光电工程  2020, Vol. 47 Issue (6): 190296      DOI: 10.12086/oee.2020.190296

A highly sensitive cantilever temperature sensor for small-area heat source temperature measurement
Xing Zhiming, Jin Tao, Zheng Lulu
School of Optical-Electrical and Computer Engineering, University of Science and Technology, Shanghai 200093, China
Abstract: In this paper, a kind of temperature sensor which can detect a small-area heat source with high sensitivity is designed by using the property of different thermal expansion coefficients of materials. The temperature sensitive element of the sensor is a silicon nitride cantilever beam which is coated with metal on its upper surface. Due to the difference of thermal expansion coefficients between the metal and silicon nitride, the cantilever beam will bend in the direction of rapid change of the temperature gradient, and the bending amount will be positively correlated with the temperature when the ambient temperature of the cantilever beam changes. In the experiment, the bending amount of the beam is measured by the optical lever, and the relationship between the temperature and the output voltage of the detector is established by calibration. The results show that the sensitivity of the sensor can reach 4.86 mV/℃ and the temperature resolution can reach 0.04 ℃. In order to verify the applicability of the sensor for measuring the small-area heat source, the heat generated by heat sources of different areas is measured depending on the calorific property of NaYF4 under laser excitation. The results show that it still can be measured even the heating area is only 0.07 mm2 and the accurate measurement for temperature of the small-area heat source can be realized.
Keywords: temperature sensor    bi-material cantilever    thermal expansion    NaYF4

1 引言

2 理论分析 2.1 悬臂梁温度传感器原理部分

 图 1 (a) 双材料悬臂梁结构示意图；(b)梁受热弯曲示意图。由于上下层材料的热膨胀系数存在差异，所以当温度发生变化时梁会产生一定幅度的弯曲 Fig. 1 (a) Diagram of bi-material cantilever beam structure; (b) Diagram of beam bending under heating. Due to the difference in thermal expansion coefficient between metal and SiNx, the beam will bend when the temperature changes
 $\frac{{{{\rm{d}}^2}z}}{{{\rm{d}}{x^2}}} = 6({\alpha _1} - {\alpha _2}) \cdot \left( {\frac{{{t_1} + {t_2}}}{{t_2^2 \cdot K}}} \right) \cdot (T - {T_0}),$ (1)

 $\begin{array}{*{20}{c}} {K = 4 + 6 \cdot n + 4 \cdot {n^2} + \frac{{{E_1}}}{{{E_2}}} \cdot {n^3} + \frac{{{E_2}}}{{{E_1}}} \cdot \frac{1}{n}, }\\ {n = \frac{{{t_1}}}{{{t_2}}}, } \end{array}$ (2)

 $z = 3({\alpha _1} - {\alpha _2}) \cdot \left( {\frac{{{t_1} + {t_2}}}{{t_2^2 \cdot K}}} \right) \cdot (T - {T_0}){x^2}。$ (3)

 ${S_{\rm{r}}} = 3 \cdot ({\alpha _1} - {\alpha _2}) \cdot \left( {\frac{{1 + n}}{{{t_2} \cdot K}}} \right) \cdot {l^2}$ (4)

 图 2 不同镀层的双材料悬臂梁厚度比n=t1/t2对传感器灵敏度Sr的影响。红色虚线为Au-SiNx的理论灵敏度，蓝色实线为Al-SiNx的理论灵敏度 Fig. 2 Effect of bi-material thickness ratio, n=t1/t2, on the sensor sensitivity Sr. The red line are the prediction data for the Au-SiNx sensor, and the blue line are the prediction data for the Al-SiNx sensor
2.2 光杠杆测量方法

 图 3 光杠杆测量悬臂梁弯曲量的原理图 Fig. 3 Schematic diagram of optical lever measurement for the bending amount of cantilever

 $\Delta D \approx L \cdot 2\theta = L \cdot \frac{{\Delta z}}{l} = \frac{{2L}}{l}\Delta z。$ (5)

 $\Delta i = 6\chi \eta P \cdot \frac{L}{{l \cdot a}}\Delta z,$ (6)

 $\Delta V = \Delta i \cdot {R_{{\rm{IV}}}} \cdot {A_{{\rm{diff}}}},$ (7)

 ${S_z} = 6\chi \eta \alpha {R_{{\rm{IV}}}}{A_{{\rm{diff}}}}\frac{{PL}}{{al}}。$ (8)

 ${S_{{\rm{sys}}}} = {S_z} \cdot {S_{\rm{r}}}。$ (9)
3 实验过程与结果分析 3.1 静态稳定性测量与温度标定

 图 4 (a) 测温实验装置结构示意图；(b) 1为悬臂梁温度传感器实验装置图，2为探测激光在梁尖端的聚焦光斑，3为显微镜下观察到的NaYF4 Fig. 4 (a) Schematic diagram of temperature measuring device; (b) 1. Experimental device diagram, 2. The focused spot of the laser on the beam tip, 3. NaYF4 observed under the microscope

 图 5 (a) 蓝色散点为1 h内探测器输出的信号，红线为满足3δ原则时的输出电压范围；(b)探测器输出信号的噪声密度谱 Fig. 5 (a) The blue scatter is the signal output by the detector within 1 hour. The red line is the output voltage range that satisfies the 3δ principle; (b) Noise density spectrum of the detector output signal

 图 6 调节电阻发热量，对每个测温点多次测量的结果计算平均值，并对测量曲线用一次函数拟合 Fig. 6 Adjust the calorific value of the resistance, calculate the average value of the results of multiple measurements at each temperature measuring point, and fit the measurement curve with a function

3.2 在相同功率密度下对不同面积的热源进行测量

NaYF4是目前氟化物类上转换荧光材料中声子能量最低、荧光效率最高的基质材料。NaYF4在受激发发光的过程中通常也会伴随着热量的产生。根据能量守恒定律，当NaYF4受激发光时会抑制光到热的转化效率，因此为了提高光热转化效率，降低辐射跃迁几率或消除辐射跃迁过程就显得尤为重要。研究表明，掺有Yb3+/Er3+的NaYF4发热离子组合在980 nm波长处具有较强的光吸收，在500 nm~570 nm波长范围内有一个比较明显的发光峰，在室温下用980 nm波长的激光激发时就可以观察到明亮的绿光，随着激发功率的增大发光强度与发热量将会增加[13]

 图 7 激发功率密度为1.12 mW/mm2时，热成像仪对每个面积下纳米材料发热情况的测量结果图 Fig. 7 Thermal images of the nanomaterial with different areas when the excitation power is 1.12 mW/mm2

 图 8 用1.12 mW/mm2的激光激发时，分别用悬臂梁与热成像仪记录材料的发热温度，并绘制出两种测温结果的对比图 Fig. 8 Comparison of measured results between cantilever beam and thermal imager

4 总结与展望

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