In this paper, some factors related to axial impurity uniformity in NTD-Si ingots are studied by means of X-ray topography, single probe spreading resistance, four-point probe, preferential etching and the measuring of voltage-current characteristics, etc. The preferential condition of high axial uniformity is also discussed.
The thermal motion of the atoms influences the intensities of the Bragg reflections. This influence is expressed by a temperature factor. Static disorder generates similar effects, which may be expressed by a pseudo temperature factor. The displacements of the atoms from their mean positions can be described by a probability density function (pdf). The temperature factors and the probability density functions are connected with each other by a Fourier transformation. An effective one particle potential can be calculated from the pdf. The so-called anisotropic temperature factors, frequently calculated in standard structure determinations, assumes a harmonic (parabolic) potential. A more general temperature factor formalism has to take into account anharmonic potentials and the corresponding anharmonic temperature factors. This article describes the mathematical basis of a general temperature factor formalism and an application of this formalism.
Bragg diffraction experiments with γ-radiation of energies of the order of 400 keV allow for high resolution studies of bulk properties of large single crystals which are relevance for the characterization of as grown single crystals as well as for the investigation of structural phase transitions. The absorption of this radiation in matter is very weak, as an example, the mean free path in copper is μo−1 ⋍ 1 cm. Therefore samples can be mounted in any cryostat, furnace or high pressure device without causing window problems. The Bragg angles are only of the order of 1° and thus the shape of the measured diffraction profile is mainly affected by lattice tilts. γ-ray diffractometry is complementary to back scattering techniques which are most suitable for lattice parameter measurements. Using a double crystal setting diffraction patterns are recorded with an angular resolution of 1 second of arc. The integrated reflecting power is measured absolutely with an accuracy of 1% or better and by using various wave lengths in the range between 0.02 and 0.04 Å, highly accurate, model independent structure factors can be determined from imperfect single crystals by means of wave length extrapolation techniques. Because of the short wave length polarization effects are neglibible. The full width at half maximum of the diffraction pattern of a perfect crystal as predicted by dynamical diffraction theory is generally less than 0.5 seconds of arc and the extinction length is of the order of 0.5 mm. Therefore small distortions from a perfect lattice cause rather large changes in the measured integrated reflecting power. Recently Pendellösung intensity beats could be measured in Si with 316 and 468 keV γ-radiation allowing to determine the 220 structure factor with an accuracy of ±- 0.1 %. In addition a surprisingly anisotropic strain field has been observed in floating-zone grown Si crystals.
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