it is expected that the LDA eigenv
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