The high frequency electron scattering rate and drude. We begin this section by studying metals and then proceed to semiconductors and insulators. Metals, insulators, and semiconductors drude model for electrons in metals linear response functions of materials paul drude 18631906 ece 4070 spring 2010 farhan rana cornell university. Drude model electrons shown here in blue constantly bounce between heavier, stationary crystal ions shown in red. Alexander graham bell used the lightsensitive property of selenium to transmit sound over a beam of light in 1880. Diode theory what is a diode, or semiconductor for that matter. Quantum physics describes the states of electrons in an atom according to the fourfold scheme of quantum numbers. Nondrude optical conductivity of iii,mn v ferromagnetic. If a conductor is suppose to conduct current does that mean a semiconductor partially conducts current. The problems in this book can be used as homework assignments in an introductory or advanced course on solid state physics for undergraduate or graduate students. 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. With no applied field, it can be seen that the electrons move around randomly. Semiconductors, diodes, transistors horst wahl, quarknet presentation, june 2001 electrical conductivity.
Depending on the type of impurity added we have two types of semiconductors. In summary, the drude theory of the optical constants of iiiv and iivi polar semiconductors can be extended into the near infrared in terms of a frequencydependent electron scattering rate formulated to give the quantum result when used in the classical drude theory. This textbook gives a complete account of electron theory in both periodic and nonperiodic metallic systems. Conductivity is determined by electrons colliding with scatterers. For semiconductors, the electrons can jump from the valence orbits but does require a small amount of energy to free the electron from the atomic core. Handout 2 sommerfeld model for metals free fermion gas.
This page contains materials for the session on the band theory of solids. Conductivity and semiconductors 1 j current density ia e electric. We can then write the wave inside the solid for this onedimensional propagation problem as ex e0e ikzt 1. I drude model derivation of freeelectron conductivity i scattering time estimates and matthiessens rule i mobility and hall coe cients. Chapter 1 optical properties of plasmonic materials. Lorentz gave an improved mathematical formulation of drude theory without essentially adding anything to its physical content. Drudelorentz model of semiconductor optical plasmons. He derives the valence and conduction band structures for electrons in metals e. Classical derivation of ohms law and drude conductivity.
Drude model conductivity frequency dependence plasma waves difficulties of classical free electron model. Drude lorentz model of semiconductor optical plasmons. Cu, be using lcaomo, and then extends this approach. Classical free electron theory of metals this theory was developed by drude and lorentz and hence is also known as drudelorentz theory. The determination of the hall mobility of the charge carriers in the respective semiconductor. And i will show you why drudes theory became celebrated theory in its time and finally, what i will start doing is 4 topic we will talk about is which i said is a wrong theory. Electrical conductivity of semiconductors and insulators could not be explained. Metals, insulators, and semiconductors drude model for electrons in metals linear response functions of materials paul drude 18631906 ece 4070 spring 2010 farhan rana cornell university inorganic crystalline materials ionic solids mostly insulators. It can also serve as a desirable reference book to solve typical problems and grasp mathematical techniques in solid state physics. Drude model conductivity frequency dependence plasma.
According to this theory, the metals containing the free electrons obey the laws of classical mechanics. Introduction to the electron theory of metals uichiro mizutani department of crystalline materials science, nagoya university. Mar 15, 2020 as per theory of semiconductor, impure semiconductors are called extrinsic semiconductors. Semiconductors have resistivities intermediate between metals and insulators at room temperature. 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. In 100 million parts of semiconductor one part of impurity is added. Drude theory of conductivity conductor in electric field assuming electrons actually behave like a gas, drude attempted to calculate the conductivity of metal. Furthermore, the noble metals are described from the generally approved data in a. The quantum extension of the drudezener theory in polar. Lecture 1 introduction to semiconductors and semiconductor.
And talk about drudes theory which really we will see is a wrong theory that is, what. Based on the drude model we arrive at the equation of motion for electrons in an. Drude s theory was used in order to calculate the freecarrier concentration and the. In pure semiconductor number of electrons n is equal to number of holes p and thus conductivity is. Metalsdrudes classical theory theory by paul drude in 1900, only three years after the electron was discovered. Li ep, hung tgg 2011 implementation of the fdtd method based on the lorentzdrude model on gpu for plasmonics applications. Electrical conductivity for semiconductors and insulators are not explained. Drudes theory was used in order to calculate the freecarrier concentration and the. In some substances, a substantial gap remains between the highest band containing electrons the socalled valence band and the next band, which is empty the socalled conduction band. Since the conduction electrons are considered to be free. Solid state physics part ii optical properties of solids mit. At 0 o k, the vb is full with all the valence electrons intrinsic semiconductors.
In drude model, due to kinetic theory of collision, that abruptly alter the velocity of an electron. Handout 2 sommerfeld model for metals free fermion gas in this lecture you will learn. Were starting out with a discussion of intrinsic semiconductors. We assume for the present discussion that the solid is thick enough so that reections from the back surface can be neglected. Classification of semiconductors on the basis of fermi level and. More 10 discussed the connection between the drude formula and radiation theory in hot dense plasmas by emphasizing their quantummechanical aspects. Barrett, electromagneticvibrationswavesandradiation, mit. Srit unit iii free electron theory engineering physics. The drude model can be visualised using the following simulation.
The classical free electron theory drude and lorentz proposed this theory in 1900. 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. A diode is a device that acts like a conductor since it allows current to pass in one direction known as forward biasing and it. Drude treated the free electrons as a classical ideal gas but the electrons should collide with the stationary ions, not with each other.
In the above energy band diagrams of a semiconductor. The quantum free electron theory somerfield developed this theory in 1928. Intrinsic conduction in an intrinsic semiconductor. The distinction between a semiconductor and an insulator is artificial, but as the gap becomes large the material usually becomes a poor conductor of e lectricity. Drude to produce a very satisfactory theory of the electrical and thermal conductivities of metals in 1900. The optical properties are evaluated based on the permittivity and permeability defined by either the drude or lorentz model. Semiconductor theory part 1 intrinsic semiconductors. Solid state physics part ii optical properties of solids. The objective of this chapter is to explore the electrical properties of materials, i. Drude theory of conductivity university of illinois. Metal treated as a gas of mobile valence electrons moving against a background of immobile ions.
Semiconductors have typically higher, substantially lower n and 14. High frequency conductivity of the highmobility twodimensional electron gas pdf. To be verified important according to classical free electron theory. This is about the right order of magnitude for many monovalent metals, such as sodium.
The high frequency electron scattering rate and drude zener. Silicon, germanium, and gallium arsenide are primary materials used in semiconductor devices. This effect consists in the appearance of an electric field called hall field eh r. Silicon and germanium are elements and are intrinsic semiconductors. Band theory of solids chapter 2 solidstate device theory pdf version. Devices using semiconductors were at first constructed based on empirical knowledge, before semiconductor theory provided a guide to construction of more capable and reliable devices. A high frequency extension of the drude theory is thus obtained which gives the observed. 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.
Conductivity frequency dependence plasma waves difficulties of classical free electron model. Pdf drudelorentz model of semiconductor optical plasmons. The theory has been developed in three main stages. Derivation of the drude conductivity from quantum kinetic. Handout 1 drude model for metals in this lecture you will learn. Nano 701t01, solid state physics and chemistry, spring 2017 assignment 2 the drude theory of metal question 1 a. These principles are extended to metals, semiconductors and insulators. Conductivity of materials, drudes theory and its failures nptel. Conduction current in metals em wave propagation in metals skin depth plasma frequency. 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. Introduction to semiconductors and semiconductor devices a background equalization lecture reading. 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.
Unit iii free electron theory engineering physics dr. Handout 1 drude model for metals cornell university. In a semiconductor insulator there is an energy gap between the filled bands and the empty bands. Alan doolittle lecture 1 introduction to semiconductors and semiconductor devices a background equalization lecture reading. Semiconductors have a small nonoverlapping gap between the valence and conduction bands. Nondrude optical conductivity ofiii,mnv ferromagnetic semiconductors s. As per theory of semiconductor, semiconductor in its pure form is called as intrinsic semiconductor. Following drudes theory in context of drudes theory, then i will talk about dc conductivity of material. Pure semiconductors are neither good insulators nor conductors. Classical, semiclassical, and quantum treatments formula 1 can be obtained easily 1 through the classical equation of motion for a single. Extrinsic semiconductor is formed by adding a small amount of impurity. 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 model of electrical conduction was proposed in 1900 by paul drude to explain the. Furthermore, the noble metals are described from the generally approved data in a general handbook of solid.
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. Drude lorentz model of semiconductor optical plasmons article pdf available in lecture notes in electrical engineering 247. Ron ballinger gives todays lecture, explaining how the behavior of electrons in aggregate solids determines their electrical and thermal conductivities, optical absorption, and other physical properties. Advanced electronic properties of materials classical drude theory of conduction contents. Drude oscillator is an extension of the single lorentz oscil lator to a case where the. Theory references refer to the list of publications given in chapter 12 a. The model, which is an application of kinetic theory, assumes that.
The drude model of electrical conduction was proposed in 1900 by paul drude to explain the transport properties of electrons in materials especially 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 metalsare all electrons moving around with about the same energy. Page 3 mobility of electrons the mobility of electrons is defined as the magnitude of drift velocity acquired by the electron in a unit field. Theory the hall effect is a galvanomagnetic effect, which was observed for the first time by e. Assume a compound semiconductor has 25% atomic concentrations of ga, 25% atomic in and 50% atomic of n. Drudes theory was used in order to calculate the freecarrier concentration and the mobilities, and these results compared well with those obtained by halleffect measurements. Pdf theoretical solutions are obtained for the propagation of electromagnetic waves at optical frequencies along a semiconductordielectric.
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