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Illustration Scattering of an Electron - Drude Model

Scattering of an Electron - Drude Model
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According to the Drude model it is assumed that the electron gas behaves classically, i.e. is not subject to the Fermi distribution but to the Boltzman distribution. Moreover, according to the Drude model, all electrons are scattered and not as it is more accurate - only the electrons with the Fermi energy. These classical assumptions have the consequence that the theoretically calculated resistance of a metal differs by many orders of magnitude from the experimentally determined resistance. Nevertheless, one can use the Drude model to derive Ohm's law or use it at very high temperatures where the Fermi distribution becomes the Boltzman distribution.

An electron is scattering at the rigid atoms of the crystal. The electron travels a mean free path length \( l \) between two collisions while flying at the thermal velocity \( \boldsymbol{v}_{\text{th}} \).

The external electric field \( \boldsymbol{E} \) causes the electron, in addition to its thermal velocity, to acquire the drift velocity \( \boldsymbol{v}_{\text d} \) directed against the E-field. In total, the electron drifts according to the applied electric field, performing a much faster thermal motion during the drift.