Paul Rago

Design of S-Graded Buffer Layers for Metamorphic ZnSySe1−y/GaAs (001) Semiconductor Devices

We present design equations for error function (or “S-graded”) graded buffers for use in accommodating lattice mismatch of heteroepitaxial semiconductor devices. In an S-graded metamorphic buffer layer the composition and lattice mismatch profiles follow a normal cumulative distribution function. Minimum-energy calculations suggest that the S-graded profile may be beneficial for control of defect densities in lattice-mismatched devices because they have several characteristics which enhance the mobility and glide velocities of dislocations, thereby promoting long misfit segments with relatively few threading arms. First, there is a misfit-dislocation-free zone (MDFZ) adjacent to the interface, which avoids dislocation pinning defects associated with substrate defects. Second, there is another MDFZ near the surface, which reduces pinning interactions near the device layer which will be grown on top. Third, there is a large built-in strain in the top MDFZ, which enhances the glide of dislocations to sweep out threading arms. In this paper we present approximate design equations for the widths of the MDFZs, the built-in strain, and the peak misfit dislocation density for a general S-graded semiconductor with diamond or zincblende crystal structure and (001) orientation, and show that these design equations are in fair agreement with detailed numerical energy-minimization calculations for ZnSySe1−y/GaAs (001) heterostructures.

Relaxation Dynamics and Threading Dislocations in ZnSe and ZnS y Se1−y /GaAs (001) Heterostructures

The design of lattice-mismatched semiconductor devices requires a predictive model for strains and threading dislocation densities. Previous work enabled modeling of uniform layers but not the threading dislocations in device structures with arbitrary compositional grading. In this work we present a kinetic model for lattice relaxation which includes misfit–threading dislocation interactions, which have not been considered in previous annihilation–coalescence models. Inclusion of these dislocation interactions makes the kinetic model applicable to compositionally graded structures, and we have applied it to ZnSe/GaAs (001) and ZnSySe1−y/GaAs (001) heterostructures. The results of the kinetic model are consistent with the observed threading dislocation behavior in ZnSe/GaAs (001) uniform layers, and for graded ZnSySe1−y/GaAs (001) heterostructures the kinetic model predicts that the threading dislocation density may be reduced by the inclusion of grading buffer layers employing compositional overshoot. This “dislocation compensation” effect is consistent with our high-resolution x-ray diffraction experimental results for graded ZnSySe1−y/GaAs (001) structures grown by photoassisted metalorganic vapor-phase epitaxy.

Initial misfit dislocations in a graded heteroepitaxial layer

We show that for a mismatched heteroepitaxial layer with linear compositional grading, the first misfit dislocations will be introduced at a finite distance yC from the substrate interface. This is of practical as well as fundamental importance; it alters the value of the critical layer thickness for lattice relaxation and it moves the misfit dislocations away from the interface, where contaminants and defects may cause dislocation pinning or mobility reduction. We have calculated the position of the initial misfit dislocations yC for linearly graded Si1−xGex/Si(001) heteroepitaxial layers with lattice mismatch given by f=Cfy, where Cf is the grading coefficient and y is the distance from the interface. The distance of the first misfit dislocations from the interface yC decreases with increasing grading coefficient but can exceed 40 nm in layers with shallow grading (|Cf|<12 cm−1). For the range of grading coefficients investigated, yC varies from 6% to 11% of the critical layer thickness. Based on the mo...

Comparison of the phase-invariant and mosaic crystal models for dynamical x-ray diffraction from metamorphic InxGa1−xAs/GaAs (001) structures

In this paper, the authors present a mosaic crystal model for the calculation of dynamical x-ray rocking curves from metamorphic semiconductor device structures containing dislocations. This model represents an extension of the previously reported phase-invariant model, which is applicable to most metamorphic heterostructures and serves as the basis for their x-ray characterization, allowing determination of the depth profiles of strain, composition, and dislocation density. The new model can be applied similarly but avoids the limitations of the phase invariant model, namely, a loss of accuracy in some structures with closely lattice matched layers and layers containing large dislocation densities. In this paper, the authors present the computational details of the new mosaic crystal model, demonstrate its application to graded InxGa1−xAs/GaAs (001) metamorphic buffers and device structures, and make quantitative comparisons between the results of the phase-invariant and mosaic crystal models.

X-ray diffraction analysis for step and linearly graded InxGa1−xAs/GaAs (001) heterostructures using various hkl reflections

In this paper, the authors present dynamical x-ray rocking curves for step and linearly graded InxGa1−xAs/GaAs (001) heterostructures containing dislocations. The x-ray rocking curve analysis for a number of reflection profiles including 002, 004, 006, 044, 135, 335, 444, and 117 was conducted assuming Cu kα1 radiation. The analysis provides an accurate estimation for the threading dislocation density in step graded structures from the broadening of the individual rocking curve peaks. The rocking curve has little sensitivity to the threading dislocation density for linearly graded InxGa1−xAs/GaAs (001) buffer layers regardless of the hkl reflection which is chosen, but the dislocation density for a uniform layer on top of a linearly graded buffer may be estimated from its rocking curve width.

Apparent critical layer thickness in ZnSe/GaAs (001) heterostructures and the role of finite experimental resolution

The critical layer thickness hc for the onset of lattice relaxation has important implications for the design of pseudomorphic and metamorphic II–VI device structures on lattice-mismatched substrates. Several theoretical models have been developed for the critical layer thickness, including the well-known force-balance model of Matthews and Blakeslee [J. Cryst. Growth 27, 188 (1974)]. Experimentally measured critical layer thicknesses in ZnSe/GaAs (001) heterostructures are often at variance with one another as well as the Matthews and Blakeslee model. By assuming that the lattice relaxation is a fixed fraction of the equilibrium relaxation (constant γ/γeq), Fritz [Appl. Phys. Lett. 51, 1080 (1987)] has shown that the measured hc may be much larger than the equilibrium value when using a finite experimental resolution. However, the assumption of constant fractional relaxation is not applicable to any heterostructure exhibiting kinetically limited lattice relaxation. In order to reconcile the conflicting r...