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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 physics and engineering, a free body diagram (FBD; also called a force diagram) [1] is a graphical illustration used to visualize the applied forces, moments, and resulting reactions on a free body in a given condition. It depicts a body or connected bodies with all the applied forces and moments, and reactions, which act on the body(ies).
In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence band is the highest range of electron energies in which electrons are normally present at absolute zero temperature, while the conduction band is the lowest range of vacant electronic states.
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 .
Aside from being in practically every semiconductor device in use today, two dimensional systems allow access to interesting physics. The quantum Hall effect was first observed in a 2DEG, [9] which led to two Nobel Prizes in physics, of Klaus von Klitzing in 1985, [10] and of Robert B. Laughlin, Horst L. Störmer and Daniel C. Tsui in 1998. [11]
In electronics and semiconductor physics, the law of mass action relates the concentrations of free electrons and electron holes under thermal equilibrium.It states that, under thermal equilibrium, the product of the free electron concentration and the free hole concentration is equal to a constant square of intrinsic carrier concentration .
The mean free path can be increased by reducing the number of impurities in a crystal or by lowering its temperature. Ballistic transport is observed when the mean free path of the particle is (much) longer than the dimension of the medium through which the particle travels. The particle alters its motion only upon collision with the walls.
Band diagram for p–n junction at equilibrium. The depletion region is shaded. φ B denotes band shift for holes and charges level. See P–n diode. The inner workings of a light emitting diode, showing circuit (top) and band diagram when a bias voltage is applied (bottom).