Alexander Gröschel

Diffusion-driven precipitate growth and ripening of oxygen precipitates in boron doped silicon by dynamical x-ray diffraction

X-ray Pendellosung fringes from three silicon single crystals measured at 900 °C are analyzed with respect to density and size of oxygen precipitates within a diffusion-driven growth model and compared with TEM investigations. It appears that boron doped (p+) material shows a higher precipitate density and a higher strain than moderately (p-) boron crystals. In-situ diffraction reveals a diffusion-driven precipitate growth followed by a second growth regime in both materials. An interpretation of the second growth regime in terms of Ostwald ripening yields surface energy values (around 70 erg/cm2) similar to published data. Further, an increased nucleation rate by a factor of ∼13 is found in the p+ sample as compared to a p- sample at a nucleation temperature of 450 °C.

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

The thickness dependence of the integrated Bragg intensities for Czochralski-grown silicon was measured with the characteristic tungsten Kα1-line at 59.3 keV. In contrast to previous experiments the sample is wedge shaped, which allows to take data over a wide range of Pendellosung fringes in one exposure only and without any mechanical movement of the sample. The period length, the oscillation amplitude, and the mean value of the Bragg intensity can be explored to identify the presence of point defects, and the temperature dependence of the period length allows to quantify the thermal Debye-coefficient with high precision.

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

Annealed Czochralski Silicon wafers containing SiOx 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 SiOx 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 = 0.39 (+0.28/−0.12) to e = 0.48 (+0.34/−0.16) 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 = 0.26 ± 0.05....

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

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 Pendellosung 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.

In Situ Observation of the Oxygen Nucleation in Silicon with X-Ray Single Crystal Diffraction

The measurement of Pendellösungs oscillations was used to observe the time dependent nucleation of oxygen in a Czochralski grown single crystal at 750°C. It is shown, that the theoretical approach of the statistical dynamical theory describes the data well. Within the framework of this theory it is possible to determine the static Debye-Waller-factor as a function of the annealing time by evaluating the mean value of the Bragg intensity and the period length. The temperature influence on the Pendellösungs distance was corrected for by measurement of a Float-zone sample at the same temperature.

Structural Defect Studies of Semiconductor Crystals with Laue Topography

A defocused Laue diffractometer setup operating with the white beam of a high energy X-ray tube has been used for a topographic visualization of structural defects in semiconductor wafers. The laboratory white beam X-ray topograph of a Czochralski Si wafer with oxygen precipitates grown in an annealing process is compared to a μPCD image. Further, the dislocation network in a VGF GaAs wafer is studied under thermal annealing up to 1140°C and the in-situ capability of the setup is demonstrated.

Strain relief via silicon self-interstitial emission in highly boron-doped silicon: A diffuse X-ray scattering study of oxygen precipitation

Oxygen precipitation in highly boron-doped Czochralski silicon (5 mΩ cm resistivity) was studied, and a strain-relieving mechanism involving the emission of silicon interstitial atoms (ISi) was identified. Strain-sensitive X-ray diffraction was employed, and through a comparison with complementary electron microscopy measurements a linear misfit strain ϵ=0.01 was determined. Different behavior concerning strain relaxation was measured for wafer-type samples (760 μm thickness) and thick samples (2 mm thickness), which was explained with out-diffusion of ISi in the thinner samples. Based on the experimental findings, a model was developed which invokes an increase in the solubility of interstitial silicon atoms upon boron doping. The model successfully accounts for different effects of boron doping on oxygen precipitation in silicon, which were reported on in literature such as preferential octahedral morphology of precipitates, enhanced nucleation, and relaxed accommodation of the precipitates with respect...

Elastic deformations in a perfect bulk Si crystal studied by high‐energy X‐rays

Long-range strain fields induced in highly perfect bulk crystals during the manufacturing process significantly affect the quality and may even lead to spontaneous fracturing. Obviously a quantitative assessment of these deformations is crucial. A possible means is to examine the diffraction of X-rays by strained crystals, as the deformations bear on the diffraction characteristics of such crystals. In this report a quantitative examination of the diffraction characteristics of a perfect silicon bulk crystal with long-range strain fields in a well defined geometry is presented. The experiments were carried out using a high-energy X-ray laboratory source. By simulating the elastic deformation of the crystal by a finite element program the strain fields of the diffracting crystal are accessed. From these, simulated data values for integrated intensities can be derived on the basis of the dynamical diffraction theory for slightly distorted crystals. The theoretical calculations show good agreement with the experimental measured values. The smallest deformation yielding a noticeable change of the integrated intensity can be associated with a bending radius of the diffracting lattice planes of 16 km.