17 Bandstructure 2 - Fundamentals of Fundamentals of...

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Unformatted text preview: Fundamentals of Fundamentals of Nanoelectronics Nanoelectronics Prof. Supriyo Datta ECE 453 Purdue University Network for Computational Nanotechnology 10.04.2004 Lecture 17: Bandstructure 2 Ref. Chapter 5.1 Review 00:03 • The principle of bandstructure helps us to find the eigenvalues of a periodic matrix. This is important for us because solids that we are interested in have periodic structures. Consider the example of last day: • Regardless of the details of the problem, the matrix that we write will be periodic. • Notice that as long as every row looks the same, the principle of bandstructure applies regardless of how each row looks. The nth row is: • This solution satisfies the Schrödinger equation if the E-k relationship below is met. • 2 in 1 Æ • As long as the above E-k relationship is met, the solution we chose will satisfy the Schrödinger equation. ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ N φ φ φ # 2 1 = ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ N E φ φ φ # 2 1 ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ % % % t t t t t ε ε ε 1 2 3 n-1 N " x 1s 1s (1) 1 1 + − + + = n n n n t t E φ εφ φ φ (2) φ φ inka n e = ka t E cos 2 + = ε ika ika te te E + + = − ε Review 05:30 • What we’ll learn today is a generalization of bandstructure method to a solid where the unit cell consists of two atoms.the unit cell consists of two atoms....
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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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17 Bandstructure 2 - Fundamentals of Fundamentals of...

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