The electronic charge distribution in crystalline silicon: comparison of ab initio theory and experiment

Lu, Zhong-Yi; Zunger, Alex

doi:10.1107/s0108767392001831

Cited by 23 publications

(31 citation statements)

References 20 publications

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“…Several experimental charge-density studies have been carried out for both silicon (Spackman, 1986;Lu & Zunger, 1992;Lu et al, 1993) and beryllium (Stewart, 1977;Larsen & Hansen, 1984;Iversen et al, 1995). In particular, the existence of non-nuclear maxima (NNM for short) in the electron-density distribution for these systems, suggested on the basis of theoretical (Zou & Bader, 1994) and experimental (Sakata & Sato, 1990;Takata et al, 1994;Iversen et al, 1995;Takata & Sakata, 1996) evidence, has been recently questioned (de Vries, Briels, Feil, te Velde & Baerends, 1996;.…”

Section: Me Model Studies On Si and Bementioning

confidence: 99%

Accurate Charge-Density Studies as an Extension of Bayesian Crystal Structure Determination

Roversi¹,

Irwin²,

Bricogne³

1998

Acta Crystallogr A Found Crystallogr

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Many hopes and much controversy have surrounded the application of the maximum-entropy (ME) method to accurate charge-density studies. This paper shows that viewing such studies as an extension of Bayesian crystal structure determination provides practical means of ful®lling many of the hopes invested in the ME method, while essentially eliminating its controversial aspects, the latter being explained in terms of a number of computational artefacts. The positional probability distribution of scatterers having maximum entropy relative to a given`prior prejudice' is computed so as to reproduce a set of phased structure-factor amplitudes; core electrons can optionally be treated as a ®xed fragment' and described using atomic core densities derived from ab initio wave functions. Fragment and prior-prejudice density distributions are computed by fast Fourier transforms and are thermally smeared by aliasing. These various algorithms have been implemented within the BUSTER computer program. Model studies on noise-free synthetic data sets for -glycine, silicon and beryllium show that all-electron calculations give rise to artefacts when a uniform prior prejudice is used, while valence-only calculations using valence monopole priors are essentially free from artefacts. The maximum-entropy approach is thus optimally implemented by incorporating the prior knowledge of the existence of sharp atomic cores in the form of a fragment not subjected to entropy maximization. These results contribute to settling the debate about the putative existence of non-nuclear density maxima at special positions for crystalline silicon and beryllium, and prepare the ground for developing maximumlikelihood multipolar re®nement.

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Section: Me Model Studies On Si and Bementioning

confidence: 99%

Accurate Charge-Density Studies as an Extension of Bayesian Crystal Structure Determination

Roversi¹,

Irwin²,

Bricogne³

1998

Acta Crystallogr A Found Crystallogr

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“…The refined parameters show good agreement with the already available literature values and are presented in table 3. The refined κ parameter of Si shows slight expansion of the valence region as agreed upon by Lu and Zunger [1]. For Ge, there is slight contraction of valence shell as indicated by κ and k .…”

Section: Multipole Refinementmentioning

confidence: 52%

“…The neutral atom wave functions are taken from Clementi tables [35] and the Slater-type radial functions are used with n l = 4, 4, 6, 8 for l ≤ 4 according to [17]. The atomic orbitals up to hexadecapole were considered with double zeta function ξ taken as per Lu and Zunger [1]. As described by Dawson [36] and Stewart [37], the multipole deformation functions allowed for the tetrahedral site symmetry of the germanium atom are one octupole (i.e., P 32− ) and one hexadecapole, the latter being a combination of P 40 and P 44 while the other terms vanish due to the site symmetry of the Si and Ge atoms beinḡ 43m.…”

Section: Multipole Refinementmentioning

confidence: 99%

“…To date, there have been many studies on the electron densities for Si and Ge both experimentally and theoretically because of their importance as semiconductors, e.g., for Si, Lu and Zunger [1] compared the measured electron density distribution with ab initio theoretical calculations within the local density formalism; Deutsch [2] used the multipole expansion for analysing the data of Si; Spackman [3,4] derived deformation and valance electron density via Fourier summation and used the multipole refinement for Si and diamond; Sakata and Sato [5] evolved the precise electron density of Si by maximum entropy method. For Si and Ge, Deutsch et al [6] have studied theoretically and experimentally the charge density.…”

Section: Introductionmentioning

confidence: 99%

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Electron density distribution in Si and Ge using multipole, maximum entropy method and pair distribution function analysis

Ramachandran¹,

Ali²,

Israel

2008

Pramana - J Phys

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The local, average and electronic structure of the semiconducting materials Si and Ge has been studied using multipole, maximum entropy method (MEM) and pair distribution function (PDF) analyses, using X-ray powder data. The covalent nature of bonding and the interaction between the atoms are clearly revealed by the two-dimensional MEM maps plotted on (1 0 0) and (1 1 0) planes and one-dimensional density along [1 0 0], [1 1 0] and [1 1 1] directions. The mid-bond electron densities between the atoms are 0.554 e/Å 3 and 0.187 e/Å 3 for Si and Ge respectively. In this work, the local structural information has also been obtained by analyzing the atomic pair distribution function. An attempt has been made in the present work to utilize the X-ray powder data sets to refine the structure and electron density distribution using the currently available versatile methods, MEM, multipole analysis and determination of pair distribution function for these two systems.

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“…For example, Lu and Zunger [6] com pared the measured electron density distribution with ab initio theoretical calculations within the local den sity formalism. Sakata and Sato [7] evolved the precise electron density of silicon by maximum entropy method (MEM) [8].…”

Section: Introductionmentioning

confidence: 99%

Comparison of electronic structure of as grown and solar grade silicon samples

Ramachandran

Sheeba

2012

Semiconductors

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A comparison of the electronic structure of two different types of silicon materials viz., (i) as grown silicon and (ii) solar silicon has been carried out utilizing maximum entropy method and pair distribution function using powder X-ray data sets. The precise electron density maps have been elucidated for the two samples. The covalent nature of the bonding between atoms in both the samples is found to be well pro nounced and clearly seen from the electron density maps. The electron densities at the middle of the Si Si bond are found to be 0.47 and 0.45 e/Å 3 for as grown silicon and solar silicon respectively. In this work, the local structural information has also been obtained by analyzing the atomic pair distribution functions of these two samples.

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The electronic charge distribution in crystalline silicon: comparison of ab initio theory and experiment

Cited by 23 publications

References 20 publications

Accurate Charge-Density Studies as an Extension of Bayesian Crystal Structure Determination

Accurate Charge-Density Studies as an Extension of Bayesian Crystal Structure Determination

Electron density distribution in Si and Ge using multipole, maximum entropy method and pair distribution function analysis

Comparison of electronic structure of as grown and solar grade silicon samples

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