Origin of residual strain in heteroepitaxial films

Heterogeneous integration of diverse materials structures is critical to the scaling of electronic and photonic integrated circuits. For a model system of Ge-on-Si, we experimentally examine the roles of lattice misfit and thermal expansion misfit in determining the residual strain in as-grown and annealed heteroepitaxial films. We present data for Ge-on-Si growth from 400 to 730 degrees C followed by heat treatment from 500-900 degrees C. We show that strain fluctuations of 5.02% enable misfit dislocation formation, and we propose a comprehensive model for the conversion of compressive misfit strain to tensile elastic strain. The model is expressed in terms of three regimes: (1) misfit control for the low temperature growth regime at 400 degrees C; (2) point defect control via annealing in the point defect recovery regime at 500-650 degrees C; and (3) thermal expansion control for growth or anneal at T > 650 degrees C in the dislocation recovery regime. Growth from 400 to 730 degrees C exhibits near complete misfit strain relief by misfit dislocations leaving a consistent residual compressive strain of 0.09%. Growth at 400 degrees C followed by post growth heat treatment at 600 degrees C results in vertical threading dislocation density reduction via a point defect-mediated climb mechanism that gives minimal strain relief. Anneal above 650 degrees C promotes strain relief by dislocation glide. Temperature excursions at T > 730 degrees C followed by cooling to room temperature yield plastic strain in the Ge film that cannot be further relieved by thermal expansion misfit accommodation. Growth at 400-730 degrees C retains a residual compressive strain that represents the nucleation threshold for misfit dislocations.