Phonon scattering related to oxygen precipitation in Cz-silicon

Zeller, Fabian; Laßmann, Kurt; Eisenmenger, Wolfgang

doi:10.1016/s0921-4526(98)01204-6

Cited by 4 publications

(1 citation statement)

References 7 publications

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“…For concentrations below 5×10 11 cm −3 , electrically active impurities can be detected, for example, by electron spin or photothermal ionization spectroscopy. Oxygen concentrations below 10 13 cm −3 were recently determined by means of phonon spectroscopy (Zeller et al 1999) with superconducting tunnelling junctions. Besides optical spectroscopy, a wide range of mass spectroscopy methods can also be used to obtain impurity concentrations.…”

Section: Materials Characterizationmentioning

confidence: 99%

History and progress in the accurate determination of the Avogadro constant

2001

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The Avogadro constant, N A , is a fundamental physical constant that relates any quantity at the atomic scale to its corresponding macroscopic scale. Inspired by the kinetic gas theory Avogadro proposed his hypothesis in 1811, in order to describe chemical reactions as an atomic process between atoms or molecules. Starting from his pioneering findings, the determination of this large number has fascinated generations of scientists up to this day. The review of methods aimed at finding a value for N A starts with the calculations made by Loschmidt (1865; N A ≈ 72 × 10 23 mol −1 ) who evaluated the number of molecules in a given gas volume, derived from estimates of molecular diameters and the mean free path length. Consideration of Brownian motion led to some more accurate determinations of N A around the beginning of the 20th century (Perrin (1908); N A ≈ 6.7 × 10 23 mol −1 ). Other methods developed in the following years are based on Millikan's oil drop experiment (1917, N A ≈ 6.064(6) × 10 23 mol −1 ), on the counting of alpha particles emitted from radium or uranium (Rutherford (1909); N A ≈ 6.16 × 10 23 mol −1 ) and on investigations of molecular monolayers on liquids (Nuoy (1924); N A ≈ 6.004 × 10 23 mol −1 ).A modern method to derive N A from the density, the relative atomic mass, and the unit cell length was introduced by Bragg in 1913. It makes use of the diffraction of x-rays by the interatomic spacings of a crystal lattice and its periodic arrangement. The accuracy of this method is extremely affected by the fact that the lattice scale of the structurally imperfect lattice can be calibrated only approximately in SI units. Data of N A were, therefore, found to be in disagreement with other fundamental constants (Bearden (1931); N A ≈ 6.019(3) × 10 23 mol −1 ). A break though was achieved with perfect crystals of silicon and x-ray interferometry making available very precise data of atomic distances, expressed in SI units (Bonse and Hart 1965).Today, metrology has re-discovered the Avogadro constant and uses it as one of several possible routes to a re-definition of the kilogram because the old platinum iridium artefact exhibits long-term stability problems. This application of the Avogadro constant presupposes a final measurement uncertainty of about 1×10 −8 , a challenge for the experimental determination of the quantities involved, i.e. macroscopic density, isotopic composition, and unit cell volume of a silicon crystal. Many years of research work were centred on the problem of how far the perfection of a real crystal is away from the ideal state. At present, it is widely accepted that,

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Section: Materials Characterizationmentioning

confidence: 99%

History and progress in the accurate determination of the Avogadro constant

2001

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Phonon scattering of oxygen-related defects in annealed silicon crystals

Zeller

Laßmann

Eisenmenger

2002

Physica B: Condensed Matter

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Reassessment of the intrinsic carrier density in crystalline silicon in view of band-gap narrowing

Altermatt

Schenk

Geelhaar

et al. 2003

Journal of Applied Physics

187

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The commonly used value of the intrinsic carrier density of crystalline silicon at 300 K is ni=1.00×1010 cm−3. It was experimentally determined by Sproul and Green, J. Appl. Phys. 70, 846 (1991), using specially designed solar cells. In this article, we demonstrate that the Sproul and Green experiment was influenced by band-gap narrowing, even though the dopant density of their samples was low (1014 to 1016 cm−3). We reinterpret their measurements by numerical simulations with a random-phase approximation model for band-gap narrowing, thereby obtaining ni=9.65×109 cm−3 at 300 K. This value is consistent with results obtained by Misiakos and Tsamakis, J. Appl. Phys. 74, 3293 (1993), using capacitance measurements. In this way, long-prevailing inconsistencies between independent measurement techniques for the determination of ni are resolved.

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Phonon scattering related to oxygen precipitation in Cz-silicon

Cited by 4 publications

References 7 publications

History and progress in the accurate determination of the Avogadro constant

History and progress in the accurate determination of the Avogadro constant

Phonon scattering of oxygen-related defects in annealed silicon crystals

Reassessment of the intrinsic carrier density in crystalline silicon in view of band-gap narrowing

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