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Solids

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This article provides a comprehensive overview of different types of solids, including ionic, covalent, molecular, and metallic. It also discusses the band theory, temperature dependence of resistivity, and the behavior of electrons in semiconductors.

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Solids

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  1. Solids Eisberg & Resnick Ch 13 & 14 RNave: http://hyperphysics.phy-astr.gsu.edu/hbase/solcon.html#solcon Alison Baski: http://www.courses.vcu.edu/PHYS661/pdf/01SolidState041.ppt Carl Hepburn, “Britney Spear’s Guide to Semiconductor Physics”. http://britneyspears.ac/lasers.htm

  2. http://hyperphysics.phy-astr.gsu.edu/hbase/solcon.html#solconhttp://hyperphysics.phy-astr.gsu.edu/hbase/solcon.html#solcon

  3. OUTLINE • Review Ionic / Covalent Molecules • Types of Solids (ER 13.2) • Band Theory (ER 13.3-.4) • basic ideas • description based upon free electrons • descriptions based upon nearly-free electrons • ‘Free’ Electron Models (ER 13.5-.7) • Temperature Dependence of Resistivity (ER 14.1)

  4. Ionic Bonds RNave, GSU at http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html#c4

  5. Ionic Bonds

  6. Ionic Bonding RNave, Georgia State Univ at hyperphysics.phy-astr.gsu.edu/hbase/molecule

  7. Covalent Bonds RNave, GSU at http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html#c4

  8. Covalent Bonding SYM ASYM spatial spin ASYM SYM spatial spin space-symmetric tend to be closer

  9. Covalent Bonding not really parallel, but spin-symmetric Stot = 1 Stot = 0 not really anti, but spin-asym space-symmetric tend to be closer

  10. TYPES OF SOLIDS (ER 13.2)CRYSTALINE BINDING • molecular • ionic • covalent • metallic

  11. most organics inert gases O2 N2 H2 Molecular Solids • orderly collection of molecules held together by v. d. Waals • gases solidify only at low Temps • easy to deform & compress • poor conductors

  12. NaCl NaI KCl Ionic Solids • individ atoms act like closed-shell, spherical, therefore binding not so directional • arrangement so that minimize nrg for size of atoms • tight packed arrangement  poor thermal conductors • no free electrons  poor electrical conductors • strong forces  hard & high melting points • lattice vibrations absorb in far IR • to excite electrons requires UV, so ~transparent visible

  13. Ge Si diamond Covalent Solids • 3D collection of atoms bound by shared valence electrons • difficult to deform because bonds are directional • high melting points (b/c diff to deform) • no free electrons  poor electrical conductors • most solids adsorb photons in visible  opaque

  14. Fe Ni Co Metallic Solids config dhalf full • (weaker version of covalent bonding) • constructed of atoms which have very weakly bound outer electron • large number of vacancies in orbital (not enough nrg available to form covalent bonds) • electrons roam around (electron gas ) • excellent conductors of heat & electricity • absorb IR, Vis, UV  opaque

  15. BAND STRUCTURE

  16. Isolated Atoms

  17. Diatomic Molecule

  18. Four Closely Spaced Atoms

  19. Six Closely Spaced Atomsas fn(R) the level of interest has the same nrg in each separated atom

  20. Two atoms Six atoms Solid of N atoms ref: A.Baski, VCU 01SolidState041.ppt www.courses.vcu.edu/PHYS661/pdf/01SolidState041.ppt

  21. Four Closely Spaced Atoms conduction band valence band

  22. Solid composed of ~NA Na Atomsas fn(R) 1s22s22p63s1

  23. Sodium Bands vs Separation Rohlf Fig 14-4 and Slater Phys Rev 45, 794 (1934)

  24. Copper Bands vs Separation Rohlf Fig 14-6 and Kutter Phys Rev 48, 664 (1935)

  25. Differences down a column in the Periodic Table: IV-A Elements same valence config Sandin

  26. The 4A Elements

  27. Band Spacingsin Insulators & Conductors electrons free to roam electrons confined to small region RNave: http://hyperphysics.phy-astr.gsu.edu/hbase/solcon.html#solcon

  28. How to choose eFandBehavior of the Fermi function at band gaps

  29. Fermi Distribution for a selected eF

  30. How does one choose/know eF If in unfilled band, eF is energy of highest energy electrons at T=0. If in filled band with gap to next band, eF is at the middle of gap.

  31. FermionsT=0 RNave: http://hyperphysics.phy-astr.gsu.edu/hbase/solcon.html#solcon

  32. Fermions T > 0

  33. Number of Electrons at an Energy e In QStat, we were doing Number of ways to have a particular energy distrib fn Number of electrons at energy e

  34. # states probability of this nrg occurring # electrons at a given nrg

  35. SemiconductorsER13-9, -10

  36. Semiconductors ~1/40 eV • Types • Intrinsic – by thermal excitation or high nrg photon • Photoconductive – excitation by VIS-red or IR • Extrinsic – by doping • n-type • p-type ~1 eV

  37. Intrinsic Semiconductors Silicon Germanium RNave: http://hyperphysics.phy-astr.gsu.edu/hbase/solcon.html#solcon

  38. Doped Semiconductors lattice p-type dopants n-type dopants

  39. 5A doping in a 4A lattice 5A in 4A lattice 3A in 4A lattice

  40. 5A in 4A lattice 3A in 4A lattice

  41. ‘Free-Electron’ Models • Free Electron Model (ER 13-5) • Nearly-Free Electron Model (ER13-6,-7) • Version 1 – SP221 • Version 2 – SP324 • Version 3 – SP425 • .

  42. ********************************************************* • Free-Electron Model • Spatial Wavefunctions • Energy of the Electrons • Fermi Energy • Density of States dN/dE E&R 13.5 • Number of States as fn NRG E&R 13.5 • Nearly-Free Electron Model (Periodic Lattice Effects) – v2 E&R 13.6 • Nearly-Free Electron Model (Periodic Lattice Effects) – v3 E&R 13.6

  43. Free-Electron Model (ER13-5) classical description

  44. Quantum Mechanical Viewpoint In a 3D slab of metal, e’s are free to move but must remain on the inside Solutions are of the form: With nrg’s:

  45. At T = 0, all states are filled up to the Fermi nrg A useful way to keep track of the states that are filled is:

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