Elemental Semiconductors

The constitutive equation for the generation of a vacancy in Si is

$$E_{form}=E_{total}-n^{Si}\mu_{Si}$$ (2)

E$_{total}$ is the total energy of the system, n$^{Si}$ is the number of Si atoms in the system and $\mu_{Si}$ is the chemical potential of a reference reservoir of crystalline silicon. Equation 2 gives the formation energy by subtracting the reference energy of n$^{Si}$ Si in a perfect crystal from the total energy of the defect system composed of n$^{Si}$ Si and a vacancy.