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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.
In this model the conduction is supposed to be carried by a free electron system moving in a self-consistent periodic potential. On the contrary, Frenkel derived his formula describing the dielectric (or the semiconductor) as simply composed by neutral atoms acting as positively charged trap states (when empty, i.e. when the atoms are ionized).
This intraband absorption is different from interband absorption because the excited carrier is already in an excited band, such as an electron in the conduction band or a hole in the valence band, where it is free to move. In interband absorption, the carrier starts in a fixed, nonconducting band and is excited to a conducting one.
Here t is the time, p is the average momentum per electron and q, n, m, and τ are respectively the electron charge, number density, mass, and mean free time between ionic collisions. The latter expression is particularly important because it explains in semi-quantitative terms why Ohm's law , one of the most ubiquitous relationships in all of ...
Ionic conduction [ edit ] Similar to electron conduction, the electrical resistance of thin-film electrolytes depends on the applied electric field, such that when the thickness of the sample is reduced, the conductivity improves due to both the reduced thickness and the field-induced conductivity enhancement.
In this case, the carrier density (in this context, also called the free electron density) can be estimated by: [5] n = N A Z ρ m m a {\displaystyle n={\frac {N_{\text{A}}Z\rho _{m}}{m_{a}}}} Where N A {\displaystyle N_{\text{A}}} is the Avogadro constant , Z is the number of valence electrons , ρ m {\displaystyle \rho _{m}} is the density of ...
Relativistic heat conduction refers to the modelling of heat conduction (and similar diffusion processes) in a way compatible with special relativity. In special (and general ) relativity, the usual heat equation for non-relativistic heat conduction must be modified, as it leads to faster-than-light signal propagation.
Electrical conduction of metals is a well-known phenomenon and is attributed to the free conduction electrons, which can be measured as sketched in the figure. The current density j is observed to be proportional to the applied electric field and follows Ohm's law where the prefactor is the specific electrical conductivity .