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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 the free electron model with scattering, the value of ′ / is of order / (), where is the Fermi temperature, and so a typical value of the Seebeck coefficient in the Fermi gas is / (the prefactor varies somewhat depending on details such as dimensionality and scattering).
The Peltier effect can be considered as the back-action counterpart to the Seebeck effect (analogous to the back-EMF in magnetic induction): if a simple thermoelectric circuit is closed, then the Seebeck effect will drive a current, which in turn (by the Peltier effect) will always transfer heat from the hot to the cold junction.
A thermoelectric generator (TEG), also called a Seebeck generator, is a solid state device that converts heat (driven by temperature differences) directly into electrical energy through a phenomenon called the Seebeck effect [1] (a form of thermoelectric effect).
For electrons or electron holes in a solid, the effective mass is usually stated as a factor multiplying the rest mass of an electron, m e (9.11 × 10 −31 kg). This factor is usually in the range 0.01 to 10, but can be lower or higher—for example, reaching 1,000 in exotic heavy fermion materials , or anywhere from zero to infinity ...
Free electron model [ edit ] After taking into account the quantum effects, as in the free electron model , the heat capacity, mean free path and average speed of electrons are modified and the proportionality constant is then corrected to π 2 3 ≈ 3.29 {\displaystyle {\frac {\pi ^{2}}{3}}\approx 3.29} , which agrees with experimental values.
In 1810, at Jena, Seebeck described the action of light on silver chloride sensitised paper (a technique used by Johann Ritter). [7] [8] He observed that the exposed chemical would sometimes take on an approximate, pale version of the color of the solar spectrum as projected from a prism to which it had been exposed, and also reported the action of light for a wavelengths beyond the violet end ...
The model also explains partly the Wiedemann–Franz law of 1853. Drude formula is derived in a limited way, namely by assuming that the charge carriers form a classical ideal gas. When quantum theory is considered, the Drude model can be extended to the free electron model, where the carriers follow Fermi–Dirac distribution. The conductivity ...