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The Physics of Non–Equilibrium Reliability Phenomena

3.5 Vibrational Spectrum

The interplay of the Si–H bond with its environment is one of the fundamental interactions which strongly influences the bond dynamics by governing its vibrational lifetime. The coupling strength between a phonon bath and the motion of a bond, i.e. a particular vibrational mode, can be quantified using the phonon spectrum.

The system studied here is the Si/SiO\(_2\) model described in Sec. 3.1 which contains 472 atoms. A normal–mode analysis based on DFT, which uses a finite–difference scheme to calculate the dynamical matrix, yields the spectrum shown in Fig. 3.17. The resulting density of states (DOS) can be divided into collective vibrations from the Si/SiO\(_2\) system (low and intermediate frequencies) and sharp peaks at higher frequencies related to particular movements of individual atoms, e.g. Si–H and O–H stretching modes. Furthermore, by projecting the phonons onto particular atom types and regions one can split the collective modes into contributions form the \(c\)–Si lattice (yellow), the amorphous oxide (red) and the interfacial regions (blue). One can see that the silicon spectrum nicely resembles the phonon DOS of its bulk counterpart, while the phonon mode spectrum of SiO\(_2\) is slightly distorted due to the interface.

Additionally, the applicability of the classical force–field ReaxFF has been tested for further calculations, see Chapter 4.


Figure 3.17: Left: Phonon density of states (DOS) of a Si/SiO\(_2\) interface model together with the fundamental frequency of the Si–H bond breaking potential, see Sec. 3.2. Right: The projected phonon spectra for the Si and the SiO\(_2\) part compared to their calculated bulk counterparts.