Bunches of misfit dislocations on the onset of relaxation of Si0.4Ge0.6/Si(001) epitaxial films revealed by high-resolution x-ray diffraction

Abstract

The experimental x-ray diffraction patterns of a Si0.4Ge0.6/Si(001) epitaxial film with a low density of misfit dislocations are modeled by the Monte Carlo method. It is shown that an inhomogeneous distribution of 60° dislocations with dislocations arranged in bunches is needed to explain the experiment correctly. As a result of the dislocation bunching, the positions of the x-ray diffraction peaks do not correspond to the average dislocation density but reveal less than a half of the actual relaxation.

Microstructure of epitaxial Mg3N2 thin films grown by MBE

“…This observation points towards its origin being located close to the filmsubstrate interface, with the initially correlated defects being overgrown by a disordered Mg 3 N 2 displaying correlations at much smaller spatial scales. Such line shapes have been reported previously in various heteroepitaxial systems and are usually interpreted as originating from different types of correlated defects, including threading dislocations [11][12][13][14][15][16] , stacking faults 17 , misfit dislocations located at the film-substrate interface 16,[18][19][20][21][22][23][24] , misorientations 12,22,23 or grain boundaries 17,25 . Consistent with these previous reports, the intensity of the coherent peak decreases significantly when going from the (222)…”

“…The reason for this lies most probably in increased roughness and/or decreased crystallinity, as will be discussed in the following. At this stage, we assume that the coherent x-ray scattering phenomenon leading to this peak is associated with a regular distribution of some crystalline defect displaying very long correlation distances, as observed previously in other material systems [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] .…”

“…Starting from Equation ( 8), Kaganer et. al constructed proper 𝐺(𝒓) functions that allowed them to identify types and arrangements of dislocations by simulating XRD patterns in a number of different heteroepitaxial systems 11,16,18,19,24 . In our case, a regular columnar structure was revealed by TEM, where the columns correspond to different twin domains that are correlated in the initial growth stages and lead to the narrow rocking curves.…”

“…Consequently, line widths of diffraction rocking curves increase as a function of the defect density. However, if the position and, eventually, the orientation of the defects are correlated, coherent scattering can be preserved even in the presence of large defect densities, leading to extremely narrow line widths in transverse ω scans [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] . While XRD gives a global view of the crystal's microstructure and lattice parameters, transmission electron microscopy (TEM) enables a local insight into the film structure that allows the identification of lattice defects and the determination of their spatial arrangement.…”

Computational Analysis of Low-Energy Dislocation Configurations in Graded Layers

“…The distance between the defects in the array is close (by construction) to the optimal value d 0 = b x /ε xx , ensuring on average full relaxation of the strain in the layer, as confirmed by the strain map of Figure 1b. This results is well known in heteroepitaxy, and, while experimentally deviations from this simple picture are often encountered [32,33,49], it is often reported as a useful first approximation of the expected distribution of dislocations [4].…”