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Dividing the thermal conductivity by the electrical conductivity = eliminates the scattering time and gives = At this point of the calculation, Drude made two assumptions now known to be errors. First, he used the classical result for the specific heat capacity of the conduction electrons: c v = 3 2 n k B {\displaystyle c_{v}={\tfrac {3}{2}}nk ...
In solid-state physics, the free electron model is a quantum mechanical model for the behaviour of charge carriers in a metallic solid. It was developed in 1927, [1] principally by Arnold Sommerfeld, who combined the classical Drude model with quantum mechanical Fermi–Dirac statistics and hence it is also known as the Drude–Sommerfeld model.
Paul Drude (c. 1900) realized that the phenomenological description of conductivity can be formulated quite generally (electron-, ion-, heat- etc. conductivity). Although the phenomenological description is incorrect for conduction electrons, it can serve as a preliminary treatment.
Moreover, the thermal fluctuation of each electron should be taken into account. Therefore, a statistical approach is needed. To predict the optical transition with appropriate precision, one chooses an approximation, called the assumption of quasi-thermal distributions, of the electrons in the conduction band and of the holes in the valence band.
Although the Drude model was fairly successful in describing the electron motion within metals, it has some erroneous aspects: it predicts the Hall coefficient with the wrong sign compared to experimental measurements, the assumed additional electronic heat capacity to the lattice heat capacity, namely per electron at elevated temperatures, is also inconsistent with experimental values, since ...
Since the Drude law also depends on scattering time, which varies greatly, this effective mass is rarely used; conductivity is instead usually expressed in terms of carrier density and an empirically measured parameter, carrier mobility.