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Unformatted text preview: Dr. P. Lucas U of A MSE 110 Band Structures SUMMARY FROM LAST CLASS • There are three types of band structures associated with each types of primary bonding which determine the properties of electrical conductivity of solid materials. • Metals are conductors and have either a partially filled s, p, or d band or an overlapping full and empty bands which generate an overall partially filled energy band. • Ionic solids are insulators. They are composed of atoms of very different electronegativity having orbitals of very different energy which generate two separate bands. An empty conduction band and a full valence band separated by a large band gap. • Semiconductors are tetrahedrally connected covalent solids. They are formed of a network of sp3 hybrid orbitals generating a full bonding valence band and a empty antibonding conduction band separated by a small band gap (<4eV) that some electrons can cross. • Binary and ternary semiconductor have an average of four electrons per atom that can form four covalent bonds each. • Visible light is not sufficiently energetic to excite electrons across the gap of insulators which appear transparent, but can excite electrons across the bandgap of semiconductors which appear opaque. • The transparency cutoff wavelength of a material is then g c E hc = λ Dr. P. Lucas U of A MSE 110 (macroscopic) definition of conductivity σ : CONDUCTIVITY IN SOLIDS • When a potential V is applied across a material, it induces a flow of charge: the current I (number of charge per second) that depends on the resistance R. I R V = • We can express the same equation for a solid of dimensions l=length and A=crosssectional area according to: j E ρ = l V E = • Where E is the electric field created by a potential V is applied to a material of length l : A I j = • j is the current density or flow of charge per unit area A. l A R = ρ • And ρ is the resistivity or resistance per unit distance ( Ω ·m). • The quantity R depends on the shape and size of a material while ρ is define for a certain type of material regardless of its size and shape. Dr. P. Lucas U of A MSE 110 (macroscopic) definition of conductivity σ : CONDUCTIVITY IN SOLIDS • The quantity that is experimentally measured is R while the quantity that describes the physical property of the material is ρ . Hence the need to convert one into the other....
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 Spring '07
 Lucas
 Electron, Condensed matter physics, Dr. P. Lucas U, Dr. P. Lucas

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