The formation energy of the silicon (001) surface

The formation energy of the silicon (001) surface is one of the easier surfaces to calculate, due to the fact that the stoichiometry is that of a single species. The approach outlined below applies to any single species system with a surface.

To calculate the formation energy of a surface you:

• 1) Simulate a slab of material, ideally as thick as possible and get the total energy from that calculation (DFT, MD etc). This is $(E_{slab}$
• 2) Simulate the bulk material, and divide by the number of atoms in the basis to get the energy per atom. This $E_{Bulk}$
• 3) Calculate the unit surface area of your slab. This is $A$. Most commonly this is the unit cell dimensions of the two axis parallel to the surface.
• 3) Solve the following equation.

$E_{f}={\frac {(E_{slab}-nE_{Bulk})}{A}}$

where $E_{f}$ is the formation energy (this number is normally given in eV/A²) and $n$ is the number of atoms in your slab.