sensors Article
Sensitivity and Frequency-Response Improvement of a Thermal Convection–Based Accelerometer Maeum Han 1,2 , Jae Keon Kim 3,4 , Jin-Hyoung Park 2 , Woojin Kim 5 , Shin-Won Kang 1 , Seong Ho Kong 1, * and Daewoong Jung 4, * 1 2 3 4 5
*
School of Electronics Engineering, College of IT Engineering, Kyungpook National University, Daegu 41566, Korea;
[email protected] (M.H.);
[email protected] (S.-W.K.) Construction Equipment R&D Group, Korea Institute of Industrial Technology (KITECH), Daegu 42994, Korea;
[email protected] Department of Sensor and Display Engineering, Kyungpook National University, Daegu 41566, Korea;
[email protected] Aircraft System Technology Group, Korea Institute of Industrial Technology (KITECH), Daegu 42994, Korea Mechatronics Technology Convergence R&D Group, Korea Institute of Industrial Technology (KITECH), Daegu 42994, Korea;
[email protected] Correspondence:
[email protected] (S.H.K.);
[email protected] (D.J.); Tel.: +82-53-950-7579 (S.H.K.); +82-54-339-0624(D.J.)
Received: 26 June 2017; Accepted: 28 July 2017; Published: 2 August 2017
Abstract: This paper presents a thermal convection–based sensor fabricated using simple microelectromechanical systems (MEMS)-based processes. This sensor can be applied to both acceleration and inclination measurements without modifying the structure. Because the operating mechanism of the accelerometer is the thermal convection of a gas medium, a simple model is proposed and developed in which the performance of the thermal convection–based accelerometer is closely associated with the Grashof number, Gr and the Prandtl number, Pr . This paper discusses the experiments that were performed by varying several parameters such as the heating power, cavity size, gas media, and air pressure. The experimental results demonstrate that an increase in the heating power, pressure, and cavity size leads to an increase in the accelerometer sensitivity. However, an increase in the pressure and/or cavity size results in a decrease in the frequency bandwidth. This paper also discusses the fact that a working-gas medium with a large thermal diffusivity and small kinematic viscosity can widen the frequency bandwidth and increase the sensitivity, respectively. Keywords: accelerometer; frequency; acceleration; heat convection
1. Introduction Microelectromechanical systems (MEMS)-based devices integrate various mechanical elements, sensors, actuators, and electronics onto a silicon substrate to achieve a multitude of different tasks over a diverse range of fields. MEMS-based sensors are increasingly being used for commercial and industrial applications, such as pressure sensors, gas sensors, RF (Radio frequency) switches, and flow sensors. One of the most important MEMS devices is the accelerometer. Many types of accelerometers used to measure vibration, shock, and inertial motion have been developed for application in various industrial fields. Most conventional accelerometers detect the acceleration using a solid proof mass and are based on the changes in the capacitance [1,2] or the piezo effect [3,4]. However, MEMS-based accelerometers based on the proof-mass system suffer from problems such as electromagnetic interference (EMI), the effect of parasitic electrostatic force, and fabrication complexity [5–9]. To overcome these problems, a thermal type of MEMS-based accelerometer that does not require a solid proof mass has been developed and fabricated, as described in previous
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complexity [5–9]. Sensors 2017, 17, 1765 To overcome these problems, a thermal type of MEMS-based accelerometer 2that of 9 does not require a solid proof mass has been developed and fabricated, as described in previous papers [5–12]. The key features of these accelerometers are that they have no solid proof mass, and papers [5–12]. The key features these accelerometers that they have no with solid a proof mass, andintheir their operation is based on airofconvection through aare thermal exchange microheater an operation is based on air convection through a thermal exchange with a microheater in anwith enclosed enclosed chamber. The researchers found that gas is a good working medium compared solid chamber. The researchers that gas isparts a good medium compared with solid liquid or liquid medium becausefound no mechanical are working present and they are anticorrosive and or stable in medium because no mechanical parts are present and they are anticorrosive and stable in the atmosphere. the atmosphere. Our group group previously previously reported reported aa thermal thermal convection–based convection–based sensor sensor for fortilting tiltingmeasurement measurement[13]. [13]. Our The sensor sensor can can be be applied applied to to both both acceleration acceleration and and inclination inclination measurements measurements without without modifying modifying the the The structure. The current paper presents the experiments carried out to examine the parameters that affect structure. The current paper presents the experiments carried out to examine the parameters that the sensitivity and frequency characteristics of thermalofconvective accelerometers. Special efforts were affect the sensitivity and frequency characteristics thermal convective accelerometers. Special made considering improvements to the frequency response of the accelerometer because currently efforts were made considering improvements to the frequency response of the accelerometer availablecurrently reports on experimental studies concerning the frequency response few [14].response To improve because available reports on experimental studies concerning the are frequency are the sensitivity and frequency response, the current study concentrated on optimizing these different few [14]. To improve the sensitivity and frequency response, the current study concentrated on parameters: these the heating power, operatingthe frequency, medium, operating pressure, cavity optimizing different parameters: heating gas power, operating frequency, gasand medium, volume of an encapsulated microchamber. In addition, the proposed thermal convection–based operating pressure, and cavity volume of an encapsulated microchamber. In addition, the proposed accelerometer response wasaccelerometer theoretically evaluated, and its operating characteristics were thermal convection–based response was theoretically evaluated, and its measured operating through experimentation. Various simple models were used to better understand the sensitivity and characteristics were measured through experimentation. Various simple models were used to better frequency response of the accelerometer. The more influential were then account understand the sensitivity and frequency response of theparameters accelerometer. The taken moreinto influential in the sensor design. parameters were then taken into account in the sensor design. 2. Materials and Methods 2. Materials and Methods 2.1. Device Structure 2.1. Device Structure Figure 1a,b show the structure of the thermal convection–based accelerometer. It consists of Figure 1a,b show to theheat structure the thermal convection–based It consists of a a central microheater the gasofmedium in the cavity, and fouraccelerometer. temperature sensors located central microheater to heat the gas medium in the cavity, and four temperature sensors located from from either sides of the heater where the gas medium flows across the temperature sensors through either sides of theFigure heater1cwhere the gas flows acrossofthe through free free convection. illustrates themedium fabrication process thetemperature sensor. The sensors silicon (Si) substrate convection. Figure the fabrication process of the sensor. was prepared with1c theillustrates 0.5 µm thickness of silicon dioxide layer. The The backsilicon side of(Si) thesubstrate Si wafer was was prepared with the 0.5 μm thickness of silicon dioxide layer. The back side of the Si was etched and the heater and temperature sensors at the bottom wafer are made of platinum wafer (Pt), which etched and the heater andproperties temperature at with the bottom are made of platinum (Pt), which has very stable physical andsensors operates a high wafer temperature coefficient of resistance of has very stable physical properties and operates with a high temperature coefficient of resistance –3 ◦ − 1 3.93 × 10 ( C) . The frond side of Si was removed by wet etching to form thermal isolation of in 3.93 × 10–3 (°C)−1. The frond the sidesensor of Si was removed wet etching to form thermal isolation in the the microchamber. Finally, is packaged inby a sealed microchamber that contains a working microchamber. Finally, the sensor medium, e.g., air or nitrogen (N2 ). is packaged in a sealed microchamber that contains a working medium, e.g., air or nitrogen (N2).
Figure 1. 1. (a) (a) Schematic PCB board and (c) (c) fabrication process of the Figure Schematic view, view,(b) (b)fabricated fabricatedsensor sensorononthe the PCB board and fabrication process of thermal convection–based accelerometer. the thermal convection–based accelerometer.
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2.2. Principles of Operation 2.2. Principles of Operation Figure 2a shows the temperature distribution in the cavity when the accelerometer is not Figure 2a shows the temperature distribution in the cavity when the accelerometer is not subjected subjected to acceleration. When power is introduced to the heater, the temperature around the to acceleration. When power is introduced to the heater, the temperature around the heater rises, heater rises, creating thermal convection in the cavity. In this case, the temperature profile of the gas creating thermal convection in the cavity. In this case, the temperature profile of the gas medium medium in the cavity is symmetrically sensed by both temperature sensors, as shown by the straight in the cavity is symmetrically sensed by both temperature sensors, as shown by the straight line. line. No temperature difference is detected between the two temperature sensors; thus, identical No temperature difference is detected between the two temperature sensors; thus, identical electrical electrical resistances and/or voltages are produced. When the accelerometer is subjected to resistances and/or voltages are produced. When the accelerometer is subjected to acceleration, acceleration, the temperature profile shifts along the direction of the applied acceleration, as shown the temperature profile shifts along the direction of the applied acceleration, as shown Figure 2b. Figure 2b. This condition results in an increase in temperature around one temperature sensor and a This condition results in an increase in temperature around one temperature sensor and a decrease in decrease in temperature around the other sensor, generating a temperature difference between the temperature around the other sensor, generating a temperature difference between the two temperature two temperature sensors that is proportional to the magnitude of the applied acceleration. By sensors that is proportional to the magnitude of the applied acceleration. By measuring the electrical measuring the electrical signal produced from the temperature difference, the acceleration can be signal produced from the temperature difference, the acceleration can be determined. determined.
Figure 2. The proposed convective sensor (a) basic principle and (b) simulation analysis (1 g at 450 K Figure 2. The proposed convective sensor (a) basic principle and (b) simulation analysis (1 g at 450 K and atmospheric pressure). and atmospheric pressure).
2.3. Theory of Operation 2.3. Theory of Operation Because the working mechanism of the convective accelerometer is based on thermal convection, Because the working mechanism of provide the convective accelerometer is environment based on thermal a method to improve its performance is to an appropriate convection to the convection, a method to improve its performance is to provide an appropriate accelerometer. Generally, two non-dimensional parameters, namely the Grashof number convection Gr and the environment to the accelerometer. twothe non-dimensional Prandtl number Pr , are introduced Generally, to investigate effect of thermalparameters, convection namely [15]. the Grashof number Gr and the Prandtl number Pr, are introduced to investigate the effect of thermal convection [15]. gρ2 βL3 ∆T Gr = (1) 2 2µ 3
Gr =
g ρ β L ΔT
Pr =
µ
μα 2
(1) (2)
Here g, ρ, β, L, ∆T, µ, and α are the applied acceleration, gas density, coefficient of μ Pr = denotes the cavity size), temperature difference (2) volumetric expansion, characteristic size (generally α between the heater and boundary of the sensor, kinematic viscosity, and thermal diffusivity, Here g, ρ,As β, expressed L, ΔT, μ, and α are the applied gas density, of predict volumetric respectively. in Equations (1) and acceleration, (2), these parameters cancoefficient be used to the expansion, characteristic size (generally denotes the cavity size), temperature difference between the heater and boundary of the sensor, kinematic viscosity, and thermal diffusivity, respectively. As expressed in Equations (1) and (2), these parameters can be used to predict the effects of the
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effects of the working-fluid properties on the sensitivity and frequency response of the thermal convection-based accelerometer. Previous works have shown that the temperature difference in the thermal convection-based sensor is linearly proportional to the Gr number; thus, a larger Gr number results in higher sensitivity of the thermal convection-based accelerometer for a given acceleration [10–12]. Therefore, increasing the value of the Gr number is essential to obtain good sensitivity of the thermal accelerometer. According to Equation (1), the following design parameters can be considered to increase the sensitivity of the thermal accelerometer: (i) Large heating power and lower ambient temperature, which corresponds to increasing T, (ii) Increase in the characteristic size, which corresponds to increasing L, (iii) Selection of a gas medium with large gas density ρ and small kinematic viscosity µ. Previous papers on thermal accelerometer have discussed the dependence of performance on Gr and Pr , important factors in sensitivity and frequency response [11–14,16,17]. In particular, the frequency response of a thermal accelerometer can therefore be improved by taking into account the thermal variations in the gas properties and the dependence on the air thermal conductivity [12]. To obtain a fast and wider frequency response, we need to highly influence the thermal physical properties of the gas medium. A large thermal conductivity (α) and a small gas density (ρ) will accelerate the thermal diffusion, which consequently facilitates the heat balance in the cavity of the accelerometer and provides a fast frequency response to the accelerometer. In addition, the frequency response is associated with the cavity dimensions and the distance between the heater and temperature sensor. We can deduce that achieving heat uniformity in a larger cavity of an accelerometer at given heater power takes a longer time and shows a slower frequency response. On the other hand, the gas medium around the heater can quickly reach the temperature sensor when the distance between the heater and temperature sensor is small. All the above-mentioned methods to improve the sensitivity and frequency response of the thermal convection-based accelerometer must be experimentally carried out based on Gr and Pr parameters to optimize the sensor structural design and maximize the performance of the accelerometer. 3. Results and Discussion 3.1. Effects of the Heating Power The sensitivities of the thermal accelerometer were measured by two methods that rely on field applications. One method that measures the sensitivity, which is called static sensitivity, was undertaken from −90◦ (−g) to +90◦ (+g) by rotating the accelerometer under standard conditions (room temperature and atmospheric pressure) where the axis is parallel to the Earth’s gravitational force. Figure 3a shows the sensitivity of the accelerometer under gravitation. This result demonstrates that the accelerometer operates well and exhibits quite a linear performance even in the whole range from −90◦ to +90◦ . With the rotation, the resistance of the temperature sensor changes due to the shifting of the temperature profile in the cavity. The magnitude of the resistance change is measured as the sensitivity of the accelerometer under given conditions. The static sensitivity of the accelerometer is 360 µV·g−1 under a heater power of 50 mW. The other method of measuring the sensitivity of the accelerometer, which is called dynamic sensitivity, is to intentionally apply acceleration to the accelerometer using a vibration shaker within a certain range of frequencies. Figure 3b shows that the accelerometer displays linear sensitivities with the range from 0 to 10 g at 30 Hz. In this case, the slope of the graph can be considered as the dynamic sensitivity of the accelerometer. We note that the dynamic sensitivity of the accelerometer is 277 µV·g−1 at an operating power of 50 mW. The static sensitivity is larger than the dynamic sensitivity under equal heating power.
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Figure 3.3.The The output voltage of the as of (a) angles and Figure output voltage of the as a function of (a) tilting and (b) accelerations. Figure3. The output voltage ofaccelerometer the accelerometer accelerometer as aa function function of angles (a) tilting tilting angles and (b) (b) accelerations. accelerations.
Figure 4a shows the effect of the heating power on the sensitivity of the accelerometer. Figure the heating power the of accelerometer. The Figure 4a 4a shows shows the effect effect of of the the heating power on onunder the sensitivity sensitivity of the thepower. accelerometer. The sensitivity of the accelerometer is shown to increase a large heating As shownThe in sensitivity of the accelerometer is shown to increase under a large heating power. As shown sensitivity the accelerometer showncan to raise increase under a large heating in power. As shown Figure 4b,c,of increasing the heatingispower the temperature difference the cavity of the in power can raise difference in the inFigure Figure4b,c, 4b,c,increasing increasingthe theheating heating power can raisethe thetemperature temperature difference thecavity cavityof ofthe the accelerometer, simultaneously providing high sensitivity. A powered heater within high temperature accelerometer, simultaneously providing high sensitivity. A powered heater with high temperature accelerometer, providing high sensitivity. A powered heater withorhigh temperature contains a largesimultaneously amount of thermal energy compared to an unpowered heater a heater with a contains aalarge amount of thermal energy compared to an unpowered heater or aaheater with aalow contains large amount of thermal energy compared to an unpowered heater or heater with low low temperature. The law of conversion of energy states that the total energy of an isolated system temperature. The law of conversion of energy states that the total energy of an isolated system temperature. TheEnergy law of can conversion energynor states that theHowever, total energy isolated system remains constant. neither beofcreated destroyed. it canofbean transformed from remains constant. Energy can neither be created nor destroyed. However, ititcan be transformed from remains constant. Energy can neither be created nor destroyed. However, can be transformed from one form to another. In other words, powered heaters with high temperature can transfer a large one form to another. In other words, powered heaters with high temperature can transfer aalarge one form to another. In other words, powered heaters with high temperature can transfer large amount of thermal energy to the working gas medium, which leads to high sensitivity of the thermal amount energy gas which to of the amountof ofthermal thermalaccelerometer energyto tothe theworking working gasmedium, medium, whichleads leads tohigh highsensitivity sensitivity thethermal thermal convection–based [18]. In practical applications, however, we need toofconsider the convection–based accelerometer [18]. In practical applications, however, we need to consider the convection–based accelerometer [18]. In practical applications, however, we need to consider the power consumption and sensitivity of the accelerometer. power powerconsumption consumptionand andsensitivity sensitivityof ofthe theaccelerometer. accelerometer.
Figure 4. 4. (a)The The outputvoltage voltage of the accelerometer as a function of acceleration with respect to Figure Figure 4.(a) (a) Theoutput output voltageof ofthe theaccelerometer accelerometeras asaafunction functionof ofacceleration accelerationwith withrespect respecttotothe the the applied heater power and simulation results at a heater temperature of (b) 400KKand and (c)450 450 K applied appliedheater heaterpower power and and simulation simulation results results atat aa heater heater temperature temperature of of (b) (b) 400 400 K and (c) (c) 450 KK (acceleration of 1 g and atmospheric pressure). (acceleration (accelerationof of11ggand andatmospheric atmosphericpressure). pressure).
3.2. Effects of the Medium Type 3.2. 3.2.Effects Effectsof ofthe theMedium MediumType Type Because the thermal convection–based accelerometer detects the temperature distribution profile Because convection–based accelerometer detects the distribution Because the the thermal thermal convection–based accelerometer detects the temperature temperature distribution of the gas medium that fillsthat the fills cavity, conditions such as the pressure, size, andsize, gas medium profile of cavity, cavity such as and profile ofthe thegas gasmedium medium that fillsthe thecavity cavity, cavityconditions conditions such asthe thepressure, pressure, size, andgas gas are critical parameters that affect the sensitivity of the accelerometer. medium mediumare arecritical criticalparameters parametersthat thataffect affectthe thesensitivity sensitivityof ofthe theaccelerometer. accelerometer. The performance of the accelerometer filled with different gas media has been experimentally The Theperformance performanceof ofthe theaccelerometer accelerometerfilled filledwith withdifferent differentgas gasmedia mediahas hasbeen beenexperimentally experimentally tested and analyzed. Figure 5a shows the effect of a gas medium on the sensitivity of the accelerometer tested and analyzed. Figure 5a shows the effect of a gas medium on the sensitivity of tested and analyzed. Figure 5a shows the effect of a gas medium on the sensitivity of the the with respect to different gas media, namely air, N , and CO . We can clearly observe that the accelerometer with respect to different gas media, namely air, N 2, and CO2. We can clearly observe 2 2 accelerometer with respect to different gas media, namely air, N2, and CO2. We can clearly observe accelerometer filled with COwith shows highest whereas the lowest sensitivity is observed that filled CO 2 shows the sensitivity, highest sensitivity, whereas the lowest sensitivity is 2with thatthe theaccelerometer accelerometer filled COthe 2 shows the highest sensitivity, whereas the lowest sensitivity is observed in the accelerometer filled with air. The difference in the sensitivities under different gas observed in the accelerometer filled with air. The difference in the sensitivities under different gas
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Sensors 2017, 17, 1765 6 ofmedia 9 in the accelerometer filled with air. The difference in the sensitivities under different gas is due to the different properties, densities, and kinematic viscosities. As shown Table 1, CO2 has the media is due to the different properties, densities, and kinematic viscosities. As shown Table 1, CO2 largest density and smallest kinematic viscosity among these media, and its corresponding Gr value has the largest density and smallest kinematic viscosity among these media, and its corresponding is the largest. In contrast, air has a small density and a large kinematic viscosity, thus yielding a low Gr value is the largest. In contrast, air has a small density and a large kinematic viscosity, thus sensitivity. viscosity makes a gas medium resistant to gas flow,to leading to leading lower sensitivity. yielding aHigh low sensitivity. High viscosity makes amore gas medium more resistant gas flow, to Thesensitivity. frequency response of the accelerometers under different gas media has also been measured, lower and theThe results are shown in Figure 5b. accelerometers The frequencyunder response of the gas accelerometer frequency response of the different media has filled also with been air gas measured, and the results are shown in Figure 5b. The frequency response of the accelerometer filled media is nearly flat up to approximately 80 Hz. Beyond 80 Hz, the sensitivity substantially decreases withfrequency air gas media is nearly flat to approximately Hz. Beyond 80 Hz, the sensitivity as the increases. When theupacceleration is kept 80 constant, the accelerometer moves a shorter substantially decreases as the frequency increases. When the acceleration is of kept the distance at a higher frequency, which leads to a decrease in the sensitivity theconstant, accelerometer [11]. accelerometer moves a shorter distance at a higher frequency, which leads to a decrease in the Another reason is ascribed to the fact that higher frequencies induce a greater admixture of the sensitivity of the accelerometer [11]. Another reason is ascribed to the fact that higher frequencies hot and cold gas media surrounding the temperature sensors in the microchamber, thus degrading induce a greater admixture of the hot and cold gas media surrounding the temperature sensors in thethe sensitivity. Furthermore, the gas can change from a laminar to a can turbulent microchamber, thus degrading theflow sensitivity. Furthermore, the gas flow changeflow fromat a higher frequencies 70 Hz) [19]. frequencies (normally > 70 Hz) [19]. laminar to(normally a turbulent>flow at higher OnOn the other hand, the experiment results reveal air can accurately the acceleration the other hand, the experiment results reveal thatthat air can accurately detectdetect the acceleration in frequency 80 Hz, Hz,whereas whereasthe the CO barely measure Hz. The medium in frequencyranges rangesof of up up to 80 CO 2 can barely measure up toup 60 to Hz.60The medium 2 can propertiesdirectly directly determine rapidly the gases move temperature sensor. Gases sensor. properties determinehow how rapidly the can gases cantoward movethe toward the temperature withwith a lighter density and larger diffusivity are advantageous as a working for medium a Gases a lighter density and thermal larger thermal diffusivity are advantageous as medium a working higher frequency response. A larger thermal diffusivity and a lighter density take less time to deliver for a higher frequency response. A larger thermal diffusivity and a lighter density take less time to deliver the heated gas from the central microheater to the temperature sensor. From these factors, we can the heated gas from the central microheater to the temperature sensor. From these factors, we can assume assume that the sensitivity of the accelerometer has a trade-off relationship with the frequency that the sensitivity of the accelerometer has a trade-off relationship with the frequency response.
response.
Figure 5. 5. The output characteristics Figure The output characteristicsofofthe theaccelerometer accelerometer as as aafunction function of of the the gas gas medium medium with with respect to:respect (a) acceleration and (b) and frequency. to: (a) acceleration (b) frequency. ◦ C [20]. Table1.1.The Thegas gas medium properties 50[20]. Table medium properties at 50at°C
Air Air N2 N2 CO2CO2
Density Density 3) 3 (kg/m (kg/m )
Specific SpecificHeat Heat (kJ/kg·K) (kJ/kg·K)
1.092 1.092 1.0564 1.0564 1.6597 1.6597
1.007 1.007 1.042 1.042 0.8666 0.8666
Kinematic Viscosity Diffusivity Conductivity Kinematic Viscosity Thermal Thermal Diffusivity Thermal Thermal Conductivity −6 −4) (m 6 ) 2(m −4 2)/s) (×10 /s) 2 /s) (×10 (W/m·K) (×10)−(m (×10 (m2 /s) (W/m·K) 19.6 0.248 0.02735 19.6 0.248 0.02735 17.74 0.249 0.02746 17.74 0.249 0.02746 9.71 0.129 0.01858 9.71 0.129 0.01858
Effects theGas GasPressure Pressure 3.3.3.3. Effects ofofthe The physical states of a gas medium in the cavity highly influence the sensitivity of the thermal The physical states of a gas medium in the cavity highly influence the sensitivity of the thermal accelerometer. A larger Gr number is beneficial for a sensitive thermal sensor. When the heater accelerometer. A larger Gr number is beneficial for a sensitive thermal sensor. When the heater power, power, structural dimensions, and gas medium are given, the gas density is the only variable to be structural dimensions, and gas medium are the gastodensity is thepressure. only variable to be considered. considered. The gas density ρ in Equation (1)given, corresponds the ambient Thus, higher gas
The gas density ρ in Equation (1) corresponds to the ambient pressure. Thus, higher gas pressure increases the Gr number, improving the sensitivity of the thermal accelerometer. Figure 6a shows
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pressure increases the Gr number, improving the sensitivity of the thermal accelerometer. Figure 6a shows that better sensitivities are observed at higher gas pressure, as expected. Mailly et al. reported that better the thermal boundary layer ofatthe temperature profile decreasesMailly whenetthe gas pressure sensitivities are observed higher gas pressure, as expected. al. reported that (density) increases (the layer thermal boundary layer isprofile defined as the distance in which the temperature the thermal boundary of the temperature decreases when the gas pressure (density) rise is 10%(the of the heaterboundary temperature [21]. Asasshown in the simulation results in Figure 6c,d, the increases thermal layerrise) is defined the distance in which the temperature rise is 10% reduced thermal boundary layer observed at simulation higher gasresults pressure. Although thermal of the heater temperature rise) [21].was As shown in the in Figure 6c,d, the reduced boundary layer islayer limited the cavity size gas or volume the accelerometer, to this thermal boundary wasby observed at higher pressure.ofAlthough the thermal according boundary layer is definition, the cavity temperature sensor can detect higher temperatures atthis higher gas pressures without limited by the size or volume of the accelerometer, according to definition, the temperature structural the accelerometer. Thisgas feature is thewithout special advantage of this sensoroftype sensor canmodification detect higheroftemperatures at higher pressures structural modification the because we can possibly achieve high sensitivity by packaging at higher pressure. In contrast, the accelerometer. This feature is the special advantage of this sensor type because we can possibly achieve proof-mass–type sensor requires modification of the structural to improve therequires sensor high sensitivity by packaging at higher pressure. In contrast, theparameters proof-mass–type sensor performance. modification of the structural parameters to improve the sensor performance. On the other other hand, hand, an an inferior inferiorfrequency frequencyresponse responseisisobserved observedatathigher higher pressure, shown airair pressure, as as shown in in Figure revealed the expressionofofthe thethermal thermaldiffusivity, diffusivity,αα==k/ρ k/ρ·c, the density (ρ) of the Figure 6b.6b. AsAs revealed byby the expression ·c, the gas is thermal conductivity (k)(k) and specific heat (c) is linearly linearlyproportional proportionaltotothe thepressure, pressure,whereas whereasthe the thermal conductivity and specific heat undergo very small variations even if if the (c) undergo very small variations even thepressure pressureincreases increases[22]. [22].These Thesefactors factors explain explain why why the frequency response of the sensor decreases as its internal pressure pressure increases. increases.
Figure 6. The Figure 6. The output output characteristics characteristics of of the the accelerometer accelerometer as as aa function function of of pressure pressure with with respect respect to: to: (a) acceleration and (b) frequency. Simulation results at gas pressure of (c) 1 bar and (d) (a) acceleration and (b) frequency. Simulation results at gas pressure of (c) 1 bar and (d) 1.8 1.8 bar bar (heater: K). (heater: 450 450 K).
3.4. 3.4. Effects Effects of of the the Cavity Cavity Volume Volume The The volume volume of of the the gas gas medium medium cavity cavity also also influences influences the the sensitivity sensitivity and and frequency frequency response response of of the the sensor sensor because because it it is is related related to to the the gas gas density density and and the the heat heat quantity quantityper perunit unitvolume volumeof ofthe thesensor. sensor. The encapsulated microcavity accommodate various The encapsulated microcavity is is designed designed to to accommodate various sizes sizes to to determine determine the the optimum optimum cavity cavity volume. volume. Figure Figure 7a 7a shows shows the the output output characteristics characteristics of of the the accelerometer accelerometer as as aa function function of of the the cavity size. The experiment reveals that the measurement results of the accelerometer show a higher cavity size. The experiment reveals that the measurement results of the accelerometer show a higher sensitivity smaller cavity the flow flow circulation circulation [23]. [23]. Gas sensitivity for for aa larger larger cavity cavity because because aa smaller cavity retards retards the Gas flow flow is is restricted which substantially substantially suppresses restricted by by aa small small cavity cavity boundary, boundary, which suppresses the the flow flow action action induced induced by by thermal thermal convection convection and and reduces reduces the the sensitivity. sensitivity. Therefore, Therefore, manufacturing manufacturing using using aa large large cavity cavity size size will increasethe the sensitivity of accelerometer. the accelerometer. are consistent those of will increase sensitivity of the These These results results are consistent with thosewith of previously previously reported papers [15–18]. Figure 7b shows response the frequency response convective of the proposed reported papers [15–18]. Figure 7b shows the frequency of the proposed sensor convective sensor with different cavity volumes. We find that a larger chamber has a lower with different cavity volumes. We find that a larger chamber has a lower frequency, which implies
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that a longer time is required for the temperature to reach equilibrium [12]. Thus, small sizes might be frequency, which implies that a longer time is required to see reach [12]. more desirable to enhance the frequency response. Basedfor onthe thistemperature result, we can thatequilibrium simultaneously Thus, smallboth sizesthe might be more to response enhance the frequency response. Based on result, improving sensitivity anddesirable frequency by optimizing the gas medium, gasthis pressure, we can see that simultaneously improving both the sensitivity and frequency response by and cavity size is not possible. Therefore, in designing the thermal accelerometer, we need to consider optimizing the gas medium, gas pressure, and cavity size is not possible. Therefore, in designing the the practical applications of the accelerometer. thermal accelerometer, we need to consider the practical applications of the accelerometer.
Figure 7.7.The Theoutput outputcharacteristics characteristics of the accelerometer as a function the volume cavity volume with Figure of the accelerometer as a function of the of cavity with respect respect to: (a) acceleration and (b) frequency (inset: different cavity size). to: (a) acceleration and (b) frequency (inset: different cavity size).
4. Conclusions Conclusions 4. An accelerometer accelerometer based on convection was fabricated this characterizations study. Several An based on convection was fabricated and tested and in thistested study. in Several characterizations derived through experimentation demonstrated that the thermal convection–based derived through experimentation demonstrated that the thermal convection–based accelerometer exhibits accelerometer exhibits better linearity, preferable frequency response, and higher sensitivity by better linearity, preferable frequency response, and higher sensitivity by optimizing various parameters. optimizing various parameters. Thistostudy paid particular attention the frequency response of the This study paid particular attention the frequency response of the to convection-based accelerometer convection-based accelerometer based on thermal exchanges. The characteristics of the sensor have based on thermal exchanges. The characteristics of the sensor have been experimentally investigated as experimentally investigated as aheater function of the medium, heater results power,have and abeen function of the gas medium, pressure, power, andgas cavity volume.pressure, The experiment cavity volume. The experiment results shown that the frequency response can be extended by shown that the frequency response can have be extended by optimizing various factors, such as a smaller optimizing various factors, such as a smaller cavity volume, a lower gas pressure, and a gas medium cavity volume, a lower gas pressure, and a gas medium with a large thermal diffusivity. with a large thermal diffusivity. Acknowledgments: This study was supported by the BK21 Plus project funded by the Ministry of Education, Acknowledgments: This study was supported by the BK21 Plus project funded by the Ministry of Education, Korea (21A20131600011). Korea (21A20131600011). Author Contributions: M.H., J.K., S.K. and D.J. conceived the idea and designed the experiment. M.H., J.K. and S.K. fabricated the experimental sensor. the characteristics the sensor. analyzed the sensor Author Contributions: M.H., J.K., S.K.W.K. and simulated D.J. conceived the idea and of designed the J.P. experiment. M.H., J.K. and J.K. and analyzed the experimental results. M.H., S.K., and D.J.of wrote the paper discussed and efficiency. S.K. fabricated theJ.P. experimental sensor. W.K. simulated the characteristics the sensor. J.P.and analyzed the the contents. sensor and efficiency. J.K. and J.P. analyzed the experimental results. M.H., S.K., and D.J. wrote the paper and Conflicts Interest: The authors declare no conflict of interest. discussedof the contents.
Conflicts of Interest: The authors declare no conflict of interest.
References
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