The movement of adatoms across a surface can be described by the Burton, Cabrera and Frank (CBF) model. The model treats adatoms as a 2D gas on top of the surface. The adatoms diffuse with a diffusion constant D; they are desorbed back to the medium above with a rate of  per atom and adsorbed with flux F.
The diffusion constant can be, when the concentration of particles is small, expressed as:
Where a is the hopping distance for the atom. E is the energy needed to pass the diffusion barrier. ν is the attempt frequency.
The CBF model obeys the following continuity equation:
Combining the steady states () with the following boundary conditions can lead to an expression for the velocity of the adatoms at each adsorption site.
The boundary conditions:
And: