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Crystal Planes in Semiconductors


Miller Indices

All lattice planes and lattice directions are described by a mathematical description known as a Miller Index. This allows the specification, investigation, and discussion of specific planes and directions of a crystal. In the cubic lattice system, the direction [hkl] defines a vector direction normal to surface of a particular plane or facet. The Miller Indices h,k,l are defined as follows:
type: <100>
Equivalent directions:
[100],[010],[001]
type: <110>
Equivalent directions:
[110], [011], [101],
[-1-10], [0-1-1], [-10-1],
[-110], [0-11], [-101],
[1-10], [01-1], [10-1]
type: <111>
Equivalent directions:
[111], [-111], [1-11], [11-1]


  1. Miller Conventions -- a guide for when to use { } vs ( ) and [ ] vs < >
  2. Algorithm for determining [hkl]





Cubic Unit Cells
   

A crystal can always be divided into a fundamental shape with a characteristic shape, volume, and contents. In many crystals, the unit cell may be chosen as a cube, with atoms placed at various points within the cube.

Simple Cubic (sc)
Body-Centered Cubic (bcc)
Face-Centered Cubic (fcc)
Sodium Chloride (NaCl)
Cesium Chloride (CsCl)
ZincBlend (ZnS)
Diamond (C)  (Silicon and Germanium have the Diamond structure)

Diamond Unit Cell {100} planes {110} planes {111} planes


Angles Between Planes

ANGLE

100

110

010

001

101

       

Plane Intersection Angle Calculator

Miller indicies of first plane:
Miller indicies of second plane:

Angle between the planes: See example graphic (popup)

100

0.00

45.0

90.0

90.0

45.0

011

90.0

60.0

45.0

45.0

60.0

111

54.7

35.3

54.7

54.7

35.3

211

35.2

30.0

65.9

65.9

30.0

311

25.2

31.4

72.4

72.4

31.4

511

15.8

35.2

78.9

78.9

35.2

711

11.4

37.6

81.9

81.9

37.6



Wafer Flats

Purpose and Function

1. Orientation for automatic equipment

2. Indicate type and orientation of crystal.

 

Primary flat The flat of longest length located in the circumference of the wafer. The primary flat has a specific crystal orientation relative to the wafer surface; major flat.

Secondary flat Indicates the crystal orientation and doping of the wafer. The location of this flat varies.

  1. These links provide specific information on each orientation.
  2. <100>

  3. <111>

  4. <110>

  5. <311>

  6. <511>

  7. <711>

  8. For large crystals no flats are ground. Instead a notch is machined for positioning and orientation purposes.



For more information on cleaving or semiconductor substrates in general, see this link


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