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Basics of Crystallography: Solid Types, Dimensions, and Structures

Learn about the three general types of solids - Amorphous, Polycrystalline, and Single Crystal - along with crystallographic dimensions, unit conversion, lattice descriptions, crystal structures, and more.

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Basics of Crystallography: Solid Types, Dimensions, and Structures

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  1. Basic Crystallography 13 January 2017 Three general types of solids • Amorphous ― with order only within a few atomic and molecular dimensions (Fig. (a)) • Polycrystalline ― with multiple single-crystal regions (called grains) separated by grain boundary (Fig.(b)) • Single crystal ― with geometric periodicity throughout the entire material (Fig. (c)) (c) (a) (b) 1

  2. DIMENSIONS AND UNITS • 1 micrometer (1 mm) = 10-6m = 10-4cm • 1 Å = 10-10m = 10-8cm (Å =Angstrom) • 10,000 Å = 1 mm = 1000 nm • 1 nanometer (1 nm) = 10-9 m = 10 Å • Wavelength of visible light 0.4 mm(violet) to 0.7 mm(red) {400 nm to 700 nm, 4,000 Å to 7,000 Å } • 1 mil = 0.001 inch = 25.4 mm • Sheet of notebook paper about 4 mils = 100 mm • 1 human hair = 75 mm to 100 mm = 75,000-100,000 nm • Atomic spacing in a crystal ~ 3 to 5 Å • Fingernail growth rate about 1-3 mm/hour (Not personally verified) • Aggressive production minimum feature sizes, tens of nm, 20 nm used in the iPhone 6 A8 microprocessor, 14 nm in state-of-the-art memory from Micron • Speed of Light c= 3x108m/sec = 300 m/μsec = 0.3 m/nsec (About 1 foot/nsec) • 3 GHz clock speed T = 0.33 nsec Signal or Photon Travels About 4 inches

  3. Lattice: lattice: the periodic arrangement of atoms in the crystal Geometric Description of Single-Crystal — Space Lattices Unit cell: unit cell: the smallest volume that can be used to repeat and form the entire crystal. Unit cells are not necessary unique. http://www.bing.com/images/search?q=silicon+crystal+lattice&qs=n&form=QBIR&pq=silicon+crystal+lattice&sc=3-23&sp=-1&sk=#view=detail&id=7BEED0A1927191D72C8552F99D050C522960DCF5&selectedIndex=14 http://www.ibiblio.org/e-notes/Cryst/Cryst.htm 3

  4. c b a Space lattices A general 3D unit cell is defined by three vectors Every equivalent lattice point in the 3D crystal can be found by c b a General case Special case 4 Refer to Text Figure 1.4

  5. Basic Crystal Structures Three common types: Simple cubic Body-centered cubic (bcc) Face-centered cubic (fcc) and (c) (a) (b) Text Figure 1.5 5

  6. Volume Density of Atoms • Volume density Number of atoms per unit volume = Total number of atoms / volume occupied by these atoms = number of atoms per unit cell/volume of the unit cell Unit: m-3 or (cm)-3 • Example For Silicon a= 5.43 Å = 5.43 x 10-8 cm Volume density = Important Numbers for Si Preferred 6

  7. Why Are Crystal Planes Important? • real crystals are eventually terminate at a surface • Semiconductor devices are fabricated at or near a surface • many of a single crystal's structural and electronic properties are highly anisotropic

  8. Computation of Miller Indices • Find the intercept on the x, y, and z • Reduce to an integer. i.e. lowest common denominator • Take the reciprocal and reduce to the smallest set of integers (h, k, l) These are called the Miller Indices

  9. INDICES

  10. (111) Plane with normal direction [111] (111) Plane with normal direction [111] (100) Plane with normal direction [100] (100) Plane with normal direction [100] (110) Plane with normal direction [110] (110) Plane with normal direction [110] Examples of Lattice Planes in Cubic Lattices

  11. (001) (010) Set of Planes Due to the high degree of symmetry in simple cubic, bcc and fcc, the axis can be rotated or parallel shift in each of three dimensions, and a set of plane can be entirely equivalent. {100} set of planes: (100), (010), (001) Similarly, {110} set of planes: (110), (101), (011) 12

  12. (001) (010) Set of Planes Due to the high degree of symmetry in simple cubic, bcc and fcc, the axis can be rotated or parallel shift in each of three dimensions, and a set of plane can be entirely equivalent. {100} set of planes: (100), (010), (001) Similarly, {110} set of planes: (110), (101), (011) 13

  13. The Diamond Structure • Materials possess diamond structure: Si, Ge • 8 atoms per unit cell • Any atom within the diamond structure will have 4 nearest neighboring atoms 14

  14. Raw material ― Polysilicon nuggets purified from sand Si crystal ingot Crystal pulling Slicing into Si wafers using a diamond saw A silicon wafer fabricated with microelectronic circuits Final wafer product after polishing, cleaning and inspection Procedure of Silicon Wafer Production 16

  15. Identification of Wafer Surface Crystallization Flats can be used to denote doping and surface crystallization 17

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