handbook of modern sensors

372 11 Flow Sensors
Fig. 11.12. Micromachined gas flow sensor.
11.6 Microflow Sensors
In some applications, such as process control in precise semiconductor manufacturing,
chemical and pharmaceutical industries, and biomedical engineering, miniaturized
gas flow sensors are encountered with increasing frequency. Most of them operate on
the method of thermal transport (see Section 11.3) and are fabricated from a silicon
crystal by using micromachining technology. Many of the microflow sensors use a
thermopile as a temperature sensor [6]; however, the thermoelectric coefficient [Eq.
(3.91) of Chapter 3] of standard elements used in the integrated circuit (IC) processing
(silicon and aluminum) is smaller than that of conventional thermocouples by factors
ranging from 10 to 100. Thus, a resulting output signal may be very small, which
requires amplification by amplifiers integrated directly into the sensor.
A cantilever design of a microflow sensor is shown in Fig. 11.12. The thickness
of the cantilever may be as low as 2 µm. It is fabricated in the form of a sandwich
consisting of layers of field oxide, chemical vapor deposition (CVD) oxide, and
nitrate [7]. The cantilever sensor is heated by an imbedded resistor with a rate of 26
K/mW of applied electric power, and a typical transfer function of the flow sensor
has a negative slope of about 4 mV/m/s.
The heat is removed from the sensor by three means: conductance L b through
the cantilever beam, gas flow h(v), and thermal radiation, which is governed by the
Stefan–Boltzmann law:
P = L b (T s − T b ) + h(v)(T s − T b ) + aσε(Ts 4 − T b 4 ), (11.24)
where σ is the Stefan–Boltzmann constant, a is the area along which the beam-togas
heat transfer occurs, ε is surface emissivity, and v is the gas velocity. From the
principles of energy and particle conservation, we deduce a generalized heat-transport
equation governing the temperature distribution T (x,y) in the gas flowing near the