Misfit dislocations in an annular film grown on a cylindrical nanowire with different elastic constants

The critical thickness condition of the misfit dislocation formation in the system of a nanowire surrounded by a co-axial film with different elastic constants is investigated. The influence of the shear modulus ratio of the film to the nanowire (cylinder), the misfit strain and the radius of nanowire on the critical thickness of the film is discussed. The results show that the critical thickness of the film for the formation of the MDs decreases monotonically with the increment of the ratio of the shear modulus. However, if the ratio of the shear modulus is reached at a certain value, the generation of MDs is energetically favorable only when the film thickness is in some range. At last, the generation of MDs is energetically unfavorable at any value of the film thickness with the ratio of the shear modulus larger than a critical value.