On the thermodynamic size limit of nanowires grown by the vapor-liquid-solid process

For nanowires grown by the vapor-liquid-solid (VLS) process, expressions of the thermodynamically allowed minimum sizes of the nanowire and the liquid phase droplet as functions of the relevant thermodynamic variables have been obtained using Si nanowires (SiNW) grown from metal-silicon (M-Si) systems as the model case. In these expressions the binary nature of the M-Si system, which involves four phases of materials, is accounted for. The liquid droplet minimum size is determined by a unique set of the external M and Si vapor phase pressure values. The SiNW minimum size expression contains two contributions, one due to the liquid droplet composition and one due to the droplet size. These expressions do not predict a limit on the attainable VLS SiNW minimum size, implying ever smaller SiNW can be grown until reaching some growth kinetic limit which is presently unknown. A set of size data of the smallest experimentally grown SiNW appears to have approached an effective limit set by the liquid composition.