Page 36 - An Introduction to Microelectromechanical Systems Engineering

Silicon-Compatible Material System 15

z, [001] z, [001] (110) z, [001]
(110)

y, [010] y, [010] y, [010]

x, [100] x, [100] x, [100]
(010) (110) (111)
(a)

(111) = (111) (111) = (111)

(111) = (111) (111) = (111)

(b)
Figure 2.1 (a) Three crystallographic planes and their Miller indices for a simple cubic crystal.
Two planes in the {110} set of planes are identified. (b) The four planes in the {111} family. Note
that (111 is the same plane as (111).
)

discussed as if it were simple cubic. In other words, the primitive unit—the smallest
repeating block—of the crystal lattice resembles a cube. The three major coordinate
axes of the cube are called the principal axes. Specific directions and planes within
the crystal are designated in reference to the principal axes using Miller indices [1], a
special notation from materials science that, in cubic crystals, includes three integers
with different surrounding “punctuation.” Directions are specified by brackets; for
example [100], which is a vector in the +x direction, referred to the three principal
axes (x,y,z) of the cube. No commas are used between the numbers, and negative
numbers have a bar over the number rather than a minus sign. Groups of directions
with equivalent properties are specified with carets (e.g., <100>, which covers the
[100 ]=+x ,[100 ]=−x ,[010 ]=+y ,[010 ]=−y ,[001 ]=+z and [001 ]=−z direc-
,
tions). Parentheses specify a plane that is perpendicular to a direction with the same
numbers; for example, (111) is a plane perpendicular to the [111] vector (a diagonal
vector through the farthest corner of the unit cube). Braces specify all equivalent
planes; for example, {111} represents the four equivalent crystallographic planes
),
),
(111), (111 (111 and (111 ).