Lattice scattering

A temperature coefficient for these data may be obtained from the equation for lattice scattering... 

The proportionality factor is the electron mobility, xn, which has units of square centimeters per volt per second. The mobility is determined by electron-scattering mechanisms in the crystal. The two predominant mechanisms are lattice scattering and impurity scattering. Because the amplitude of lattice vibrations increases with temperature, lattice scattering becomes the dominant mechanism at high temperatures, and therefore, the mobility decreases with increasing temperature. 

Theory predicts that the mobility decreases as T 3/2 because of lattice scattering (8). But because electrons have higher velocities at high temperatures, they are less effectively scattered by impurities at high temperatures. Consequently, impurity scattering becomes less important with increasing temperature. Theoretical models predict that the mobility increases as T3/2/nj, in which nx is the total impurity concentration (8). The mobility is related to the electron diffusivity, Dn, through the Einstein relation... 

Table 2.3. Material parameters of zinc oxide for the calculation of the lattice-scattering-limited mobility (2.7-2.14)...

Equation 6.22 predicts that electronic conductivity is dependent on the electron relaxation time. However, it suggests no physical mechanisms responsible for controlling this parameter. Since electrons exhibit wave-particle duahty, scattering events could be suspected to play a part. In a perfect crystal, the atoms of the lattice scatter electrons coherently so that the mean-free path of an electron is infinite. However, in real crystals there exist different types of electron scattering processes that can limit the electron mean-free path and, hence, conductivity. These include the collision of an electron with other electrons (electron-electron scattering), lattice vibrations, or phonons (electron-phonon scattering), and impurities (electron-impurity scattering). 

X-rays, electrons, and neutrons all have wavelike as well as particle nature, and each can be generated as a beam of a very limited energy (and therefore of a specific, or monochromatic, wavelength). X-rays and electrons are scattered when they hit electrons, and neutrons are scattered when they hit nuclei. If these electrons and nuclei are arranged in the three-dimensional regular array of a crystal lattice, scattering takes place only in specific directions that is, diffraction occurs. 

Electrical Resistivity. Electrical resistivity is composed of contributions from imperfections and impurities, both temperature dependent and temperature independent (residual resistivity), lattice scattering, magnetic interactions and electron-electron interactions (36). 

It is useful to estimate the characteristic time required to achieve primary separation of the electron-hole pair in a bulk single crystalline semiconductor electrode with a flat interface with the electrolyte. If there is a depletion layer at the interface in which an electron-hole pair is generated (see Fig. 5), the electron will move to the interior and the hole to the surface. Provided that the mean free path length for electron-lattice scattering is much smaller than the width of the depletion layer, the drift velocities of the electron and hole are described by the relationships... 

E and E represent the respective activation energies of the forward and reverse reactions. These energy values, in a solid medium, are representative of the energy needed to cause the transfer of an electrically neutral particle in the crystal lattice (scattering process) or through interfaces. 

When the crystal is irradiated by an X-ray beam, its lattice scatters the radiation selectively. A strong diffraction is observed when the wavevector of scattering for a particular angle (i.e. q) coincides with the vector of reciprocal lattice, as shown in the Ewald sphere. Fig. 5.10. The condition... 

Silicon (Si). The electronic transport is due exclusively to electrons in the [100] conduction band minima and holes in the two uppermost (heavy and light) valence bands. In samples with impurity concentrations below 10 cm , the mobilities are determined by pure lattice scattering down to temperatures of about 10 K (n-type) or 50 K (p-type), for electrons and holes, respectively. Higher impurity concentrations lead to deviations from the lattice mobility at corresponding higher temperatures. For electrons, the lattice mobility below 50 K is dominated by deformation-potential coupling... 

Germanium (Ge). Low-field electronic transport is provided by electrons in the minima of the conduction band and holes near the Fg point in the valence bands. At room temperature, the mobUity of samples with impurity concentrations below 10 cm is Umited essentially by lattice scattering higher donor or acceptor concen-... 

The mobility of electrons and holes is affected by two main scattering mechanisms chemical impurities and lattice scattering. The mobility temperature dependence due to... 

Since scattering probabilities for different mechanisms add to yield the net scattering probability that, in turn, defines the overall mean free time between collisions, mobilities (e.g., phonon scattering mobility and lattice scattering mobility) due to different mechanisms are combined as = Mphonon + ion that is, the smallest mobility dominates. 

The temperature dependence of the charge carrier mobility is dependent on the electronic stmcture of the solid. For a pure non-polar semiconductor - as in an ideal and pure covalent semiconductor - the electrons in the conduction band and the electron holes in the valence band can be considered as quasi-free (itinerant) particles. Then the mobilities of electrons and electron holes, Un and Up, are determined by the thermal vibrations of the lattice in that the lattice vibrations result in electron and electron hole scattering (lattice scattering). Under these conditions the charge carrier mobilities of electrons and electron holes are both proportional to T 3/2, e.g. 

The transport of small polarons in an ionic solid may take place by two different mechanisms. At low temperatures small polarons may tunnel between localised sites in what is referred to as a narrow band. The temperature dependence of the mobility is determined by lattice scattering and the polaron mobility decreases with increasing temperature in a manner analogous to a broad band semiconductor. 

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