Drude formulated a theory for conduction in metals using the electron concept. Due to the quantum mechanical nature of electrons, a full simulation of electron movement in a solid i. Handout 2 sommerfeld model for metals free fermion gas in this lecture you will learn. 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. Advanced electronic properties of materials classical drude theory of conduction contents. Neglecting the electronelectron interaction and the electronion interaction, it appears as if the electrons move in a confined box with periodic collision with ions in the lattice. Handout 2 sommerfeld model for metals free fermion gas. This document is highly rated by electronics and communication engineering ece students and has been viewed 1429 times. Lecture 2 drude theory of thermal conductivity the thermal. Sommerfeld theory replaces f bv of drude s theory with fv profound consequences on and c v daniele to oli january 11, 2017 5 48. Mar 29, 2018 drude theory of conduction basics of free electron theory and electrical conductivity part 1. The classical free electron theory ofmetals drude lorentz theory of metals lecture2postulates.
According to this theory, the metals containing the free electrons obey the laws of classical mechanics. This motion of electrons led to the formation of ohms law. 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. Atomic selectrons are delocalised due to overlap of outer orbits. This document is highly rated by civil engineering ce students and has been viewed 10632 times. Solid state, by providing a large and ready number of concrete prob. Im having trouble understanding the derivation of ohms law from the drude model. In drude model, when atoms of a metallic element are brought together to form a metal, the valence electrons from. This idea was given by drude and he utilized it to explain many properties of metals satisfactorily such as electrical conductivity, thermal conductivity etc. Paul drude constructed in 1900 a theory to explain the electrical and ther mal conductivity of metals. 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. The drude model can be visualised using the following simulation. Electrons in a metal behave much like particles in an ideal gas no coulombic interaction and no. I drude model derivation of freeelectron conductivity i scattering time estimates and matthiessens rule i mobility and hall coe cients i frequencydependent conductivity of freeelectron metals reading.
Drude theory of metals problems in solid state physics with. To visualize a plasma oscillation, imagine a cube of metal placed in an external electric field pointing to the right. Drude treated the free electrons as a classical ideal gas but the electrons should collide with the stationary ions, not with each other. The development of the quantummechanical electron theory of metals. Drude model conductivity frequency dependence plasma. We can then write the wave inside the solid for this onedimensional propagation problem as ex e0e ikzt 1. Carrier dynamics of electrons and holes in moderately doped silicon pdf. 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.
The assumptions of the drude lorentz classical theory of freeelectrons are the following. According to this theory, a metal consists of electrons which are free to move about in the crystal like molecules of a gas in a container. The current theory explains this with ad hoc manipulations like screening and positive charge carriers, but the correct answer is much simpler. The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals. In its more modern context, the drudelorentz model views a material as consisting of an array of the following. Drude theory of conduction basics of free electron theory. System upgrade on feb 12th during this period, ecommerce and registration of new users may not be available for up to 12 hours. Dependence on crystalline quality temperature alloying frequency.
Solid state physics part ii optical properties of solids. Sommerfeld theory of metals arnold sommerfeld 18681951 ece 407 spring 2009 farhan rana cornell university does not say anything about the electron energy distribution in metalsare all electrons moving around with about the same energy. Theory by paul drude in 1900, only three years after the electron was discovered. Classical derivation of ohms law and drude conductivity. Classical free electron theory of metals engineering. It features a 1hour lecture video, and also presents the prerequisites, learning objectives, reading assignment, lecture slides, homework with solutions, and resources for further study. 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. Conduction current in metals em wave propagation in metals skin depth plasma frequency. Then sommerfelds elementary quantum mechanical theory of metals is discussed. This idea will have many applications, even beyond the drude model. This page contains materials for the session on the band theory of solids.
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. Just 3 years after the discovery of the electron by. Drude was lucky he overestimated the electronic specific heat by 100 times electronic c v at room temperature is nowhere close to. The classical free electron theory drude and lorentz proposed this theory in 1900. Metalsdrudes classical theory theory by paul drude in 1900, only three years after the electron was discovered. He reasoned that since metals conduct electricity so well, they must contain free electrons that move through a lattice of positive ions. Ohms law derivation from drude model physics forums. The time between collisions with impurities is of order. Apr 16, 2020 classical free electron theory of metals engineering physics edurev notes is made by best teachers of civil engineering ce.
Handout 1 drude model for metals cornell university. The above relation is called wiedemannfranz law and is obeyed quite well by alkali metals over a narrow temperature range. The drude and sommerfeld models of metals in other words, the collisions produce a frictional damping term. Below is a schematic diagram of drudes model of metals. Drude theory of metals problems in solid state physics. 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. The development of the quantummechanical electron theory. Notes on the drude model assumptions of the drude model. We assume for the present discussion that the solid is thick enough so that reections from the back surface can be neglected. The treatment of a metal as containing a gas of electrons completely free to move within it. A geometrical interpretation of the electronic structure of metals by lifshits and kaganov. In this chapter we shall examine the theory of metallic conduction put forth by. Drude theory of conduction basics of free electron theory and electrical conductivity part 1. Classical free electron theory of metals this theory was developed by drude and lorentz and hence is also known as drude lorentz theory.
Thompson discovered the electrons metals valence assumption. In its more modern context, the drude lorentz model views a material as consisting of an array of the following. His approach is based upon quantization of electrical. Both assumed that the weakly bound conduction electrons could be modeled using the classical kinetic theory of gases. 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 contain free electrons that move through a lattice of positive ions. According to this theory the free electrons obey quantum laws. This is about the right order of magnitude for many monovalent metals, such as sodium. Motivation metals are excellent conductors of heat and electricity, are ductile and malleable physicists have tried to construct simple models of the metallic state that account the characteristic metallic properties theory of paul drude in 1900 came only a few years after j.
This paper continues an earlier study of the first phase of the development from 1926 to 1928 devoted to finding the general quantummechanical framework. Drude theory of conductivity university of illinois. Refractive part blue and absorptive part red of the susceptibility function. This model makes several key assumptions some of which are better approximations than others.
Drude in 1900 and developed by lorentz in 1909 to explain electrical conduction in selection from engineering physics book. 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 plasma by pulling the electrons back to their original positions. Plasma oscillations plasmons can be described in the classical picture as an oscillation of free electron density with respect to the fixed positive ions in a metal. In drudes model, electrons transport heat because the electrons thermalized. Conduction current in metals em wave propagation in metals. The drude model explains the electrodynamic properties of metals. Sommerfelds free electron theory of metals physics. Assuming electrons actually behave like a gas, drude attempted to calculate the conductivity of metal. Drude s theory of electron transport was published in the year 1900 1, and is obviously based on classical physics. Its extraordinary longevity owes to the fact that i for free electrons i. In 1928, by applying quantum mechanical principles, arnold sommerfeld succeeded in overcoming many of drawbacks of the classical free electron theory, while retaining all the essential features of the classical free electron theory. Metals and the drudelorentz model oxford scholarship. Semiconductors have resistivities intermediate between.
The drude theory of metals the model kinetic theory of gases. The quantum free electron theory somerfield developed this theory in 1928. The most important effect of putting q uantum mechanics into the theory of metals. I drude model derivation of freeelectron conductivity i scattering time estimates and matthiessens rule i mobility and hall coe cients i frequencydependent conductivity of freeelectron metals.
Below is a schematic diagram of drude s model of metals. Srit unit iii free electron theory engineering physics. The drude model provides a classical mechanics approach to describing conductivity in metals. The drude theory of metals the model free electron densities densityof the electron gas. In an atom electrons revolue around the nucleus and a metal is composed of such atoms. Notes on the drude model assumptions of the drude model the drude model provides a classical mechanics approach to describing conductivity in metals. Sommerfeld theory of metals arnold sommerfeld 18681951 ece 407 spring 2009 farhan rana cornell university does not say anything about the electron energy distribution in metals are all electrons moving around with about the same energy. 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. Drude model conductivity frequency dependence plasma waves difficulties of classical free electron model. Phases a phase is a homogeneous portion of a system with uniform physical and chemical characteristics, in principle separable from the rest of the system. To do so we need to make some further simplifying assumptions 1. Resistivity of metals 4 room temperature resistivity of single crystalline metals drude theory was successful to describe basic tendencies of metal conductivity. The drude model peter hertel overview model dielectric medium permittivity of metals electrical conductors faraday e ect hall e ect. A phase is a homogeneous portion of a system with uniform physical and chemical characteristics, in principle separable from the rest of the system.
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. This textbook gives a complete account of electron theory in both periodic and nonperiodic metallic systems. In other words, the drude model is right about thermal conductivity, but wrong about heat capacity. The development of the quantummechanical electron theory of. The drude model of electrical conduction was proposed in 1900 by paul drude to explain the transport properties of electrons in materials especially metals. Between two successive collisions of the conduction electron, its interaction both with other electrons and with ions is neglected. In the metal for a wave propagating in the z direction z ee kz ikz t e ikz t. Electrons in a metal behave much like particles in an ideal gas no coulombic interaction and no collisions between particles.1559 1569 834 1468 1258 52 599 1399 1009 952 838 717 425 1328 209 217 746 1177 348 463 33 547 647 992 832 1394 1484 1476 1322 264 90 126 89 739 891 1048 286 1440 1298 784