ece495nf07hw5(to be print)

ece495nf07hw5(to be print) - φ n = e ik na to find the...

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10/12/07 ECE 495N, Fall’07 MSEE B010, MWF 330P – 420P Fundamentals of Nanoelectronics HW#5: Due Friday Oct.19 in class. All exercises, page numbers refer to S.Datta, Quantum Transport: Atom to Transistor, Cambridge (2005) HW#5: Due Friday Oct.19 in class. None of these problems require the use of MATLAB. Problem 1: Exercise E.5.4, Page 128. Problem 2: Consider an infinitely long linear 1-D lattice (lattice constant: a) with one s- orbital per atom (assumed orthogonal) and having a site energy of E 0 , so that the Hamiltonian looks like H = ε te i ϕ 0 0 te - i te i 0 0 te - i te i ⋯ ⋯ ⋯ Impose periodic boundary conditions and assume a solution of the form
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Unformatted text preview: φ n = e ik na to find the dispersion relation E(k). Problem 3: The E(k x ,k y ) relation for a two-dimensional solid is written in the form E = E-2V (cosk x a + cosk y a + 2 α cosk x a cos k y a) where α is a dimensionless number. How would you choose the nearest neighbor and next nearest neighbor overlap matrix elements in a square lattice of side 'a' so as to correspond to this dispersion relation ? 10/12/07 - t- t ' Nearest neighbor overlap : - t Next nearest neighbor overlap : - t'...
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ece495nf07hw5(to be print) - φ n = e ik na to find the...

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