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Single-Crystal Silicon Carbide MEMS: Fabrication, Characterization, and Reliability 7-13
−0.0014
25C N = 2 × 10 19 cm −3
d
−0.0012 100C
150C
Transverse dR/R −0.0008 250C
−0.001
200C
−0.0006
−0.0004
−0.0002
0
0 10 100 150
−6
Strain (10 )
FIGURE 7.8 Relative change in resistance of the transverse piezoresistors as a function of strain at different
19
3
temperatures (N 2 10 cm ).
d
18
16 Beam 1
Net bridge output (mV) 12
14
Beam 2
10
8
6
4
2
0
0 5 10 15 20 25 30 35 40
Pressure (psi)
FIGURE 7.9 Net bridge output as function of pressure of two different beam sensors. In both cases the dependence
is linear (N 2 10 cm ).
19
3
d
The bridge GF decreases linearly with temperature, as seen in Figure 7.7(b). The relative change in
resistance versus strain of the transverse piezoresistors is shown in Figure 7.8, from which the transverse GF
can also be calculated. In order to check the reproducibility of the measurements, another beam transducer
structure was assembled, and the bridge output as a function of pressure was measured. For comparison,
Figure 7.9 shows the results obtained on both beams. In both cases, the dependence between the bridge
output and the applied pressure is linear; however, one of the beams exhibited a slightly lower sensitivity.
This lowered sensitivity was probably a result of either a geometrical factor (i.e., the metal diaphragm in
both cases did not have exactly the same dimensions) or the mounting procedure, or both. Random tem-
perature variations made it difficult to measure the GF of the individual resistor elements, especially the
transverse resistors, which exhibited very small changes in resistance with pressure.
7.3.2 Temperature Effect on Resistance
Another important consideration in the selection of aresistor for high or low temperature applications
is how the resistor’s electrical resistance changes with temperature. Resistance variation with temperature
is usually expressed as a TCR, which is defined as:
1 R R
f
o
β (7.12)
R T T
o f o
© 2006 by Taylor & Francis Group, LLC
