(Color online) Atomic force microscopy (AFM) images of the surfaces of 100-nm-thick, coherently strained GaAsN films grown with =(a) 7, (b) 18, and (c) 29. A 250-nm-thick, partially-relaxed GaAsN film is shown in (d). The gray-scale ranges displayed are (a) 100, (b) 5, (c) 5, and (d) 70 nm. Cuts of the tip height defined by the arrows are shown below each AFM image.
Stress-thickness product vs thickness for (a) 500-nm-thick films and (b) the first 250 nm of films. In (a), the slope is approximately constant for all films, indicating negligible stress relaxation. In (b), the slope is approximately constant for films with , while for the slope begins to decrease, indicating stress relaxation. Inset: (004) XRC for the same films. For , there is one distinct epilayer peak, while for there is a split epilayer peak.
(a) Stress measured by in situ multibeam optical stress sensor (MOSS) (triangles and squares) measurements and calculated from ex situ x-ray rocking curve (XRC) (diamonds and circles) measurements using a linear interpolation of lattice parameter and elastic constants. For samples with N composition greater than , indicated by the dotted line, the apparent stress difference is significantly greater than the error bars of the measurements. All samples were grown with a high ratio , unless otherwise noted. N compositions were determined from XRCs using a linear interpolation of lattice parameters and elastic constants. (b) Composition dependence of the bowing parameter, , for which the MOSS and XRC stresses are equal, shown as open diamonds and solid circles for and 15, respectively. Weighted linear fits to the data points for and 15 are indicated by the dashed and solid lines, respectively. N compositions were determined from XRCs, with bowing of the elastic constants included. (c) Composition dependence of and using for which the MOSS and XRC stresses are equal, with (solid lines) and (dashed lines).
Dark-field cross-sectional transmission electron microscopy (TEM) images for films with =(a) 2.4% and (b) 3.0%, collected with a  two-beam condition. In addition, bright-field cross-sectional TEM images collected with a  two-beam condition are shown for =(c) 2.4% and (d) 3.0%. Finally, cross-sectional high-resolution TEM images are shown for =(e) 2.4% and (f) 3.0%. In both cases, the zone axis is .
GaAsN alloy lattice parameter vs nitrogen concentration, predicted by various lattice-parameter models, as well as observed experimentally by x-ray rocking curves ( axis) and nuclear reaction analysis (Ref. 29) ( axis). The model assumes a linear interpolation of the binary lattice parameters (i.e., Vegard’s law), the model assumes a linear interpolation of the binary unit-cell volumes, the model assumes a quadratic interpolation of the binary unit-cell volumes, the model uses Murnaghan’s equation of state to minimize the strain energy, and in the model, the linearly interpolated lattice parameter is modified to include the effect of lattice expansion due to the incorporation of N–N split interstitials. The gray line indicates the least-squares fit to the experimental data.
Elastic constants and lattice parameters for GaAs and GaN used for x-ray rocking curve analysis.
Stress measured by multibeam optical stress sensor (MOSS) and determined from x-ray rocking curve (XRC) measurements assuming different models for the film lattice parameter, for six samples with various N compositions. The model assumes a linear interpolation of the binary lattice parameters (i.e., Vegard’s law). The model accounts for deviation from a linear interpolation due to lattice expansion caused by the incorporation of N–N split interstitials.
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