The free electron model the quantum state of an electron is described by the timeindependent schrodinger equation. The electrons are, however, bound to move within the metal due to electrostatic attraction between the positive ion cores and the electrons. The drude model can be visualised using the following simulation. The relationship between theory and potential applications is also emphasized. The drude model of a metal considers a sea of mobile electrons that have equilibrium average charge density. Since the dielectric function is additive, it can be written as the sum of free electron and interband. The current theory explains this with ad hoc manipulations like screening and positive charge carriers, but the correct answer is much simpler. Deviations from the drude theory were observed, and the values of the optical mass and relaxation time of the conduction electrons are discussed. Drudes classical theory of electrical conduction drude assumed that a metal is composed of ions, which are stationary, and valence electrons, which are free to move.
Drude model electrons shown here in blue constantly bounce between heavier, stationary crystal ions shown in red. Basic assumptions of drude model a gas of conduction electrons of mass m, which move against a background of heavy immobile ions electron density a z n m 0. Elements can be more clearly classified as metals and nonmetals on the basis of their chemical properties. Handout 1 drude model for metals cornell university. Ueep2024 solid state physics topic 3 free electron in metals 2. The time between collisions with impurities is of order. Alan doolittle for metals, the electrons can jump from the valence orbits outermost core energy levels of the atom to any position within the crystal free to move throughout the crystal with no extra energy needed to be supplied. The origin of mooij correlations in disordered metals.
This is a simple classical model, and many of its concepts extend to the quantum case. Drude theory of metals poisson in the drude model the probability of an electron suffering a collision in any in finitesimal interval dt is just dt. In these intervals, the interband transitions cannot be excited and the dielectric function has the form 2. Drude lorentz theory drude, in 1900, postulated that the metals consist of positive ion cores with the valence electrons moving freely among these cores. The model, which is an application of kinetic theory, assumes that the microscopic behaviour of electrons in a solid may be treated classically and looks much like a pinball machine, with a sea of constantly jittering electrons bouncing. The origin of mooij correlations in disordered metals npj. Optical and thermal properties book chapter iopscience.
Einstein and the early theory of superconductivity, 1919. Only at a temperatures t f that the particles in a classical gas attain kinetic energies as high as e f. In other words, the drude model is right about thermal conductivity, but wrong about heat capacity. One component is the drude freeelectron term, and the second component is the substantial contribution of the bound or interband electrons. Charge neutrality of the system at equilibrium is guaranteed by the presence of an assumed uniform positive charge background from ion cores that exactly cancel the equilibrium average electron charge density. Introduction to the electron theory of metals uichiro. Conduction current in metals em wave propagation in metals skin depth.
Semiclassical theory of conduction in metals drudes law. The classical free electron theory of metals drude lorentz theory of metals postulates. Einsteins early thoughts about superconductivity are discussed as a case study of how theoretical physics reacts to experimental findings that are. Classical derivation of ohms law and drude conductivity. Nondrude like behaviour of metals in the terahertz spectral. Debyes contribution to specific heat theory einsteins oscillator treatment of specific heat gave qualitative agreement with experiment and gave the correct high temperature limit the law of dulong and petit.
Tarea 1 tarea 1 1 drude theory of metals poisson in the. This idea will have many applications, even beyond the drude model. An empirical polarizable force field based on the classical. Drude formulated a theory for conduction in metals using the electron concept. The drude theory and the hall effect before considering the effect of magnetic fields on conductors, we need some model to describe the flow of currents in response to electric fields. The drude theory of metals the model kinetic theory of gases. Discussion on the drude theory of metal usually begin with the case of zero magnetic field so that the force acting on the electrons is just the one from the electric field. The model, which is an application of kinetic theory, assumes that. Einstein and the early theory of superconductivity, 19191922. Nondrude like behaviour of metals in the terahertz. For the traditional model metals, au and ag, the detailed dielectric function eq. Effective medium theory of nanodielectrics for embedded. Charge neutrality of the system at equilibrium is guaranteed by the presence of an assumed uniform positive charge background from ion cores that. The completed drude20 dna force field was shown to quantitatively reproduce the extent of charge neutralization by ions around dna, in accordance with counterion condensation cc theory.
Show that an electron picked at random at a given moment had no collision during the preceding t seconds with probability e. The simple approach is to regard the conduction band electrons as noninteracting electron gas and yields a fairly accurate description of metals like silver, gold or aluminium. Hall effect experiment utk department of physics and. In practice metals vaporize before the temperature t f is reached. The valence electrons of atoms are free to move about the whole volume of the metals like the molecules of a perfect gas in a container. This is about the right order of magnitude for many monovalent metals, such as sodium. This simple model uses classical mechanical theory of free electron. Drude was lucky he overestimated the electronic specific heat by 100 times electronic c v at room temperature is nowhere close to and underestimated the average electronic speed by a factor of 10.
The absorption edge was investigated very accurately. On thermal conduction in metals for a thermal conduction process along the xdirection since half of the electron density n m at x comes from the high temperature side and half of it comes from the low temperature side the thermal current density can be written as. Electrons in a metal behave much like particles in an ideal gas no coulombic interaction and no. Deriving the conductivity and permittivity of metals the drude model explains the electrodynamic properties of metals. S5 is reduced to the classical drude function in the wavelength interval where the interband transitions become inactive. Lecture notes on condensed matter physics a work in.
Drude theory of conductivity conductor in electric field assuming electrons actually behave like a gas, drude attempted to calculate the conductivity of metal. Metals drudes classical theory theory by paul drude in 1900, only three years after the electron was discovered. Typical mechanical properties of metals the yield strength and tensile strength vary with prior thermal and mechanical treatment, impurity levels, etc. Introduction to the electron theory of metals the electron theory of metals describes how electrons are responsible for the bonding of metals and subsequent physical, chemical and transport properties. Chapter 19 electrical properties university of tennessee. With no applied field, it can be seen that the electrons move around randomly. In an atom electrons revolue around the nucleus and a metal is composed of such atoms. Lecture 1 introduction to semiconductors and semiconductor. Show that it will have no collision during the next t seconds with the same probability. Elements can be more clearly classified as metals and non metals on the basis of their chemical properties. Handout 2 sommerfeld model for metals free fermion gas. But we know that electrons are quantum particles, speci. Semiconductor devices introduction to materials science for engineers, ch.
But elastic moduli are relatively insensitive to these effects. But then, this electric field is related to a charge current density. Drudes model 1900 is based on the kinetic theory of electrons in a metal which assumes that the material has motionless positive ions and a noninteracting electron gas. The potential field of these ion cores, which is responsible for such an interaction, is assumed to. It was constructed in order to explain the transport properties of conduction electrons in metals. The wellknown approximation of 1 is also tested for noble metals. Only at temperatures t f will the free electron gas behave like a classical gas. The authors accessible approach allows for comparisons with experimental results as much as possible. This model makes several key assumptions some of which are better approximations than others.
Chapter outline mechanical properties of metals how do. A more careful account of the drude model can be found in the first chapter of solid state physics by ashcroft and mermin. To do so we need to make some further simplifying assumptions 1. Drude model assumes that the mean electronic velocity at a point vanishes this cannot be rigorously justified. This textbook gives a complete account of electron theory in both periodic and nonperiodic metallic systems. This variability is related to the behavior of dislocations in the material, chapter 7. Fundamental relations for optical phenomena, drude theoryfree carrier contribution to the optical properties, interband transitions, the joint density of states and critical points, absorption of light in solids, optical properties of solids over a wide frequency range, impurities and excitons. Azad bachelor of science university of dhaka dhaka, bangladesh 1996 master of science oklahoma state university stillwater, ok usa 2003 submitted to the faculty of the graduate collage of oklahoma state university in partial fulfillment of the requirements for. The drude model of electrical conduction was proposed in 1900 by paul drude to explain the transport properties of electrons in materials especially metals. Chapter 5 the drude theory of metals delaware physics. Supporting information whats so hot about electrons in. In the models of noble metals, such as au and ag, the detailed dielectric function eq s1 is reduced to the simplified classical drude function for the longwavelength intervals, interband. Sommerfeld theory replaces f bv of drudes theory with fv profound consequences on and c v daniele to oli january 11, 2017 5 48. To do so we will use the drude theory of conductors.
Pines, elementary excitations in solids perseus, new york, 1999 an advanced level text on the quantum theory of solids, treating phonons. Drude theory of conductivity university of illinois. The drude and sommerfeld models of metals in other words, the collisions produce a frictional damping term. May 11, 2016 the completed drude 20 dna force field was shown to quantitatively reproduce the extent of charge neutralization by ions around dna, in accordance with counterion condensation cc theory. The drude model envisions a conductor as a gas of free currentcarrying charges. For metals, the electrons can jump from the valence orbits outermost core energy levels of the atom to any position within the crystal free to move throughout the crystal with no extra energy needed to be supplied for insulators, it is very difficult for the electrons to jump from the valence orbits and requires a huge. In these intervals, the interband transitions cannot be excited and the dielectric function has the form 2 p, drude metal, drude b, drude drude. In the present analysis, the drude region can be identified during the test for the fermi liquid behavior in noble metals. Averitt, ucsd the lycurgus cup the oldest known plasmonic device. The book starts with the basics of oneelectron band theory and progresses to cover high tc superconductors and quasicrystals. It is important to apply the drude model in the correct drude region. Drudelorentz theory drude, in 1900, postulated that the metals consist of positive ion cores with the valence electrons moving freely among these cores. The relationship between theory and potential applications is.
Drude treated the free electrons as a classical ideal gas but the electrons should collide with the stationary ions, not with each other. Notes on the drude model assumptions of the drude model the drude model provides a classical mechanics approach to describing conductivity in metals. Lecture notes on condensed matter physics a work in progress. The quantitative fit to experiment was improved by debyes recognition that there was a maximum number of modes of vibration in a solid. Some confusion in drude theory of metals physics stack exchange. F for selected metals we define the fermi temperature t f by e f k b t f. L z the electrons inside the box are confined in a threedimensional infinite.