Page 37 - An Introduction to Microelectromechanical Systems Engineering

16 Materials for MEMS

The determinants of plane and direction equivalence are the symmetry opera-
tions that carry a crystal lattice (including the primitive unit) back into itself (i.e., the
transformed lattice after the symmetry operation is complete is identical to the start-
ing lattice). With some thought, it becomes evident that 90º rotations and mirror
operations about the three principal axes are symmetry operations for a simple cubic
crystal. Therefore, the +x direction is equivalent to the +y direction under a 90º rota-
tion; the +y direction is equivalent to the –y direction under a mirror operation, and
so forth. Hence, the +x,–x,+y,–y,+z, and –z directions are all equivalent. Vector
algebra (using a dot product) shows that the angles between {100} and {110} planes
are 45º or 90º, and the angles between {100} and {111} planes are 54.7º or 125.3º.
Similarly, {111} and {110} planes can intersect each other at 35.3º, 90º, or 144.7º.
The angle between {100} and {111} planes is of particular importance in
micromachining because many alkaline aqueous solutions, such as potassium
hydroxide (KOH), selectively etch the {100} planes of silicon but not the {111}
planes (discussed in detail in Chapter 3). The etch results in cavities that are bounded
by {111} planes (see Figure 2.2).
Material manufacturers cut thin circular wafers from large silicon boules along
specific crystal planes. The cut plane—the top surface of the wafer—is known as the
orientation cut. The (100) wafers dominate in both MEMS and CMOS technology,
but wafers are also readily available with (111) orientation and, to a lesser degree,
(110) orientation. It should be noted that saying that the surface of a wafer has a
particular orientation such as (100) is arbitrary; any orientation within the equiva-
lent {100} group of planes, such as (001), can alternatively be selected. It should be
further noted that when referring to the wafer surface (e.g., (100)), the group of
planes (e.g., {100}) or direction normal to the surface (e.g., [100]) is often used
instead; all are intended to mean the same thing. The (100) and (111) wafers, with n-
and p-type doing, are produced with a minor flat at a specific location relative to a
wider, major flat, as shown in Figure 2.2.
Crystalline silicon is a hard and brittle material deforming elastically until it
reaches its yield strength, at which point it breaks. Its tensile yield strength is 7 GPa,
which is equivalent to a 700-kg (1,500-lb) weight suspended from a 1-mm area. Its
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Young’s modulus is dependent on crystal orientation, being 169 GPa in <110>
directions and 130 GPa in <100> directions—near that of steel. The dependence of
the mechanical properties on crystal orientation is reflected in the way a silicon wafer
preferentially cleaves along crystal planes . While large silicon wafers tend to be
1
fragile, individual dice with dimensions on the order of 1 cm×1cmor less are rugged
and can sustain relatively harsh handling conditions. As a direct consequence of
being a single crystal, mechanical properties are uniform across wafer lots, and
wafers are free of intrinsic stresses. This helps to minimize the number of design
iterations for silicon transducers that rely on stable mechanical properties for their
operation. Bulk mechanical properties of crystalline silicon are largely independent

1. A (100) silicon wafer can be cleaved by scratching the surface with a sharp diamond scribe along a <110>
direction (parallel or perpendicular to the flat), clamping the wafer on one side of the scratch, and applying a
bending force to the free side of the wafer. Fracture occurs preferentially along <110> directions on the
surface. The newly exposed fracture surfaces tend to be {111} planes, which are sloped at 54.7° with respect
to the surface.