Abstract
Experimental transmission infrared spectra of <i>γ</i>-Al<sub>2</sub>O<sub>3</sub> and ZnO films are collected from heat-treated thin oxide films deposited with uniform thickness on Si(100) using atomic layer deposition. We show that the Berreman thickness, i.e. the upper limit for a linear relationship between oxide film thickness and phonon absorbance in the infrared region in transmission configuration, is a concept that applies to both transverse and longitudinal optical phonons. We find that for aluminum oxide films the Berreman thickness is 125 nm, and we estimate that it is around approximately 435 nm for zinc oxide films. Combining experiment and simulation, we also show that the Berreman thickness is the maximum distance allowed between interfaces for Snell's law and Fresnel's formulas to determine the optical properties in the infrared region and in transmission configuration for a layer system including an oxide film. Below the Berreman thickness, a Taylor series expansion of the absorbance coefficient determines the linear relationship between phonon absorbance and oxide film thickness <i>t</i>, so that as <i>t</i> → 0 absorption A<sub>p</sub> ∞ 4πω<sub>ph</sub><i>t</i>, where ω<sub>ph</sub> indicates optical phonon frequency. Above the Berreman thickness, field boundary conditions at the air/oxide film interface effectively contribute with a single interface in explaining optical phonon absorbance. Preliminary infrared spectra in reflection configuration for γ-Al<sub>2</sub>O<sub>3</sub>/Si(100) are discussed, and the obtained data support the conclusions reported for the transmission configuration.
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