Basic Crystallography

26 January 2015

Three general types of solids 1. Amorphous ― with order only within a few atomic and molecular

dimensions (Fig. (a))2. Polycrystalline ― with multiple sing-crystal regions (called grains)

separated by grain boundary (Fig.(b))3. Single crystal ― with geometric periodicity throughout the entire material

(Fig. (c))

(a) (b) (c)1

DIMENSIONS AND UNITS

1 micrometer (1 m) = 10-6m = 10-4cm 1 Å = 10-10m = 10-8cm (Å =Angstrom) 10,000 Å = 1 m = 1000 nm 1 nanometer (1 nm) = 10-9 m = 10 Å Wavelength of visible light 0.4 m(violet) to 0.7 m(red)

{400 nm to 700 nm, 4,000 Å to 7,000 Å } 1 mil = 0.001 inch = 25.4 m Sheet of notebook paper about 4 mils 1 human hair = 75 m to 100 m = 75,000-100,000 nm Atomic spacing in a crystal ~ 3 to 5 Å Fingernail growth rate about 1-3 m/hour (Not personally verified) Aggressive production minimum feature sizes, tens of nm, 20 nm used in the iPhone 6 A8 microprocessor.

Geometric Description of Single-Crystal — Space Lattices

lattice: the periodic arrangement of atoms in the crystal

Lattice:

unit cell: a small volume that can be used to repeat and form the entire crystal. Unit cells are not necessary unique.

Unit cell:

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Space lattices

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A general 3D unit cell is defined by three vectors cba

, ,Every equivalent lattice point in the 3D crystal can be found by

csbqapr

a

b

c

General casea

b

c

Special case

Basic Crystal Structures

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Three common types:

a) Simple cubicb) Body-centered cubic (bcc) c) Face-centered cubic (fcc)

(a) (c)(b)

cba

and

constant lattice cba

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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

1. Find the intercept on the x, y, and z

2. Reduce to an integer. i.e. lowest common denominator

3. Take the reciprocal and reduce to the smallest set of integers (h, k, l) These are called the Miller Indices

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cba ,,

cba ,,

8

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(100) Plane with normal direction [100]

(110) Plane with normal direction [110]

(111) Plane with normal direction [111]

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]

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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)

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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)

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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

Refer To Crystal WEB Link 12

Volume Density of Atoms

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• 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 =

3223

atoms/cm10x58

a

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Procedure of Silicon Wafer Production

Raw material ― Polysilicon nuggets purified from sand

Crystal pulling

Si crystal ingot

Slicing into Si wafers using a diamond sawFinal wafer product after polishing,

cleaning and inspection

A silicon wafer fabricated with microelectronic circuits

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Identification of Wafer Surface Crystallization

Flats can be used to denote doping and surface crystallization