ECE453Fall2010HW2[1]

# ECE453Fall2010HW2[1] - = 300 nm and compare with the...

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Fall 2010 ECE 453 HW #2 Due 9/10 HW # 2 Due Friday, September 10 This homework is based on Chapters 6, 7 of the notes. Equations σ = q 2 d dE - f 0 E -∞ + D ( E ) AL ν 2 ( E ) τ ( E ) N ( p ) = K N p h d where K N = 2 L , π WL , 4 3 AL for d = 1, 2, 3 { } dimensions D ( E ) = dN dE D ( E ) ( E ) p ( E ) = N ( E ) . d M ( p ) = 1, 2 W h / p , A h / p ( 29 2 2.1. Calculate the density of states, D(E) and the mode number, M(E) for a conductor with a parabolic dispersion (Eq.(6.2a)), in one-, two- and three dimensions. 2.2. Obtain the following expression for the conductivity (at low temperatures) = GL W = q 2 h λ L + L 4 sn s in terms of the electron density n s using the concepts discussed in this course. Here s is equal to the number of spins times the number of valleys = 2 x 2 = 4 for graphene. Plot versus n s , assuming L = 4 μm using (a) = 2 μm and with (b)
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Unformatted text preview: = 300 nm. and compare with the experimental data on graphene reported in field Phys. Rev. Lett. 101, 096802 (2008). Note that the values of the mean free path indicated in the paper are half those suggested for this problem. This is because our definition of mean free path differs from the standard one by the factor of 2/ K v d (see Eq.(4.5b)). (You need to hand in Matlab code and the plot generated from that code as well, along with the derivation of the expression). Take n s values ranging from 11 11 2 2 10 to2 10 cm-- × × Hint: Show that at low temperatures. n s = sk 2 4 , M = kW , G = s q 2 h M + L and then combine the results appropriately....
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