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Unformatted text preview: 11 Lorentz-Drude models for conductivity and susceptibility and polarization current In this lecture we will describe simple microscopic models for conductivity σ and electric susceptibility χ e of material media composed of free and bound charge carriers. The models were first developed by Lorentz and Drude prior to the establishment of quantum mechanics. In these models free charge carriers motions are described using Newtonian dynamics and atoms are represented as electric dipoles p =- e r ( r is electron displacement from atomic nucleus) behaving like damped 2nd order systems. Conductivity: Conducting materials such as copper, sea water, ionized gases (plasmas) contain a finite density N of mobile and free charge carriers at the microscopic level (in addition to neutral atoms and molecules sharing the same macroscopic space) — these elementary mobile carriers can be electrons, positive or negative ions, or positive “holes” (in semi-conductor materials). (a) (b) E = 0 E q > q > In the absence of an applied electric field E, free charge q exhibits a "random walk" between collisions such that its average velocity v is zero. By collisions we refer to the inreactions of q with zero-mean miscroscopic electric fields within the conductor due to charges entrapped in the lattice. In the presence of an applied electric field E, the mean position of free charge q>0 drifts in the direction of field vector E with some non-zero mean velocity v. Avg. drift velocity v reperesents a balance between acceleration force due to E and an opposing friction force produced by collisions of q with the lattice at random intervals with some mean value . τ • Each elementary charge carrier with a charge q and mass m and subject to a macroscopic electrical force q E will be modelled by a dynamic equation m d v dt = q E- m v τ , which is effectively Newton’s second law — “force equals mass times acceleration” — in which v denotes the macroscopic velocity 1 of charge 1 Think of microscopic velocity of each charge carrier as v + δ v , where δ v is an independent zero-mean 1 carriers and- m v τ denotes a macroscopic friction force proportional to- v . Friction is a consequence of “collisions” of charge carriers with the neutral background at a frequency of ν = 1 τ collisions per unit time, and causes the decay of v as v ( t ) = v (0)...
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This note was uploaded on 05/05/2010 for the course ECE ece 442 taught by Professor Kim during the Spring '10 term at University of Illinois at Urbana–Champaign.
- Spring '10