Real-space Green's tensors for stress and strain in crystals with cubic anisotropy

Real-space Green's tensors are presented for the calculation of the stress or strain in infinite cubic crystals containing buried quantum wires or dots of arbitrary shape and composition, including the cubic anisotropy of elastic constants. The Green's tensors are obtained as a polynomial series to second order in Delta, an expansion coefficient defined in terms of the elastic stiffnesses. The zeroth-order term in the series is the usual isotropic Green's tensor. The results agree extremely well with the numerical, exact formulation of Pan and Yang [E. Pan and B. Yang, J. Appl. Phys. 90, 6190 (2001)] but compute considerably faster and are easier to implement. The present approach is used to determine the strain in the direction normal to the plane of a quantum well in different orientations. This constitutes a stringent test of the approximate Green's tensor series and results are found to be in excellent agreement with standard solutions. The Green's-function expansion for the hydrostatic strain is presented and found to be of a simple form for both dots and wires. (c) 2005 American Institute of Physics.