University of California, Berkeley Spring 2008 EE230 Solid State Electronics Prof. J. Bokor pset 1.fm 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
This is the end of the preview.
access the rest of the document.