MEMS-based gas flow sensors

Abstract

Micro-electro-mechanical system (MEMS) devices integrate various mechanical elements, sensors, actuators, and electronics on a single silicon substrate in order to accomplish a multitude of different tasks in a diverse range of fields. The potential for device miniaturization made possible by MEMS micro-fabrication techniques has facilitated the development of many new applications, such as highly compact, non-invasive pressure sensors, accelerometers, gas sensors, etc. Besides their small physical footprint, such devices possess many other advantages compared to their macro-scale counterparts, including greater precision, lower power consumption, more rapid response, and the potential for low-cost batch production. One area in which MEMS technology has attracted particular attention is that of flow measurement. Broadly speaking, existing micro-flow sensors can be categorized as either thermal or non-thermal, depending upon their mode of operation. This paper commences by providing a high level overview of the MEMS field and then describes some of the fundamental thermal and non-thermal micro-flow sensors presented in the literature over the past 30 years or so.

1 Origin and applications of MEMS technology

The concept of micro-electro-mechanical systems (MEMS) dates back to the early 1960s, but only became an achievable reality when the tools and techniques originally developed for integrated circuit (IC) manufacturing became sufficiently advanced. Whereas electronic semiconductor devices are fabricated using IC process sequences, MEMS devices are produced by selectively etching away parts of the underlying silicon wafer or adding and patterning additional metallic and polymer layers to form the required mechanical and electromechanical devices. Typical MEMs micro-fabrication techniques include deposition [e.g. electroplating, sputtering, chemical vapor deposition (CVD), etc.], photolithography, and etching (e.g. wet etching, reactive ion etching (RIE), etc.]. Although still an emerging technology, MEMS devices are being increasingly deployed for mainstream commercial and industrial applications such as pressure sensors, accelerometers, gas sensors, RF switches, micro-mirrors, etc. (Löfdahl and Gad-el-Hak 1999). In addition to the obvious advantages accruing from their diminutive scale (including a greater portability, a more discrete implementation and a reduced power consumption), MEMS devices permit the bulk manufacturing of multiple machines on the surface of a single silicon wafer, and therefore yield a huge reduction in the unit cost. Furthermore, today’s micro-fabrication techniques enable multiple functional units to be integrated on a single chip, thereby making possible such concepts as lab-on-chip (LoC) and micro-total analysis systems (μ-TAS) for the pharmaceutical and food-processing industries, wearable drug delivery systems for the medical field, miniaturized wireless sensors for environmental monitoring, and battlefield surveillance applications, etc.

Measuring the velocity of gas flows is an essential requirement in many commercial and industrial applications, including environmental monitoring systems, medical instrumentation, process control, and gas pipelines. Flow measurement applications were traditionally implemented using large-scale mechanical flow meters of one form or another. However, the increasing sophistication of modern micro-fabrication techniques has led to the development of many MEMS-based micro-flow meters in recent years. Reviewing the literature, it is found that the majority of these sensors can be classified as either thermal or non-thermal, depending on their mode of operation. Furthermore, non-thermal sensors can be further classified as either differential pressure-based, lift force-based, or cantilever-based (Table 1). The remainder of this paper presents a systematic review of the operational principles and advantages of each of the major thermal and non-thermal flow meters presented in the literature over the past 30 years or so (Nguyen 1997).

Table 1 Performance of MEMS-based flow sensors for gas flow velocity measurement

2 Thermal flow sensors

Thermal flow sensors are based on mechanical–thermal–electrical transport principles. Figure 1 shows the general signal transport principles of thermal flow sensors. There are two classifications (Nguyen 1997):

Fig. 1

Signal transport of thermal flow sensors with three signal domains (Nguyen 1997)

• a. Hot-wire sensors: thermal flow sensors measure the effect of the fluid flow on a hot body by either increase of heating power with constant heater temperature or decrease of heater temperature with constant heating power.

• b. Calorimetric sensors: thermal flow sensors measure the asymmetry of temperature profile around the heater which is modulated by the fluid flow.

The first thermal flow sensor based on silicon technology was presented by Van Putten and Middelhoek of the University of Technology, Delft back in 1974 (Van Putten and Middelhoek 1974). In 1983, the same authors utilized a hot-film mechanism to develop an integrated silicon double-bridge anemometer (Van Putten and Middelhoek 1983). Several years later, Tai et al. (1985) applied newly emerging MEMS micro-fabrication techniques to construct a polysilicon bridge for anemometer applications. The experimental results confirmed the feasibility of using micro-fabrication techniques to produce miniaturized, low-cost, high-performance devices for flow sensing applications, and prompted a tremendous interest in the development of MEMS-based micro-flow sensors which continues until this day. Thus, a series of research works start to focus on micro thermal flow sensors (Petersen and Brown 1985; Tabata et al. 1985; Tanaka et al. 1986; Johnson and Higashi 1987; Tai and Muller 1988). In 1987, Johnson and Higashi (1987) developed a highly sensitive silicon-based microtransducer for air flow and differential pressure-sensing applications. The device is still manufactured by Honeywell. The microtransducer consists of a heater and two symmetric temperature-sensing elements whose thickness and width are 1 μm and 2 mm, respectively. When airflow passes the microtransducer, the resistances of the sensing elements vary due to the temperature changes, and determine the flow rate through the electric output of a bridge circuit.

In 1990, Van Oudheusden and Van Herwaarden (1990) presented a two-dimensional thermal flow sensor. A thermally isolated floating-membrane structure was formed in the chip by a two-step etching process. Flow was measured by detecting flow-induced temperature differences in two directions on the heated membrane, and allowed directional flow measurements over a full range of 360°. The response time was found to be 150 ms. In comparison to a thick-silicon-based flow sensor of similar dimensions, the structure possessed a much higher sensitivity, and an improved offset, and better time response performance.

In 1991, Moser et al. (1991) presented two types of silicon-based gas flow sensors utilizing industrial CMOS and bipolar IC technologies, respectively. Both sensors were based on the Seebeck effect. Integrated thermopiles were placed on free-standing cantilever beams and measured the temperature differences between the heated tips of the beams and the bulky silicon substrates as the gas flow varied. The sensitivities of the CMOS sensors and the bipolar sensors were 1.78 and 0.26 V (m/s)^−1/2 W⁻¹, respectively.

In 1992, Löfdahl et al. (1992) presented a MEMS-based sensor with the form shown in Fig. 2 for measuring the mean velocity and turbulence intensity of gas flows. Although the operational principle of the device is similar to that of a conventional hot-wire sensor, a number of fundamental differences exist. For example, rather than using a bridge-balance mechanism, the device detects the flow velocity by measuring the voltage difference between two temperature-sensitive PN-junction diodes. The “hot” diode monitors the temperature of the chip, which is electrically heated by an integrated resistor and is cooled by the gas flow, while the “cold” diode adjusts the temperature of the device relative to that of the ambient air in order to achieve the specified overheat ratio. Thus, the power dissipated in the heated resistor varies as a function of the instantaneous flow velocity. In their study, the authors presented two device configurations, namely the single-wire sensor shown in Fig. 2 for measuring a single velocity component, and the double-chip sensor illustrated in Fig. 3 for measuring two orthogonal velocity components.

Fig. 2

Schematic of a single-wire MEMS sensor (left “hot” diode; right “cold” diode) (Löfdahl et al. 1992)

Fig. 3

Double chip sensor for the determination of fluctuating velocity correlations (Löfdahl et al. 1992)

In 1992, Yoon and Wise (1992) presented an integrated mass flow sensor with on-chip CMOS interface circuits, which were capable of measuring gas type, flow velocity, direction, temperature, and pressure. The sensors were suspended on micromachined dielectric windows with areas of 0.5 mm × 0.5 mm (L × W) (Fig. 4). In flow velocity sensing, the heater and detector were interleaved to achieve tight thermal coupling. With the window heated and maintained at constant temperature, gas was allowed to flow over the chip surface with increasing the convective heat flow. The input power was required to be increased to maintain the window temperature. The increased electrical power was used to indicate the flow velocity. The flow sensitivity was found to be independent of window temperature. In flow direction sensing, the temperature distribution across the window was symmetrical; however, when flow was introduced, the gas was heated while passing over the heater so that the upstream thermocouple was cooled while the downstream thermocouple was heated. The flow angle can generally be resolved within ±5° and the circuit has a resolution of about 0.1°C and a sensitivity of 4 mV/°C.

Fig. 4

Schematic of monolithic mass flowmeter a top-view and b cross-section-view (Yoon and Wise 1992)

In 1996, Kälvesten et al. (1996) presented an integrated pressure-flow sensor for correlated measurements in turbulent gas flows. The flow-sensor area was 300 μm × 60 μm with an edge-to-edge distance of 100 μm between the different sensor areas. The flow sensor performed with a response time of 25 μs as the sensor was operated at constant temperature using feedback electronics. The measured steady-state flow-sensor power dissipation was P = 34 + 0.4τ ^0.47₀  mW (where τ₀ is the time-average flow-dependent wall shear stress) in a turbulent wall boundary layer at an over-temperature of 100°C.

In the same year, Qiu et al. (1996) presented a micro gas-flow sensor with an integrated heat sink and a flow guide for gas-flow sensing applications with high sensitivity (700 mV at a flow velocity of 2.7 m/s and a supply voltage of 3 V), low power consumption (8 mW at 55 K over-temperature and an airflow velocity of 0.8 m/s) and short response time (lower than 150 ms). The chip and the diaphragm size were 4 mm × 6 mm and 1.5 mm × 2.0 mm, respectively.

In 1997, Nguyen and Dötzel (1997) develop a multi-range electrocaloric mass-flow sensor based on an asymmetrical relative positioning of heaters and temperature sensors, which was realized by using an array of heaters or temperature sensors (Fig. 5a). The asymmetrical relative positioning of heaters and temperature sensors is shown in Fig. 5b. In their study, a linear sensitivity was shown for a nitrogen flow from 0 to 50 ml/min.

Fig. 5

Schematic of multi-range electrocaloric mass flow sensor a perspective view and b heater array and temperature sensors on the sensor (Nguyen and Dötzel 1997)

In 1998, Ebefors et al. (1998) presented a MEMS-based triple-hot-wire sensor with polyimide joints. As shown in Fig. 6, the x- and y-hot wires were located in the wafer plane, while the z-wire was rotated out of the plane by a radial joint formed by the curing-induced shrinkage of polyimide resin pads deposited within V-shaped grooves in the silicon substrate. Overall, the silicon chip measured 3.5 × 3.0 × 0.5 mm³, while the three hot wires each had dimensions of 500 × 5 × 2 μm³. The time-constants of the hot-wire resistance change caused by heating without any flow were found to be 120 μs (cooling) and 330 μs (heating), respectively. Furthermore, it was shown that both response times were improved by operating the sensor at a constant temperature.

Fig. 6

MEMS triple hot-wire (Ebefors et al. 1998)

In 1999, Kaltsas and Nassiopoulou (1999) presented a C-MOS compatible silicon gas flow sensor, as shown in Fig. 7. The principle of operation was based on heat transfer from a polysilicon resistor to the fluid and the detection of the flow-induced temperature difference by polysilicon thermopiles, integrated at both sides of the heater. The input current was either introduced directly to the heater through the aluminum contact pads 5 and 6, or through a compensation resistor with exactly the same characteristics as the heater through aluminum pads 7 and 8. This resistor was used to compensate the resistance change of the heater due to its heat exchange with the gas. In their study, different sensor designs were considered and fabricated in order to determine optimum sensor performances. The distance between the polysilicon heater and the hot thermopile contacts was taken between 20 and 40 μm and the number of thermopiles between 12 and 23, with stripe thickness between 5 and 10 μm, respectively. Different values of the width of porous silicon isolation area were also considered between 180 and 320 μm. The sensor was evaluated in nitrogen flows from 0 to 0.4 m/s. Its sensitivity per heating power is 6.0 mV/(m/s) W and the chip size is 1.1 mm × 1.5 mm.

Fig. 7

Top-view of silicon gas flow sensor with porous silicon thermal isolation (Kaltsas and Nassiopoulou 1999)

In 1999, Liu et al. (1999) presented a micro-hot-film shear-stress sensor consisted of a suspended silicon–nitride diaphragm with 200 × 200 μm area and 1.5 μm thickness, which was located on top of a vacuum-sealed cavity, as shown in Fig. 8a. A heating and heat-sensing element, made of polycrystalline silicon material, was located on top of the diaphragm. The underlying vacuum cavity greatly reduced conductive heat loss to the substrate and therefore increased the sensitivity of the sensor. As shown in Fig. 8b, the diaphragm was separated from the bottom of the cavity by approximately 2 μm, with the pressure inside the cavity being lower than 300 mtorr. Two metallization wires of 10 μm width connected the polysilicon resistor to the external electronics. Due to the effective thermal isolation between the heated element and the substrate, the heat isolation could be further improved by increasing the depth of the cavity, thus enhancing the thermal resistance from the diaphragm to the substrate.

Fig. 8

Schematic of a top- and b side-views of a thermal shear-stress sensor (Liu et al. 1999)

In 2000, Hung et al. (2000) developed a thermal flow sensor with the mesh-membrane structure shown in Fig. 9. The sensor was fabricated by using an E-Gun evaporation technique to deposit an initial titanium barrier layer with a thickness of approximately 200 Å on a silicon substrate and then a platinum layer with a thickness of 1,800 Å. Finally, the thermoresistor was patterned using a standard lift-off technique. By curve fitting the experimental data obtained at temperatures ranging from 30 to 600°C, the temperature coefficient of resistance (TCR) of the sensor was found to be 0.00249 (1/°C). In addition, for flow velocities greater than 1.5 m/s, the flow meter incurred a power consumption of 14.56 mW and demonstrated a sensitivity of approximately 0.01433 mA (m/s)^−1/2 when operated in a constant-voltage mode. Finally, in a constant-current mode, the device was found to have a sensitivity of more than 7.98 mV (m/s)^−1/2 and a power consumption of 45.10 mW. Overall, the experimental results demonstrated that compared with traditional macro-scale membrane-structure flow sensors, the proposed device not only had a simpler fabrication, but also provided an improved reproducibility, a greater sensitivity, an enhanced linearity, a more rapid response and an improved robustness toward thermal fluctuations.

Fig. 9

Design of a thermal sensor with the mesh-membrane supporting structure (Hung et al. 2000)

In 2002, Makinwa and Huijsing (2002) exploited a wind sensor realized in a standard CMOS process, which consisted of a two-dimension thermal flow sensor and three auto-zeroed comparators on a single chip. The wind sensor chip was composed of a square silicon substrate on which four heaters, four thermopiles and a central diode were integrated, as shown in Fig. 10. The comparators formed the basis of three thermal sigma-delta modulators that controlled and digitized the heat distribution on the chip. In their study, it showed the sensor was capable of measuring wind speed and direction with an accuracy of ±4% and ±2°, respectively, over the range 2–18 m/s.

Fig. 10

Schematic layout of a CMOS wind-sensor (Makinwa and Huijsing 2002)

In 2003, Chen et al. (2003) presented a hot-wire anemometer (HWA) which was enabled by a three-dimension assembly technique called plastic deformation magnetic assembly (PDMA). As shown in Fig. 11, the HWA used a thermal element (hot wire) made of Pt/Ni/Pt film with a measured TCR of 2,700 ppm/°C. The thermal element was elevated from the substrate to a predetermined height that corresponded to the length of the support prongs. By elevating the thermal element away from the bottom of the velocity boundary layer, the thermal element could experience greater fluid flow velocity and exhibit better sensitivity.

Fig. 11

Schematic of a single out-of-plane HWA (Chen et al. 2003)

In 2004, Sabaté et al. (2004) presented a multi-range silicon micromachined sensor as shown in Fig. 12. It facilitated the measurement of both low (i.e. 0–200 sccm) and high (8 SLM) velocity flows. As shown in the cross-sectional illustration in Fig. 13, the device featured a total of seven resistors arranged symmetrically about the center of a nitride membrane measuring 750 × 750 μm² and positioned such that a distance of 120 μm remained between the last resistor and the silicon substrate in order to ensure a proper thermal isolation effect. The upstream resistors (i.e. R ₁, R ₂ and R ₃) served as both heaters and sensing elements, while the downstream resistors (i.e. R ₄, R ₅ and R ₆) served as sensing elements only. As a result, the temperatures of the upstream resistors decreased with an increasing flow rate, whereas those of the downstream resistors increased gradually at low flow rates, but decreased slightly at higher flow rates.

Fig. 12

Cross-section scheme of the multi-range silicon micromachined flow sensor (Sabaté et al. 2004)

Fig. 13

Top-view of the multi-range silicon micromachined flow sensor (wind direction left to right) (Sabaté et al. 2004)

In 2008, Yu et al. (2008) presented a micro channel integrated with gas flow sensor to enhance measurement accuracy, as shown in Fig. 14. Due to the air flow on both sides of the diaphragm of the flow sensor, the forced convective thermal transfer between the diaphragm and fluid would be present on both sides of diaphragm. The temperature characteristics of the novel flow sensor were simulated at different flow rates, from 0 to 5.0 m/s, and the optimized positions of the test resistor pair on the membrane were obtained. As the incoming flow velocity was 3 m/s, its temperature difference between the upstream and the downstream could reach about 38.6 K, which was much higher than those of the traditional flow sensors. The results illustrated that the measurement accuracy increased, but the measurement range narrowed with increase of the heater temperature. The measurement accuracy could increase and the measurement range could widen with the increase of the heater width.

Fig. 14

Cross-section scheme of the flow sensor structure a without and b with flow guide (Yu et al. 2008)

In summary, thermal flow sensors such as those reviewed above have a high sensitivity and a wide measurement range. However, many silicon-based thermal sensors produce a non-linear output signal and therefore require some form of biasing scheme. Moreover, the successful operation of thermal sensors is reliant upon the existence of a temperature differential between the sensor mechanism and the gas flow, respectively. Consequently, developing improved thermal isolation structures such as membranes or micro-bridges is essential in further enhancing the performance of thermal sensor designs.

3 Non-thermal flow sensors

As discussed in the following, the existing proposals for non-thermal flow sensors can be broadly categorized as either resonating, differential pressure-based, lift-force-based, or cantilever-based, respectively.

3.1 Resonating flow sensors

In 1990, Bouwstra et al. (1990) proposed a resonating microbridge mass flow sensor with a frequency output based on standard IC and MEMS fabrication technologies. Figure 15a illustrates the operation of the sensor. The microbridge was suspended at the center of a flow channel. Thin-film resistors were embedded within the microbridge for excitation and detection of forced vibrations. AC and a DC electrical voltage were superimposed and applied to the excitation resistors. The generated dynamic heat forced the microbridge into a bending mode of vibration by thermal expansion of its upper layers. The vibration could be detected by thin-film strain gauges in a Wheatstone bridge arrangement. A feedback loop amplifier off-chip completed the electrothermo-mechanical oscillator.

Fig. 15

a Operation of the resonating flow sensor and b experimental set-up with a gain/phase analyzer for measuring the transfer function of the resonating flow sensor (Bouwstra et al. 1990)

Figure 15b shows the working principle of the resonating flow sensor. A gain/phase analyzer was used to measure the transfer function of the vibrating microbridge with thermal excitation and piezoresistive detection. The static temperature elevation of the microbridge, caused by the dissipation in the resistors, was dependent on the heat transfer by conduction and forced convection, and strongly influenced the natural frequencies of the microstructure. The oscillation frequency, which was a function of the mass flow, could be converted into a digital signal for further manipulation. An additional advantage of the type of flow sensors is that they required few electromechanical transduction properties of the applied thin film and balance of Wheatstone bridge.

3.2 Differential pressure flow sensors

Differential pressure flow sensors are based on the fundamental physical property that the pressure drop induced in a gas flow as it travels over a surface varies in direct proportion to its velocity. The correlation between the pressure drop and the flow velocity can be formulated as follows:

$$ \Updelta p = \frac{C}{2}\frac{L}{{D_{\text{h}}^{2} }}U\mu $$

(1)

where Δp is the pressure drop, C is the friction coefficient, L is the length of the channel in the flow direction, D _h is the hydraulic diameter, U is the average velocity of the fluid, and μ is the dynamic viscosity of the fluid (Gravesen et al. 1993).

In 1998, Berberig et al. (1998) presented a Pyrex-based micro-flow sensor with the configuration shown in Fig. 16 and demonstrated that for certain ranges of the fluid velocity and viscosity, the sensor output signal could be related to the flow velocity via the following Bernoulli equation

$$ \rho gz + p_{\text{stat}} + \frac{{\rho u^{2} }}{2} = {\text{const}}. $$

(2)

with ρ is the fluid density, g is the gravitational constant, z is the height, p is the pressure, and u is the velocity.

Fig. 16

Schematic of the Prandtl micro flow sensor structure (Berberig et al. 1998)

Rearranging Eq. 2, it was shown that the flow velocity could be determined in accordance with

$$ u = \sqrt {\frac{2}{\rho }\left( {P_{\text{tot}} - P_{\text{stat}} } \right)} $$

(3)

where P _tot is the total pressure at the stagnation point (see Fig. 17).

Fig. 17

Schematic of the operation principle (Berberig et al. 1998)

In general, pressure flow sensors have two major advantages compared to their thermal counterparts, namely (1) the electrical contacts are typically fully insulated from the fluid and are therefore less prone to corrosion and damage, and (2) the requirement for a heating element is removed and therefore the device tends to be more easily fabricated and more power efficient. Thus, the main issue in developing high-performance pressure flow sensors is to enhance the sensitivity of the detection mechanism such that the interference imposed by the sensor on the gas flow is minimized whilst a high level of measurement accuracy is still retained.

3.3 Lift-force flow sensors

In 1997 and 1998, Svedin et al. (1997) presented a bi-directional gas-flow sensors based on lift force and (1998) a lift-force flow sensor designed for acceleration insensitivity. It is a silicon gas-flow sensor comprising two thin plates connected to a rigid center beam (see Fig. 18). It was shown that when the sensor was positioned at a small angle to the flow direction (i.e. less than 25°), the passage of the air over the thin plates created an upward force similar to that produced under an airplane wing. As a result, both plates experienced a small deflection, which was then detected by an array of strain gauges mounted on the frame of the sensor and converted into an equivalent flow velocity measurement. The results indicated that the sensor had an average flow sensitivity of 0.054 μV/V/(1/min)².

Fig. 18

Schematic of the lift force sensor structure (Svedin et al. 1998)

In general, a body located in a flow experiences a drag force acting in the direction of the flow and a lift force acting in the direction perpendicular to the flow. These two forces can be formulated as follows:

$$ F_{\text{drag}} = C_{\text{D}} \frac{{\rho V^{2} }}{2}bc $$

(4)

$$ F_{\text{lift}} = C_{\text{L}} \frac{{\rho V^{2} }}{2}bc $$

(5)

where C _D and C _L are the drag- and lift-force coefficients, respectively, b and c are the width and length of the body, respectively, ρ is the fluid density and V is the mean flow velocity. The distribution of the lift force experienced by the two thin plates in the sensor shown in Fig. 19 can be obtained from the theory of thin airfoils. Assuming that the rigid center support beam induces a negligible flow disturbance, the normalized force distribution, q(x), acting on the surface of the two plates can be expressed as

$$ q(x) = \frac{1}{{F_{\text{lift}} }}\frac{{{\text{d}}F_{\text{lift}} }}{{{\text{d}}x}} = \frac{2}{c\pi }\sqrt {\frac{c}{x} - 1} $$

(6)

where c is the cord length, i.e. the length of the structure in the direction of the flow (Anderson 1991).

Fig. 19

Front and rear parts of the airfoil structure deflect differently under the influence of the lift force (Svedin et al. 1998)

In 2003, Svedin et al. (2003) improved the sensing performance of their original lift force sensor through the addition of a thermal hot-chip sensor (see Fig. 20). The experimental results showed that the integration of two different flow sensor techniques enabled a high measurement sensitivity to be obtained over a wide flow range. Specifically, the thermal sensor provided an optimal measurement sensitivity in the low-velocity regime, while the lift-force sensor provided an enhanced sensing capability in the high-velocity regime (see Fig. 21). Moreover, it was shown that the addition of the thermal hot-chip sensor not only improved the sensing capability of the original lift-force sensor presented (Svedin et al. 1998) such that the flow direction could be detected as well as the flow rate, but also rendered the sensing structure more robust to the effects of accidental damage to one or other of the two sensing mechanisms.

Fig. 20

Schematic of the lift force sensor with integrated hot-chips (Svedin et al. 2003)

Fig. 21

General outline of the output signals from the lift force and thermal principles (Svedin et al. 2003)

3.4 Cantilever type flow sensors

In general, a cantilever deflection caused by air flow can be obtained by combining the effects of the loads acting separately

$$ \delta_{\text{t}} = \frac{{qa^{3} }}{24EI}(4L - a) + \frac{{Fb^{2} }}{6EI}(3L - b) $$

(7)

where δ_t is the total deflection of the cantilever, q is the uniform load intensity on the beam part, E is the Young’s modulus of cantilever, I is the moment of inertia, L is the length of the cantilever, F is the concentrated load on the paddle part, a is the distance from the fixed end to the uniform load and b is the distance from the fixed end to the concentrated load. Please note that q (the uniform load intensity) and F (the concentrated load) are applied by the wind pressure calculated by the Bernoulli’s equation:

$$ P_{\text{wind}} = 0.5\rho_{\text{air}} V_{\text{wind}}^{2} $$

(8)

where P _wind is the wind pressure, ρ_air is the intensity of the air and V _wind is the air flow velocity. The flow velocity is determined by measuring the resistance variation of pizeoresistor as the cantilever beam deflects under the influence of a fluid flow passing through it. The resistance R of the piezoresistor is given by

$$ R = \frac{{l_{\text{R}} \rho }}{A} = \frac{{l_{\text{R}} \rho }}{wt} $$

(9)

where l _R is the resistor length, ρ is the resistivity, A is the cross-sectional area, w is the width and t is thickness. The derivative of Eq. 9 is

$$ \frac{{{\text{d}}R}}{R} = \frac{{{\text{d}}\rho }}{\rho } + \frac{{{\text{d}}l_{\text{R}} }}{{l_{\text{R}} }} - \frac{{{\text{d}}w}}{w} - \frac{{{\text{d}}t}}{t} $$

(10)

where defines $\varepsilon_{\text{l}} = \frac{{{\text{d}}l_{\text{R}} }}{{l_{\text{R}} }},\;{\text{d}}l = \Updelta l,\;{\text{d}}w = \Updelta w,\;{\text{and}}\;{\text{d}}t = \Updelta t,$ then it could be rearranged to

$$ \frac{{{\raise0.7ex\hbox{${{\text{d}}R}$} \!\mathord{\left/ {\vphantom {{{\text{d}}R} R}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$R$}}}}{{\varepsilon_{\text{l}} }} \approx (1 + 2v) $$

(11)

where v is Poission’s ratio. The working principle of the cantilever type flow sensors shows that the resistance variation dR of the piezoresistor depends on the strain ε_l of the cantilever which deformation is caused by the deflection δ_t in Eq. 7 (Wang et al. 2007).

In 1997, Zhang et al. (1997) presented a cantilever-based flow sensor of the form illustrated in Fig. 22. As shown, the device comprised an open paddle-type cantilever structure. When exposed to a gas flow, the paddle-type cantilever experienced a downward deflection, causing a corresponding movement of the cantilever beam. This in turn generated a change in the resistance signals of an array of piezo-resistors attached to the root of the beam from which the air flow velocity was subsequently derived. It was shown theoretically that the device was capable of detecting water flow rates as low as 100 μl/min and air flows with a minimum velocity of 5 ml/min. In addition, the experimental results showed that the sensor maintained a linearity of 25% for air flow rates ranging from 10 to 200 ml/min.

Fig. 22

Schematic of cantilever paddle micromachined flow sensor (Zhang et al. 1997)

In 2002, Su et al. (2002) fabricated an ultra-thin micromachined silicon cantilever-based flow sensor with an integrated strain gauge at its root (see Fig. 23). The sensing performance of the device was characterized by conducting airflow measurement tests in a steel pipe with an inner diameter of 7.0 mm. The piezo-resistive sensitivity (ΔR/R)/y(0) of the device was found to vary in the range of 0.23–2.89 × 10⁻⁶ nm⁻¹ when characterized using beam bending tests, while the flow sensitivity (ΔR/R)/V ²_gas was determined in the airflow tests to lie in the range 0.652–4.489 × 10⁻⁵ (ms⁻¹)⁻². Finally, the minimum detectable airflow velocity was found to be 7.0 cm s⁻¹, which is broadly comparable to that for a conventional HWA.

Fig. 23

Schematic diagram of a cantilever beam with an attached square (Su et al. 2002)

In 2003, Chen et al. (2003) presented a flow sensor based on momentum transfer principles. As shown in Fig. 24, the sensor consisted of an in-plane fixed-free cantilever with a vertical artificial cilium attached at the tip of the free end. External flow parallel to the sensor substrate imparted upon the vertical cilium. Due to the rigid connection between the in-plane cantilever and the vertical cilium, a mechanical bending moment was transferred to the horizontal cantilever beam, inducing strain at the base of the cantilever beam. The strain, measured by using piezoresistive sensors embedded at the base of horizontal cantilevers, could correlate to the flow rate. The length, width, and thickness of the in-plane cantilever are 1,100, 180, and 17 μm, respectively. The height, width, and thickness of the vertical cilium are 820, 100, and 10 μm, respectively.

Fig. 24

Design of single artificial haircell sensor (Chen et al. 2003)

In 2007, Kao et al. (2007) presented a MEMS-based flow sensor for the measurement of gas flow. The flow sensor had an array of curved-up cantilever beams that were surface-micromachined with two layers of depositions under two sets of different process parameters. The differential residual stress between the two layers of the polysilicon depositions caused the beams to curve upward from the substrate surface as the sacrificial layer was released. As shown in Fig. 25, the length of the shortest beam is 200 μm, with beam lengths increasing in a step of 200 μm to the longest beam of 2,000 μm. The thickness of the beam was typically about 1 μm.

Fig. 25

Photographs of the surface-micromachined MEMS flow sensor with curved-up cantilever beams (Kao et al. 2007)

In 2007, Wang et al. (2007) exploited the tip deflection effect caused by manufacturing-induced residual stresses to fabricate a micro flow sensor comprising a free-standing cantilever structure (see Fig. 26). The sensitivity of the flow sensor was evaluated for a constant platinum piezo-resistor length of 1,500 μm and three cantilever beam widths, namely 400, 1,200 and 2,000 μm, respectively. The average sensitivities of the corresponding sensors were found to be 0.0134, 0.0227 and 0.0284 Ω/(m/s), respectively, with a maximum error of 2%. In other words, the flow rate sensitivity increased as the width of the cantilever beam was increased. The experimental results also showed that the maximum detectable flow rate was 45 m/s when using the cantilever beams.

Fig. 26

Schematic illustration of flow sensor (Wang et al. 2007)

4 Conclusions

Advances in MEMS techniques in recent years now make possible the fabrication of sophisticated sensors for a diverse range of applications. Compared to their traditional macro-scale counterparts, micro-scale sensors have a greater sensitivity, a lower cost, an improved portability and a more straightforward integration with IC circuit devices. This paper has presented a systematic review of the major MEMS-based micro-flow sensors presented in the literature over the past 30 years or so. It has been shown that depending on their mode of operation, these sensors can be broadly categorized as either thermal or non-thermal (i.e. pressure differential-based, force-lift based, or cantilever-based). The operational principles and sensing performance of each type of sensor have been systematically discussed, and their relative advantages and disadvantages highlighted where appropriate. Overall, the results presented in this review confirm the applicability of MEMS-based sensors for a diverse range of low-cost, high-performance gas flow sensing applications.