Origin of Diameter-Dependent Growth Direction of Silicon Nanowires

A nucleation thermodynamic model was developed to clarify the diameter-dependent crystallographic orientation of silicon nanowires (SiNWs) grown via the vapor-liquid-solid (VLS) mechanism with an Au catalyst. The calculated critical energies (E(r*)) and corresponding critical radii (r*) of the SiNWs with <111> and <110> orientations as a function of Au-catalyst size (D(Au)) revealed that the 110-oriented SiNW with r is preferred below D(Au) = approximately 25 nm, but the preferred direction changes to <111> above D(Au) = approximately 25 nm. The model indicated that the nucleated SiNW with a radius (r) above r is stable and continues to grow until the diameter becomes equal to D(Au) but that the crystallographic orientation is maintained. Thus, the predicted growth direction of the final SiNW with a size of D(Au) is <110> for D(Au) < approximately 25 nm and <111> for D(Au) > approximately 25 nm, which is in excellent agreement with reported experimental results.