Role of Dislocation Interactions in Decreasing Mobile Threading Dislocation Density and Limiting Strain Relaxation in Si
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EXPERIMENTAL PROCEDURES The SiI-xGex epilayers used in this study were grown on (001) Si wafers using a variety of deposition techniques (molecular beam epitaxy (MBE), conventional chemical vapor deposition (CVD) and limited reaction processing (LRP)) and growth parameters. The films contained Ge fractions between 10 and 35 atomic % and their Ge content remained uniform over the entire thickness of the film. Film thicknesses varied between 40 and 130 nm. All films underwent isothermal annealing after growth. For thicker films, we report previous results published by Volkert et al.4 and Hauenstein et al.5 Including these data allows us to increase the range over which we compare the predictions of different models with experimental data. The biaxial misfit strains due to lattice mismatch present in the films after growth were determined at room temperature using a laser scanning technique to measure the curvature of the wafers. Then, the annealing procedure was as follows: the sample was inserted into the furnace which was previously stabilized at the desired annealing temperature. An inert atmosphere was provided using an argon back pressure. The sample reached the target temperature within 3 minutes. Starting immediately after insertion, substrate curvature was measured in situ every 2 minutes until strain relaxation was complete. For details on the furnace and wafer curvature measurement system used in these experiments, readers should refer to von Preissig. 6 After completion of the annealing (when the strain rate became too small to be measurable), the sample was removed from the furnace and allowed to cool in air. The curvature was then measured at room temperature to determine the elastic strain remaining in the film, Cr. Sil-xGex films on Si (001) substrates are under a biaxial compressive stress state and the edge forces exerted on the substrate cause it to bend elastically. In (001) oriented Si, the biaxial modulus is isotropic in the plane of the substrate and the film/substrate system takes the shape of a spherical shell. In this case, the biaxial strain in the film, £-f, is related to the substrate curvature through the following relation 7 : Ef- MS h 2 (K1-K0) (1) Mf 6 hf where M is the biaxial modulus in the (001) plane, h represents thickness and the subscripts "s" and "f' refer to substrate and film respectively. Here, K0 is the curvature of the bare wafer and K1 is the curvature of substrate plus film. Since substrate curvature is measured in situ during isothermal annealing, the elastic strain in the film as a function of annealing time, ef(t), can be determined using equation (1). The plastic strain rate, t(t), can also be found by taking the first derivative of Srm- eS(t). Here, 5 m represents the initial misfit strain in the film after growth. If the effect of stress and temperature on threading dislocation velocity is known, the variation of dislocation velocity, v(t), during the course of an annealing experiment can be predicted. We use HVTEM measurements of dislocation velocities in similar
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