1ECE 4070 – Spring 2010 – Farhan Rana – Cornell UniversityECE 4070: Physics of Semiconductors and NanostructuresKMK’ECE 4070 – Spring 2010 – Farhan Rana – Cornell UniversityECE 4070: Physics of Semiconductors and NanostructuresInstructor: Farhan RanaOffice: PH316Email: [email protected]: The course covers fundamentals of solid state physics relevant to semiconductors, electronic and photonic devices, and nanostructures.Crystal lattices and the reciprocal lattice; Electron states and energy bands in molecules and solids; Metals, insulators, and semiconductors; Graphene, 2D atomic materials, and carbon nanotubes;Lattice dynamics and phonons in 1D, 2D, and 3D materials; Electron statistics and dynamics in energy bands; Effective mass theorem; Electron transport and Boltzmann equation; Optical transitions and optical interband and intraband processes;Optical loss, optical gain, and Kramers-Kronig relations;Excitons and polaritons; Semiconductor heterostructures; Electron states in zero, one, and two dimensional nanostructures; Quantum wells, wires, and dots; Quantum transport in nanostructures and ballistic transport;2ECE 4070 – Spring 2010 – Farhan Rana – Cornell UniversityCourse Website and Homeworks• All course documents, including:- Lecture notes- Homeworks and solutions- Exam solutions- Extra course related materialwill appear on the course website:http://courses.cit.cornell.edu/ece407/Homeworks• Homeworks will be due on Tuesdays at 5:00 PM• New homeworks and old homework solutions will appear on the course website by Tuesday night• Homework 1 will be due next Tuesday and will be available on the course website by tomorrow nightECE 4070 – Spring 2010 – Farhan Rana – Cornell UniversityCourse Grading and Textbooks• Course grading will be done as follows:- Homeworks (25%)- 2 Evening Prelims (20% each) – dates TBD- Final exam (35%) – date TBD• No in-class quizzes, no pop-quizzes• Final exam will be comprehensiveTextbooks• There are no required textbooks. Highly recommended textbooks are:- Introduction to Solid State Physics, by Charles Kittel (8thedition)- Electronic and Optoelectronic Properties of Semiconductor Structures, by Jasprit Singh- Solid State Physics, by Ashcroft and Mermin3ECE 4070 – Spring 2010 – Farhan Rana – Cornell UniversityHandout 1Drude Model for MetalsIn this lecture you will learn:• Metals, insulators, and semiconductors• Drude model for electrons in metals• Linear response functions of materialsPaul Drude (1863-1906)ECE 4070 – Spring 2010 – Farhan Rana – Cornell UniversityInorganic Crystalline MaterialsIonic solidsMostly insulators Example: NaCl, KClCovalent solidsSemiconductorsSi, C, GaAs, InP, GaNPbSe, CdTe, ZnO InsulatorsSiO2, Si3N4MetalsAu, Ag, Al, Ga, InMetals1- Metals are usually very conductive2- Metals have a large number of “free electrons” that can move in response to an applied electric field and contribute to electrical current3- Metals have a shiny reflective surface4ECE 4070 – Spring 2010 – Farhan Rana – Cornell UniversityProperties of Metals: Drude ModelBefore ~1900 it was known that most conductive materials obeyed Ohm’s law (i.e. I =V/R).In 1897 J. J. Thompson discovers the electron as the smallest charge carrying constituent of matter with a charge equal to “-e” C106.119eIn 1900 P. Drude formulated a theory for conduction in metals using the electron concept. The theory assumed:1) Metals have a large density of “free electrons” that can move about freely from atom to atom (“sea of electrons”)2) The electrons move according to Newton’s laws until they scatter from ions, defects, etc. 3) After a scattering event the momentum of the electron is completely random (i.e. has no relation to its momentum before scattering)+ + + ++ + + ++ + + +ionssea of electrons+ ++ +electron pathECE 4070 – Spring 2010 – Farhan Rana – Cornell UniversityDrude Model - I+ ++ +electron pathApplied Electric Field:In the presence of an applied external electric field the electron motion, on average, can be described as follows: ELet be the scattering time and 1/be the scattering ratetpThis means that the probability of scattering in small time interval time dt is: The probability of not scattering in time dt is then:dtdt1Let be the average electron momentum at time t , then we have:  01dtdttEetpdtdttpIf no scattering happens then Newton’s lawIf scattering happens then average momentum after scattering is zerotptEedttpd5ECE 4070 – Spring 2010 – Farhan Rana – Cornell UniversityDrude Model - IICase I: No Electric Field tpdttpdSteady state solution:0tpElectron pathCase II: Constant Uniform Electric Field Steady state solution is:EetpEElectron pathElectron “drift” velocity is defined as:EEmemtpv= e/m = electron mobility (units: cm2/V-sec)EEenvenJElectron current density (units: Amps/cm2) is:JWhere:mnenen23 )Siemens/cm :(units tyconductivi electron)/cm# :(units density electronECE 4070 – Spring 2010 – Farhan Rana – Cornell UniversityDrude Model - IIItptEedttpdCase III: Time Dependent Sinusoidal Electric FieldThere is no steady state solution in this case. Assume the E-field, average momentum, and currents are all sinusoidal with phasors given as follows:  tieEtERe  tieptpRe  tieJtJRe   EimempvEieppEepitptEedttpd11Electron current density:   EvenJiimne1012Where:Drude’s famous result !!6ECE 4070 – Spring 2010 – Farhan Rana – Cornell UniversityLinear Response Functions - IThe relationship:EJis an example of a relationship between an applied stimulus (the electric field