Page 145 - MEMS Mechanical Sensors

134 Pressure Sensors

back and patterns the bosses and ribs on the front of the diaphragm. The resistors
were positioned in the standard layout (Figure 6.15) and were located on the top
surface of the rib, which served to magnify the stress by removing the resistor further
from the neutral axis. The bosses were stiffened regions along each side of the dia-
phragm leaving the center unstiffened like a standard diaphragm.
Meandering resistors have also been applied to basic and bossed diaphragms
[29]. The meander incorporates different levels of doping in each direction, which
maximizes the strain sensitivity of the resistor. The meander pattern increases the
length of the resistor, and this approach improves sensitivity compared with stan-
dard resistors.
The temperature cross-sensitivity is an obvious drawback of silicon piezoresis-
tors. The change in resistance due to temperature will often exceed that arising from
the change in the measurand. Several techniques are therefore employed to compen-
sate for temperature. The first technique arises from the use of a full bridge with the
resistors arranged as shown in Figure 6.15. In such an arrangement the change in
temperature is a common mode effect acting on all resistors simultaneously, and
therefore, the temperature effects should cancel out. Due to manufacturing toler-
ances, however, the temperature coefficients of each resistor will invariably be
slightly different. The change in resistance due to temperature and its resulting effect
on the output of the bridge can be expressed in the following equations [30]:

() =
RT R ( )( +01 α T + β T 2 ) (6.38)
()
∆VT R ()R0 () 0
0 = 1 2 × ( [ α −α )T + (β − β ) ]
2
T
V ()] 2 1 2 1 2
A [R () R0 + 0
1 2 (6.39)
()R 0
R 0 ()
) ]
− 1 2 2 × ( [ α 1 −α 2 ) + (β 1 − β T 2
T
2
[R 0 ()]
()R 0
1 2
The incorporation of a temperature sensor onto the sensor chip can enable
temperature compensation via a look-up table or algorithm. Such an approach,
however, requires extensive temperature and pressure calibration, which is a time
consuming and expensive operation. An alternative technique is to include a dummy
bridge on the sensor chip in addition to the pressure sensitive bridge. The dummy
resistors should be positioned at least 100 µm away from the edge of the diaphragm
to ensure they do not experience any pressure-induced stresses [31]. This compensa-
tion technique has been applied with the dummy resistors arranged in either a full
bridge [29] or a half-bridge [32]. The temperature limits of the implanted piezoresis-
tive approach are approximately 120°C due to the limitations of the p-n junction.
This temperature limit can be extended by using doped polysilicon resistors depos-
ited on the top surface of the diaphragm. Polysilicon resistors are, however, less sen-
sitive to applied stress (see Chapter 5).
Over the years, developments in materials and fabrication processes have also
had an effect on piezoresistive pressure sensors. Silicon fusion bonding, for example,
has enabled a reduction in chip size by enabling a diaphragm wafer to be bonded to
the back of an anisotropically etched cavity as shown in Figure 6.17 [33]. The use of
SOI wafers has improved performance in several ways. The buried oxide can act as
an etch stop, facilitating fabrication [34] and precisely controlling the diaphragm