Equilibrium critical thickness for Si1−xGex strained layers on (100) Si

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Abstract
The critical thickness for Si1−xGex strained layers for the alloy range 0<xannealed 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 2 7, 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 .