Screening of an applied electric field inside a metallic layer described by the Thomas-Fermi-von Weizsäcker model. (English) Zbl 1174.82342

Blanc, X.; Monneau, R.

Adv. Differ. Equ. 7, No. 7, 847-876 (2002).

Summary: We are interested in the effect of a constant electric field on the electronic structure of a crystal. We model it by a density-functional theory, and derive from this microscopic model macroscopic features of the system by letting the ratio between atomic spacing and the size of the crystal go to zero. Although many aspects are disregarded in this approach, we show that the effect of the electric field is negligible inside the crystal and estimate its vanishing rate with respect to the distance from the boundary of the crystal.

MSC:

82D20	Statistical mechanics of solids
82D35	Statistical mechanics of metals
35A15	Variational methods applied to PDEs
35J20	Variational methods for second-order elliptic equations
35J50	Variational methods for elliptic systems
35Q40	PDEs in connection with quantum mechanics

Keywords:

Thomas-Fermi-von Weizsäcker theory; variational methods; electric field; exponential decay