EE606_s09_hw3

EE606_s09_hw3 - %PDF-1.2% 15 0 obj< /Linearized 1 /O 17...

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1 EE606: Solid State Devices Homework 3: Energy Band Theory 1. Solve problems 3.6, 3.9, and 4.5 from the textbook. 2. For a 2D Graphene sheet, assume that the unit lattice vectors are given by 1 ˆˆ ax a y b =+ ! and 2 a y b =− ! with 00 3/ 2 a n d 2 aa b a ≡≡ with a 0 =1.42A. a) Sketch the real space lattice. Which one of the five 2D Bravais lattice is this? b) Calculate the reciprocal lattice vector by using the formula 1 A ! = 2 π ) ( 3 2 1 3 2 a a a a a ! ! ! ! ! × × 2 A ! = 2 π ) ( 1 3 2 1 3 a a a a a ! ! ! ! ! × × where 3 a ! = z ˆ c) Draw the Brillouin Zone by Wigner-Seitz algorithm. Indicate the Γ -point of the Brillouin Zone. What is the volume of this zone. d) Calculate the co-ordinates of the locations of the edges of Brillouin zone perpendicular to the [10], [01] and [11] directions. e) If the conduction band minimum of the BZ occurs along the [11] direction, then how many ellipsoid do we need to consider for calculating electron density. f) Assuming that the solution of the Schrodinger equation for Graphene is given by 2 1 4cos cos 4cos iy xy E tk
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EE606_s09_hw3 - %PDF-1.2% 15 0 obj< /Linearized 1 /O 17...

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