Electron-acoustic phonon scattering

Figure 49. The mobility of the excess electrons in various SnCh samples determined by means of the Hall effect and conductivity. The high temperature behavior points to acoustic phonon scattering. Both samples differ in purity. According to Ref..155. (Reprinted from H. J. van Daal, Polar Optical-Mode Scattering of Electrons in SnC>2. , Solid State Commun. 6, 5-9. Copyright 1968 with permission from Elsevier.)...

Figure 18 Temperature dependence of the electron mobility for 6H-SiC. The broken lines show the calculated values of the mobility determined by the impurity scattering by the piezophonon scattering Itpiez by polar optical phonon scattering (Xp i, and by acoustic phonon scattering The solid hne shows the values for the mobility determined by acoustic phonon and optical phonon scatterings, which is in...

For TMDs, the temperature dependence of the electron mobility is usually formed to be much stronger than expected for acoustic phonon scattering. The resistivity for materials with a temperature independent extrinsic carrier concentration is usually fit by the empirical reladmi ... 

Until now we have mainly treated electrons and holes analogously to the ionic defects. As far as the mobility is concerned, quantum mechanical eflfects cause severe differences. There is no energy of activation (AH = 0) in the case of perfect band conduction and, formally speaking, the temperature dependence of the mobility is effectively determined by the prefactor. The determining process for the finite mobility is scattering by lattice vibrations and/or imperfections. The T / relation for acoustic phonon scattering is a typical law in this context (see Chapter 3) (see Fig. 6.14). Unless the electronic charge concentration has been fixed by dop-... 

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 ... 

Bulk silicon is a semiconductor with an indirect band structure, as schematically shown in Fig. 7.12 c. The top of the VB is located at the center of the Brillouin zone, while the CB has six minima at the equivalent (100) directions. The only allowed optical transition is a vertical transition of a photon with a subsequent electron-phonon scattering process which is needed to conserve the crystal momentum, as indicated by arrows in Fig. 7.12 c. The relevant phonon modes include transverse optical phonons (TO 56 meV), longitudinal optical phonons (LO 53.5 meV) and transverse acoustic phonons (TA 18.7 meV). At very low temperature a splitting (2.5 meV) of the main free exciton line in TO and LO replicas can be observed [Kol5]. 

The most orthodox model involving a quasi-one-dimensional tight-binding band with electron scattering by acoustic phonons and molecular vibrations (one-phonon processes) has been analyzed carefully and in great detail [43,44]. Good agreement with experimental data is claimed by the proponents of this model. 

Figure 3. Schematic Illustration of dispersion curves of an acoustic phonon, a band electron, and the SWAP. The Incident phonon -q Is scattered as q2. (Reproduced with permission from reference 5. Copyright 1985 Nljhoff.)...

The effect of device temperature on the electrical behavior of the device occurs due to the lattice temperature dependence of the electron scattering rate. When the LO phonon and acoustic phonon temperatures rise, the electron scattering rate increases, thus increasing the electrical resistance or decreasing the carrier mobility. The coupling of electrical and thermal characteristics suggest that these must be analyzed concurrently. 

Values for both the hole and electron mobilities and carrier densities in various SiC polytypes are listed. Ionized and neutral impurity, acoustic phonon, piezoelectric and polar optical phonon scattering mechanisms are all found in SiC. In general, mobilities have increased and carrier concentrations decreased with time, reflecting the improvement in crystal quality whether bulk or epitaxially-grown material is considered. 

Robinson and co-workers have analyzed ESR TTc as a fimction of temperature measured at 9.5 and 16 GHz and as a function of frequency at rt, as shown in Figure 6.34 [164]. They assumed a model that the mechanism for is the modulation of the electron-electron dipolar interaction due to scattering of the spins by acoustic phonons. They also assumed two levels of diffusion (1) almost free rapid motion within a domain of 50 carbons as proposed by the ENDOR analysis in an unoriented C enriched sample [117], which dominates the ESR 77,. at the X-band and (2) slow migration of such a domain which assures compatibility with the motional narrowing of the ESR linewidth. The rapid diffusion within the domain is not of activation type and the diffusion rate increases with decreasing temperature. On the contrary, the migration is of activation type. However, such an analysis of the ENDOR data [117] was pointed out to be incorrect in section 3.2.5 [105]. Then, it is probable that this model will give rise to some inconsistency with other observations as follows. 

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