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3-6 MEMS: Design and Fabrication

[001]
a
a

a

[100]

(100)
[010]
[a]
[001] a
a

a

[100]
(110)

[010]
[110]
[b]
[001] a
(111) [111]
a

a

[100]

[010]
[c]

FIGURE 3.2 Miller indices in a cubic lattice: planes and axes. Shaded planes are (a) (100), (b) (110), (c) (111).

[Maluf, 2000]. Wafers polished on both sides, often used in MEMS, are about 100 µm thinner than
standard thickness substrates (see the 425 µm thick Si substrate in Figure 3.1).

3.3.2 Miller Indices

The periodic arrangement of atoms in a crystal is called the lattice. The unit cell in a lattice is a segment
that is representative of the entire lattice. For each unit cell, basis vectors (a , a , and a ) can be defined
1
2
3
such that if the unit cell is translated by integral multiples of these vectors a new unit cell identical to the
original is obtained. A simple cubic-crystal unit cell for which a a a and the axes angles are
2
3
1
α β γ 90° is shown in Figure 3.2. In this figure, the dimension a is known as the lattice constant.
To identify a plane or a direction, a set of integers h, k, and l, called the Miller indices, are used. To deter-
mine the Miller indices of a plane, one takes the intercept of that plane with the axes and expresses these
intercepts as multiples of the basis vectors a , a , a .The reciprocal of these three integers is taken, and to
1
3
2
obtain whole numbers the three reciprocals are multiplied by the smallest common denominator. The
resulting set of numbers is written down as (hkl). By taking the reciprocal of the intercepts, infinities ( )

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