Lecture 2 drude theory of thermal conductivity the thermal. The model, which is an application of kinetic theory, assumes that. The drude model of electrical conduction was proposed in 1900 1 2 by paul drude to explain the transport properties of electrons in materials especially metals. The electrons are, however, bound to move within the metal due to electrostatic attraction between the positive ion cores and the electrons. The time between collisions with impurities is of order.
Drude model conductivity frequency dependence plasma. 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. A drude model approach to dispersion interactions in dipolebound anions by feng wang bs, peking university, beijing, 1998 submitted to the graduate faculty of arts and sciences in partial fulfillment of the requirements for the degree of doctor of philosophy university of pittsburgh april 2003. Between two successive collisions of the conduction electron, its interaction both with other electrons and with ions is neglected. Below is a schematic diagram of drudes model of metals. A procedure to determine the electrostatic parameters has been developed for a polarizable empirical force field based on the classical drude oscillator model.
Drude formulated a theory for conduction in metals using the. Thompson discovers the electron as the smallest charge carrying constituent of matter with a charge equal to e e 1. Pdf overview of drudelorentz type models and their applications. Carrier dynamics of electrons and holes in moderately doped silicon pdf. The model is optimized with an emphasis on condensedphase properties and is validated against a variety of experimental data. Drude model of electrical conduction march 29, 2015 december 29, 2010 by mini physics drude model is a model in which the free electrons in a metal are treated like a classical ideal gas with a maxwellboltzmann distribution of kinetic energies, with an average thermal energy 32kt. Advanced electronic properties of materials classical drude theory of conduction contents. The values of rs also vary between those of these two metals, from 5. Schematic of the electronic potential assumed in the drude and sommerfeld models of metals a. If the electrons in a plasma are displaced from a uniform background of ions, electric fields will be built up in such a direction as to restore the neutrality of the. L z the electrons inside the box are confined in a threedimensional infinite.
Theory by paul drude in 1900, only three years after the electron. Pdf drudelorentz model of semiconductor optical plasmons. Conduction current in metalsconduction current in metals 2 2. The current theory explains this with ad hoc manipulations like screening and positive charge carriers, but the correct answer is much simpler. 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 problem statement. Handout 1 drude model for metals cornell university.
This simple model uses classical mechanical theory of. Assumptions the drude model considers the metal to be formed of a mass of positivelycharged ions from. 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. Srit unit iii free electron theory applied physics. Transferability of the developed parameters is emphasized by the use of a single electrostatic model for the hydroxyl group. We assume for the present discussion that the solid is thick enough so that. The conduction electrons are modeled as a gas of particles with no coulomb repulsion screening 2. Between two successive collisions of the conduction electron, its interaction both. Many measurements of the optical properties of solids involve the normal incidence reectivity which is illustrated in fig. Drude theory of conductivity conductor in electric field assuming electrons actually behave like a gas, drude attempted to calculate the conductivity of metal. Theoretical model 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. Drude model before 1900 it was known that most conductive materials obeyed ohms law i. Electrical conductivity in the absence of collisions, the average momentum of free electrons. Notes on the drude model assumptions of the drude model the drude model provides a classical mechanics approach to describing conductivity in metals.
At room temperature, by using the kinetic theory of gases to estimate the drift velocity, the drude model gives. A polarizable empirical force field based on the classical drude oscillator has been developed for the aliphatic alcohol series. We assume for the present discussion that the solid is thick enough so that reections from the back surface can be neglected. Drudes theory treated the electrons as an ordinary classical gas. The drude model provides a classical mechanics approach to describing conductivity in metals. Drudelorentz model of semiconductor optical plasmons article pdf available in lecture notes in electrical engineering 247. Drude theory in the calculations above, we didnt consider the electron collisions. The drude model explains the electrodynamic properties of metals. Atomic charges and polarizabilities for a given molecule of interest were derived from restrained fitting to quantummechanical electrostatic potentials esp calculated at the b3lyp ccpvdz or b3lypaugcc. Based on the drude model we arrive at the equation of motion for electrons in an. Independent electron approximation the response to applied fields is calculated for each electron separately.
Generalized drude model and electromagnetic screening in. The quantum free electron theory somerfield developed this theory in 1928. 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. Theoretical model the lorentz classical theory 1878 is based on the classical theory of interaction between light and matter and is used to describe frequency dependent polarization due to bound charge. There are occasional hints at the rst and the fourth, leaving the others largely untouched. This is about the right order of magnitude for many monovalent metals, such as sodium. Metals drudes classical theory theory by paul drude in 1900, only three years after the electron was discovered. Basic assumptions of the model the drude theory of metals the model kinetic theory of gases. 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. Note that the technical notes classical dispersion model and drude dispersion model are complementary to this one. With no applied field, it can be seen that the electrons move around randomly. Drude theory of metals 1 four assumptions in the drude theory i a given conduction electron in a metal interacts with an ion only when it makes a collision with the ion.
Drude constructed his theory of electrical and thermal conduction in metals by 1 considering the electrons to be a gas of negatively charged particles traversing in a medium of uniformly distributed positive ions, and 2 applying the kinetic theory of gas to the electron sea. According to this theory, the metals containing the free electrons obey the laws of classical mechanics. The drudesmith model has been used extensively in fitting the thz conductivities of nanomaterials with carrier confinement on the mesoscopic scale. Drude theory of conductivity university of illinois. 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 model, which is an application of kinetic theory, assumes that the. Drude attributed them to the electrons bouncing off the. We argue that it can be used to study both metals and superconductors for superfluid electrons although the underlying physics 16 cannot be explained in our phenomenological model effectively. Polarizable empirical force field for the primary and. This is due to overestimation of by about a factor of 100 as we shall when we study the sommerfeld model. The classical free electron theory drude and lorentz proposed this theory in 1900. Electrons in a metal behave much like particles in an ideal gas no coulombic interaction and no. Notes on the drude model assumptions of the drude model.
Also sometimes the measured value of q is positive drude model has no answer to this. In such a picture, the ionic cores merely maintain. You may notice the very high electron density found in metals, which is about. Chapter 5 the drude theory of metals delaware physics. This simple model uses classical mechanical theory of free electron. Doitpoms tlp library introduction to thermal and electrical. Im having trouble understanding the derivation of ohms law from the drude model. The drude smith model has been used extensively in fitting the thz conductivities of nanomaterials with carrier confinement on the mesoscopic scale. To do so we need to make some further simplifying assumptions 1. The drude model can be visualised using the following simulation. Note that the technical notes classical dispersion model. The classical theory of electrons in metals is used to describe the basics of metallic behavior. Averitt, ucsd the lycurgus cup the oldest known plasmonic device.
The free electron model the quantum state of an electron is described by the timeindependent schrodinger equation. 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. Ohms law derivation from drude model physics forums. Handout 2 sommerfeld model for metals free fermion gas in this lecture you will learn. If we treat the collisions using the drude approximation assuming that the collisions are described by a single parameter. The drude model peter hertel overview model dielectric medium permittivity of metals electrical conductors. Drude model electrons shown here in blue constantly bounce between heavier, stationary crystal ions shown in red. 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. The model, which is an application of kinetic theory, assumes that the microscopic behavior of electrons in a solid may be treated classically and looks much like a pinball machine, with a sea of constantly jittering.
Superelectron model of perfect conductivity first london equation perfect conductor vs perfect conducting regime 3. Lorentz 18531928 hendrik antoon lorentz was a dutch physicist in the late 19. Drudelorentz theory drude, in 1900, postulated that the metals consist of positive ion cores with the valence electrons moving freely among these cores. The theory has been developed in three main stages. 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. In other words, the drude model is right about thermal conductivity, but wrong about heat capacity.
The potential field of these ion cores, which is responsible for such an interaction, is. Coliisons in the drude model are instantaneous events that abruptly alter the velocity of an electron. In drudes model, electrons transport heat because the electrons thermalized at the. This model makes several key assumptions some of which are better approximations than others.
Classical model of a superconductor september 20, 2005 massachusetts institute of technology 6. L z the electrons inside the box are confined in a. Equation is the constitutive equation and can be viewed as a generalization of the conventional drude model with and. Drude model, the ratio of the thermal to the electrical conductivity does. Jun 06, 2008 im having trouble understanding the derivation of ohms law from the drude model. These include their electrical conductivity, heat conductivity, reflection. The smallscale details of the potential due to the ionic cores shown schematically in b are replaced by an average potential v 0.
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