Quantum size oscillations in optical and electric properties of superthin metal films

Interference of bulk and boundary scattering in films with a quantum size effect

“…Each such term is given by the correlation function of inhomogeneities on the corresponding wall with a simple coefficient that reflects the permeability of the interlayer boundary and the overall structure of the system. Straightforward analysis shows that if the bulk scattering within all layers is the same, then the effective relaxation time τ (eff ) j (q) is still determined by equation (10) with W jj (q, q ) given not by equation (11), but by a similar equation from reference [27] for multilayer systems. If the bulk scattering is not the same in different layers, then the calculations should be performed for each layer separately.…”

“…The integral in equation ( 13) depends on the relation between three length scales, R, L b , L. The numerator, W (0) jj (q j , q ), equation (11), represents a peak in the momentum space q which is centred around q j = (2mµ − (πj/L) 2 ) 1/2 and has the width 1/R . For example, if the surface inhomogeneities are Gaussian as in (6), the zeroth angular harmonic of the scattering probabilities (11) over the angle between the vectors q and q is equal to…”

“…In non-degenerate semiconductor films with a QSE this dependence is smoother because of a more uniform occupancy of quantized states. Though we do not know of any direct observation of such sawor step-like curves in transport measurements without magnetic field (with the exception of, maybe, reference [11]), the QSE has been observed in both metal and semiconductor films (see, e.g., references [12,13] and references therein) by scanning tunnelling microscopy [14], ultraviolet electron spectroscopy, photoemission, and dozens of other optical experimental techniques (see references [3,15] and references therein). Recently a QSE has also been observed in confined 3 He at ultralow temperatures [16].…”

“…Though we do not know of any direct observation of such saw-or step-like curves in transport measurements without magnetic field (with the exception of, maybe, Ref. [11]), QSE has been observed in both metal and semiconductor films (see, e.g., Refs. [12,13] and references therein) by scanning tunnel microscopy [14], ultraviolet electron spectroscopy, photoemission, and dozens of other optical experiments (Refs.…”

Quantum size effect on dielectric function of ultrathin metal film: a first-principles study of Al(1 1 1)

“…Laref el al [17] studied the thickness dependence of the optical permittivity of ultrathin gold films for a more accurate design of plasmonic device based on density functional theory (DFT) calculation. Experimentally, Kuzik et al [18,19] observed the periodic oscillation of optical conductivity as a function of film thickness in Nb, Cu, Mo, W, Ni and Ti, which is possibly an indication of QSE.…”