[Paper Review] Morphological influence on surface--wave propagation at the planar interface of a metal film and a columnar thin film

Akhlesh Lakhtakia, John A. Polo|ArXiv.org|Jun 28, 2007

Fluid Dynamics and Thin Films5 references21 citations

TL;DR

This paper investigates how the vapor deposition angle during columnar thin film (CTF) growth affects surface-wave propagation at a metal–CTF interface. By modeling the CTF as a biaxial dielectric with anisotropic permittivity controlled by the vapor incidence angle 𝜒𝑣, the study shows that higher 𝜒𝑣 reduces surface wave phase velocity and propagation range, requiring larger incidence angles in a modified Kretschmann configuration to excite the wave.

ABSTRACT

The selection of a higher vapor deposition angle when growing a columnar thin film (CTF) leads to surface-wave propagation at a planar metal-CTF interface with phase velocity of lower magnitude and shorter propagation range. Acordingly, a higher angle of plane-wave incidence is required to excite that surface wave in a modified Kretschmann configuration.

Motivation & Objective

• To investigate the influence of columnar thin film (CTF) morphology—controlled by vapor deposition angle—on surface-wave propagation at a planar metal–CTF interface.
• To establish a link between the vapor incidence angle 𝜒𝑣 and the resulting optical anisotropy in CTFs, particularly in their permittivity dyadic.
• To determine how morphological changes in CTFs affect the phase velocity and propagation range of surface waves.
• To analyze the excitation conditions of surface waves in a modified Kretschmann configuration, focusing on the required incidence angle.
• To quantify the relationship between 𝜒𝑣 and the critical incidence angle needed for surface wave excitation.

Proposed method

• Model the CTF as a biaxial dielectric material with principal permittivities 𝜀𝑎, 𝜀𝑏, 𝜀𝑐, dependent on the column inclination angle 𝜒, which is influenced by the vapor incidence angle 𝜒𝑣.
• Use a Cartesian coordinate system where the morphologically significant plane is the xz-plane, with unit vectors 𝐮𝑛, 𝐮𝜏, and 𝐮𝑏 defining the principal axes of the CTF.
• Derive the surface wave wavenumber 𝜅 at the metal–CTF interface using boundary-value analysis of the electromagnetic field phasors in both half-spaces.
• Formulate the reflection and transmission coefficients via a matrix method involving the permittivity dyadics and wave vector components.
• Apply energy conservation constraints to validate the solution and compute absorbance 𝐴𝑝 as a function of incidence angle 𝜃₁.
• Simulate the absorbance 𝐴𝑝 vs. 𝜃₁ for varying 𝜒𝑣 values (5° to 90°), identifying peaks corresponding to surface wave excitation.

Experimental results

Research questions

• RQ1 How does the vapor deposition angle 𝜒𝑣 influence the anisotropic permittivity and morphology of a columnar thin film?
• RQ2 What is the effect of CTF morphology on the phase velocity and propagation range of surface waves at a metal–CTF interface?
• RQ3 How does the required incidence angle for surface wave excitation in a modified Kretschmann configuration vary with 𝜒𝑣?
• RQ4 To what extent does the surface wave excitation peak in absorbance correspond to the real part of the surface wave wavenumber?
• RQ5 How do the principal permittivity components and column inclination angle affect the coupling efficiency of surface waves?

Key findings

• Increasing the vapor deposition angle 𝜒𝑣 leads to a reduction in the phase velocity of surface waves at the metal–CTF interface.
• Higher 𝜒𝑣 results in a shorter propagation range for surface waves due to increased attenuation and reduced group velocity.
• The critical incidence angle 𝜃₁ required to excite surface waves increases with 𝜒𝑣, reaching 62.168° at 𝜒𝑣 = 90°.
• The real part of the surface wave wavenumber 𝜅 increases with 𝜒𝑣, from 1.3037 at 5° to 2.6530 at 90°, indicating higher wavevector magnitude.
• The rightmost absorbance peaks in the simulated 𝐴𝑝 vs. 𝜃₁ curves correspond to surface wave excitation, with peak positions matching the real parts of the surface wave wavenumbers.
• The absorbance peaks are most pronounced when the CTF is grown at higher 𝜒𝑣, confirming enhanced surface wave coupling under these morphological conditions.