Carrier-phonon scattering

If these holes emit phonons, they will move to the edge of the HOMO band edge, and if they absorb phonons, they will move away from the HOMO band edge. Each hole will experience a different sequence of phonon absorption and emission events that have probabihties given by the carrier-phonon scattering rate, as a function of carrier... 

It is clear from Equation 11.3 that resistivity should approach within 10% of the bulk value when the film thickness exceeds about four times the mean free path. The better the conductor, the smaller the mean free path. Thus, the resistivity approaches the bulk value as the film thickness reaches typical values of 100-200 nm for metallic conductors, or perhaps as much as several micrometers for semiconductors, depending on the intrinsic or doped carrier density. For sufficiently thick metallic films with K 1, the temperature coefficient of resistivity becomes positive, as bulk electron-phonon scattering becomes the primary contribution to resistivity [5]. Conduction in semiconductor films remains activation-limited, and retains a negative temperature coefficient. Figure 11.1 illustrates the dependence of resistivity on film thickness for sputtered... 

The optical excitation of electron-hole pairs represents a non-equilibrium state. The subsequent relaxation processes from the initial state includes both carrier-carrier interactions and coupling to the bath phonons. In some treatments, there is a distinction made between carrier-carrier and carrier-phonon interactions in which the latter is referred to as thermalisation. A two-temperature model is invoked in that the carrier-carrier scattering leads to a statistical distribution that can be described by an elevated electronic temperature, relative to the temperature characterising the lattice phonons (Schoenlein et al, 1987 Schmuttenmaer et al, 1996). This two-temperature model is valid only if the carrier-carrier energy redistribution occurs on time scales much faster (>10 times) than relaxation into phonons. This distinction has limited value when there is not a sufficient separation in time scale to make a two-temperature model applicable. The main emphasis in this section is on the dynamics of the energy distribution of the carriers as this is most relevant to energy storage applications. 

The other phonon-scattering events involve k states and phonons in which the carriers remain within the same valley (conserve symmetry). These intravalley scattering processes are described by the rate (A.op) (Kash et al, 1985 Zhou, 1990)... 

At the injection conditions employed, the observation is a convolution of carrier-carrier scattering and phonon scattering and both would be increased by the presence of surface defects. Lower injection conditions need to be achieved to completely eliminate carrier-carrier scattering from the dynamics and permit a definitive elucidation of the dynamics relevant to surface photoelectrochemistry under majority-carrier depletion conditions. 

The main message from this class of experiments is that the details of the surface do affect the carrier relaxation. In the presence of surface defects associated with conventional surface preparation, the carrier relaxation in the surface region is exceptionally fast relative to bulk processes (10-100 fs dynamics). As can be seen by comparing the dynamics shown in Fig. 2.9, the effect of the surface is to increase the rate of relaxation and thermalisation. The asymmetry, more anharmonic character to the surface modes and increased mixing of states at defect sites all conspire to speed up the relaxation processes. With proper attention to surface structure, it is possible to intervene in the relaxation process and achieve carrier and phonon scattering rates that approach bulk processes. In this limit, 200 fs to picosecond dynamics define the operative time scales. 

V is the speed of sound, 6 is the Debye temperature, tc is the total phonon-scattering rate, w is the phonon-scattering rate due to three phonon normal processes. In this model, two additional scattering mechanisms of phonon (by point defects and by charge carriers) are considered. 

Up to this point, the mobility of the electronic carriers and their temperature dependencies were not discussed. The effect of temperature on the mobility of the electrons and holes will depend on several factors, with the width of the conduction and/or valence bands being the most important. For wideband materials (not to be confused with wide-band-gap materials), the mobility of the electronic carriers decreases with increasing temperature as a result of lattice or phonon scattering, not unlike what happens in metallic conductors. It can be shown that in this case both p and pp are proportional to Thus the temperature dependence of... 

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. 

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