It is necessary to have at least 1D confinement to observe the effect of the model. Regarding meshing, it is the most important portion of the device structure you have to decide where you should use finer meshing or coarser meshing. If you use finer meshing everywhere then your code will not converge or you get message "too many nodes generated". You can use coarser meshing in less important regions particularly in bulk but at the interfaces you should use finer meshing.

Thanks Imroze....

Agree with Fiheon