Angular behavior of the Berreman effect investigated in uniform Al2O3 layers formed by atomic layer deposition

Experimental transmission absorbance infrared spectra of γ-Al(2)O(3) showing evidence of the angular dependence of the peaks of surface modes appearing next to the longitudinal optical phonon frequency ω(LO) (the Berreman effect) are collected from heat-treated thin oxide films deposited with thickness uniformity on Si(100) using atomic layer deposition. The peak area of the most intense surface longitudinal optical mode is plotted versus the infrared beam incidence angle θ(0). The experimental points closely follow the sin(4)(θ(0)) function in a broad thickness range. The best match occurs at a critical thickness, where a linear relationship exists between the surface longitudinal optical mode intensity and film thickness. Simulations suggest that below the critical thickness the sin(4)(θ(0)) behavior can be explained by refraction phenomena at the air/thin film and thin film/substrate interfaces. Above the critical thickness, the experimentally obtained result is derived from field boundary conditions at the air/thin film interface. The sin(4)(θ(0)) functional trend breaks down far above the critical thickness. This picture indicates that infrared radiation has a limited penetration depth into the oxide film, similarly to electromagnetic waves in conductors. Consequently, surface longitudinal optical modes are viewed as bulk phonons excited down to the penetration depth of the infrared beam. Comparison with simulated data suggests that the infrared radiation absorptance of surface longitudinal optical modes tends to approach the sin(2)(θ(0)) trend. Reflection phenomena are considered to be the origin of the deviation from the sin(4)(θ(0)) trend related to refraction.