Thickness dependence of the integrated Bragg intensity for statistically disturbed silicon crystals

Journal of Applied Physics

Bergmann

et al. 2014

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Residual strains in cubic silicon carbide measured by Raman spectroscopy correlated with x-ray diffraction and transmission electron microscopy Annealed Czochralski Silicon wafers containing SiO x precipitates have been studied by high energy X-ray diffraction in a defocused Laue setup using a laboratory tungsten tube. The energy dispersive evaluation of the diffracted Bragg intensity of the 220 reflection within the framework of the statistical dynamical theory yields the static Debye-Waller factor E of the crystal, which gives access to the strain induced by the SiO x precipitates. The results are correlated with precipitate densities and sizes determined from transmission electron microscopy measurements of equivalent wafers. This allows for the determination of the constrained linear misfit e between precipitate and crystal lattice. For samples with octahedral precipitates the values ranging from e ¼ 0.39 (þ0.28/À0.12) to e ¼ 0.48 (þ0.34/À0.16) indicate that self-interstitials emitted into the matrix during precipitate growth contribute to the lattice strain. In this case, the expected value calculated from literature values is e ¼ 0.26 6 0.05. Further, the precise evaluation of Pendell€ osung oscillations in the diffracted Bragg intensity of as-grown wafers reveals a thermal Debye-Waller parameter for the 220 reflection B 220 (293 K) of 0.5582 6 0.0039 Å 2 for a structure factor based on spherically symmetric scattering contributions. V C 2014 AIP Publishing LLC. [http://dx.

Section: Discussionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Misfit strain of oxygen precipitates in Czochralski silicon studied with energy-dispersive X-ray diffraction

Journal of Applied Physics

Bergmann

et al. 2014

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“…[10][11][12][13] The thickness dependent Bragg intensity of an ideal crystal can be described analytically 14 and shows a characteristic oscillatory behavior around the average Bragg intensity. The oscillation period is called the Pendell€ osung length, and for X-rays it is typically a) will@krist.uni-erlangen.de.…”

Section: B Pendell € Osung Oscillationsmentioning

confidence: 99%

Oxygen diffusivity in silicon derived from dynamical X-ray diffraction

Journal of Applied Physics

Kot

et al. 2013

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Diffusion of the vacancy defect leading to the formation of multi-shell structures in the nanowire and nanobridge J. Appl. Phys. 112, 114301 (2012) Characterization of defect evolution in ultrathin SiO2 layers under applied electrical stress J. Appl. Phys. 112, 103513 (2012) Fluid like behavior of oxygen in cubic zirconia under extreme conditions Appl. Phys. Lett. 101, 181906 (2012) Out-diffusion of deep donors in nitrogen-doped silicon and the diffusivity of vacancies J. Appl. Phys. 112, 013519 (2012) Additional information on J. Appl. Phys. Thickness dependent Pendell€ osung oscillations are highly sensitive to strain fields from defects in a host crystal. Based on this, we present a novel technique to measure the precipitation kinetics of oxygen in silicon already at its early stage of clustering at high temperatures. At 900 C, precipitates with a radius smaller than 4 nm and with a density of 1 6 0:5 Â 10 13 1/cm 3 were observed. The technique was calibrated by complementary scanning transmission electron microscope and energy dispersive X-ray measurements in the range of normal diffusivity yielding a diffusion constant of 1:7 6 0:1 Â 10 À12 cm 2 =s, which is close to the literature value of 2:074 Â 10 À12 cm 2 =s. The measurements have been made with the characteristic K a1 -line of a high voltage tungsten X-ray tube at 59.31 keV, which provides the opportunity to illuminate through complex sample environments like high temperature scattering furnaces. V C 2013 American Institute of Physics. [http://dx

“…21 In this paper, a deeper insight into the O kinetics in pþ Si compared to pÀ material is presented by comparing the precipitation behavior at 780 C with and without a nucleation step at 450 C. Four crystal wedges (see Table I) were prepared and the thickness dependence of the 400 Bragg reflection was investigated in-situ at 780 C by the Pendell€ osung method. 22,23 The diffraction energy was 59.3 keV, which corresponds to the K a1 -line of the tungsten X-ray tube. The Pendell€ osung lengths were measured accurately by exploiting high order oscillations O (10).…”

mentioning

confidence: 99%

“…More details to the experimental setup and the sample preparation can be found in previous publications. 23,24 The Pendell€ osung oscillations measured in-situ during annealing at 780 C of the wedges p þ I and p À I are displayed in Figure 1 (top left and right). The wedges were first annealed for 30 h at 450 C and then directly ramped with 5 K/min to 780 C where the first data set shown were acquired (light grey curves in Figure 1).…”

mentioning

confidence: 99%

Growth and nucleation regimes in boron doped silicon by dynamical x-ray diffraction

Applied Physics Letters

Bergmann

et al. 2014

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The oxygen precipitation of highly (17.5 mΩ cm) and moderately (4.5 Ω cm) boron (B) doped silicon (Si) crystals at 780 °C is investigated by following in-situ the evolution of diffraction Pendellösung oscillations. All samples show an initial diffusion-driven growth process which may change over into Ostwald ripening. For the highly doped sample and involving a nucleation step at 450 °C for 30 h, the precipitate density ρ is enhanced by a factor of 8 as compared to the moderately doped sample. The influence of a high B concentration on ρ is dramatically higher for the samples directly heated to 780 °C, where an enhancement factor of 80 is found. Considering Ostwald ripening as a second growth regime reveals consistent ripening rates and surface energies σ with those found at 900 °C in a previous publication.