The theory has been developed in three main stages. During the establishment processes of the electromagnetic wave theory. Drude theory of conductivity conductor in electric field assuming electrons actually behave like a gas, drude attempted to calculate the conductivity of metal. Thompson discovers the electron as the smallest charge carrying constituent of matter with a charge equal to e e 1. Carrier dynamics of electrons and holes in moderately doped silicon pdf. The drude theory of metals and the hall e ect by michele laino july 12, 2015 abstract in this brief tutorial i show the basic assumption of the drude model of conduction in metals, actually this tutorial represents a simpli ed version of the real drude model, since some properties, and.
Apply the classical kinetic theory of gases to the conduction electrons. Drude constructed his theory of electrical and thermal conduction in metals by 1. Conduction current in metalsconduction current in metals 00 0 00 0. Charge neutrality of the system at equilibrium is guaranteed by the presence of an assumed uniform positive charge background from ion cores that. Uses pauli principle to distribute them in the available energy states. For future reference, we note that the typical length scale in metals is a. This simple model uses classical mechanical theory of free electron. These may be thought to have become delocalized when the valence levels of the atom came i. Before discussing the results of the drude model, we examine how the scattering rate can be included in the equations of motion of the electrons. Metals drudes classical theory theory by paul drude in 1900, only three years after the electron was discovered. Lecture 8 lossy media, lorentz force law, drudelorentz.
With no applied field, it can be seen that the electrons move around randomly. 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. Pdf overview of drudelorentz type models and their applications. The typical density of electrons in 1610 m 3or 1022cm. In drudes model, electrons transport heat because the electrons thermalized at the.
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. Understanding of physics on electrical conductivity in. The current theory explains this with ad hoc manipulations like screening and positive charge carriers, but the correct answer is much simpler. Drude optical properties of metals 8 plasma frequency 1 to improve accuracy of drude model, effective number of free electron is usually introduced damping frequency damping frequency scattering time generally correlates with conductivity but not accurately 12 2 0 p 2 qn m z sq h. Chapter 5 the drude theory of metals delaware physics.
Classical model of a superconductor september 20, 2005 massachusetts institute of technology 6. The modern electromagnetic wave theory has been developed from the group work in theory by james clerk maxwell, oliver heaviside, and josiah willard gibbs from 1861 to 1865, and verified experimentally by heinrich hertz in 1887. Why metals have some finite resisitivty and how it depends on temperature. Drude treated the free electrons as a classical ideal gas but the. In the macroscopic maxwells equations, the total electric charge density r is factorized into a bound component rb and a free counterpart rf, just as the total current density j is separated into a free component jf and a bound component jb. Extension of the drude model an extension of the drude model is proposed that accounts for the spin and spinorbit interaction of charge carriers. The dispersion energy an introduction and some surprises. This is due to overestimation of by about a factor of 100 as we shall when we study the sommerfeld model. Due to the simple nature of the hamiltonian, the drude oscillator model is a good start for learning the standard electronic structure methodsi, and it is for this reason that i began my ph. While providing an explanation of ohms law and joule heating, drude theory leaves open the question of why there is such a large difference in conductivity between.
The current script will give you all the information you need for following this introductory course. Handout 2 sommerfeld model for metals free fermion gas. Jun 08, 20 the success of drude s model, why is the heat capacity of metals so low. Applications of the quantum drude oscillator model for. Introduction to condensed matter phy 251phy 420 prof. The drude model considers the metal to be formed of a mass of positively charged ions from which a number of free electrons were detached. Also sometimes the measured value of q is positive drude model has no answer to this. Drude formulated a theory for conduction in metals using the. Lecture 2 drude theory of thermal conductivity the thermal. Metal as gas of electrons drude constructed his theory of electrical and thermal conduction by applying the kinetic theory of gases to a metal. This is about the right order of magnitude for many monovalent metals, such as sodium. You may notice the very high electron density found in metals, which is about. Sommerfeld theory of metals arnold sommerfeld 18681951 ece 407 spring 2009 farhan rana cornell university. The values of rs also vary between those of these two metals, from 5.
Theoretical model drude s 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. In 1905, einstein interpreted the photoelectric effect in 1911 rutherford proved that atoms are composed of a pointlike positively charged, massive nucleus surrounded by a sea of electrons. Recognizes that their energies are discrete treats them like a particle in a box of constant energy. The drude theory of metals and the hall e ect by michele laino july 12, 2015 abstract in this brief tutorial i show the basic assumption of the drude model of conduction in metals, actually this tutorial represents a simpli ed version of the real drude model, since some properties, and consequences, have been omitted. In the classical drude model, the optical conductivity has a maximum at zero frequency. For a typical metal, p is 100 or even times larger. Drude model assumptions ions are arranged in fixed positions and cannot move collisions between es and ions are instantaneous, uncorrelated events ignore all other interactions independent electron approximation free electron approximation electron experiences a collision with a probability per unit time 1 is the mean time between collisions. Superelectron model of perfect conductivity first london equation perfect conductor vs perfect conducting regime 3. Understanding of physics on electrical conductivity in metals.
It explains the electrical, thermal and magnetic properties of solids etc. Basic assumptions of the model the drude theory of metals the model kinetic theory of gases. Lorenz model harmonic oscillator model without restoration force that is, free electrons which are not bound to a particular nucleus linear dielectric response of matter. The drude model links optical and electric properties of a material with the behavior of its electrons or holes the model dielectric permittivity permittivity of metals conductivity faraday e ect hall e ect. Please consult the book if you want to delve deeper into the subject. The classical drude model and how it attempts to explain conductivity and the hall effect form the starting point. Drude s theory was used in order to calculate the freecarrier concentration and the mobilities, and these results compared well with those obtained by halleffect measurements. Drude model, valence electrons in metals delocalise and scatter o defects. Bridging the hydrodynamic drude model and local transformation optics theory rub en a. Observed values of q are vk about 100 times too small. Pdf drudelorentz model of semiconductor optical plasmons.
Basic assumptions of the drude model understanding of basic metallic. This is usually just known as the drude model or the. If we treat the collisions using the drude approximation assuming that the collisions are described by a single parameter. Drude sommerfeld model drude model assumes boltzmann distribution noninteracting electrons although nearly independent and free on average, electrons are much closer to each other than molecules in ideal gas. Chapter 1 optical properties of plasmonic materials. The classical free electron theory drude and lorentz proposed this theory in 1900. Recall from drude theory, that 1014 sec, so 1 1014 hz.
The drude model of electrical conduction was proposed in 1900 by paul drude to explain the transport properties of electrons in materials especially metals. Department of chemistry uci department of chemistry. Drude theory in the calculations above, we didnt consider the electron collisions. Srit unit iii free electron theory applied physics. Classical theory drude model drude model, 1900ad, after thompsons discovery of electrons in 1897 based on the concept of kinetic theory of neutral dilute ideal gas apply to the dense electrons in metals by the free electron gas picture success. I drude model derivation of freeelectron conductivity i scattering time estimates and matthiessens rule i mobility and hall coe cients i frequencydependent conductivity.
Drude model before 1900 it was known that most conductive materials obeyed ohms law i. To do so we need to make some further simplifying assumptions 1. Basic assumptions of the model drude based his model of metallic conductivity on applying the kinetic theory of gases to a metal which he regarded as a gas of electrons. Electrons move freely inside the metal, except for collisions with ions. Handout 1 drude model for metals cornell university. In its simplest form kinetic theory treats the molecules of a gas as identical solid spheres moving in straight lines until they collide with one another. Drude dispersion model drude s 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. 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. Sommerfeld model for metals free fermion gas in this lecture you will learn.
The drude model peter hertel overview model dielectric medium permittivity of metals electrical conductors. Drude model conductivity frequency dependence plasma. This model makes several key assumptions some of which are better approximations than others. The model, which is an application of kinetic theory, assumes that the. In other words, the drude model is right about thermal conductivity, but wrong about heat capacity.
The drude model peter hertel overview model dielectric medium permittivity of metals electrical conductors faraday e ect hall e ect paul drude, german physicist, 18631906. Notes on the drude model assumptions of the drude model the drude model provides a classical mechanics approach to describing conductivity in metals. Drude treated the free electrons as a classical ideal gas but the electrons should collide with the stationary ions, not with each other. The drude model of a metal considers a sea of mobile electrons that have equilibrium average charge density. Retains almost all aspects of drude model with the following modifications. The extended drude model edm 3 is widely used and successfully applied to high tc superconductors to reveal nonfermi liquid behaviors 6. Electrical conductivity in the absence of collisions, the average momentum of free electrons.
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