pset 1 - University of California Berkeley EE230 Solid...

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University of California, Berkeley Spring 2008 EE230 Solid State Electronics Prof. J. Bokor pset PROBLEM SET 1 (Due Tues., Feb. 12, 2008) 1. [Kittel, 1.1] Find the angles between the tetrahedral bonds of the diamond lattice. 2. Derive the Bragg condition: a) Prove that the reciprocal lattice vector G = h a * + k b * + l c * is perpendicular to the (hkl) lattice plane. b) Show that the distance between two parallel planes of the lattice is: d(hkl) = 2 π /| G|. c) Now show that the result derived in class: 2 k•G = G 2 is equivalent to the more familiar Bragg condition: 2dsin θ = n λ. 3. [Kittel, 2.5] The crystal structure of diamond can be considered as a simple cubic lattice with a basis of 8 atoms (conventional cube cell). a) Find the structure factor S for this basis. b) Find the zeroes of S and show that the allowed reflections of the diamond structure sat- isfy: (v 1 + v 2 + v 3 ) = 4n, where all indices are even and n is any integer, or else all indices are odd. 4. Determine the Bragg angles for the (111), (220), (311), and (400) reflections of germanium
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