A miniature Fabry-Perot interferometric sensor with an ultra-high temperature sensitivity was constructed by using an approximate 8-layer graphene diaphragm. The extremely thin diaphragm was transferred onto the endface of a ferrule with an inner diameter of 125 μm, and van der Waals interactions between the graphene diaphragm and its substrate created a low finesse Fabry-Perot interferometer with a cavity length of 42.86 μm. Temperature testing demonstrated a temperature-induced cavity length change of 352 nm/°C with a good linearity in the range of 20-60 °C. The result conformed well to the proposed analytical models relating to thermal expansion of trapped gas, thermal-optical property of graphene diaphragm and deflection behavior of bulged graphene blister. However, the ultra-thin diaphragm exhibited a small deflection deformation characteristic due to the applied higher loads.
© 2015 Optical Society of America
Interest has increased in utilizing miniature fiber optic Fabry-Perot (FP) sensors in biomedical, environmental, microsystem applications due to their advantages over conventional sensors; such as immunity to electromagnetic interference, high resolution, fast response and compact size [1,2 ]. The FP sensor is typically constructed directly on a fiber end face and consists of a cleaved optical fiber and a sensitive diaphragm known as an extrinsic Fabry-Perot interferometric (EFPI) sensor structure. The sensitivity of the diaphragm in the FP sensor is defined as the ratio of the FP cavity’s length variation to the detected parameters , which is closely related with the used materials and the thickness of the diaphragm. Taking pressure measurement as an example, several of the miniature FP pressure sensors referred to in the research literature used different types of elastic materials as a pressure-sensitive diaphragm, such as metal, SiO2/silica, polymer, silver and graphene membrane [4–8 ]. Compared with other materials, the ultra-thin thickness of graphene can significantly improve the pressure sensitivity of FP sensors. Recently, Ma et al. fabricated a FP acoustic sensor with a dynamic pressure sensitivity of 1100 nm/kPa by using a ~100-nm-thick graphene diaphragm with a diameter of 125 μm . Then Li et al. further achieved a dynamic pressure sensitivity of 2380 nm/kPa using a 13-layer graphene diaphragm with a diameter of 125 μm, which was the highest reported . Hence, graphene, with a single-layer thickness of ~0.335 nm, is being utilized more since it was first isolated by Novoselov et al.  because of its extreme elasticity , ultrastrong adhesion , impermeability to gases  and optical far-infrared properties . The unique combination of optical and mechanical properties makes graphene an ideal material for FP sensor applications. However, it is no denying that the temperature sensitivity of FP sensors should be investigated to enhance the thermal applicability of such sensors. Recently, multiple FP temperature sensors employing various smart structures and non-graphene materials have been reported. A single micro-air-gap based intrinsic FP interferometric fiber-optic sensor exhibited an optical path difference of 2.9 μm from 50 °C to 700 °C . And a FP temperature sensor with a sensitivity of 0.95 pm/°C was developed by etching a multimode graded index fiber . Also, an ultra-high sensitivity of ∼5.2 nm/°C was obtained by using a partially polymer-filled glass capillary to form an air micro-cavity . These aforementioned FP sensors are adequate to measure high temperature variation whereas not suitable for measuring small temperature variation. In contrast, it is possible that graphene diaphragm is much more sensitive to low temperature fluctuations due to the properties of extremely thinness, high strength and large deflection deformation to allow the thermal expansion of air micro-cavity. In a recent study , it was stated that a miniature FP temperature sensor had a resonant wavelength sensitivity of 1.56 and 1.87 nm/°C at the temperature range of 500 - 510 °C and 1000 - 1008 °C respectively, by using a more than 4-layer graphene diaphragm with a diameter of 125 μm. However, the physics behind the cavity length variation verse temperature is not discussed in detail. Moreover, based on the thin-film optical theory and the Fresnel’s equations for reflection and refraction , the stated reflectivity (9.04%) of graphene film should indicate an approximate thickness above 12 nm. The thicker diaphragm in a miniaturized sensor head imposes a limit on its temperature sensitivity due to the restriction of thermal expansion of trapped gas in FP cavity.
In this paper, we fabricate a FP cavity using an ultra-thin ~8-layer graphene diaphragm with a diameter of 125 μm. The sensor proposed here exhibits an ultra-high temperature sensitivity of 352 nm/°C in the tested range of 20-60 °C. The diaphragm structure breaks the sensitivity limitations imposed by the increased thickness and the decreased dimension of a diaphragm used in traditional FP temperature sensors. Furthermore, thermal tests show that the cavity length variation of the FP sensor conforms well to the theoretical model on basis of the thermal expansion of trapped gas, thermal optical property of graphene diaphragm and the spherical shell equation used for the geometrically nonlinear response of a clamped circular elastic graphene diaphragm subjected to a pressure difference across the diaphragm.
2. Sensor fabrication and temperature-sensitive principle
Figure 1(a) shows the schematic diagram and the physical picture of the presented FP sensor that comprises of a zirconia ferrule, a standard single mode fiber (SMF) and a multi-layer graphene diaphragm. The diaphragm, working as a light reflector made directly on the end of the SMF, is adhered to the zirconia substrate by van der Waals forces as shown in Fig. 1(b), and the separation between the fiber end and the ferrule endface is controlled by using a 1-μm resolution translation stage. The ferrule and the SMF are held together by an epoxy adhesive (3M®). The graphene diaphragm is prepared from a 5~8-layer commercial Trivial Transfer Graphene sample in which the graphene film is grown by chemical vapor deposition (CVD) on a 20-μm thick Cu foil deposited on a polymer substrate (ACS Material®, www.xfnano.com). The process for preparing the graphene membrane and transferring it onto the fiber tip to an FP cavity is similar to that in .
When external temperature occurs to change, the thermal expansion of trapped gas and the different thermal expansion coefficients between the zirconia ferrule and the SMF will cause the change of the length of FP cavity and then generate the FP interference. Referring to the theory of multiple-beam interference, the interference intensity Ir in FP cavity can be expressed as
As seen from Eq. (1), the temperature sensitivity for FP sensors shows a strong dependence on L and R 2. According to the law of thermal expansion of trapped gas and thermal deformation characteristics, the length change ΔL of FP cavity can be described as20], ω is supposed to consist of the deflection ωP caused by pressure change imposing on the clamped circular elastic graphene diaphragm and the deflection ωT caused by thermal expansion of the diaphragm.
After the graphene film is adhered to the ferrule endface at normal temperature T 0 and pressure p 0, the internal pressure in the micro-cavity, pint, is equal to the initial tension, resulted from adhesion energy between graphene film and ferrule substrate, plus the external pressure, pext, which is atmospheric pressure p 0. In other words, the graphene membrane is not flat, because a calibrated AFM tip test had showed a few nanometers of dip along the edges of the suspended regions where the graphene met the SiO2 sidewalls . Considering the ideal gas law, when the temperature increases to T from T 0, the internal pressure pintT at T becomes21].
For the purpose of modeling the load-deflection behavior, the graphene diaphragm is approximated as a clamped circular membrane made of a linear isotropic elastic material based on the spherical shell equation. The relationship between the diaphragm deflection ω and the pressure change ΔP may be expressed as 
It is noted that ΔL can be measured by the interference spectrum. In combination with the available calculated ω and ΔVT, the pressure difference ΔP between internal and external sides of the diaphragm can be solved using Eq. (7), as well as the volume ΔVω under the bulge using Eq. (6). However, the relationship between the internal pressure and the volume under the pressurized blister should be in agreement with Eq. (5).
3. Experiment and analysis
It can be inferred from Eq. (1) that it is necessary to determine the reflectivity R 1 of the graphene diaphragm suspended onto the fiber-tip so as to analyze the change of cavity length because of the multiple optical interference. Moreover, the reflectance and transmittance of graphene in the optical region are a function of frequency, temperature and carrier density; i.e., R 1 is affected by the temperature. In terms of the wavelength range (1528-1608 nm) of used broadband source (ALS-CL-17), R 1 can be calculated by the complex refractive index, which depends on the temperature-dependent dynamical conductivity for high frequencies [23, 24 ]. Thus, the calculated reflectivities of 7- and 8-layer graphene diaphragm verse temperature are shown in Fig. 2 . Since the visibility of the fringe pattern for the FP cavity is related to the reflectivity of the fiber end and the graphene diaphragm, R 1 can be fitted by the measured interference spectrums of a FP sensor. Firstly, R 2 was measured to be approximately 2.5% with an optical spectrum analyzer (AQ6370C). Next, R 1 was measured to be within the range of 0.613% to 0.683%, as shown in Fig. 2. The result showed that the measured R 1 was not much sensitive to the temperature, which agreed well with the theoretical solution. The average value of R 1 was approximately 0.652%, in close proximity to the calculated reflectivity of 0.727% for an 8-layer graphene diaphragm. Therefore, the thickness of the diaphragm was approximated as 2.68 nm, i.e. an 8-layer thickness. It could also be inferred that the interference intensity was mostly generated by the cavity length variation.
Referring to Fig. 3 , the developed FP sensor and a thermocouple sensor were put inside a thermostat. The reference temperature for the FP sensor was offered by a thermocouple thermometer (testo 925) with an accuracy of ± (0.5 °C + 0.3% of measured value) in the range of −40 °C to + 900 °C and an associated Type K thermocouple probe with an accuracy of Class 2 in the range of −60 °C to + 400 °C according to standard EN 60584-2. A broadband laser was used to illuminate the FP sensor, and the interference intensity was received by a photoelectric detector (PD) with a preamplifier through the use of an optical circulator. The 3dB bandwidth of the PD was up to 200 kHz. The reflection spectrum was then monitored by an optical spectrum analyzer (AQ6370C) with a wavelength resolution of 0.02 nm. In consideration of the use of room temperature curable adhesive and common SMF, the tested temperature was arranged as 20-60 °C, where the set interval was 2 °C in the first 10 °C and 5 °C in the remaining range, respectively.
Figures 4(a)-4(c) illustrate the cavity length change verse temperature at three cycles of temperature rise/drop measurements, respectively. Although the increased cavity length was not uniform as the temperature rose, the temperature sensitivity of the FP sensor was estimated to be 352 nm/°C by using a least square fitting method with a fitting R-square of 99.83%, in combination with the measured average cavity lengths respectively corresponding to the three cycles of temperature rise and drop measurements. And the sensor’s hysteresis error was calculated to be 2.79% in the tested range of 20-60 °C. Then derived by Eqs. (5) and (7) , the corresponding internal pressure in the cavity and the diaphragm deflection in Fig. 5 indicated that the volume thermal expansion under pressurized graphene blister made the pressure in the cavity, PintT, become slightly larger as the temperature rose, therefore leading to a slight increase in ωP. The thermal expansion of air micro-cavity induced the enlargement of bulged film deformation ω. Hence as shown by the symbol ‘Δ’ in Fig. 5, another factor ωT, in relation to the thermal expansion of the diaphragm, was introduced to examine the thermal mechanical behaviors of the FP sensor. This factor was solved by ω-ωP, and its fitted result was close to 208 nm/°C, which was a major contribution to the measured temperature sensitivity of 352 nm/°C. It could also be concluded from Fig. 5 that the higher load applied to the diaphragm, instead of the prestress, exerted a dominating effect on the pressure-deflection behavior of graphene membrane as a result of thermal expansion. That is to say, the diaphragm exhibited a small deflection characteristic at higher loads.
Taking the interference intensities at 35°C, 36°C and 37°C as examples, the measured reflection spectrums of the fabricated FP sensor is presented in Fig. 6 , where the average shift of dip wavelengths 1541 nm, 1555 nm and 1566 nm is 12.5 nm /°C. Furthermore, due to the variation in temperature, the theoretical dip wavelength shift can be approximated as
As demonstrated in Fig. 7 , the fitted period of temperature variation is less than 3 °C at the wavelength of 1541 nm. This phenomenon is not suitable for use of the wide-temperature intensity demodulation. For a typical wavelength of 1550 nm, a maximum linear range is generally defined as 387.5 nm, i.e., λ/4, which means that a variation of less than 1 °C for the temperature sensitivity mentioned here will possibly enable the order of interference spectrum to move forward or backward.
Therefore, the change of FP cavity length is available to effectively estimate the current temperature. The possible error existing in the distribution of measured sensitivity is mainly due to the ideal gas modeling and thermal deformation induced by the transferring of graphene sheets suspended onto the ferrule substrate, which is dependent on the kinetic adhesion characteristics and mechanical properties [25, 26 ]. As a result, further research on the thermal deformation of graphene diaphragm in FP sensors over a wider temperature range is needed to investigate the physics behind it.
This study demonstrated the effectiveness of designing and analyzing an ultra-high temperature sensitivity sensor using a nanothick graphene diaphragm. A sensitive FP cavity of 42.86 μm in length was fabricated by suspending the graphene diaphragm and adhering it onto the endface of a ferrule with a bore diameter of 125 μm. The diaphragm, whose reflectivity was essentially independent of temperature, was equivalent to an 8-layer thickness. The thermal variation of cavity length was measured to be approximately 352 nm/°C in the tested range of 20-60 °C, which was primarily induced by the thermal deformation of graphene diaphragm on basis of the established analytical models. However, the intensity and phase shifts at common temperatures featured a periodic appearance even due to a narrow thermal fluctuation. Thermal adaptability analysis presented here would be applicable in highly sensitive graphene-based FP temperature, pressure or other sensors for biomedical and aerospace applications.
This work is supported by the National Nature Science Fund of China (61573033), the Program for Changjiang Scholars and Innovative Research Team in University (IRT1203), the China Academy of Space Technology (CAST) Innovation Foundation and the Graduate Innovation Fund of Beihang University (YCSJ-01-2015-01).
References and links
1. S. Avino, J. A. Barnes, G. Gagliardi, X. Gu, D. Gutstein, J. R. Mester, C. Nicholaou, and H.-P. Loock, “Musical instrument pickup based on a laser locked to an optical fiber resonator,” Opt. Express 19(25), 25057–25065 (2011). [CrossRef] [PubMed]
3. F. Xu, D. Ren, X. Shi, C. Li, W. Lu, L. Lu, L. Lu, and B. Yu, “High-sensitivity Fabry-Perot interferometric pressure sensor based on a nanothick silver diaphragm,” Opt. Lett. 37(2), 133–135 (2012). [CrossRef] [PubMed]
4. G. Beheim, K. Fritsch, and R. N. Poorman, “Fiber-linked interferometric pressure sensor,” Rev. Sci. Instrum. 58(9), 1655–1659 (1987). [CrossRef]
5. W. Wang, N. Wu, Y. Tian, C. Niezrecki, and X. Wang, “Miniature all-silica optical fiber pressure sensor with an ultrathin uniform diaphragm,” Opt. Express 18(9), 9006–9014 (2010). [CrossRef] [PubMed]
6. G. C. Hill, R. Melamud, F. E. Declercq, A. A. Davenport, I. H. Chan, P. G. Hartwell, and B. L. Pruitt, “SU-8 MEMS Fabry-Perot pressure sensor,” Sens. Actuators A Phys. 138(1), 52–62 (2007). [CrossRef]
7. F. Guo, T. Fink, M. Han, L. Koester, J. Turner, and J. Huang, “High-sensitivity, high-frequency extrinsic Fabry-Perot interferometric fiber-tip sensor based on a thin silver diaphragm,” Opt. Lett. 37(9), 1505–1507 (2012). [CrossRef] [PubMed]
8. J. Ma, H. F. Xuan, H. L. Ho, W. Jin, Y. H. Yang, and S. C. Fan, “Fiber-optic Fabry-Perot acoustic sensor with multilayer graphene diaphragm,” IEEE Photonics Technol. Lett. 25(10), 932–935 (2013). [CrossRef]
9. C. Li, X. Y. Gao, T. T. Guo, J. Xiao, S. C. Fan, and W. Jin, “Analyzing the applicability of miniature ultra-high sensitivity Fabry-Perot acoustic sensor using a nanothick graphene diaphragm,” Meas. Sci. Technol. 26(8), 085101 (2015). [CrossRef]
10. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004). [CrossRef] [PubMed]
13. J. S. Bunch, S. S. Verbridge, J. S. Alden, A. M. van der Zande, J. M. Parpia, H. G. Craighead, and P. L. McEuen, “Impermeable atomic membranes from graphene sheets,” Nano Lett. 8(8), 2458–2462 (2008). [CrossRef] [PubMed]
14. L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B Condens. Matter 76(15), 153410 (2007). [CrossRef]
16. P. A. R. Tafulo, P. A. S. Jorge, J. L. Santos, F. M. Araújo, and O. Frazão, “Intrinsic Fabry-Perot cavity sensor based on etched multimode graded index fiber for strain and temperature measurement,” IEEE Sens. J. 12(1), 8–12 (2012). [CrossRef]
17. G. Zhang, M. Yang, and M. Wang, “Large temperature sensitivity of fiber-optic extrinsic Fabry-Perot interferometer based on polymer filled glass capillary,” Opt. Fiber Technol. 19(6), 618–622 (2013). [CrossRef]
18. L. Li, Z. Y. Feng, X. G. Qiao, H. Z. Yang, R. H. Wang, D. Su, Y. P. Wang, W. J. Bao, J. C. Li, Z. H. Shao, and M. Hu, “Ultrahigh sensitive temperature sensor based on Fabry–Pérot interference assisted by a graphene diaphragm,” IEEE Sens. J. 15(1), 505–509 (2015). [CrossRef]
19. C. Li, J. Xiao, T. T. Guo, S. C. Fan, and W. Jin, “Interference characteristics in a Fabry-Perot cavity with graphene membrane for optical fiber pressure sensors,” Microsyst. Technol. 21(11), 2297–2306 (2015). [CrossRef]
21. N. G. Boddeti, S. P. Koenig, R. Long, J. L. Xiao, J. S. Bunch, and M. L. Dunn, “Mechanics of adhered, pressurized graphene blisters,” J. Appl. Mech. 80(4), 040909 (2013). [CrossRef]
22. J. W. Beams, The Structure and Properties of Thin Film (Wiley, 1959).
23. L. A. Falkovsky, “Optical properties of graphene,” J. Phys. Conf. Ser. 129, 012004 (2008). [CrossRef]
26. M. A. N. Dewapriya, A. Srikantha Phani, and R. K. N. D. Rajapakse, “Influence of temperature and free edges on the mechanical properties of graphene,” Model. Simul. Mater. Sci. Eng. 21(6), 065017 (2013). [CrossRef]