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Handout 3 Free Electron Gas in 2D and 1D

1 ECE 407 Spring 2009 Farhan Rana Cornell UniversityHandout 3 Free Electron Gas in 2D and 1 DIn this lecture you will learn: Free Electron gas in two dimensions and in one dimension Density of States in k-space and in energy in lower dimensionsECE 407 Spring 2009 Farhan Rana Cornell UniversityElectron Gases in 2D In several physical systems Electron are confined to move in just 2 dimensions Examples, discussed in detail later in the course, are shown below:Semiconductor quantum Wells:GaAsGaAsInGaAs quantum well (1-10 nm)Graphene:Semiconductor quantum wells can be composed of pretty much any semiconductor from the groups II, III, IV, V, and VI of the periodic tableGraphene is a single atomic layer of carbon atoms arranged in a honeycomb lattice TEM micrographSTM micrograph2 ECE 407 Spring 2009 Farhan Rana Cornell UniversityElectron Gases in 1D In several physical systems Electron are confined to move in just 1 dimension Examples, discussed in detail later in the course, are shown below:Semiconductor quantum Wires (or Nanowires):GaAsInGaAsNanowireGaAsSemicon ductor quantum Point Contacts (Electrostatic Gating):GaAsInGaAsQuantum wellCarbon Nanotubes (Rolled Graphene Sheets):metalmetalECE 407 Spring 2009 Farhan Rana Cornell UniversityElectrons in 2D Metals: The Free Electron ModelThe quantum state of an Electron is described by the time-independent Schrodinger equation: rErrVrm 222 Consider

Electron Gases in 2D • In several physical systems electron are confined to move in just 2 dimensions • Examples, discussed in detail later in the course, are shown below: Semiconductor Quantum Wells: GaAs GaAs InGaAs quantum well (1-10 nm) Graphene: Semiconductor quantum wells can be composed of pretty much any semiconductor from the

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