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handbook of modern sensors

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346 10 Pressure Sensors<br />

As a result, pressure sensitivity a p and temperature sensitivity <strong>of</strong> the circuit b T can<br />

be found by taking partial derivatives:<br />

a p = 1 E<br />

∂V out<br />

∂p = π 44<br />

4<br />

∂(σ 1y − σ 1x )<br />

, (10.14)<br />

∂p<br />

b T = 1<br />

a p<br />

∂a p<br />

∂T = 1<br />

π 44<br />

∂π 44<br />

∂T . (10.15)<br />

Since ∂π 44 /∂T has a negative value, the temperature coefficient <strong>of</strong> sensitivity is<br />

negative; that is, sensitivity decreases at higher temperatures.<br />

There are several methods <strong>of</strong> fabrication which can be used for silicon pressure<br />

sensor processing. In one method [8], the starting material is an n-type silicon<br />

substrate with (100) surface orientation. Piezoresistors with 3 × 10 18 -cm −3 surfaceimpurity<br />

concentration are fabricated using a boron ion implantation. One <strong>of</strong> them<br />

(R 1 ) is parallel and the other is perpendicular to the 〈110〉 diaphragm orientation.<br />

Other peripheral components, like resistors and p-n junctions used for temperature<br />

compensation are also fabricated during the same implantation process as that for the<br />

piezoresistors. They are positioned in a thick-rim area surrounding the diaphragm.<br />

Thus, they are insensitive to pressure applied to the diaphragm.<br />

Another approach <strong>of</strong> stress sensing was used in the Motorola MPX pressure sensor<br />

chip shown in Fig. 10.5 The piezoresistive element, which constitutes a strain gauge, is<br />

ion implanted on a thin silicon diaphragm. Excitation current is passed longitudinally<br />

through the resistor’s taps 1 and 3, and the pressure that stresses the diaphragm is<br />

applied at a right angle to the current flow. The stress establishes a transverse electric<br />

field in the resistor that is sensed as voltage at taps 2 and 4. The single-element<br />

transverse voltage strain gauge can be viewed as the mechanical analog <strong>of</strong> a Hall effect<br />

device (Section 3.8 <strong>of</strong> Chapter 3). Using a single element eliminates the need to closely<br />

match the four stress- and temperature-sensitive resistors that form a Wheatstone<br />

Fig. 10.5. Basic uncompensated piezoresistive element <strong>of</strong> Motorola MPX pressure sensor.<br />

(Copyright Motorola, Inc. Used with permission.)

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