Basic Crystallography 18 And 23 January 2019 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)) (a) (b) (c) 1

DIMENSIONS AND UNITS 1 micrometer (1 mm) = 10-6m = 10-4cm * DIMENSIONS AND UNITS 07/16/96 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 or less, iPhone for 2019 rumors A13 processor 7 nm (70 Å or about 15 atoms wide), 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 *

Geometric Description of Single-Crystal — Space Lattices lattice: the periodic arrangement of atoms in the crystal Lattice: 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

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

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

Volume Density of Atoms 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

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

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

INDICES

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

Set of Planes (001) (010) 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

Set of Planes (001) (010) 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

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

Procedure of Silicon Wafer Production Raw material ― Polysilicon nuggets purified from sand Crystal pulling Si crystal ingot A silicon wafer fabricated with microelectronic circuits Final wafer product after polishing, cleaning and inspection Slicing into Si wafers using a diamond saw (1) Raw material from sand and made into the polysilicon nuggests (2) The polysilicon nuggets are placed into the quartz crucible. Quartz crucible, surrounded by graphite heater, 1600degree C. Metling it rotated. The melted nuggets can be pulled out slowly using a crystal seed. The crystal seed the shape is long thin needle. When it pull out and colled and formed the cylinder shpaed inget. The ingot is single crystal slicon.The diameter of the ingot is deciced by the temperature when melting and the rotating speed when it pulled out. Pure crystal cylindar ingets.temparatue and rate decide the diameter 16

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