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7-8 MEMS: Design and Fabrication

are thickness and radius. Since the radius is generally a fixed value determined by the pressure range and
package specification, thickness is left as the main controlling variable. Therefore, the process of etching
of the diaphragm to achieve a desired thickness and shape is of primary importance in diaphragm-based
pressure sensor technology.
Until recently, the application of SiC diaphragms as pressure sensing devices was almost nonexistent.
Fortunately, SiC microfabrication technology has advanced significantly over the last decade, largely
because of the ability to perform high-energy plasma etching of various types of structures. Some struc-
tures have been selectively etched in SiC using reactive ion etching (RIE), but the etch rates reported were
too low for practical use in the wafer thinning and shaping [Palmour et al., 1987] needed for pressure sen-
sor fabrication. Rapid progress has been made in DRIE with etch rates up to 1µm/min already reported
[Khan and Adesida, 1999].

7.3 Characterization of 6H-SiC Gauge Factor

The piezoresistive effect is associated with changes in resistance as a result of an applied mechanical stim-
ulus. The resistance can be measured by incorporating the gauge within a Wheatstone bridge circuit con-
figuration, and the resultant output voltage is related to the applied force. The piezoresistive effect is
rather small in metals, but in semiconductors it is much more pronounced. The explanation can be found
in Equation (7.1) for the gauge factor,

dR dρ
GF 1 2ν (7.1)
Rε ρε

where R electrical resistance (Ω); ρ electrical resistivity (Ω-cm) of the gauge material; ν Poisson
ratio (a geometrical effect); and ε applied strain.
The change in the resistance with strain is dependent on two terms: one is associated with the geomet-
rical piezoresistive effect, and the second originates from the strain dependency of the resistivity, as shown
in Equation (7.1). In metals, this latter term is zero, whereas it is significantly nonzero in semiconductors.
In semiconductors, the contribution of the geometrical term to the GF is of the same order as in metals.
Therefore, the gauge factor in semiconductors is related to the large strain sensitivity of the resistivity.
This fact can be explained on the basis of the energy-band structure of semiconductors. In n-type semi-
conductors such as 6H-SiC that have multiple valleys in the conduction band, the piezoresistive effect is
associated with a change in the relative energy positions of the multivalley minima under applied stress.
This effect causes the electrons to transfer among the valleys, causing a net change in the mobility, which
in turn has a dominant effect on the strain (stress) dependency of the resistivity [Herring and Vogt, 1956].
In order to measure the GF of 6H-SiC, resistors were etched in 6H-SiC epilayers (p- and n-type). The
configuration of the resistors was such that two of the elements were transversely oriented, whereas the
other two were oriented longitudinally. The substrate was then diced into rectangular chips, each con-
taining a pair of Wheatstone bridge circuits, one of which is shown in Figure 7.4(a). The equivalent cir-
cuit of the Wheatstone bridge is shown in Figure 7.4(b). It depicts the transverse and longitudinal
piezoresistors arranged alternately. With current flowing parallel to their length, the transverse resistors
R and R would experience a perpendicular strain (strain perpendicular to current flow), and the longi-
4
1
tudinal resistors R and R would experience a parallel strain (strain parallel to current flow).
2 3
The purpose of using two Wheatstone bridges (only one shown here) on a single chip is to simultane-
ously compare the measured responses from both the tensile and the compressive states of the bridges.
The rectangular chip was then attached to a machined metal diaphragm made of Incoloy™ with high-
temperature glass, as shown in the cross section schematic of Figure 7.5. One set of Wheatstone bridges
was placed at the edge of the metal diaphragm, and the other one was on the push rod. Pressure was applied
to the diaphragm through a back port (not shown), which caused the push rod of the metal diaphragm to
deflect the SiC beam. One set of piezoresistors, closer to the center of the metal diaphragm, was placed in
tension, whereas the other, closer to the periphery of the diaphragm, was in compression. The ∆R of each

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