1 Introduction Free-standing strained axial nanowire (NW) heterostructures have been intensively studied due to the inherent potentials as building blocks for novel optoelectronic applications [1][2][3]. Performances of such devices with lattice misfit would strongly degrade due to crystalline defects, thus tremendous interest exists in how to avoid generating dislocations on the hetero-interface. Experimentally, high-quality axial Ge/Si [4], GaP/GaAs [5], InAs/InP [6], InAs/GaAs [7] and InP/Si [8] NW hetero-structures without onset of plastic relaxation, concluded by transmission election microscopy (TEM), have been successfully fabricated in the last decade. Compared with conventional planar epitaxy, axial NW heterostructure can accommodate much greater misfit because NW sidewall acts as free surface for elastic strain relaxation [9]. Moreover, two groups [8, 10] observed critical diameters (CDs) of coherent cylindrical NW epilayers on foreign bulk substrate, grown by Au-assisted molecular beam epitaxy (MBE) and metal organic chemical vapor deposition (MOCVD), respectively. When NW diameter is larger than the critical value, NWs will lose coherency or NWs cannot grow [8,10].