Size dependence of the transmittance for metal nanofilms in the infrared region

The Dielectric Function of Metal 1D-systems

“…Let us compare the calculation results of the dielectric function of metal nanowires with similar results for thin films [14]. The starting point, which can be formula (4) at…”

“…For a film of thickness l and longitudinal dimensions a and b (l a, b), the expression for the dielectric function has the form of [14]…”

“…The square brackets in (17) denote the integer part of the number. Since the calculation in [14] was performed for a well of finite depth U 0 , then the quantities k xm are the roots of equation…”

Size oscillations of the work function of a metal film on a dielectric substrate

“…At α = α m , we can write (9) Let us derive an equation for determining α m + 1 . To this end, we use the relation (10) Combining formulas (9) and (10), we obtain the expression (11) Equating the right hand sides of Eqs.…”

“…The transverse momentum component បk xm is defined by boundary conditions for the electron wave function in the system and by the solution to the equation (1) Here, the subscript m numbers subbands. Integrating the density of states of the two dimen sional electron gas over k || and equating the number of occupied states to the number of conduction electrons [9], we obtain the equation for determining the size dependent Fermi energy ε F : (2) where ប 2 = 2m e ε F ; is the conduction electron density in a 3D metal; and m F is the number of the last occupied or in part occupied subband.…”