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Unformatted text preview: 11/20/06 ECE 495W, Fall’06 MSEE 13010,er 330P —— 420P Fundamentals of N anoelectronics All exercises, section numbers and page numbers refer to S.Datta, Quantum Transport: Atom to Transistor, Cambridge (2005)
HW#8: Due Friday Dec.1 in class. Please turn in a copy of your MATLAB code for Problem 1.
You can use the MAT LAB codes at the end of the text as a guide, but the codes you turn in should be your own work, not copied from the text. Please study the examples in Section 9.5, page 240. Problem 2: Consider an infinite wire modeled as a discrete lattice with points spaced by ‘ , a having a Hamiltonian with H n,” = 2t0 and H WM =— t0 = Hn,n_1 (all other elements are zero), such that the dispersion relation is given by E = 2t0 (1— cos ka). What is the local density of states at the point “0”, D(O,E) ? Problem 3: Suppose we cut the wire in Problem 2 into two separate semiinﬁnite wires as shown so
that H01 = H10 = 0 (other elements of the H—matrix remain unchanged). cut What is the local density of states at the point “0”, D(O,E) ? £
4‘ 2/1 74:0]; H ’ [we] ) 5.1 3 [#606 a] _ who *i
g : [wa'fed J Problem 4: Consider the wire in Problem 3 channel source The transmission WE) for this wire is obviously zero since electrons cannot go from left to right.
But suppose we Wish to get this result formally by evaluating the expression Trace [I‘IGI‘ZG+] 2: 0
We treat points “0” and “1” as the channel described by the Hamiltonian [H] = [O 0% J
0 and the rest as the source and drain contacts described through (2x2) self—energy matrices. (a) What are 21 and 22? (b) What are 1‘1 and F2? (c) What is [G]? (d) Show that Trace [I‘IGI‘ZG+] = 0. 21: *WW' 0 22"[0 0 mil ...
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 Fall '06
 SupriyoDatta
 Fundamental physics concepts, Wire, Phonon, local density, MAT LAB codes, separate semiinﬁnite wires

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