Strain relaxation kinetics in Si1−xGex/Si heterostructures

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Abstract
A semiempirical kinetic model is presented which maps out the thermal budget for processing of strained layer devices through epitaxial growth and postgrowth anneals. Misfit strain relaxation in Si1−xGex/Si heterostructures by the injection and propagation of a/2 〈110〉 60°‐type misfit dislocations has been studied for a range of geometries and dimensions. Strained layer superlattices, Si1−xGex alloy layers, 0<xgrown by molecular‐beam epitaxy on (100) Si substrates and subjected to post‐growth thermal cycles. Velocity and nucleation rate data from Nomarski interference microscopy of defect‐etched surfaces were correlated with electron beam induced current microscopy transmission electron microscopy and x‐ray diffraction results to define Arrhenius relationships for misfit dislocation injection rates and propagation velocities. A unified kinetic model for misfit strain relaxation that incorporates both nucleation and propagation is then developed, which is applicable for all heterostructures and thermal cycles in the low dislocation density regime 3 mm−1. Nonuniform strain distribution in graded device heterostructures is considered by defining the effective stress acting on misfit dislocations for an arbitrary geometry. The effective stress was varied from 0 to 750 MPa in Si1−xGex/Si heterostructures by varying both layer dimensions and Ge concentration. Misfit dislocation nucleation rates varied from 10−3 to 103 mm−2 s−1 and misfit extension velocities of 25 nm s−1 to 2 mm s−1 were obtained over the temperature range 450–1000 °C for anneals of duration 5–2000 s. Activation energies, stress exponents, and prefactors in the Arrhenius relations were found to be independent of Ge concentration, effective stress, and heterostructure geometry allowing a comprehensive model to be developed. The onset of strain relaxation during epitaxial growth cycles (the ‘‘apparent critical thickness’’ or metastability limit) characteristic of molecular‐beam epitaxy and chemical vapor deposition was measured and correlated with the simulation of misfit dislocation injection and propagation in typical growth sequences. The kinetic model is also used to define the maximum time‐temperature envelope, or thermal budget (t, T), for the misfit dislocation‐free processing of Si1−xGex/Si heterostructures subjected to post‐growth thermal treatme