Thin-film physics — condensed-matter sub-discipline covering the formation, structure, optical / electronic properties, and applications of films with thickness ≲ 1 µm (and usually ≪ optical wavelength). Foundations: (1) Film growth modes…
thin-films
Film growth modes: Frank-van-der-Merwe / Volmer-Weber / Stranski-Krastanov
The Bauer 1958 surface-energy criterion selects between the three canonical film growth modes by comparing γ_f (film surface energy) + γ_fs…
Thin-film interference: 2·n_f·d·cos(θ) = m·λ (constructive)
Thin-film interference arises when light reflects from the top and bottom surfaces of a transparent film of thickness d and refractive…
Epitaxial misfit strain: ε = (a_f - a_s)/a_s; critical thickness
Epitaxial film-on-substrate growth forces the film to conform to the substrate in-plane lattice parameter, generating a coherency strain ε…
Fresnel constructive thickness: d(θ=0)=λ/(2n_f); d(θ=π/3)=λ/n_f
Sympy-exact witness of the thin-film constructive-interference thickness formula at m=1. Setup: d = λ/(2·n_f·cos(θ)). Identity 1 (normal…
Sheet resistance R_s = ρ/t; R_s(2t) = R_s(t)/2
Sympy-exact witness of the sheet-resistance scaling law. Setup: a thin conducting film of bulk resistivity ρ and thickness t has sheet…
Misfit-strain anchor: a_f = 51/50·a_s ⇒ ε = 1/50
Sympy-exact witness of the misfit-strain anchor. Setup: ε = (a_f - a_s)/a_s. Identity 1 (lattice-matched, a_f = a_s): ε = 0 — no…