Phonon emission

MaxweU-Boltzmann distribution. At high electric fields, E > 10 kV/cm, no longer increases with electric field and approaches a limiting saturation speed, determined primarily by optical phonon emission. Eigure 3 shows the variation of drift speed with electric field for electrons and holes in various semiconductors. 

The role of two-phonon processes in the relaxation of tunneling systems has been analyzed by Silbey and Trommsdorf [1990]. Unlike the model of TLS coupled linearly to a harmonic bath (2.39), bilinear coupling to phonons of the form Cijqiqja was considered. In the deformation potential approximation the coupling constant Cij is proportional to (y.cUj. There are two leading two-phonon processes with different dependence of the relaxation rate on temperature and energy gap, A = (A Two-phonon emission prevails at low temperatures, and it is... 

For insulating surfaces, the friction p can be only due to phonon emission into the substrate, but on metal surfaces damping to vibration may result from both phononic and electronic excitations so that p= %/+ pp. The damping coefficient is assumed to be in the form of a diagonal matrix. 

A transition linearly coupled to the phonon field gradient will experience, from the perturbation theory perspective, a frequency shift and a drag force owing to phonon emission/absorption. Here we resort to the simplest way to model these effects by assuming that our degree of freedom behaves like a localized boson with frequency (s>i. The corresponding Hamiltonian reads... 

Figure 4.10(b) shows the temperature dependence of the absorption spectrum expected for an indirect gap. It can be noted that the contribution due to becomes less important with decreasing temperature. This is due to the temperature dependence of the phonon density factor (see Equation (4.37)). Indeed, at 0 K there are no phonons to be absorbed and only one straight line, related to a phonon emission process, is observed. From Figure 4.10(b) we can also infer that cog shifts to higher values as the temperature decreases, which reflects the temperature dependence of the energy... 

The nonradiative rate. Am, from a (RE) + ion level is also strongly related to the corresponding energy gap. Systematic studies performed over different (RE) + ions in different host crystals have experimentally shown that the rate of phonon emission, or multiphonon emission rate, from a given energy level decreases exponentially with the corresponding energy gap. This behavior can be expressed as follows ... 

Quenching of narrow-line emissions (as observed for many Ln3+ ions) has been explained by phonon emission to the lattice modes. Moos and co-workers (60) and others (67) have given many examples. Usually the nonradiative rate is described by Kiel s formula (62) for a single-frequency p-phonon process,... 

The most interesting aspect of this work is that the authors are able to rule out resonance exchange as the mechanism by which energy is transferred between the ions. They believe that transference takes place via phonon emission. It would be extremely interesting to determine the rates of ene/gy transfer between the ions, for this would then yield information concerning the rate of liberation of phonons. A study of the temperature... 

A similar situation exists for carrier capture by surface states. Relatively large capture cross sections are observed but no adequate theoretical treatment exists. Theory to describe the capture process is greatly complicated by presence of the surface. The carrier motion as well as the vibrational behavior of the crystal is perturbed by the surface. What does seem clear, however, is that the surface state should be tightly enough bound to the crystal lattice so that phonon emission is possible. In addition, the state should be close enough to the semiconductor to overlap the wave function of the semiconductor carrier. 

At higher temperatures, the transfer rate of the impurity molecule between sites is enhanced by phonon emission or absorption this can be viewed as a phonon-dressed state transfer. When these off-diagonal processes are included in the analysis, the transition probability can be broken up into phonon processes of different order. One-phonon processes do not contribute, because momentum is not conserved in these events. Among the two-phonon processes, only Raman events contribute. These lead to a I7 dependence of the transition probability (see, for example, Flynn and Stoneham [1970]). This regime takes place when kBT... 

This interaction Hamiltonian describes the fe-phonon emission due to a periodical local field. 

Figure 7.6 Schematic representation of fundamental absorption processes in (a) direct bandgap and (b) indirect bandgap semiconductors. Phonon emission and phonon absorption processes are marked in red. (Adapted from Yacobi [211)...

Fourth, the excited states in Si-based electronics must decay by phonons, and thus at DR = 3 nm a huge heat dissipation problem exists for nanoscale inorganic electronic components. In contrast, molecular devices can also decay from their excited state by photon emission (so far at 3%) [112] this photon decay channel must be maximized. If this is successful—that is, if the chosen unimolecular device does decay to its ground state by photon emission rather than by phonon emission—then unimolecular devices will have an inherent practical advantage over inorganic ones. 

The optical absorption arising from the defect transitions is weak because of the low defect densities and in a thin film cannot be measured by optical transmission. The techniques of PDS, CPM and photoemission yield, described in Section 3.3, have sufficient sensitivity. Photocapacitance, which measures the light-induced change in the depletion layer capacitance, is similarly sensitive to weak absorption (Johnson and Biegelsen 1985). PDS measures the heat absorbed in the sample and detects all of the possible optical transitions. At room temperature virtually all the recombination is non-radiative and generates heat by phonon emission. CPM detects photocarriers and so is primarily sensitive to the optical transitions which excite electrons to... 

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