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The critical thickness for Si1−xGex strained layers for the alloy range 0<x<0.15 has been determined from annealed epilayers using mapping techniques which allow single dislocation detection and composition thickness measurements over large areas (∼50 cm2 ). A series of Si1−xGex layers was deposited by molecular beam epitaxy in which the composition (x) and thickness (h) were continuously varied across the substrate to produce a slowly changing strain energy density through the stable/metastable transition. On annealing at either 750 or 900 °C for 30 min, an abrupt transition in relaxation behavior was found at critical values of thickness and composition (hc,xc ). Increasing the anneal temperature or time did not shift the transition giving identical (hc,xc ) values. At strain thicknesses above these critical values a large increase in defect density was observed (>∼104 , cm−2) whereas in thinner strained epilayers, below the thermodynamic stability curve, no misfit dislocations were found. Nomarski microscopy of defect etched surfaces and x-ray topography were used to reveal misfit dislocations formed during the initial stages of relaxation. The appearance of single misfit dislocations at a density ≊1 cm−2 was taken as the criterion for a ‘‘relaxed’’ layer. The critical strain and thickness in the vicinity of these transition points were determined on the as-grown wafer by x-ray diffraction and Rutherford backscattering spectrometry with confirmation of layer thicknesses by cross-sectional transmission electron microscopy. The Matthews–Blakeslee [J. Cryst. Growth 27, 118 (1974)] equilibrium critical thickness he (nm), vs Ge atom fraction curve given by xe =0.55/he  ln(4he /b) for 1/2 a0〈110〉, 60° glide dislocations with a Burgers vector b ∼0.4 nm, is an excellent fit to these experimental data, i.e., xc =xe and hc =he .

The direct energy gap of thin, undoped epitaxial layers of Al1−xInxAs grown on (100) InP has been measured as a function of In content for values of x between 0.46 and 0.55 using catholuminescence spectroscopy. For the composition lattice matched to InP it was measured to be 1.450 eV at room temperature, and 1.508 eV at 4 K. Over the limited range of compositions studied, it varied as Eg =1.450+2.29 Δx eV at room temperature, and as Eg =1.508+2.22 Δx eV at 4 K, where Δx=(0.52−x), the deviation of x from the lattice-matched value.

A series of Si/Si,-,Ge, strained-layer superlattice structures has been studied by x-ray double-crystal diffractometry, Raman spectroscopy and transmission electron microscopy. The periodicity of the superlattices, the alloy composition and the degree of relaxation have been measured. The precisions of the three techniques are discussed and the results critically compared.

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