Recent Highlights in Materials Reliability Division
Strain in Compound Semiconductor Photonic Systems
Strain is used for the self-assembly of quantum dots (QDs) or for tuning the energy band structure of heteroepitaxial layers. Deleterious effects of strain can lead to delamination of buried oxide apertures in vertical cavity surface-emitting lasers (VCSELs) or shifting of operating wavelengths for InGaAsP/InP-based devices. We have begun an effort, which is partially ATP-funded, to understand and control strain development in III-V semiconductor materials systems. One aspect of the work involves developing experimental methods for measuring elastic strains with spatial resolution in the range of tens of nanometers. This involves the use of electron diffraction in the scanning electron microscope (SEM) and also in the transmission electron microscope (TEM). At present, this is being applied to strains induced by phase transition arising from the wet oxidation of AlGaAs layers confined between GaAs layers. Such oxides are used as optical apertures for VCSELs and, upon formation, result in volumetric compressive strains in the semiconducting layers in excess of 6%.
The second aspect of our contribution to solving this problem is to develop a multi-scale theoretical method for modeling the self-assembly of InAs QDs on GaAs substrates. This involves the combined use of Green’s functions (GF) and boundary element methods (BEMs) incorporating anisotropic elasticity. Strain, in this case, occurs from the mismatch in natural lattice parameters between the two materials. We determine both numerically and analytically the elastic strain energy distribution in these systems. A nice aspect of the work is that we are able to provide experimental data for direct incorporation into the theoretical model using electron microscopy, due to the well-defined conditions often present during epitaxial growth of crystals.
Figure 1 shows a cross-sectional SEM image of an AlGaAs/GaAs multilayer structure, with an aluminum oxide layer partially grown in. The diffuseness of the electron backscatter diffractoin (EBSD) patterns is an indication of the amount of strain present around the oxide growth front. More specifically, pattern diffuseness is a direct measure of the magnitude of the elastic strain gradient present within the sampling volume of the electron beam. The strain is greater near the growth front. With automated beam scanning and pattern collection, we are able to determine the spatial extent of the distortion field caused by the oxidation. Preliminary measurements suggest that the distortion field associated with a single oxide layer extends more than 1 µm beyond the position of the front. The diffraction measurements are made only in crystalline portions of the specimen and, hence, do not sample the oxide strain directly, but rather the resulting effect on AlGaAs and GaAs layers in the vicinity.
Figure 1: SEM image of multilayer structure, with oxide growth front visible. EBSD patterns obtained from positions indicated by line segments. Scale bar = 200 nm.
We are developing advanced theoretical techniques using Green’s functions (GF) and boundary element methods (BEMs) to model the self-assembly of arrays of quantum dots in anisotropic semiconductors. We consider the energetics of growth of a small QD in the strain field of an existing "grown" QD. We introduce a new parameter G, the elastic energy release rate (EERR), that determines the growth of a QD. The EERR, as in fracture mechanics, is defined as the elastic relaxation energy per unit volume of growth and is given by dW/dVQD, where W is the elastic strain energy and VQD is the volume of the growing QD. Assuming uniform misfit strain in QDs,
where the first term is the work done by external traction, the second term is the work done by the intrinsic traction at the boundary of QDs, and the last term represents the energy of the reference state.
We have applied our theory to InAs QDs in GaAs. We have calculated EERR for a QD growing on the free (001) surface for a buried seed dot as well as a seed dot on the surface (Figure 2). We find that the grown QD reduces the EERR of a new QD. For the grown QD at the surface, the EERR for the new dot is lower in the <100> and <010> directions. However, the change in EERR is small when the grown QD is at the surface. In contrast, the effect of a buried QD on EERR of the new QD is very pronounced.
Figure 2:
Formation of a new QD under the influence of a grown surface QD (a) or buried QD (b).We find that the maximum of EERR occurs vertically above the grown QD only for some values of the depth of the QD (Figure 3). This shows that, for QDs covered by a thick spacer medium, a vertical array of self-assembled QDs is energetically favorable. In the case of a thin covering, an oblique stacking of QDs could occur. We also find that there is an optimum depth of the buried QD for the formation of a new QD vertically above it. where the first term is the work done by external traction, the second term is the work done by the intrinsic traction at the boundary of QDs, and the last term represents the energy of the reference state.
Figure 3:
Variation of the EERR for formation of a new QD with locations at different depths of the buried QD (Figure 2b): (a) h = 0.1a; (b) h = 0.6a.
Last modified on April 30, 2003
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