Constructing a Crystal Once you specify the lattice, you can then - - PowerPoint PPT Presentation

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“Constructing” a Crystal

• Once you specify the lattice, you can

then “hang” a collection of atoms off of each position in the lattice

– Important: every lattice point (point on the scaffold) must have the exact same

• environment. i.e. the structure must

possess translational symmetry from point to point.

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Crystal Bravais Lattices

• Simple Base

Centered Triclinic Monoclinic Orthorhombic

Simple Body centered Base centered Face Centered

Hexagonal

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Crystal lattices ( cont.)

Rhombohedral Tetragonal Simple Body Centered

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Simple Cubic lattices

Simple Body-Centered Face-centered

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Atomic Order of a Crystal Structure

Figure 4.2

Plummer

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Amorphous Atomic Structure

Figure 4.3

Plummer

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4

• Rare due to poor packing (only Po has this structure)
• Close-packed directions are cube edges.
• Coordination # = 6

(# nearest neighbors)

SIMPLE CUBIC STRUCTURE (SC)

back

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Unit Cell in 3-D Structure

Unit cell

Figure 4.4

Plummer

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10

• Coordination # = 12
• ABAB... Stacking Sequence
• APF = 0.74
• 3D Projection
• 2D Projection

A sites B sites A sites Bottom layer Middle layer Top layer

Adapted from Fig. 3.3, Callister 6e.

Hexagonal Close-Packed Structure (hcp)

Note: this structure is NOT cubic back

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Body-Centered Cubic (BCC)

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Specifying Directions in Crystals

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Silicon Crystal Structure and Growth (Plummer - Chapter 3)

Click to edit Master text styles Second level

• Third level
• Fourth level
• Fifth level

Plummer

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Miller Indices of Crystal Planes

Z X Y (100) Z X Y (110) Z X Y (111)

Figure 4.9

lummer

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Silicon Crystal Structure

• Planes and directions are defined using x, y, z coordinates.
• [111] direction is defined by a vector of 1 unit in x, y and z.
• Planes defined by “Miller indices” – Their normal direction (reciprocals of intercepts of

plane with the x, y and z axes).

Crystals are characterized by a unit cell which repeats in the x, y, z directions.

Plummer

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Silicon has the basic diamond crystal structure – two merged FCC cells offset by a/4 in x, y and z.

Plummer

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Various types of defects can exist in a crystal (or can be created by processing steps). In general, these cause electrical leakage and are result in poorer devices.

(Extra line of atoms)

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Point Defects

Vacancy defect Interstitial defect Frenkel defect

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