3 represents the same spatial direction in both layers. In a lattice dynamics simulation, one period is included as a unit cell. Despite the similarity, however, there is a subtle difference between the transfer matrix method and the lattice dynamics simulation. The stop bands correspond to the minigaps in the superlattice phonon dispersion. 4(a), which plots the phonon transmissivity of a 5- × 5- Å Si–Ge-like superlattice, obtained from the transfer matrix method ( Chen, 1999). The effect of phonon interference is clearly seen in Fig. Minigaps are also created at the zone boundaries and inside the Brillouin zone ( Tamura et al., 1989) as a result of the phonon interference and mode conversion. The folded phonons are the optical branches of the new unit cell. One way to understand this reduced zone representation is to imagine a new unit cell for the superlattice structure that contains four atoms as a basis. This is because of the phonon folding in the reduced zone representation. Compared to bulk materials, more phonon branches show up in the superlattice. Figures 3(a) to 3(d) show the lattice dynamics calculation of the phonon dispersion of a 2 × 2 Si–Ge-like superlattice (two monoatomic layers of Si and two monoatomic layers of Ge) in the direction perpendicular and parallel to the superlattice plane ( Bao and Chen, 2000a). In a superlattice, for example, the transfer matrix method ( Naranyamamurti et al., 1979 Tamura et al., 1989), the elasticity equations ( Colvard et al., 1985), and the lattice dynamics ( Tamura et al., 1999) method have been used to obtain the phonon dispersion relations. The phonon drag peak is absent in impure materials. In a crystal with defects or impurities, both electrons and phonons can dissipate momentum by scattering from defects at all temperatures. The coupled equations are usually solved by a variational technique. The Boltzmann equations for electrons and phonons become coupled. The theory of phonon drag includes electrons and phonons. The thermopower is the only measurement that shows the peak from phonon drag. That rate is not affected by phonon drag and there is no peak in the conductivity or resistivity. σ is only affected by the rate that the electrons and phonons scatter from each other. Phonon drag does not affect the electrical resistivity. The Seebeck is a measure of the energy content of the current, and attains high values. The amount of energy carried by the combined system is quite large. As the electrons drift along in the electric field, the phonons drift along with them. The electrons and phonons form a closed system that exchange energy back and forth. There is a bottleneck in the dissipation of energy. The phonons can only dissipate their energy by giving it back to the electrons. Īs they accelerate, they emit phonons, thereby transferring the energy gain from the electric field into phonon energy.The electrons are accelerated by the electric field. There are relatively few other phonons thermally excited, and three-phonon processes become rare. Both of these concepts are very important in physics.At low temperatures, the anharmonic phenomena is ineffective. A phonon is a collective vibration of several atoms. A photon is a package of energy that is the foundation of quantum mechanics. Phonon and photon are two very close words that can be mistaken by many beginners in physics and science. What is difference between photon and phonon? Borders between the bands of colors will then show the dispersion curves. The straightforward method of plotting the curves is to evaluate the function point by point, varying both frequency and velocity over the ranges of interest, and plotting positive results in one color and negative results with another. Elementary particles, considered as matter waves, have a nontrivial dispersion relation even in the absence of geometric constraints and other media. Dispersion may be caused either by geometric boundary conditions (waveguides, shallow water) or by interaction of the waves with the transmitting medium.

Phonon dispersio dash vertical