Electron-phonon interaction semiconductors

Alfred Leitenstorfer and Alfred Laubereau, Ultrafast Electron-Phonon Interactions in Semiconductors Quantum Kinetic Memory Effects... 

A QD Hamiltonian includes both Coulomb and electron-phonon interactions. Apparently, the phonon modes (denoted as QD) in the quantum dot are different from the semiconductor ones. The electron-phonon interaction determines relaxation processes in quantum dot (hot electrons or excitons). Thus, the QD Hamiltonian yields... 

Electron-phonon interaction in a semiconductor is the main factor for relaxation of a transferred electron. There are two different relaxation processes that decrease the efficiency of light conversion in a solar system (1) relaxation of an electron from a semiconductor conduction band to a valence band and (2) a backward electron transfer reaction. The forward and backward electron transfer processes have been already included in the tunneling interaction, HSm-qd, described by Eq. (108). However, the effect of SM e-ph interaction is important for the correct description of electron transfer in the SM-QD solar cell system. In the previous section, we have gradually considered different types of interactions in the quantum dot and obtained the exact expression for the photocurrent (128) where the exact nonequilibrium QD Green s functions determined from Eq. (127) have been used. However, in... 

For the particular case of longitudinal optical modes, we found in Eq. (9-27) the electrostatic electron-phonon interaction, which turns out to be the dominant interaction with these modes in polar crystals. Interaction with transverse optical modes is much weaker. There is also an electrostatic interaction with acoustic modes -both longitudinal and transverse which may be calculated in terms of the polarization generated through the piezoelectric effect. (The piezoelectric electron phonon interaction was first treated by Meijer and Polder, 1953, and subsequently, it was treated more completely by Harrison, 1956). Clearly this interaction potential is proportional to the strain that is due to the vibration, and it also contains a factor of l/k obtained by using the Poisson equation to go from polarizations to potentials. The piezoelectric contribution to the coupling tends to be dominated by other contributions to the electron -phonon interaction in semiconductors at ordinary temperatures but, as we shall see, these other contribu-... 

Such electron-phonon interactions directly proportional to the dilatation are called deformation potentials, a concept first introduced by Bardeen and Shockley (see, for example, Shockley, 1950). This is indeed the dominant mechanism for electron-phonon interaction in covalent semiconductors, and the interaction with transverse waves is weaker. 

Takagahara T. (1993b), Electron-phonon interactions and excitonic dephasing in semiconductor nanocrystals Phys. Rev. Lett. 71, 3577-3580. 

Various scientists consider the time-fluctuating energy levels (Fig. 6.7) as bands of energy levels. Such a description is very convenient, especially for semiconductor-liquid interfaces, but must be used with caution. As Morrison has already pointed out in his book [12], these bands arise from the fluctuation of the solvent and they have different properties from the fixed bands in solids. There is an essential difference in concept between, on the one hand, electron-phonon interactions causing a fluctuation of electronic energy in a static distribution of levels, and, on the other hand, ion-phonon interactions causing a fluctuation of the energy levels themselves. For instance, it is not possible to have an optical transition between the occupied and unoccupied levels. 

When temperature is lowered, the band gaps usually increase [15]. There again, a few materials like lead sulphides or some copper halides are exceptions with a band gap increasing with temperature [96]. A quantitative analysis of the temperature dependence of the energy gaps must consider the electron-phonon interaction, which is the predominant contribution, and the thermal expansion effect. The effect of thermal expansion can be understood intuitively on the basis of the decrease of the interatomic distances when the temperature is decreased. A quantitative analysis of the electron-phonon contributions is more difficult, and most calculations have been performed for direct band-gap structures [75], Multi-parameter calculations of the temperature dependence of band gaps in semiconductors can be found in [81],... 

An additional complication arises from the fact that the probability of an electron (or hole) being self-trapped due to the electron - phonon interaction increases strongly as the electronic wave function shrinks in size to the order of atomic dimensions (Emin, 1982). A consequence of this is that electrons in disorder-induced localized states are believed to be more susceptible to small polaron formation and self-trapping than are ordinary extended-state electrons (Emin, 1984 Cohen et al, 1983). Thus, not only does the disordered structure of amorphous semiconductors introduce new physical phenomena, namely, the mobility edge, but also the effect of known phenomena, such as the electron - phonon interaction, can be qualitatively different. 

Contrary to inorganic crystalline semiconductors, where charge is transported in general by electrons in the conduction band and holes in the valence band, in doped conjugated polymers charged solitons, polarons, and bipolarons act as charge carriers. These quasi-particles are the direct consequence of the strong electron-phonon interaction present in these quasi-one-dimensional polymers. 

Conjngated polymers differ from crystalline semiconductors and metals in several aspects and are often treated theoretically as a one-dimensional system. The formation of the band gap is explained taking into account either electron-phonon interactions or electron-electron interactions among 7t-electrons. If electron-phonon interaction dominates in real 7t-conjugated polymers, these systems could be treated using Peierls theory. In contrast, when electron-electron interactions dominate, the Hubbard model could be used to explain the physical properties of polymers. 

Strong electronic-vibrational interaction in the electrolyte renders the tunneling process from the semiconductor irreversible, obviating oscillations which increase residence time in the semiconductor and thus intraband thermalization therein. This irreversibility has its basic origin in the electronic particle tunneling from the semiconductor where the electron-phonon interaction is weak to a strongly-coupled state of the electrolyte where the electronic-vibrational interaction is strong. 

A mechanism that would always reduce the mobility of a carrier, be it free or coulombically bound to a countercharge, as compared to the value expected for a wide-band semiconductor is polaron formation. In fact, by calculating ground state and lowest-lying excited states of a PDA chain using a tight-binding Hamiltonian which includes electron-phonon interactions yet no electron-electron re-... 

The paper is organized as follows. Section II contains a discussion of band bounds in disordered materials, distinguishing between band edges and band limits. Section III introduces the mobility-edge concept. Section IV introduces the current version of the simplest band model of an amorphous semiconductor. Section V contains a discussion of the band-edge features in the electronic structure of a disordered material and classifies them according to the degree to which they can be represented as universal. In Section VI the effects of electron-phonon interaction are discussed. In Section VII there is a brief dicussion of fast processes such as the optical absorption and in Section VIII of slow processes such as the dc transport properties. We conclude in Section IX with an overall summary of the present status of the theory. 

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