Longitudinal Vibrational Absorption Modes of Hydrogenated Amorphous Silicon Nitride Thin Films
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produce a p-polarized probe beam and Harrick Brewster's angle sample holder was used to adjust the beam's incident angle. THEORETICAL FUNDAMENTALS An unpolarized beam from an ordinary light source consists of a very large number of randomly oriented atomic emitters and its overall polarization changes in a completely unpredictable fashion. However, the randomness of the polarization can be represented by two orthogonal vibrating electric fields [5]. These vectors can be chosen as one parallel to (p-vector), and another perpendicular to the incident plane (s-vector), respectively. The vibration orientations of p- and s-vector are shown in Fig. 1 (a) by a line with double arrows and a dot, respectively. The p- and s-vectors can further be treated as sum of subvectors parallel (pl1 or s,) or perpendicular (p 1 or s, ) to the film's surface as illustrated in Fig. 1 (b). The s-vector only has s, component independent of light incident angle. The p-vector (a) will have p_Lcomponent if the light beam strikes film with an oblique incidence. The magnitudes of p_L and p,, are proportional and inversely p-vector P proportional to light incident angle, respectively; and at normal incidence, p, vanishes. If a certain P 11 bond in atomic structure is absorptive dependent on external field's vibration orientation, p1 is (b) responsible for LO mode resonance while pl, causes TO mode resonance. Therefore, at normal Fig. 1 Illustration of (a) p-polarized beam incidence incidence, p, -vector vanishes and no LO modes on thin film at an oblique angle, (b) decomposican be observed in the vibrational absorption tion of p-vector. spectrum. With the increase of light incident angle 0, magnitudes of p1 and p,, increases and decreases, respectively. Correspondingly, an increased LO density and a decreased TO density should be observed in vibrational absorption spectrum. The longitudinal optical modes of thin films of cubic crystals were first discovered by Berreman upon non-normal angle incidence of p-polarized light [6]. In general, the frequencies of longitudinal and transverse optical mode phonons are different, the LO mode being the higher. The frequency splitting of a vibrational mode into an LO-TO pair is the result of the interaction of the mode's vibrational motion with electromagnetic field of the film through the electric charge present on the vibrating atoms [7]. The bond exhibiting LO-TO pair splitting are dominated by long-range electric forces which are sensitive to longitudinal components of infrared-active vibrations, while bond showing no LO-TO splitting are dominated by short-range interatomic forces that affect both modes [8,9]. Theoretically, the frequencies of LO (cot,) and TO (w,) phonons can be related by the Lyddane-Sachs-Teller relation [6,10]: (0t
E
Ot
(1)
E_.
where E0 and e- are dielectric constants at low- and high-frequencies, respectively. 536
RESULTS AND DISCUSSION A. Identification of Longitudinal Modes Figure 2 shows vibrational absorption spectra of a-SiN,.73:H collected at p-polarized incidence
with a
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