2.2 Formal Transport Theory

The behavior of solid-state matter under the influence of external fields is one main subject of solid-state physics. The external field may be an electric field, a magnetic field, an optical signal, or a temperature gradient. Those external fields modify the distribution of the internal energy which in turn modifies or alters some electronic properties, such as the carrier concentration or the carrier mobility.

Besides the carrier mobility the electric current is also affected by the magnetic field by deflecting its direction. Modeling the electric current implies to determine the number of electrons with given momentum at a given location as a function of time. Those distribution functions are modeled by solving the Boltzmann equation and with them the electron and energy transport equations are derived. The transport equations can be obtained from the thermodynamics of irreversible processes. The advantage of this solution is a direct evaluation of the equation coefficients with respect to the driving forces, and a direct link to experiments [22].