# High-Pressure Sensors Based on Laser-Manufactured Sintered Silicon Carbide
## 3 Results and Discussion  
Several S-SiC membranes have been fabricated with thickness ranging from 100 \(\upmu\)m to 300 \(\upmu\)m and diameter from 2.0 to 3.5 mm. Good results have been gained for membrane diameters around (\(2.4\pm 0.05\)) mm. Figure 7 shows experimental results for a (\(160\pm 10\)) \(\upmu\)m thick membrane (S1 sample). As shown in Figure 7a, in the 0-10 MPa range photocurrent amplitude displays the expected behavior of an interference signal given by [41]:  
\[I(\lambda,d)=A^{2}+B^{2}+2 ABcos\left(\frac{4\uppi d}{\lambda}\right) \tag{1}\]  
where \(d\) is the cavity length and \(\lambda\) (= 1550 nm) the wavelength of light emitted by laser-diode, whereas \(A\) and \(B\) are the intensities of light reflected at the fiber end-face and the inner diagram surface, respectively (see Figure 5a). The observed signal periodicity corresponds to a \(\lambda\)/2 diaphragm shift, i.e., 775 nm. Continuous red line represents best fit of data according to Equation (1). Up to a pressure of 1.5 MPa, a monotonic behavior of the photocurrent signal is observed, confirming the feasibility of the fabricated sensing element (see Figure 7b). In the 0-1 MPa range, the sensor shows a full scale range non-linearity lower than 4%. In order to evaluate sensor performances in terms of non-linearity and repeatability, according to Equation (1), fit of data reported in Figure 7 has been used to compile a look-up table (LUT) relating the photocurrent amplitude to the diaphragm deflection. Due to the non-monotonic nature of Equation (1), repeated measurements were performed increasing the pressure from 0 to about 10 MPa. Results are summarized in Figure 8a, where each point refers to pressure values recorded in correspondence of the photocurrent threshold values (i.e., membrane displacement) saved in the LUT. Obtained results displayed almost the same values at each test within the \(\pm 20\) kPa (error bars for data in the figure are within the symbols). The sensor displays a good linearity, with a slope 0.163 nm/kPa (i.e., 16.3 nm/bar). In order to quantify the linearity error, the residuals between experimental and estimated values were  
Figure 7: Photocurrent signal as a function of the applied pressure acquired for a 160 \(\upmu\)m thick S-SiC diaphragm. (**a**) In the 0–10 MPa range the expected sinusoidal behavior stated by Equation (1) is clearly found. The period of signal corresponds to a \(\lambda\)/2 = 775 nm deflection of membrane. (**b**) The plot shows the absolute value of the relative photocurrent change obtained subtracting the value acquired at 0 Pa. In the investigated 0–1 MPa range sensor non-linearity is around 4%. evaluated by linear fit of data of Figure 8a. Results, reported in Figure 8b, depict that errors are lower than \(\pm 20\) nm, i.e., \(\pm 0.6\%\) on the investigated full scale range. The same characterization has been performed for a (\(260\pm 10\)) um thick diaphragm (sample S2). Figure 9 summarizes the experimental results where membrane deflection \(\Delta d\) was evaluated at voltages corresponding to a phase shift of interference signal of 0\({}^{\circ}\), 45\({}^{\circ}\), 90\({}^{\circ}\), 135\({}^{\circ}\), and 180\({}^{\circ}\). As expected, sensor sensitivity of 0.038 nm/kPa is lower than that found for the S1 thinner membrane. Moreover, in the investigated 0-30 MPa range, non-linearity is around 3% of the full scale. As depicted in Figure 5a, diaphragm is compressed towards the fiber end-face by the applied pressure. Being the optical fiber core diameter much lower than the diaphragm diameter, optical interference is mainly induced by the center deflection of membrane. Assuming a uniform  
Figure 8: (a) Diaphrag deflection as a function of pressure for a membrane 160 μm thick. (b) Residuals calculated by the difference of values of (a) and those calculated by linear best fit of data. Figure 9: Diaphrag deflection as a function of pressure for a membrane 260 μm thick.