Theoretical Determination of the Surface Structure

T (n) is the kinetic energy of noninteracting electrons, the second term describes the interaction with an external potential, and the third term describes the electrostatic energy of the electrons. E is a functional that includes all exchange-correlation interactions and also the contributions of the electron-electron interaction to the kinetic energy, which are not considered in T n). The dependence of the exchange-correlation energy on the electron density n r) is not known 

The electronic ground-state energy E n) for a given atomic structure can now be calculated. The TE of the system is then given as the sum of E(n) and the electrostatic interaction energy of the ions (for a temperature T = 0 K). 

In order to compare the energetic stability of different atomic structures for a given surface orientation but different surface stoichiometries, the TEs are plotted in a surface phase diagram. Here the surface energy S2 of the various structure models is presented versus the thermodynamic chemical potential of one of its elements A/r with respect to its bulk value. 

The surface composition of a compound semiconductor, that is, the concentration of the individual compound materials, can be characterized by the chemical 

B at the surface, respectively. The upper limit for the chemical potential of both species is given by the condensed phase in the bulk of the respective element  

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