Lecture%2003

# Lecture%2003 - EEE 352 Lecture 03...

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1 EEE 352: Lecture 03 Crystal Structure * Diamond Crystal * Basis of the FCC * Bonds * Tetrahedral coordination * X-Ray Diffraction * Laue and Braggs http://www.fulton.asu.edu/~ferry/ECE352.htm Here we consider some important crystal structures encountered in nature * The first of these is the DIAMOND crystal structure Which is one of the crystal forms of CARBON In crystallography it is typical to break crystals down to their PRIMITIVE CELL * A basic BUILDING BLOCK that can be used to construct the crystal * The cell of the diamond structure, shown below, IS NOT THE PRIMITIVE CELL THE NORMAL CELL OF DIAMOND FOUR ATOMS ARE CONTAINED WITHIN THIS CELL MAKING IT EXTREMELY COMPLEX ! Crystal Structure of Diamond The PRIMITIVE CELL is formed by the primitive vectors and the basis. The normal cell is larger, but is more suitable for building the lattice. Crystal Structure of Diamond Silicon The inter-atomic distance is twice the covalent radii , or 2.346 Angstrom in Si. The PRIMITIVE LATTICE vector has a length that is times the nearest neighbor distance, or 3.83 Angstrom in Si. 3 / 2 2 The edge of the NORMAL CELL is times the inter- atomic spacing or 5.418 Angstrom in Si. 3 / 4 4 1 , 4 1 , 4 1 0 , 2 1 , 2 1 (0,0,0) (1,0,0) This is the NN distance. Each atom has 4 NN. These are the 4 covalent bond directions. This is the 2 nd NN distance. Each atom has 12 2 nd neighbors. This is the 3 rd NN distance. Each atom has 6 3 rd NN. Recall that when describing lattice structures we used TRANSLATION VECTORS * That allow us to MAP from one lattice point to another We must also introduce translation vectors to describe the BASIS unit of the crystal * These vectors indicate the spatial relation of atoms WITHIN the basis unit * The translation vectors for the basis unit of diamond are shown below Where we have assumed the primitive cell size is a Crystal Structure of Diamond d Relative to each lattice point: * The FIRST atom of the basis is located at: * The SECOND atom of the basis is located at: [ ] 0 , 0 , 0 [] z y x ˆ , ˆ , ˆ 4 d

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2 Crystal Structure of Diamond Basis on “bottom face” atom Basis on “front face” atom Basis on “left face” atom Basis on “corner (origin)” atom Crystal Structure of Diamond The “basis” results in 4 new atoms in the face-centered cubic cell (BUT only 4 as the new structure is not “close packed” but rather open) : We recall the tetrahedral coordination of the four atoms that arise from the simple bonding picture. Left face Front face Bottom face Center atom sits ¼ of distance along cube diagonal We will see later that the 14 electrons in Si separate into core electrons (10) and bonding electrons—the outer 4 electrons serve this latter purpose. n E 1 s 2p 2 s 3p 3 s 3d 123 K L M shell filled empty -13.55 eV - 6.52 eV These outer 4 electrons form the covalent bonds.
3 The two s and two p wave functions from each atom will share with their neighbors in a manner that gives one s and three p contributions ( s, p x , p y , p z ) in each bond, known as a sp 3 hybrid .

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## This note was uploaded on 09/19/2009 for the course EEE 352 taught by Professor Ferry during the Spring '08 term at ASU.

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Lecture%2003 - EEE 352 Lecture 03...

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