Section 08_Electron_Transport

Section 08_Electron_Transport - Physics 927 E.Y.Tsymbal...

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Physics 927 E.Y.Tsymbal 1 Section 8: Electronic Transport Drude model The simplest treatment of the electrical conductivity was given by Drude. There are four major assumptions within the Drude model. 1. Electrons are treated as classical particles within a free-electron approximation. Thus, in the absence of external electromagnetic fields each electron is taken to move uniformly in a straight line, neglecting the interactions with other electrons and ions. In the presence of external fields each electron is taken to move according to Newton's laws of motion. 2. Electrons move free only between collisions with scattering centers. Collisions, as in kinetic theory, are instantaneous events that abruptly alter the velocity of an electron. Drude attributed them to the electrons scattering by ion cores. However, as we will see later, this is not a correct picture of electron scattering on ordered periodic structures. A particular type of scattering centers does not matter in the Drude model. An understanding of metallic conduction can be achieved by simply assuming that there is some scattering mechanism, without inquiring too closely into just what that mechanism might be. Fig.1 Trajectory of a conduction electron scattering off the ions, according to the picture of Drude. 3. An electron experiences a collision, resulting in an abrupt change in its velocity, with a probability per unit time 1/ τ . This implies that the probability of an electron undergoing a collision in any infinitesimal time interval of length dt is just dt / . The time is therefore an average time between the two consecutive scattering events. It known as, the collision time (relaxation time), it plays a fundamental role in the theory of metallic conduction. It follows from this assumption that an electron picked at random at a given moment will, on the average, travel for a time before its next collision. The relaxation time is taken to be independent of an electron's position and velocity. 4. Electrons are assumed to achieve thermal equilibrium with their surroundings only through collisions. These collisions are assumed to maintain local thermo-dynamic equilibrium in a particularly simple way: immediately after each collision an electron is taken to emerge with a velocity that is not related to its velocity just before the collision, but randomly directed and with a speed appropriate to the temperature prevailing at the place where the collision occurred. Now we consider the application of the Drude model for electrical conductivity in a metal. According to Ohm's law, the current I flowing in a wire is proportional to the potential drop V=V 2 V 1 along the wire: V = IR, where R, the resistance of the wire, depends on its dimensions. It is much more convenient to express the Ohm's law in a form which is independent of the dimensions of the wire because these factors are irrelevant to the basic physics of the conduction.
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Physics 927 E.Y.Tsymbal 2 Fig.2
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This note was uploaded on 03/11/2012 for the course PHYSICS 927 taught by Professor Staff during the Fall '11 term at UNL.

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Section 08_Electron_Transport - Physics 927 E.Y.Tsymbal...

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