Determination of precipitate concentration using Laue diffraction

S. Bernatová, O. Caha

Institute of Condensed Matter physics, Masaryk University, Kotlářská , 611 37 Brno, Czech Republic

author@muni.cz

Structural quality of semiconductor wafers and epitaxial layers is an important parameter substantially influencing their electrical properties and the performance of fabricated integrated circuits. A reliable control of the defect nucleation and growth during the semiconductor technology is an important issue, since the defects may affect detrimentally the electric parameters of the semiconductor structures, but they can also be beneficial, because they can getter out impurities, especially heavy metal atoms.

The x-ray scattering methods, especially diffuse scattering around reciprocal lattice points, were often used in past for the defect characterization. The diffuse scattering provides us the information about precipitate shapes, sizes and deformation field around them. However, the determination of their absolute concentration is not straightforward; the diffuse scattered intensity from the defects has to be normalized, for instance to the thermal diffuse scattering [1]. This drawback can be overcome by measurement of the rocking curve in a two-crystal setup without analyzer, which can be normalized directly to the intensity of the primary beam. This method was used in the Bragg diffraction geometry by several authors [2]. We have used the Laue geometry, which allows us to measure both the diffraction curve and the transmission curve simultaneously, and therefore gives us more information.

We have used x-ray diffractometer with Cu tube and germanium 220 Bartels (4 crystal) monochromator without analyzer. We have checked the diffractometer angular resolution on a float zone (defect free) silicon crystal. The sample was polished and etched to the thickness of 0.122 mm. The measured diffraction and transmission curves are shown in the figure 1. The experimental curves were compared with the dynamical theory of x-ray diffraction [3]. The slight disagreement of the theoretical and experimental dependences can be explained by inhomogeneity in the sample thickness.

Figure 1. The dependence of the diffracted (squares) and transmitted (crosses) intensity on the angle of incidence in 220 diffraction on a float zone (defect free) silicon crystal. The measured intensity is compared to the theoretical diffraction curves (dashed and solid lines). The angle of incidence is measured with respect to the Bragg position.

The sample of a Czochralski grown silicon underwent a three stage annealing process (600°C/8 h, 800°C/4 h and 1000°C/16 h). The sample was polished and etched to the thickness 0.180 mm. The experimental diffraction and transmission curves strongly differs from the theoretical diffraction curves of ideal crystal, see figure 2. Especially, the intensity of the transmitted beam is much lower than from an ideal crystal. The diffraction profiles of the defected crystal was calculated using statistical dynamical theory [4], where the defects were assumed as amorphous spheres randomly displaced inside the crystal lattice. The best coincidence was found for the precipitate radius 1.2 μm and their volume ratio of 3%, which corresponds to the absolute precipitate concentration of 0.9∙10¹⁰cm^-3.

Figure 2. The dependence of the diffracted (squares) and transmitted (crosses) intensity on the angle of incidence in 220 diffraction on the sample with precipitates. Thin line shows the calculation of diffracted intensity, dotted line shows the calculation of transmitted intensity, by the statistical dynamical theory of x-ray diffraction and. Dot-and-dash line and dash line show curves of the perfect crystal.

References

1. L. A. Charni, K. D. Scherbachev, V. T. Bublik, phys. stat. sol. (a) 99, (1991), 267.

2. V.B. Molodkin, S.I. Olikhovskii, E.N. Kislovskii, T.P. Vladimirova,E.S. Skakunova, R.F. Seredenko, B.V. Sheludchenko, Phys. Rev. B 78 (2008), 224109.

3. see for instance A. Authier, Dynamical theory of x-ray diffraction, (Oxford university press, 2001).

4. V. Holý & K.T. Gabrielyan, phys. stat. sol. (a) 140, (1987), 39.

Acknowledgements.

The authors would like to acknowledge prof. V. Holý for providing the simulation code.