Finite-element methods in electronic-structure theory

Pask, John E.; Klein, Bern; Sterne, P. A.; Fong, C. Y.

doi:10.1016/s0010-4655(00)00212-5

Cited by 116 publications

(88 citation statements)

References 58 publications

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“…The finite-difference method has also been used with the conjugate-gradient solver (Seitsonen, Puska, and Nieminen, 1995) and the Rayleigh quotient multigrid method (Heiskanen et al, 2001); see Torsti et al (2003Torsti et al ( , 2006. Pask et al (1999Pask et al ( , 2001) and Sterne, Pask, and Klein (1999) used finite-element modeling for electron-positron systems.…”

Section: F Numerical Approaches For Self-consistent Calculationsmentioning

confidence: 99%

Defect identification in semiconductors with positron annihilation: Experiment and theory

2013

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Positron annihilation spectroscopy is particularly suitable for studying vacancy-type defects in semiconductors. Combining state-of-the-art experimental and theoretical methods allows for detailed identification of the defects and their chemical surroundings. Also charge states and defect levels in the band gap are accessible. In this review the main experimental and theoretical analysis techniques are described. The usage of these methods is illustrated through examples in technologically important elemental and compound semiconductors. Future challenges include the analysis of noncrystalline materials and of transient defect-related phenomena.

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Section: F Numerical Approaches For Self-consistent Calculationsmentioning

confidence: 99%

Defect identification in semiconductors with positron annihilation: Experiment and theory

2013

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“…Since we focus on the analysis of the NOR, SHG and THG, in our work the parameter λ is taken to be 4. The four lowest electron states in electric field-tunable Morse quantum well have been calculated numerically via finite element method [37,38]. In order to calculate the coefficients of NOR, SHG and THG, one considers that the system is irradiated by a light field with frequency ω applied with polarization along the growth direction of the quantum well.…”

Section: Methodsmentioning

confidence: 99%

Electric-field-induced Nonlinear Optical Rectification, Second- and Third-harmonic Generation in Asymmetrical Quantum Well

Şakiroğlu

2017

SDÜ Fen Bil Enst Der

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Abstract:The effects of a static electric field on the nonlinear optical rectification, second-and third-harmonic generation in a quantum well described by Morse potential are theoretically investigated. Analytical expressions for the optical coefficients due to intersubband optical transitions with an applied electric field are extracted from the compact-density matrix approach and iterative scheme. Numerical results presented for a typical GaAs quantum well reveal the feasibility of control of optical transitions between the size-quantized subbands. In addition, we have to emphasize the fact that the optical response of the system is remarkably sensitive to the electric field and structural range parameter.

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“…There are several techniques for band structure calculations for classical continuous systems such as photonic and phononic crystals. These include the plane-wave method (Ho et al 1990;Leung & Liu 1990;Zhang & Satpathy 1990;Meade et al 1993;Johnson & Joannopoulos 2001), the transfer matrix method (Pendry & MacKinnon 1992), the multiple scattering method (Leung & Qiu 1993;Wang et al 1993), the finite-difference time-domain method (Chan et al 1995), the finite-difference method (Yang 1996), the finite-element (FE) method (Axmann & Kuchment 1999;Dobson 1999;Pask et al 2001), the meshless method (Jun et al 2003), the multiple multipole method (Moreno et al 2002), the wavelet method (Checoury & Lourtioz 2006;Yan & Wang 2006) and the pseudospectral method (Chiang et al 2007), among others (Botten et al 2001;Marrone et al 2002;Yuan & Lu 2006) (see Busch et al (2007) for a review). Some of the methods involve expanding the periodic domain (or potential) and the wave field using a truncated basis.…”

Section: (A) Classical Calculationsmentioning

confidence: 99%

Reduced Bloch mode expansion for periodic media band structure calculations

2009

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Reduced Bloch mode expansion (RBME) is presented for fast periodic media band structure calculations. The expansion employs a natural basis composed of a selected reduced set of Bloch eigenfunctions. The reduced basis is selected within the irreducible Brillouin zone at high symmetry points determined by the medium's crystal structure and group theory (and possibly at additional related points). At each of the reciprocal lattice selection points, a number of Bloch eigenfunctions are selected up to the frequency/energy range of interest for the band structure calculations. As it is common to initially discretize the periodic unit cell and solution field using some choice of basis, RBME is practically a secondary expansion that uses a selected set of Bloch eigenvectors. Such expansion therefore keeps, and builds on, any favourable attributes a primary expansion approach might exhibit. Being in line with the well-known concept of modal analysis, the proposed approach maintains accuracy while reducing the computation time by up to two orders of magnitudes or more depending on the size and extent of the calculations. Results are presented for phononic, photonic and electronic band structures.

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Finite-element methods in electronic-structure theory

Cited by 116 publications

References 58 publications

Defect identification in semiconductors with positron annihilation: Experiment and theory

Defect identification in semiconductors with positron annihilation: Experiment and theory

Electric-field-induced Nonlinear Optical Rectification, Second- and Third-harmonic Generation in Asymmetrical Quantum Well

Reduced Bloch mode expansion for periodic media band structure calculations

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