Investigation of dislocations in semiconductor epilayers

In order to increase the carrier mobility in Si-based electronic devices, strained layers have a great potential. Strained layers are realized by growth on plastically relaxed SiGe layers as pseudo-substrates. The relaxation of the pseudosubstrates takes place via dislocation formation. The growth conditions determine sensitively the particular properties of the dislocation networks, e.g., the average length of dislocation segments and the density of threading dislocations, i.e., dislocations running through the SiGe layer and epilayers grown on top of it to the sample surface. In order to optimize the fabrication process and hence minimize the threading dislocation density, a reliable characterization technique is desired. We propose to use x-ray diffraction (XRD) for this purpose. XRD has successfully been employed to determine the dislocation density in metals, but for epitaxial semiconductor layers it can so far be applied only in certain cases: either if long misfit segments dominate the dislocation network, or for very particular dislocation types in GaN. A full characterization of dislocations in epilayers is not possible so far, as a theoretical description of the x-ray scattering from threading dislocation is largely lacking. Recently, we have investigated SiGe layers fabricated by an advanced CVD method, and found an x-ray scattering pattern completely different from that observed previously for relaxed SiGe layers: The dislocation network is dominated by comparably short misfit segments. Hence the finite length of dislocation segments needs to be taken into account for a analysis. In this proposal, we will hence pursue two main goals: (i) we will extend the scattering theory for threading dislocations in order to be able to calculate the scattering from any oblique dislocation with mixed screw and edge character. (ii) we will develop a scattering theory for dislocation half-loops with segments of finite length. For both goals, the correct description of the strain field surrounding a dislocation or dislocation half loop will be the main difficulty. We will employ numerical methods as well as develop analytical methods for these calculations. Once the x-ray scattering from dislocations in SiGe can be simulated, we will investigate sample series grown by different methods in order to determine the dependence of the dislocation network on the growth conditions, and hence contribute to optimize the growth, i.e., minimize the threading dislocation density in the topmost epilayers.

Semiconductor heterostructures are very important building blocks for almost all modern electronic devices. By the combination of different materials, their advantages can be exploited to obtain "artificial" materials with superior performance. An important feature of such heterostructures is that they are monocrystalline, i.e., the crystal lattice is continued even across the boundaries between different materials. Since they usually do not have the same natural atom spacings, crystal defects and strain occur at boundaries between different materials, often with unwanted consequences on the material performance. It was the aim of our project to provide a better characterization of these crystal defects, so-called dislocations, by means of x-ray scattering, in order to improve the tools needed for material engineering, to develop material with sufficiently low defect density. Each dislocation is accompanied by a strain field, which can be "seen" by x-ray diffraction. The analysis of diffraction data is, however, challenging due to several aspects: the strain field can be calculated analytically only for pathologically simple defects such as infinitely long, straight dislocation lines in elastically isotropic media. In real samples, however, dislocations are composed of multiple short segments, partly at the boundary between different, anisotropic crystalline materials, partly penetrating through the different layers up to a surface. The strain fields of such more realistic dislocations, consisting of misfit (at/parallel to the interface) and threading segments (penetrating through the epilayers to the surface) could be modelled in our project by means of finite element simulations, in particular a variant of it called "extended finite element modelling", which is able to describe the local rupture in the crystal lattice due to the dislocations. A second obstacle in the analysis of scattering data is the fact that they are obtained not from a single dislocation, but from a large number of dislocations, with their strain- fields overlapping. Therefore, beside fast simulation codes, a Monte Carlo scheme for the creation of random dislocation ensembles was developed. Many such ensembles, random in detail but sharing the same statistical quantities, have to be calculated, and their diffraction patterns have to be averaged to simulate the experimental data. For this purpose, a very fast computer code was developed, to calculate the diffraction pattern from finite element data on a three-dimensional grid. The algorithms and methods developed have been applied to several scientific cases: the analysis of regular dislocation networks in PbSe/PbTe heterostructures, guided dislocation networks in prepatterned Si/SiGe heterostructures, as well as for the simulation of dislocations in self-assembled SiGe islands and InAs/InAsP core-shell nanowires.