ECE 453 Assignment 1 Solutions_1[1]

ECE 453 Assignment 1 Solutions_1[1] - ECE 453 Assignment 1...

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ECE 453 Assignment 1 Solutions 1.1 a) Substituting values from attached notes: ( 29 2 2 1.6 19 38.6 6.63 34 e q S h e μ - = = - 1 25.9 38.6 k S μ = 1.1 b) 2 2 2 s s s W q M h L L q M W h W h M q σ λ λ λ λ σ σ λ = + = = Substituting values from part (a) and from question: 0.1 6 25.9 3 1.6 3 41.44 ~ 41 100 9 e m M e e S e m - = Ω× - × = -
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1.2 2 2 cos cos 2 2 cos 2 2 z v d v d v d v d v π π π π π π π π θ θ θ θ θ π θ θ π π - - - - = = = = 2 2 2 2 2 2 2 cos cos 2 1 cos2 2 2 2 z v d v d v d v d v π π π π π π π π θ θ θ θ θ π θ θ π - - - - = = + = =
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1.3 In this problem we have to find expressions for , F F - ɶ ɶ from given differential equation and boundary conditions ( 29 0 a constant, say = A d d F F dz dz d F F dz F F + - + - + - = - = - = ɶ ɶ ɶ ɶ ɶ ɶ Therefore, d d A F F dz dz λ + - = = - ɶ ɶ …(1) Thus, , F F - ɶ ɶ are linear. Now we need to apply the boundary conditions to find out A. Using equation 5.3 from the Notes (Lessons from nanoelectronics):
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