Dynamical theory of transport phenomena in solids based on their electronic dielectric properties

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Abstract
The relaxation-time approximation for the Boltzmann equation has been introduced for solving the transport problem in solids since it is generally difficult to evaluate internal friction forces. Nonetheless, it was shown recently by several authors that the reversal mobility of the free carriers could be calculated by the so-called ‘‘energy-loss’’ method. This method is based on the dielectric function of the free carriers. It allows us to calculate the work done by the relative motion of the scattering centers through the induced electrical field associated with the free carriers. Unfortunately, the energy-loss method has been reduced to an energy balance and is not able to describe complex situations such as, for instance, those including magnetic fields. This paper presents a critical analysis and proposes an extension of this method to the case of more complex situations. It leads to the evaluation of the internal scattering fields screened by the moving free carriers and allows a reformulation of the whole theory of transport properties. This theory gives an explicit expression of the internal fields, taking formally into account the real band structure of the material, the local-field effects, and the dynamical screening effects. Numerical calculations of the ionized-impurity scattering are presented in the simplified case where local-field effects are neglected and in the effective-mass approximation in order to compare Boltzmann’s theory, the energy-loss method, and the present ‘‘dynamical’’ theory.