Miller indices
Wafer Geometry
Wafer is 0.5 mm thick and 100 to 150 mm (4 to
6 inch) in dia. Good die are completely inside
the margin region
Miller indices
Miller indices (watch the video:
http://www.youtube.com/watch?v=9us_oENGoM)
1. Set the coordinate axes along the edges of
the unit cell
2. Let the plane to be indexed intercept the
axes
3. Divide it by unit cell length
4. Record these pure number set in the order
x,y,z
5. Invert these values (from 1,2,3 to 1, ½, 1/3
6. Find out LCM of the denominator and multiply
each with this (6x1, 6x½, 6x1/3 = 6,3,2)
7. Enclose the whole-number set in small
brackette (6,3,2)
Note:
1. If the plane to be indexed is parallel to a
coordinate axis, the intercept is infinity and
hence the index would be 0
2. If the plane to be indexed is in the –ve
portion of a coordinate axis, a minus sign is
placed over the corresponding index number
3. A group of equivalent planes is concisely
referenced through the use of {}, such as {100}
4. Direction of the plane is referenced through
the use of [], such as [100]
Note:
Six planes, (100), (010), (001),(100), (010) and
(001) are identical planes and hence are
represented by {100}
(100), (110) and (111) represent three different
planes.
Can you reflect on planes, (100), (200), (300) –
if these are identical planes?
Miller notation summary
Convention
Interpretation
(hkl)
Crystal plane
{hkl}
Equivalent planes
[hkl]
Crystal direction
<hkl>
Equivalent directions
The [100] direction is normal to the (100) plane
in a cubic crystal.