Diffuse x-ray scattering of misfit dislocations at Si1−xGex/Si interfaces by triple crystal diffractometry

Abstract

Heterostructure Si1−xGex layers on (001)Si substrates with different degrees of relaxation R, ranging from the nearly pseudomorphic state to the nearly relaxed state (R∼0.8), were characterized by diffuse x-ray scattering measurements. The lattice constants a⊥ and a∥, and from these the Ge content x, the relaxation R, and misfit dislocation density Dd, were determined by single crystal diffractometry. The thickness of the SiGe layers was measured in the as-grown state by double crystal diffractometry. A standard triple crystal x-ray diffractometer was used to analyze the diffuse x-ray scattering (DXS) intensity by rotation of the analyzer crystal (ΔΘ) at a fixed sample position (α). The intensities were measured around the 004 reciprocal lattice point of the Si substrate using a wide open counter and a wide range of rotation angle (ΔΘ) for the analyzer crystal. The diffuse scattering increases steeply with increasing dislocation density up to a critical value of Dd≈5×104 cm−1. Then it reaches saturation and decreases slowly as Dd increases. This behavior can be explained by the superposition of the strain fields of neighboring dislocations above a critical density, so that only the heavily distorted regions near the dislocation core participate in scattering. This is confirmed by the fact that the DXS measured for different α values follows the Stokes–Wilson scattering ( IDXS∝q−4; q being the scattering vector). We show that the diffuse scattering technique is a very sensitive tool to detect relaxation at relatively low levels of dislocation densities Dd less than 5×104 cm−1, where diffractometric techniques that measure the lattice constants are near their resolution limits.