Nano-gaps are fundamental building blocks for nanochannels, plasmonic nanostructures and superconducting Josephson junctions. We present a systematic study on the formation mechanism and resolution limit of W-C nano-gaps fabricated using focused-ion-beam chemical vapour deposition (FIB-CVD). First, the deposition size of the nanostructures is evaluated. The size averaged over 100 dots is 32 nm at FWHM. Line and space are also fabricated with the smallest size, having a spacing of only 5 nm at FWHM. Then, a model is developed to study the formation mechanism and provides the design basis for W-C nano-gaps. Both experimental and simulation results reveal that the shrinkage of W-C nano-gaps is accelerated as the Gaussian parts of the nano-wire profiles overlap. A Nano-gap with a length of 5 nm and height difference as high as 42 nm is synthesized. We believe that FIB-CVD opens avenues for novel functional nanodevices that can be potentially used for biosensing, photodetecting, or quantum computing.