Theory of equilibrium shape of an anisotropically strained island: thermodynamic limits for growth of nanowires

Using continuum elastic theory, we show that strain anisotropy removes the shape instability existing for an isotropically strained island. An anistropically strained island has always an anisotropic shape, elongating along the less-strained direction and adopting a narrow width in the more-strained direction. The sign of strain makes only a quantitative difference without changing the qualitative island shape. Our study establishes thermodynamic limits for growing nanowires with anisotropically strained islands.