Analysis of the lattice diffusion-controlled growth of metallic whiskers

Whisker growth plays an important role in determining the performance and lifetime of micro/nano electronic devices. In this work, we analyse the contribution of lattice diffusion to the whisker growth in a bilayer structure. An analytical solution of the growth rate is obtained as a function of the average chemical stress and the whisker size. The growth rate is inversely proportional to the whisker size for the growth of a whisker over a semi-infinite crystal, while it is proportional to the thickness of the surface layer for larger ratio of the whisker size to the thickness of the surface layer. The analytical result provides us a rational basis to evaluate the growth behaviour of metallic whiskers and nanowires controlled by the lattice diffusion