Image charges, method

For the application of the image charges method, similarly to [41], the model of continuous media characterized by dielectric permittivity and the effective mass approximation was used for the wave functions calculations. These two characteristics could be sufficient for the description of the principal differences between the solid and its ambience as well as between electrons and holes in dielectrics and semiconductors. 

We use the image charges method to account for the surface influence on the defects electric field [43, 47]. The geometry of the image charges induced by the surface defect with two electrons is shown in Fig. 4.1 Ic, d. 

Xu Z, Cai W, Cheng X Image charge method for reaction fields in a hybrid ion-channel model, Commun Comput Phys 9(4) 1056—1070, 2011. 

The first simulation studies of full double layers with molecular models of ions and solvent were performed by Philpott and coworkers [51,54,158] for the NaCl solution, using the fast multipole method for the calculation of Coulomb interactions. The authors studied the screening of a negative surface charge by free ions in several highly concentrated NaCl solutions. A combination of (9-3) LJ potential and image charges was used to describe the metal surface. 

There are problems with using both of these methods in the simulation of inhomogeneous systems. Because the periodicity of the system is lost in the direction normal to the interface (unless one uses image charges with the flat wall model, which effectively results in a 3D periodic system implementation of the ES method is not straightforward for certain type of systems. Hautman and Klein have presented a modified Ewald sum method for the simulation of systems that are periodic in two... 

The method of image charges determines how a charge qt located at r = (r , 6t, 4>l) in C leads to the following contributions to the induced potential ... 

Charge Image (or Virtual Charge) Method (54) (Method for Gp i calculation)... 

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