ECE495N-F08-Exam_1

# ECE495N-F08-Exam_1 - ECE 495N EXAM I CLOSED BOOK Wednesday,...

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Unformatted text preview: ECE 495N EXAM I CLOSED BOOK Wednesday, Oct.1, 2008 NAME : PUID # : Please show all work and write your answers clearly. This exam should have seven pages. Problem 1 [11. 2, 3] 8 points Problem 2 [p. 4, 5] 8 points Problem 3 [11. 6, 7] 9 points Total 25 points Problem 1: We have seen in class that the current-voltage (I-V) characteristics of a nanoscale device can be calculated from 2g rlrz 1=— dEDE—U — E— h l ( )y1+y2[f1( ) f2(E)] 1 1 where W and = 8(E—nzﬂkT +1 AlsoU : UL + U0(N —No). Assume U0 = 0 and the Laplace potential UL to be a fraction 0: of the drain potential VD (the source potential is assumed zero): U L = — q OEVD, a being a constant between 0 and 1. A channel has a density of states as shown, namely a constant non- zero value for E2 EC and zero for E< EC. Assume that the equilibrium electrochemical potential a is located above EC. as shown. Sketch the current versus drain voltage assuming that the electrostatic potential of the [J channel (a) remains fixed with respect to the source (a = O) and (b) assumes a value halfway between the source and drain potentials (a = 0.5), Expkxin year reasoning clearly. (a) Channel potential ﬁxed with respect to source: (I = 0. I (13) Channel potential halfway between source and drain: a = 0.5 Problem 2: We have seen in class that free electrons in the abSence of any external potential are described by (in one dimension) 2 2 3! 2m 3x2 whose solutions can be written in the form wag) = Q g “b 3 45m (2) man: with E and it related by the dispersion relation: E = 52kg am (3) We have also seen that if the electrons are conﬁned in a box of length L, the energy levels become discrete with the lowest energy given by E1 = T127: 2 I 2mL2 (4) (a) Can you suggest a suitable differential equation to replace (1) if you wanted the dispersion relation to look like E = Ak‘ (3’) (A being a constant) instead of (3) ? (b) If a system of electrons with a dispersion relation given by (3’) were confined in a box of length L, how would the expression for the lowest energy given in (4) be modified? Problem 3: M1 A box has four degenerate energy levels all having energy s. We know that for nor:- interacting electrons the maximum current under bias is Use the multielectl‘on picture to derive the correct expression for the maximum current if the electron-electron interaction energyr is so high that no more than one electron can be inside the box at the same time. ...
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## ECE495N-F08-Exam_1 - ECE 495N EXAM I CLOSED BOOK Wednesday,...

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