In the analytical model, the length of the channel is one of the variables in the heat equation. Thus it is interesting to know how the length of the channel influences the sensitivity. Firstly the simulation parameters will be defined, the heater’s length will be chosen as500um and without any gap between two heaters, and the length of
the channel will changes from 4000 to 1000um. And the rest of the parameters will
be the same as 3.6.
Figure 3.20 shows the simulation result. For the 4000um, 3000umand 2000 um, the output voltage remains at same level. But from the 1800 um, the output
voltage is lower. Because as the channel length decreases, the heater is closer to the boundary of the channel, then the heat-sink will force the temperature level drop to the room temperature. To have a better understanding about how the heat-sink forces the temperature to the room temperature, Appendix E shows the temperature profiles. As the output voltage decreases, the sensitivity of the sensor is also de- creasing, then to design a high sensitivity sensor, the silicon heat-sink should keep some distance from heaters.
60 CHAPTER3. BRONKHORSTSENSORS
Figure 3.20: The simulation results of changing channel length. The triangle mark is the sensor with 4000umchannel length, the blue cross is the sensor
with 3000 um channel length, the blue solid line is the sensor with
2000umchannel length and red line is s the sensor with 1000um
3.5.3 How the fabrication process influence the performance
During the fabrication process, it is difficult to make sure the thickness of the material is the same as it supposes to be. Since some material such as the heater and the SiRN wall are regarded as thin film material,the changing the thickness will cause the properties of the material to change. Thus, in this section, we will investigate how the material properties influences the performance of the sensor. The simulation parameters can be found in table 3.7.
Parameters Value Unit
G0 20 W/(km3)
Radius of Channel 31.5 um
Length of heater 500 um
Length of Channel 2000 um
Bridge Voltage of Wheatone Bridge 956 mV
Ambient Temperature 293.15 K
Amplification Factor 150
Figure 3.21: The simulation result of changing effective thermal conductivity.
Firstly, the thermal conductivity of SiRN will increase from3W/mKto9W/mK.
The figure 3.21 shows the simulation result, as the thermal conductivity of SiRN increases the sensitivity of the sensor decrease.
Secondly, the TCR of the gold heater is also relevant, because it will influence the resistance of the measuring resistor. Thus we will increase the TCR of gold to see how it will affect the performance of the sensor, see figure 3.22. As the TCR of gold decrease, the sensitivity of the sensor is decreasing.
62 CHAPTER3. BRONKHORSTSENSORS
Figure 3.22: The simulation result of changing TCR of gold.
3.6 Overview
This chapter presents both simulation results and the measurement results. There still some differences between the simulation results and measurement results. The reason behind it is we can’t build the same heat-sink structure as the real sensor, and calculation value of theG0 will be different from the actual sensor. However, we
can adjust theG0 to fit the measurement result, which also means if we can get the
accurate value for the conductivity of heat-sink, the simulation model can predict the output of sensor accurately.
From the simulation result of the Bronkhorst’s sensor, it turns out that the sen- sitivity of the sensor can be improved by increasing the radius of the channel and decrease the heater’s length. However, there still some parameters we can change to optimize the sensor. Later on, we also change some parameters in the simulation to investigate how it influences the sensor. First, we adjusted the distance between the two heaters, from the simulation result, the sensitivity of the sensor is improved by decreasing the distance between the two heaters. Second, when the channel’s length is close to the heater’s length, the sensitivity of the sensor is also decreased. What else, we also found that if the fabrication process is not accurate enough, the behavior of sensor will also change as the material’s properties changes, for exam- ple, by increasing the thickness of the SiRN wall, the thermal conductivity of SiRN will be increased, it will results in the sensitivity of the sensor decrease.
Conclusion and Discussion
This thesis presents two types of model to predict the behavior of a thermal flow sensor. The first model is built in Comsol, which is using numerically way to calculate the temperature profile of the sensor. The advantages of Comsol is that it can create the model in 3D, and it can use the multiple physical models. But it takes a long time to finish the simulation, especially if there is any thin film structure in the model, we must increase the mesh size to get an accurate result, and it will result in even longer time consumption. The second model is an analytical model which based on the heat equation. The advantage of the analytical model is that it takes much less time to generate the result, and the result is close to the Comsol simulation.
Later on, the sensors from the Bronkhorst are measured to verify the simulation results. The simulation result is close to the measurement result, but there is some difference between the simulation result and measurement result. The main reason behind it is that the heat structure in the actual sensor is too complex to construct it in the simulation. Meanwhile, we also investigate how the design parameters will influence the behavior of the thermal flow sensor. From the simulation and mea- surement result in chapter 3.4.1, the sensitivity of the sensor increases as the radius increases. For example, the sensitivity of the sensor with31.5umradius channel is
40.6mV /(ml/min), when we increase the radius of channel to 45um, the sensi-
tivity now is 48mV /(ml/min). In the chapter 3.4.2, the sensitivity of the sensor
can be improved by decreasing the heater’s length. For example, the sensitivity of the sensor with1000umheater is118mV /(ml/min), the sensitivity of the sensor
with500umheater is250mV /(ml/min). Except for these two parameters, there
still have some parameters can influence the behavior of the sensor. Thus, in chap- ter 3.5, we run the analytical model by adjusting some design parameters, such as the distance between two heaters, channel length, and material properties. It turns out that increasing the distance of two heaters, decreases the channel length and increases the thickness of SiRN will result in decreasing the sensitivity. By collecting all these information, the new thermal sensor with one heater is designed. But due
64 CHAPTER4. CONCLUSION AND DISCUSSION to the time limitation, we design a mask but doesn’t fabrication out, see the appendix F.
Outlook on future work
In this thesis, the analytical model is built to predict the behavior of the thermal flow sensor, but there are some items remain to be done:
1. The equation to approximate the G0 in this thesis is not accurate enough,
therefore it is important to find a proper way to calculate theG0.
2. Except the design parameters mentioned in this thesis, there still have some design parameters can be investigated, for example, it might help to place the sensor in the vacuum, the sensitivity might be improved by applying more heaters, the measurement range might be an increase by using multiple chan- nels, etc.
3. Base on the analytical model in this thesis, it might be interesting to develop a software can generate omptimal design parameter when we enter the sensi- tivity and measurement range.
[1] “Comsol, inc.” https://www.comsol.com/. [2] “Ansys, inc.” https://www.ansys.com/.
[3] J. Groenesteijn, M. J. de Boer, J. C. L¨otters, and R. J. Wiegerink, “A versatile technology platform for microfluidic handling systems, part i: fabrication and functionalization,” Microfluidics and Nanofluidics, vol. 21, no. 7, p. 127, Jul
2017. [Online]. Available: https://doi.org/10.1007/s10404-017-1961-0 [4] “Bronkhorst nederland b.v.” https://www.bronkhorst.nl/.
[5] H.H.Bruun.,Hot-Wire Anemometry. Oxford University Press, 1994.
[6] “Wolfram research corp.” http://www.wolfram.com/.
[7] T. L. B. A. S. L. Frank P. Incropera, David P. Dewitt,Fundamentals of Heat and Mass Transfer. JOHN WILEY SONS, 2006.
[8] K. Ohe and Y. Naito, “A new resistor having an anomalously large positive tem- perature coefficient,”Japanese Journal of Applied Physics, vol. 10, no. 1, p. 99,
1971.
[9] A. Alenitesyn and E. Butikov, “. concise handbook of mathematics and physics.”
CRC Press (Boca Raton, Fla. and Moscow), 1997.
[10] C. H. Mastrangelo, Y.-C. Tai, and R. S. Muller, “Thermophysical properties of low-residual stress, silicon-rich, lpcvd silicon nitride films,” Sensors and Actuators A: Physical, vol. 23, no. 1, pp. 856 – 860, 1990, proceedings
of the 5th International Conference on Solid-State Sensors and Actuators and Eurosensors III. [Online]. Available: http://www.sciencedirect.com/science/ article/pii/092442479087046L
[11] G. Langer, J. Hartmann, and M. Reichling, “Thermal conductivity of thin metallic films measured by photothermal profile analysis,” Review of Scientific Instruments, vol. 68, no. 3, pp. 1510–1513, 1997. [Online]. Available:
https://doi.org/10.1063/1.1147638
The method to solve the constants
In this section, we will present the way to solve the equation 2.23 to 2.28 in section 2.1: A1e−rL+B1 =A2erL+B2 =Theatsink (A.1) A1e−rxh +B1 =C1e−rxh +C2− Qxh rk (A.2) A2erxh +B2 =C1erxh +C2+ Qxh rk (A.3) A1re−rxh =C1re−rxh + Q rk (A.4) A2rerxh =C1rerxh+ Q rk (A.5)
To solve the six constant,firstly we rewrite the equation A.1 as following:
A1e−rL−A2erL =B2−B1 (A.6)
Then using equation A.3 minus A.2:
A2erxh −A1e−rxh +A1e−rL−A2erL =C1erxh −C1e−rxh + 2 Qxh
rk (A.7)
Next using equation A.5 minus A.4 to find the relation betweenC1 ,A1 andA2
A2rerxh −A1re−rxh =C1erxh −C1e−rxh (A.8)
Replacing the equation A.8 into A.7, the relation between A1 and A2 can be
found as: A1 = 2 Qxh rke−rL +A2e 2rL (A.9) 69
70 APPENDIX A. THE METHOD TO SOLVE THE CONSTANTS To solve theA1 and A2 we need using euqaiton A.4 and A.5 again, but before
subtracting them, the equation A.4 need to divide e−rxh and the equation A.5 need
to divideerxh: A1−A2 = Q r2ke−rxh − Q r2kerxh (A.10)
Replacing equation A.9 into A.10 theA2 can be solved as:
A2 =
Q(e−r(L−xh)−e−r(L+xh)−2x
hr)
r2k(erL−e−rL) (A.11) Now we have already knownA2, then theA1can be solved by replacingA2into
equation A.10,C1 can be solved by replacingA1 andA2 into equation A.8, and B1
The constant for equation 2.37
This section provide the constants for the heat equation 2.37, which is located in Chapter 2.3.
It is difficult to solve the 14 variables with 14 equations, then the software called Mathematica is used to solve the equation, the PDF file attached as following shows those 14 equations and the solution of them.
解方程
SolveA1×ⅇ-r*L+B1⩵0 && A4×ⅇr*L+B4 ⩵0 &&
A1×ⅇ-r*Xh+B1-C1×ⅇ-r*Xh-C2+Q×Xh r×k ⩵0 && A1×r×ⅇ-r*Xh-C1×r×ⅇ-r*Xh-Q r×k ⩵0 && A2×ⅇ-r*Xh1+B2-C1×ⅇ-r*Xh1-C2+Q×Xh1 r×k ⩵0 && A2×r×ⅇ-r*Xh1-C1×r×ⅇ-r*Xh1-Q r×k ⩵0 && A2×ⅇ-r*Xh2+B2-C3×ⅇ-r*Xh2-C4+Q×Xh2 r×k ⩵0 && A2×r×ⅇ-r*Xh2-C3×r×ⅇ-r*Xh2-Q r×k ⩵0 && A3×ⅇr*Xh2+B3-C3×ⅇr*Xh2-C4-Q×Xh2 r×k ⩵0 && A3×r×ⅇr*Xh2-C3×r×ⅇr*Xh2-Q r×k ⩵0 && A3×ⅇr*Xh1+B3-C5×ⅇr*Xh1-C6-Q×Xh1 r×k ⩵0 && A3×r×ⅇr*Xh1-C5×r×ⅇr*Xh1-Q r×k ⩵0 && A4×ⅇr*Xh+B4-C5×ⅇr*Xh-C6-Q×Xh r×k ⩵0 && A4×r×ⅇr*Xh-C5×r×ⅇr*Xh-Q r×k ⩵0, {A1, B1, A2, B2, A3, B3, A4, B4, C1, C2, C3, C4, C5, C6} A1 → 1 -1+ⅇ2 L rk r2 ⅇ L r-r Xh-r Xh1-r Xh2Q -ⅇL r+r Xh+r Xh1+ⅇL r+r Xh+r Xh2-ⅇL r+r Xh1+r Xh2+ⅇL r+2 r Xh+r Xh1+r Xh2-ⅇL r+r Xh+2 r Xh1+r Xh2+ ⅇL r+r Xh+r Xh1+2 r Xh2-2ⅇr Xh+r Xh1+r Xh2r X h+2ⅇr Xh+r Xh1+r Xh2r Xh1-2ⅇr Xh+r Xh1+r Xh2r Xh2, B1 →- 1 -1+ⅇ2 L rk r2 ⅇ -r Xh-r Xh1-r Xh2Q-ⅇL r+r Xh+r Xh1+ⅇL r+r Xh+r Xh2-ⅇL r+r Xh1+r Xh2+ ⅇL r+2 r Xh+r Xh1+r Xh2-ⅇL r+r Xh+2 r Xh1+r Xh2+ⅇL r+r Xh+r Xh1+2 r Xh2- 2ⅇr Xh+r Xh1+r Xh2r X h+2ⅇr Xh+r Xh1+r Xh2r Xh1-2ⅇr Xh+r Xh1+r Xh2r Xh2, A2 → 1 -1+ⅇ2 L rk r2 ⅇ -r Xh-r Xh1-r Xh2Q-ⅇ2 L r+r Xh+r Xh1+ⅇ2 L r+r Xh+r Xh2-ⅇ2 L r+r Xh1+r Xh2+ ⅇ2 r Xh+r Xh1+r Xh2-ⅇr Xh+2 r Xh1+r Xh2+ⅇ2 L r+r Xh+r Xh1+2 r Xh2- 2ⅇL r+r Xh+r Xh1+r Xh2r X h+2ⅇL r+r Xh+r Xh1+r Xh2r Xh1-2ⅇL r+r Xh+r Xh1+r Xh2r Xh2, B2 → 1 -1+ⅇ2 L rk r2 ⅇ -r Xh-r Xh1-r Xh2QⅇL r+r Xh+r Xh1-ⅇL r+r Xh+r Xh2+ⅇL r+r Xh1+r Xh2- ⅇL r+2 r Xh+r Xh1+r Xh2+ⅇL r+r Xh+2 r Xh1+r Xh2-ⅇL r+r Xh+r Xh1+2 r Xh2+ⅇr Xh+r Xh1+r Xh2r X h+ ⅇ2 L r+r Xh+r Xh1+r Xh2r X h-ⅇr Xh+r Xh1+r Xh2r Xh1-ⅇ2 L r+r Xh+r Xh1+r Xh2r Xh1+2ⅇr Xh+r Xh1+r Xh2r Xh2, A3 → 1 -1+ⅇ2 L rk r2 ⅇ -r Xh-r Xh1-r Xh2Q-ⅇr Xh+r Xh1+ⅇ2 L r+r Xh+r Xh2-ⅇ2 L r+r Xh1+r Xh2+ ⅇ2 r Xh+r Xh1+r Xh2-ⅇr Xh+2 r Xh1+r Xh2+ⅇr Xh+r Xh1+2 r Xh2-2ⅇL r+r Xh+r Xh1+r Xh2r X h+ 2ⅇL r+r Xh+r Xh1+r Xh2r X h1-2ⅇL r+r Xh+r Xh1+r Xh2r Xh2, B3 → 1 -1+ⅇ2 L rk r2 ⅇ -r Xh-r Xh1-r Xh2QⅇL r+r Xh+r Xh1-ⅇL r+r Xh+r Xh2+ⅇL r+r Xh1+r Xh2-ⅇL r+2 r Xh+r Xh1+r Xh2+ ⅇL r+r Xh+2 r Xh1+r Xh2-ⅇL r+r Xh+r Xh1+2 r Xh2+ⅇr Xh+r Xh1+r Xh2r X h+ⅇ2 L r+r Xh+r Xh1+r Xh2r Xh- ⅇr Xh+r Xh1+r Xh2r X h1-ⅇ2 L r+r Xh+r Xh1+r Xh2r Xh1+2ⅇ2 L r+r Xh+r Xh1+r Xh2r Xh2,
A4 → 1 -1+ⅇ2 L rk r2 ⅇ -r Xh-r Xh1-r Xh2Q-ⅇr Xh+r Xh1+ⅇr Xh+r Xh2-ⅇr Xh1+r Xh2+ ⅇ2 r Xh+r Xh1+r Xh2-ⅇr Xh+2 r Xh1+r Xh2+ⅇr Xh+r Xh1+2 r Xh2-2ⅇL r+r Xh+r Xh1+r Xh2r X h+ 2ⅇL r+r Xh+r Xh1+r Xh2r X