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…
Fresnel reflection at normal incidence r = (n_1 - n_2)/(n_1 + n_2); Mobius linear-fractional
Fresnel-reflection framework at normal incidence (Fresnel 1823 Memoire sur la loi des modifications de la lumiere). Setup: at the planar…
Brewster angle: tan(theta_B) = n_2/n_1; r_p(theta_B) = 0 by IVT
Brewster's-angle framework (Brewster 1815 Phil Trans R Soc). Setup: at the dielectric interface with indices n_1, n_2, the p-polarised…
Anti-reflection quarter-wave coating n_AR = sqrt(n_1 n_2); geometric-mean condition
Anti-reflection (AR) quarter-wave-coating framework (Strong 1936 J Opt Soc Am 26, 73; Macleod 2010 Thin-Film Optical Filters). Setup: a…
Theorem: R (n_1 + n_2)^2 - (n_1 - n_2)^2 = 0 (Fresnel normal-incidence intensity identity)
Theorem (Fresnel-normal-incidence-residual canonical): R = r^2 = ((n_1 - n_2)/(n_1 + n_2))^2 cleared of denominators gives R (n_1 + n_2)^2…
Theorem: n_1 sin(theta_B) - n_2 cos(theta_B) = 0 at tan(theta_B) = n_2/n_1
Theorem (Brewster-zero-residual canonical): at theta_B = arctan(n_2/n_1), sin theta_B = n_2/sqrt(n_1^2 + n_2^2) and cos theta_B =…
Theorem: n_AR^2 - n_1 n_2 = 0 (AR geometric-mean identity)
Theorem (AR-quarter-wave-residual canonical): n_AR = sqrt(n_1 n_2) squared yields n_AR^2 = n_1 n_2 exactly. Canonical sympy pins: n1, n2 =…
KMC growth (Voter)
A Voter 1997 KMC review; thin-film growth via island-nucleation + Burton-Cabrera-Frank step-flow; modern quantum-LMC ML-MD enhancements.
ALD (Suntola 1977)
T Suntola 1977 atomic-layer-deposition; modern semiconductor + battery applications; sub-nm thickness + 100% conformal.
Sputtering (Thornton 1974)
J Thornton 1974 zone-model sputter-deposition microstructure; modern HiPIMS + ion-plating; standard for hard-coatings + optical-films.
Stoney (1909)
G G Stoney 1909 sigma_film = E_s h_s^2 / (6 (1-nu_s) h_f) curvature-stress; modern fiber-optic + multi-beam strain-measurement.
Frank-van der Merwe (1949)
Frank-van-der-Merwe 1949 + Volmer-Weber + Stranski-Krastanov 3 epitaxial-growth modes; modern strain-engineering + quantum-dots.
Thin-film PV
First-Solar CdTe + Hahn-Meitner CIGS; modern CdSeTe + perovskite-silicon tandem record 33.9% Helmholtz-Berlin 2024.
Stoney equation (1909)
G Stoney 1909 σ_f = E_s h_s²/(6h_f(1-ν_s))κ; modern modern foundational text + 2024 wafer-curvature in-situ stress-monitoring CVD.
Epitaxy (Frank-van der Merwe 1949)
F Frank-J van der Merwe 1949 + Volmer-Weber + Stranski-Krastanov; modern modern foundational text + 2024 MBE 2D-materials hetero-structure.
ALD (Suntola 1977)
T Suntola 1977 ALD; modern modern foundational text + 2024 high-k gate-dielectric HfO2 + 2 nm semiconductor sub-monolayer precision.
KMC growth (Vlachos 1995)
D Vlachos 1995 + Voter 2007 kinetic-Monte-Carlo; modern modern foundational text + 2024 ML-accelerated KMC thin-film growth.
Sputter (Grove 1852)
W Grove 1852 sputter-deposition; modern modern foundational + magnetron-sputter + 2024 HiPIMS dense-coatings tool-coatings cutting-tools.
CdTe / CIGS (Britt-Ferekides 1993)
J Britt-C Ferekides 1993 + Repins 2008 CIGS 19.9% + 2024 CdTe 22%; modern modern foundational text + First-Solar 2024 utility-scale modules.