handbook of modern sensors

11.6 Microflow Sensors 373
(A)
(B)
Fig. 11.13. Gas microflow sensor with self-heating titanium resistors: (A) sensor design; (B) interface
circuit: R u and R d are resistances of the upstream and downstream heaters, respectively.
(Adapted from Ref. [7].)
sensor’s surface:
∂ 2 T
∂x 2 + ∂2 T
∂y 2 = vnc p ∂T
k g ∂x
for y>0, (11.25)
where n is the gas density, c p is the molecular gas capacity, and k g is the thermal
conductivity of gas. It can be shown that the solution of this equation for the boundary
condition of a vanishing thermal gradient far off the surface is [7]
(
)
1
V = B √
µ 2 + 1 − 1 , (11.26)
where V is the input voltage, B is a constant, and µ = Lvnc p /2πk g , and L is the gas
sensor contact length. This solution coincides very well with the experimental data.
Another design of a thermal transport microsensor is shown in Fig. 11.13A [8]
where titanium films having a thickness of 0.1 µm serve as both the temperature
sensors and the heaters. The films are sandwiched between two layers of SiO 2 . Titanium
was used because of its high TCR (temperature coefficient of resistance) and
excellent adhesion to SiO 2 . Two microheaters are suspended with four silicon girders
at a distance of 20 µm from one another. The Ti film resistance is about 2 k.
Figure 11.13B shows a simplified circuit diagram for the sensor, which exhibits an
almost linear relationship between the flow and output voltage V .
A microflow sensor can be constructed by utilizing a capacitive pressure sensor
[9] as shown in Fig. 11.14. An operating principle of the sensor is based on a
pressure gradient technique as described in Section 11.2. The sensor was fabricated
using silicon micromachining and defused boron etch-stops to define the structure.
The gas enters the sensor’s housing at pressure P 1 through the inlet, and the same
pressure is established around the silicon plate, including the outer side of the etched
membrane. The gas flows into the microsensor’s cavity through a narrow channel
having a relatively high-pressure resistance. As a result, pressure P 2 inside the cavity