Surface phonon
Similar to the ordinary lattice vibrations in a bulk solid (whose quanta are simply called phonons), the nature of surface vibrations depends on details of periodicity and symmetry of a crystal structure.
As a specific example, the decreasing size of CdSe quantum dots was found to result in increasing frequency of the surface vibration resonance, which can couple with electrons and affect their properties.
One is the "slab method", which approaches the problem using lattice dynamics for a solid with parallel surfaces,[3] and the other is based on Green's functions.
Which of these approaches is employed is based upon what type of information is required from the computation.
For broad surface phonon phenomena, the conventional lattice dynamics method can be used; for the study of lattice defects, resonances, or phonon state density, the Green's function method yields more useful results.
The surface Brillouin zone (SBZ) for phonons consists of two dimensions, rather than three for bulk.
[5] Higher order anharmonicity terms can be accounted by using perturbative methods.
The term x(l,m) is the position of the unit cell with respect to some chosen origin.
Alternatively, the atoms may vibrate side-to-side, perpendicular to wave propagation direction; this is known as a "transverse phonon”.
"Acoustic" branch phonons have a wavelength of vibration that is much bigger than the atomic separation so that the wave travels in the same manner as a sound wave; "optical" phonons can be excited by optical radiation in the infrared wavelength or longer.
Surface phonon mode branches may occur in specific parts of the SBZ or encompass it entirely across.
[3] A particular mode, the Rayleigh phonon mode, exists across the entire BZ and is known by special characteristics, including a linear frequency versus wave number relation near the SBZ center.
[1] Two of the more common methods for studying surface phonons are electron energy loss spectroscopy and helium atom scattering.
Since the interaction of low energy electrons is mainly in the surface, the loss is due to surface phonon scattering, which have an energy range of 10−3 eV to 1 eV.
[7] In EELS, an electron of known energy is incident upon the crystal, a phonon of some wave number, q, and frequency, ω, is then created, and the outgoing electron's energy and wave number are measured.
[1] If the incident electron energy, Ei, and wave number, ki, are chosen for the experiment and the scattered electron energy, Es, and wave number, ks, are known by measurement, as well as the angles with respect to the normal for the incident and scattered electrons, θi and θs, then values of q throughout the BZ can be obtained.
where G is a reciprocal lattice vector that ensures that q falls in the first BZ and the angles θi and θs are measured with respect to the normal to the surface.
[4]– Helium is the best suited atom to be used for surface scattering techniques, as it has a low enough mass that multiple phonon scattering events are unlikely, and its closed valence electron shell makes it inert, unlikely to bond with the surface upon which it impinges.
In particular, 4He is used because this isotope allows for very precise velocity control, important for obtaining maximum resolution in the experiment.
[4] There are two main techniques used for helium atom scattering studies.
The other involves measuring the momentum of the scattered He atoms by a LiF grating monochromator.
[4] EELS and helium scattering techniques each have their own particular merits that warrant the use of either depending on the sample type, resolution desired, etc.
[4] Thus, the resulting data is easier to understand and analyze for He atom scattering than for EELS, since there are no multiple collisions to account for.
He scattering is also more sensitive to very low frequency vibrations, on the order of 1 meV.
