Example of test calculation

Let us show effects of ESMs on the electronic structure of a system. As a demonstration calculation, the distribution of excess charge $\rho _{\rm ex}$ in a $1\times 1$ Al-terminated Si(111) slab under the boundary condition, 'vacuum + ideal metal' (ESM.switch = on3), is presented in Fig. 37(a) (the input file of this test calculation 'Al-Si111_ESM.dat' is found in the work directory). It can be seen that segregation of the doped charge in the slab happened due to the attractive interaction between the doped and the corresponding mirror charges. Figure 37(b) indicates the change of the Hartree potential $\Delta V_{\rm H}$ corresponding to each condition indicated in Fig. 37(a), where the potential inside the Al-Si(111) slab and the electric field between the slab and the ideal-metal medium change according to the amount of the doped charge.

Figure 37: Al-Si(111) slab model with vacuum and ideal-metal ESMs; (a) Distributions of excess charge in Al-Si(111) slab, $\rho_{\rm ex}$; (b) Bias-induced changes of Hartree potentials of Al-Si(111) slab, $\Delta V_{\rm H}$. The number of doped charge is -0.01, -0.005, +0.005, and +0.01 e. Each plot is obtained as a difference in difference charge or difference Hartree potential with reference to a neutral slab with the same ESMs.