The threading dislocation density (TDD) in plastically relaxed Ge/Si(001) heteroepitaxial films is commonly observed to progressively decrease with their thickness, owing to mutual annihilation. However, there exists a saturation limit, known as the geometrical limit, beyond which a further decrease of the TDD in the Ge film is hindered. Here, we show that such limit can be overcome in SiGe/Ge/Si heterostructures thanks to the beneficial role of the second interface.Indeed, we show that Si0.06Ge0.94/Ge/Si(001) films display a TDD remarkably lower than the saturation limit of Ge/Si(001). Such result is interpreted with the help of Dislocation Dynamics simulations. The reduction of TDD is attributed to the enhanced mobility acquired by pre-existing threading dislocations after bending at the new interface to release the strain in the upper layer.Importantly, we demonstrate that the low TDD achieved in Si0.06Ge0.94/Ge/Si layers is preserved also when a second, relaxed Ge layer is subsequently deposited. This makes the present reversegrading technique of direct interest also for achieving a low TDD in pure-Ge films.
Ge vertical heterostructures grown on deeply-patterned Si(001) were first obtained in 2012 (C.V. Falub et al., Science 2012, 335, 1330-1334, immediately capturing attention due to the appealing possibility of growing micron-sized Ge crystals largely free of thermal stress and hosting dislocations only in a small fraction of their volume. Since then, considerable progress has been made in terms of extending the technique to several other systems, and of developing further strategies to lower the dislocation density. In this review, we shall mainly focus on the latter aspect, discussing in detail 100% dislocation-free, micron-sized vertical heterostructures obtained by exploiting compositional grading in the epitaxial crystals. Furthermore, we shall also analyze the role played by the shape of the pre-patterned substrate in directly influencing the dislocation distribution.
Regular surface undulations, called cross-hatch patterns, appearing at the free surface of latticemismatched heteroepitaxial films are a key signature of plastic relaxation. Here we show that the dynamics of cross-hatch formation is accurately described by a continuum model based on strainmediated surface diffusion, provided that a realistic distribution of dislocations is considered. We demonstrate quantitative agreement between our time-dependent simulations and dedicated atomic force microscopy experiments on Si0.92Ge0.08 films grown on Si(001) at various thicknesses, finally shedding light on the origin and on the dynamical behavior of a widely-investigated pattern, first observed more than half a century ago.
We present a joint theoretical and experimental analysis of the dislocation distribution in graded epitaxial SiGe crystals grown on under-etched Si pillars by low-energy plasma-enhanced chemical vapor deposition. Dislocation dynamics simulations are used to investigate preferential positioning of 60 • dislocations introduced in the system to release the lattice misfit strain. Coupling to a finite-element solver is exploited to allow for the exact numerical treatment of the stress fields in the presence of a complex distribution of free surfaces. The results show that, by suitably under-etching the Si pillars, it is possible to reverse the sign of the Burgers vector of the dislocations. This helps explaining differences in the experimentally observed distribution of dislocations in SiGe crystals grown on vertical and under-etched pillars, leading to a strong reduction of defects in the latter case. The agreement between simulations and experiments is not simply qualitative: the predicted number of defects generated by multiplication processes in tall crystals is indeed fully consistent with the measured one.
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