Phonons in ultrathin layered structures

Diffusion of phonons through (along and across) the ultrathin crystalline films

“…For that analysis it was necessary to calculate phonon state and spectra. Those results are compatible and supplement the results obtained in previous research [23][24][25][26][30][31][32].…”

“…In the case of ε, γ < −1, characteristic of interaction wouldn't be elastic any more. For ε, γ = −1 the stiff walls effect appears, with all boundary surfaces being non-flexible and with all motives inside them being "frozen" along z-direction [30][31][32]. It should be mentioned that case with ε, γ = 0 known as the film with free boundary surfaces, is particularly interesting one, while it has exact analytical solution for the dispersion law.…”

Phonon Contribution in Thermodynamics and Transport Properties of Ultrathin Ceramic Films

“…In the cut-o case [1,23] (the approximation ρ 0 = ρ N = 0 will be called that) we obtain k z = πµ z a(N I z + 2)…”

Phonon Thermodynamics in Crystalline Nanofilms

“…In this paper we observe an ideal ultrathin film of simple cubic crystalline structure, made on a substrate with the use of some appropriate technological process (deposition, sputtering, etc. ), whose basic crystallographic parameters are [4][5][6]: a x = a y = a z ≡ a; N x,y ~ 10 8 >> N z ~ 10.…”