Are you talking about the Z-axis of your substrate or about the c-axis of ZnO? ZnO is hexagonal and is formed by atomic layers perpendicular to c and also to Z. in so far it does not surprise that you can see rods. First, the growth direction is anisotropic, and second, your transport is anisotropic as well, i.e. it flows towards the surface. From my point of view excellent conditions for a fiber- or rod-like growth perpendicular to the surface. If the misfit to Si is small you possibly can produce rods which all have the same orientation. Certainly beneficial for many applications.

Thanks for the reply Prof. Gert Nolze. I have asked about the z-axis of the substrate as viewed from SEM image.

Article Fabrication and properties of ZnO/GaN heterostructure nanoco...

It is well known that ZnO is a hexagonal crystal. It is preferentially orientated along the (002) plane and along the (001) direction (Z-axis). When ZnO is deposited on Si substrate as thin layer which is called seed layer and it acts as a nucleation agent. The shape, size and orientation of the nanorods grown on the seed layer depend on the grain size, thickness, perfectness and the orientation of the seed layer crystal. Since ZnO is a hexagonal crystal and its preferential orientation along the (002) plane. It is reported that (002) plane has lower surface compared to the others planes. Hence the ZnO NRs can grow very easily along Z-axis rather than others axis.