Phonon interactions with surfaces

Momentum conservation implies that the wave vectors of the phonons, interacting with the electrons close to the Fermi surface, are either small (forward scattering) or close to 2kp=7i/a (backward scattering). In Eq. (3.10) forward scattering is neglected, as the electron interaction with the acoustic phonons is weak. Neglecting also the weak (/-dependence of the optical phonon frequency, the lattice energy reads ... 

One of the main theoretical problems is to determine the dependence of the energy of a surface exciton on its wavevector or, in other words, to obtain the dispersion law for surface excitons. Then the next problems arise in consideration of the interactions of these excitons with light, phonons and with surface defects. 

Phonons once propagating in a crystal system undergo various other scattering interactions. Such scattering events, which cause a change in the phonon wavevector or phase, occur at crystal boundaries and as a result of interactions with lattice imperfections or with conduction electrons. It is possible experimentally to limit interactions with surfaces and electrons the latter by concentrating on insulators and semiconductors tjith low carrier concentrations. 

Jackson [15,16] proposes a quantum-mechanical theory for nonelastic scattering of particles as a result of interaction with surface phonons. Translational degrees of freedom of the gas particle are presented as a time-dependent wave packet. The wave functions describing the scattering of the particles satisfy a Schrodinger-type equation with a potential of interaction between flie gas particle and the solid surface, which depends both on time and temperature. In this model the Hamiltonian of the system is... 

Interaction with Surface Phonons-Harmonic Model... 

It should be mentioned that the magnitude of the vibrational energy of the oscillator generated by interaction with surface phonons is greater than the thermal vibration energy of the oscillator. 

In this equation v is a phonon frequency, such that hv is approximately k, with the Debye characteristic temperature of the metal. The quantity p is the product of the density of electrons in energy at the Fermi surface, N(0), and the electron-phonon interaction energy, V. 

VEM excitation energy relaxati( i. Such ways (channels) be probably chemisorption with charge transfer, production of phonons, ejection of electrons from surface states and traps, and the like. The further studies in this field will, obviously, make it possible to give a more complete characteristic of the VEM interaction with the surface of solid bodies and the possibilities of VEM detecting with the aid of semiconductor sensors. 

It is necessary to take proper account of the discreteness of energies transferred to a surface group from the substrate thermostat. If p 1, then the first excited level with the energy ifico(lJ2 lies near the potential well top and the quantum transition to it, when activated by the interaction with the substrate phonon thermostat, will enable the atom C to pass freely over the barrier or under a low barrier by tunneling. In this case, the rate of transitions from the ground to the first excited level is expected to be a good estimate for an average reorientation frequency. 

To explain the observed width, it is necessary to look for strong surface-to-bulk interactions, i.e. large magnitudes of surface-exciton wave vectors. Such states, in our experimental conditions, may arise from virtual interactions with the surface polariton branch, which contains the whole branch of K vectors. We propose the following indirect mechanism for the surface-to-bulk transfer The surface exciton, K = 0, is scattered, with creation of a virtual surface phonon, to a surface polariton (K / 0). For K 0, the dipole sums for the interaction between surface and bulk layers may be very important (a few hundred reciprocal centimeters). Through this interaction the surface exciton penetrates deeply into the bulk, where the energy relaxes by the creation of bulk phonons. The probability of such a process is determined by the diagram... 

This is a surface vibrational spectroscopic technique that involves the irradiation of the adsorbate-metal interface with a beam of low-energy (2 to 10 eV) electrons and the measurement of the energies of the backscattered electrons energy losses below 0.5 eV are due mainly to inelastic interactions with metal-surface phonons and adsorbate vibrational excitations. The extremely high sensitivity of HREELS makes possible measurements of adsor-... 

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