19 Bandstructure - Fundamentals of Nanoelectronics...

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Fundamentals of Fundamentals of Nanoelectronics Nanoelectronics Prof. Supriyo Datta ECE 453 Purdue University Network for Computational Nanotechnology 10.08.2004 Lecture 19: Bandstructure Ref. Chapter 5.1 & 5.2
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Review 00:05 • The bandstructure principle helps us to understand the energy levels of large solids and serves as a background to understand the energy levels of nanostructures. For electrical conduction we need to understand the energy levels and we need to know where the Fermi level lies because the energy levels around the Fermi level determine the I-V characteristics. • We always start from Schrödinger equation: • As long as there is spherical symmetry for the potential we can reduce this equation to three 1D equations. Solving each equation numerically then involves turning the equation to a matrix equation. To so we first set up a lattice of points. • By doing this we have discretized the quantities we are dealing with. For example the wavefunction will have a value at each lattice point. • Notice that without the spherical symmetry the problem is not separable; hence we have to deal with the 3D equation which easily gets out of hand. • To solve the problem we turn into another method, namely the idea of basis functions. ) ( ) ( 2 ) ( 2 2 r r U m r E G G = G Ψ + = Ψ x 1 2 3 n-1 n n+1 N a n Ψ = Ψ m m m r u r ) ( ) ( G G ψ
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This note was uploaded on 01/12/2011 for the course ME 305 taught by Professor Wright,j during the Spring '10 term at Birla Institute of Technology & Science, Pilani - Hyderabad.

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19 Bandstructure - Fundamentals of Nanoelectronics...

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