Scattering of charge carriers

The sublinear increase of vd(F) be interpreted with the aid of a model by Shockley [45], based on the inelastic scattering of charge carriers from longitudinal acoustic phonons. In this model, the assumption is made that the charge carriers scatter... 

In delocalized bands, the charge transport is limited by the scattering of the carriers by lattice vibrations (phonons). Therefore, an increase in the temperature, which induces an increase in the density of phonons, leads to a decrease in the mobility. 

The application of an electric field E to a conducting material results in an average velocity v of free charge carriers parallel to the field superimposed on their random thermal motion. The motion of charge carriers is retarded by scattering events, for example with acoustic phonons or ionized impurities. From the mean time t between such events, the effective mass m of the relevant charge carrier and the elementary charge e, the velocity v can be calculated ... 

This process describes the scattering of free carriers by the screened Coulomb potential of charged impurities (dopants) or defects theoretically treated already in 1946 by Conwell [74,75], later by Shockley [10] and Brooks and Herring [76,77]. In 1969, Fistul gave an overview on heavily-doped semiconductors [78]. A comprehensive review of the different theories and a comparison to the experimental data of elemental and compound semiconductors was performed by Chattopadhyay and Queisser in 1980 [79]. For nondegenerate semiconductors the ionized impurity mobility is given by [79] ... 

As described above, the electrons in a semiconductor can be described classically with an effective mass, which is usually less than the free electron mass. When no gradients in temperature, potential, concentration, and so on are present, the conduction electrons will move in random directions in the crystal. The average time that an electron travels between scattering events is the mean free time, Tm. Carrier scattering can arise from the collisions with the crystal lattice, impurities, or other electrons. However, during this random walk, the thermal motion is completely random, and these scattering processes will therefore produce no net motion of charge carriers on a macroscopic scale. 

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