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ECE495N-F08-HW_6

# ECE495N-F08-HW_6 - ECE 495N Fall’08 ME118 MWF 1130A –...

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Unformatted text preview: 10/22/08 ECE 495N, Fall’08 ME118, MWF 1130A – 1220P HW#6: Due Wednesday Oct.29 in class. This homework requires the use of the following formulas for the density of states and the mode density (S, area; L, length; W, width): = D (E) ∑ δ ( E − ε (k )) k π vx ( k ) = ∑ δ ( E − ε (k )) M(E) L k 1 ∂ε ( vx ( k ) = ) ∂k x Assume that electrons are confined to a two-dimensional layer having an ε (k ) relation of the form = 2 ( k x 2 + k y 2 ) / 2m ε (k ) 1. Obtain an expression for the (a) density of states D(E) and (b) the mode density, M(E) in terms of the energy E, the area S and constants like m and . Assume that both L and W large enough that the summations over kx and ky can both be replaced with appropriate integrals. 2. How would you write the energies of the subbands if the electrons are confined to a narrow channel of width W in the y-direction? 3. Obtain an expression for the density of states D(E) and the mode density M(E), assuming that L is large enough that the summation over kx can be replaced with an appropriate integral, but W is NOT large enough to do the same for ky . ...
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